The Economic Journal

Adda,, Jérôme;Fawaz,, Yarine

doi: 10.1093/ej/ueaa058pmid: N/A

Abstract This paper assesses the effect of import competition on the labour market and health outcomes of US workers. We first show that import shocks affect employment and income, but only in areas where jobs are more intense in routine tasks. Exploiting over 40 million individual observations on health and mortality, we find that import had a detrimental effect on physical and mental health that is concentrated in those areas and exhibits strong persistence. It decreased healthcare utilisation and increased hospitalisation for a large set of conditions, more difficult to treat. The mortality hazard of workers in manufacturing increased by up to 6% per billion-dollar import increase. Globalisation and in particular increased international trade has profoundly shaped the economies of both the developing and developed world over the last decades. While this process has enabled both the growth of poorer countries and access to cheaper consumer goods in richer ones, many worry that the effects of trade and particularly import competition have been poorly distributed across individuals in developed countries. The economic literature has focused on many aspects of the impact of trade, first on the manufacturing sector, but also on its wider consequences on wages and employment in all sectors. This line of research has shown that imports in developed countries have led locally to higher unemployment, lower labour force participation and reduced wages. Autor et al. (2013a), Autor et al. (2014), Ebenstein et al. (2014), Pierce and Schott (2016) and Autor et al. (2016) exploit the timing of imports from China on US local labour markets affected differently by those imports. The results show that the effect is concentrated on workers in the manufacturing sector, and especially those with low wages and low labour force attachment. We build on and extend this body of work, contributing to the literature on trade and health is three different ways. First, we show that the labour market effects of import competition are mediated by the average routine task intensity (RTI) in the manufacturing sector in the area. In areas where this intensity is low, import competition has no discernible effects on employment, unemployment or family income. In contrast, most of the economic effects are concentrated in areas where jobs are more characterised by routine tasks. Bernard et al. (2006) shows that firms react to trade from low-wage countries by moving to industries that are more intense in high-skilled labour and capital, when they survive. In that process, production workers are likely to be more affected than non-production workers. This trade-induced skill-biased technological change is also at the core of the work by Bloom et al. (2015). Our results align well with this body of research and characterise the geographical concentration of import competition, a distinction not made in the literature so far. Second, we characterise the dynamic effects of import competition. The extant literature has linked labour market outcomes to contemporaneous measures of imports. We show that not only do import shocks have a lasting effect of many years, but their effect on employment and income is also increasing with time. In some cases the effect doubles within a span of six years. This feature shows that import competition is of a different nature from other aggregate shocks. For instance, economic recessions last only for one or two years. A large number of studies look at the effect of recessions on labour market or health outcomes, but it is likely that import competition leads to different long-term effects, worth exploring on their own. Third, we provide a detailed picture of the effect of import shocks on health, including mental and physical health, health behaviour, access to healthcare and ultimately mortality. Our empirical analysis draws on multiple and large data sets that record individual health in the United States over the last decades. We exploit data from the Behavioral Risk Factor Surveillance System (BRFSS) to get information on morbidity, interactions (or the lack of) with the healthcare system and health behaviour. We complement these data with hospital records with detailed medical diagnosis to shed further light on the effect of import competition on morbidity, poor health behaviour and healthcare access. Finally, we use longitudinal data following manufacturing workers to investigate the effect of import competition on mortality. We investigate how the geographical concentration of economic effects and their dynamics affect the disparity and timing of a large set of health outcomes. Our empirical strategy differs with the type of data we analyse. When uncovering the effect of import competition on health, health behaviour or hospitalisation, our research design is close to Autor et al. (2013a), as we use the industry composition of local labour markets to compute an import per worker (IPW) measure at the commuting zone (CZ) level. However, when analysing the effect of import competition on mortality, we have information on the precise industry in which the respondents are working, which allows us to relate their hazard of death directly to the imports they face as well as detailed individual characteristics including their health when they are first observed. We show that the effects of import competition on health are precisely restricted to those areas where manufacturing jobs are more routine-oriented. The effect of import competition on health is also increasing in the timing of the import shock, and affects both physical and mental health. The results are remarkably similar across the different data we use, coming either from survey data or from larger hospital records. We then investigate the possible pathways leading from poorer labour market outcomes to poorer mental and physical health. We find mixed effects of import competition on health behaviour: on average, they improve following an import shock, but, at the same time, there is a worsening in the upper tail. To uncover this complex pattern requires the very large sample size of hospitalisation data as health surveys such as the BRFSS miss it. Importantly, we show that the decline in health is too large to be explained by the observed decrease in family income. Another channel can be the reduced interaction with the healthcare system that we document. Two factors could be at play: the decrease in family income and the loss of the employer-provided health insurance, which—in the case of the USA—is not replaced by public coverage in most cases. We show that the decrease in income is not enough to explain such a reduction in care. The consequence of this lack of access is that it may lead to some health conditions going untreated or diagnosed too late, leading to more serious conditions later on. Our analysis of the hospitalisation data reveals that import shocks lead patients to be admitted with more serious conditions that require longer treatments. Finally, we show that increases in import competition have a subsequent effect on mortality that is growing over time. By analysing individual and longitudinal data, we can rule out prior sorting into industries based on health. The results show that a billion-dollar increase in imports raises the hazard of dying by about 6% after seven years. Our results complement a new strand of the literature that has been looking directly at the impact of import competition on workers’ health. Hummels et al. (2016) exploits Danish employer–employee data combined with individual health data to show how rising exports may lead to increased job effort, and increased productivity and income, but also put workers at increased risk of illness and injury. McManus and Schaur (2016) combines plant-level injury outcomes at US manufacturers with measures of import competition, and shows that greater increases in imports are associated with greater increases in injury rates. Closer to our research, a small number of studies have looked at the impact of import competition on workers’ health. Colantone et al. (2019) finds a large negative impact of import competition at the industry level on workers’ mental health in Great Britain, with spillover effects on their children, whose self-esteem and well-being are undermined. This effect goes through job displacement as well as gloomier expectations and increased likelihood of job displacement for those still in their job. Lang et al. (2019) uses the BRFSS data to estimate the impact of import competition on several dimensions of health, and finds a detrimental effect on mental and general self-assessed health in the USA. As a mechanism, they find less healthcare utilisation (individuals more exposed to import competition are more likely to forgo a doctor visit due to its cost) but no effect on healthcare access (no effect on the share of individuals having a health insurance plan in the CZ). A contemporaneous work by Pierce and Schott (2020) examines the causal link between trade liberalisation and mortality, exploiting a change in US trade policy that increased US counties’ exposure to foreign competition from China differentially via their industry structure. They find that counties more exposed to the change in US trade policy exhibit relative increases in the so-called deaths of despair (at the core of Case and Deaton, 2015), especially among working-age whites, and that the impact of the policy change on mortality coincides with a deterioration in labour market conditions and uptake of disability insurance. We add to this literature in several ways by showing the geographic concentration and the timing of detrimental effects of import shocks on health. As the effects are clustered precisely where we uncover poorer labour market outcomes and follow a similar dynamic, our analysis provide a more stringent test of the role of import competition on health. We show that prior sorting cannot explain the effect of import competition on health. The data on hospitalisation we exploit allow us to uncover the unexpectedly large set of health outcomes that are affected by import shocks. While we find detrimental effects on mental health and its manifestation through suicides, substance abuse (and in particular opioid abuse), import shocks affect also many aspects of physical health that have not been documented before. Those include heart, endocrine, respiratory, skin or infectious diseases as well as cancers, revealing that import competition has a much heavier toll than previously found. The rest of the paper is organised as follows. Section 1 describes how we measure import competition and routine tasks and how they relate to each other. Section 2 shows the dynamic impact of import competition and its geographical concentration in areas that are characterised by a high RTI. Section 3 presents the effect of import competition on health, health behaviour and healthcare utilisation. Finally Section 4 concludes. 1. Import Competition and Routine Tasks 1.1. Exposure to Import Competition from China CZs: in the following analysis, we first provide new evidence about the impact of exposure to US imports from China on labour market outcomes, then investigate how exposure to import competition from China affects individual health outcomes. Whether outcomes are local labour markets or individual health (with the exception of the last section where the outcome is mortality), we follow seminal work by Autor et al. (2013a,b; 2015) (hereafter Autor–Dorn–Hanson) and define the CZ as our unit of analysis. CZs are the most logical geographical unit of analysis when looking at the impact of Chinese imports on local labour markets as well as health as we expect labour market outcomes to drive the health effects. We consider the entire US territory with the exception of Hawaii and Alaska in all our analysis because of the many changes of counties over time in those two states, which leaves us with 722 CZs. The IPW shock: definition. We construct the IPW measure defined in Autor–Dorn–Hanson for every year from 1990 to 2011, using the following definition: $$\begin{eqnarray} \textit{IPW}_{c,t}=\sum _{j\in \textit{Manuf}} \frac{L_{c,j,t}}{L_{\textit{US},j,t}} \frac{\textit{Import}_{j,t}}{L_{c,\textit{All},t}}, \end{eqnarray}$$ where Lc,j,t is the employment in industry j—which belongs to the set of manufacturing industries Manuf—and CZ c, in year t, while LUS,j,t is the employment in the same industry j across the whole country in year t. The greater the share of the CZ in the US employment in industry j (given by the ratio between these two terms in the equation), the greater the shock. Imports from China in industry j are expressed in billion 2009 US$, and denoted Importj,t. They are rescaled by total non-agriculture employment in the CZ, hence expressed ‘per worker’. We construct this measure for every year of data (1991–2011) and as a level variable, instead of a difference with respect to the previous period. This will allow us to use all available years of data when exploiting unbalanced health panel data. To put things in perspective we also rebuild the exact Δ IPW measure defined in the Autor–Dorn–Hanson literature, and replicate their findings using 20 one-year periods rather than two decennial changes. In order to tackle potential endogeneity in the impact of imports from China on manufacturing employment and subsequently workers’ health, we adopt the same instrumentation strategy as Autor–Dorn–Hanson: because the US rising imports from China could be the result of a domestic demand shock in the US rather than an exogenous supply shock in China, we use Chinese imports in eight other high-income countries to instrument for Chinese imports in the US.1 The non-US exposure-to-Chinese-export variable is defined similarly, but differs in two respects from the IPW variable: Importj,t is replaced by |$\textit{Import}_{j,t}^{\textit{OTH}}$|⁠, i.e., the imports from China to the eight countries mentioned above, in industry j in year t; second, it uses employment levels from the prior decade, precisely from ten years before, alleviating the risk of a simultaneity bias. $$\begin{eqnarray} {IPW}_{c,t}^{{OTH}}=\sum _{j\in {Manuf}} \frac{L_{c,j,t-10}}{L_{{US},j,t-10}} \frac{{Import}_{j,t}^{{OTH}}}{L_{c,{All},t-10}}. \end{eqnarray}$$ The IPW shock: data sources. Imports from China are extracted from COMTRADE. Although US imports are available from other sources for prior decades as well, the instrumentation strategy we use leads to restricting the time period to 1991–2011. Starting in 1997, we will therefore be able to look at the impact of imports from China on several outcomes allowing for up to six lags. Imports are measured at the commodity level (six-digit HS). We therefore apply a crosswalk to convert them into four-digit SIC codes (corresponding to the SIC87 classification of industries). All import values are deflated or inflated to 2009 US$. In order to construct an import shock at the CZ level, we need data on the industry composition of each CZ, i.e., the number of workers working in each four-digit SIC industry over the 1981–2011 period (since employment appears with a ten-year lag in the definition of the instrument version of the IPW shock). We extract this information from the County of Business Patterns (CBP), which is an annual series that provides subnational economic data by industry. It includes the number of employees at the county level during the week of 12 March.2 We then aggregate these numbers to the CZ level. Figures 1 and 2 show both the geographic heterogeneity of the IPW shock and the increasing pervasiveness of the shock from 1990 to 2011. 1.2. Automatability as a Source of Heterogeneity The RTI measure: in order to assign a value of RTI to each CZ, we use detailed occupations at the individual level from the census: following Autor and Dorn (2013) we assign to each occupation a routine, manual and abstract index depending on the content of the tasks defining each occupation (each occupation is assigned a value between 0 and 10 for these three dimensions of task content). We compute the RTI measure for occupation k, defined as RTIk = ln(Routinek) − ln(Manualk) − ln(Abstractk).3 The RTI index sums up the likelihood for a job of going through automation, which consists in reducing or eliminating the human labour needed to perform a task, by replacing it by machines. Because this approach is based on the task content of each occupation rather than on the use of machines or computers by industry for instance, it reflects more the concept of automatability, i.e., the propensity for workers to be displaced as a result of the computerisation or robotisation of the tasks they used to perform. It has been widely used as an indicator of computerisation or of technological change in the Autor–Dorn–Hanson literature. When computing this RTI measure at the CZ level, we consider jobs in the manufacturing sector in 1990, so that the average of the RTI measure in a CZ reflects the RTI of occupations only in the manufacturing sector and for year 1990, i.e., when exposure to import competition was still very low over all the US territory. We then sort the 722 CZs into three terciles of RTI based on the average RTI among manufacturing workers in each CZ. Each tercile is made up of around 240 CZs, as displayed in Figure 3: low, medium and high RTI (based on the average RTI in manufacturing jobs in the CZ). Darker shades, mostly present in the Midwest and more locally in South-East and North-East regions of the USA, mean that jobs within the manufacturing sector are more prone to automation in those CZs, due to their high content in routine tasks and/or their low content in abstract and manual tasks. Fig. 1. Open in new tabDownload slide IPW: Heterogeneity across US Territory in 1990. Fig. 1. Open in new tabDownload slide IPW: Heterogeneity across US Territory in 1990. Fig. 2. Open in new tabDownload slide IPW: Heterogeneity across US Territory in 2011. Notes: IPW shock in CZ c at time t is constructed as: |$\textit{IPW}_{c,t}=\sum\nolimits _{j\in \textit{Manuf}} \frac{L_{c,j,t}}{L_{\textit{US},j,t}} \frac{\textit{Import}_{j,t}}{L_{c,\textit{All},t}}$|⁠, where j is an industry belonging to the set of manufacturing industries Manuf. The first ratio corresponds to the share of the CZ in the US employment in industry j. The import shock (imports from China in industry j in billion 2009 US$) Importj,t is rescaled by total non-agriculture employment in the CZ, hence expressed ‘per worker’. Fig. 2. Open in new tabDownload slide IPW: Heterogeneity across US Territory in 2011. Notes: IPW shock in CZ c at time t is constructed as: |$\textit{IPW}_{c,t}=\sum\nolimits _{j\in \textit{Manuf}} \frac{L_{c,j,t}}{L_{\textit{US},j,t}} \frac{\textit{Import}_{j,t}}{L_{c,\textit{All},t}}$|⁠, where j is an industry belonging to the set of manufacturing industries Manuf. The first ratio corresponds to the share of the CZ in the US employment in industry j. The import shock (imports from China in industry j in billion 2009 US$) Importj,t is rescaled by total non-agriculture employment in the CZ, hence expressed ‘per worker’. Fig. 3. Open in new tabDownload slide RTI across US Territory in 1990. Notes: We match detailed occupation codes from IPUMS Census 1990 with the routine, abstract and manual task contents based on the job task requirements of each occupation as described in theDictionary of OccupationalTitles. We compute the RTI measure for occupation k, defined as RTIk = ln(Routinek) − ln(Manualk) −ln(Abstractk), for the manufacturing sector. We then average the RTI index (for manufacturing only) at the CZ level, and divide the US territory into three terciles of RTI. Fig. 3. Open in new tabDownload slide RTI across US Territory in 1990. Notes: We match detailed occupation codes from IPUMS Census 1990 with the routine, abstract and manual task contents based on the job task requirements of each occupation as described in theDictionary of OccupationalTitles. We compute the RTI measure for occupation k, defined as RTIk = ln(Routinek) − ln(Manualk) −ln(Abstractk), for the manufacturing sector. We then average the RTI index (for manufacturing only) at the CZ level, and divide the US territory into three terciles of RTI. Table 1 displays CZ characteristics across RTI tercile groups. While the highest RTI tercile accounts for less population that the first two, all demographic and labour-related characteristics are very similar across the three RTI terciles.4 The only CZ-level characteristic that differs substantially across RTI terciles is the amount of imports per worker, which increases with the RTI index. We next address the question of how import competition and automatability correlate across the USA.5 Table 1. CZ Characteristics by RTI Tercile, in 1990. . All . RTI low . RTI medium . RTI high . . Mean . SD . Mean . SD . Mean . SD . Mean . SD . Imports and RTI IPW (in $1,000) 0.30 (0.33) 0.21 (0.24) 0.32 (0.34) 0.45 (0.42) IPWOTH (in $1,000) 0.40 (0.34) 0.29 (0.21) 0.41 (0.32) 0.62 (0.47) RTI (mean) 1.27 (0.10) 1.24 (0.08) 1.29 (0.09) 1.28 (0.13) RTI (mean) in manufacturing 1.46 (0.14) 1.33 (0.09) 1.51 (0.04) 1.64 (0.09) Demographics % of male 49.33 (1.11) 49.88 (1.11) 48.99 (0.86) 48.84 (1.08) % of white individuals 81.23 (11.21) 79.02 (11.20) 83.22 (9.29) 81.90 (13.95) % of black individuals 11.51 (9.16) 10.49 (8.94) 12.28 (8.56) 12.14 (10.65) % of low-educated individuals 16.71 (5.40) 16.27 (5.17) 16.27 (4.95) 18.70 (6.36) % of individuals aged less than 25 19.42 (2.43) 19.39 (2.45) 19.43 (2.40) 19.47 (2.48) % of individuals aged 25–34 27.91 (1.94) 28.71 (2.06) 27.57 (1.63) 26.81 (1.46) % of individuals aged 35–44 23.26 (1.22) 23.56 (1.49) 23.12 (0.94) 22.88 (0.85) % of individuals aged 45–54 15.79 (1.10) 15.43 (1.12) 15.95 (0.96) 16.27 (1.08) % of individuals aged 55 and over 13.62 (2.14) 12.90 (2.48) 13.93 (1.73) 14.56 (1.54) Labour % of employed individuals 71.82 (4.58) 71.78 (5.11) 71.97 (4.12) 71.59 (4.26) % of unemployed individuals 4.57 (0.98) 4.56 (0.94) 4.60 (0.96) 4.51 (1.12) % of not in labour force 23.61 (3.91) 23.65 (4.45) 23.43 (3.52) 23.90 (3.35) % of individuals in manufacturing 12.92 (4.91) 10.95 (3.76) 14.00 (4.04) 15.02 (6.98) Income Income (mean, household equivalised) 38,738 (7,221) 39,251 (6,990) 39,075 (7,211) 36,814 (7,497) % of individuals w. eq. fam. income<$15k 18.82 (6.52) 19.12 (6.45) 17.96 (6.38) 20.03 (6.77) % of individuals w. eq. fam. income<$20k 27.57 (8.49) 27.87 (8.24) 26.39 (8.53) 29.48 (8.60) % of individuals w. income<$15k 39.01 (6.25) 38.55 (6.66) 38.87 (5.94) 40.37 (5.79) % of individuals w. income<$20k 47.26 (7.06) 46.78 (7.27) 46.95 (6.90) 49.07 (6.66) Observations 240 241 241 722 Average size of each CZ 429,880 413,836 186,930 343,429 . All . RTI low . RTI medium . RTI high . . Mean . SD . Mean . SD . Mean . SD . Mean . SD . Imports and RTI IPW (in $1,000) 0.30 (0.33) 0.21 (0.24) 0.32 (0.34) 0.45 (0.42) IPWOTH (in $1,000) 0.40 (0.34) 0.29 (0.21) 0.41 (0.32) 0.62 (0.47) RTI (mean) 1.27 (0.10) 1.24 (0.08) 1.29 (0.09) 1.28 (0.13) RTI (mean) in manufacturing 1.46 (0.14) 1.33 (0.09) 1.51 (0.04) 1.64 (0.09) Demographics % of male 49.33 (1.11) 49.88 (1.11) 48.99 (0.86) 48.84 (1.08) % of white individuals 81.23 (11.21) 79.02 (11.20) 83.22 (9.29) 81.90 (13.95) % of black individuals 11.51 (9.16) 10.49 (8.94) 12.28 (8.56) 12.14 (10.65) % of low-educated individuals 16.71 (5.40) 16.27 (5.17) 16.27 (4.95) 18.70 (6.36) % of individuals aged less than 25 19.42 (2.43) 19.39 (2.45) 19.43 (2.40) 19.47 (2.48) % of individuals aged 25–34 27.91 (1.94) 28.71 (2.06) 27.57 (1.63) 26.81 (1.46) % of individuals aged 35–44 23.26 (1.22) 23.56 (1.49) 23.12 (0.94) 22.88 (0.85) % of individuals aged 45–54 15.79 (1.10) 15.43 (1.12) 15.95 (0.96) 16.27 (1.08) % of individuals aged 55 and over 13.62 (2.14) 12.90 (2.48) 13.93 (1.73) 14.56 (1.54) Labour % of employed individuals 71.82 (4.58) 71.78 (5.11) 71.97 (4.12) 71.59 (4.26) % of unemployed individuals 4.57 (0.98) 4.56 (0.94) 4.60 (0.96) 4.51 (1.12) % of not in labour force 23.61 (3.91) 23.65 (4.45) 23.43 (3.52) 23.90 (3.35) % of individuals in manufacturing 12.92 (4.91) 10.95 (3.76) 14.00 (4.04) 15.02 (6.98) Income Income (mean, household equivalised) 38,738 (7,221) 39,251 (6,990) 39,075 (7,211) 36,814 (7,497) % of individuals w. eq. fam. income<$15k 18.82 (6.52) 19.12 (6.45) 17.96 (6.38) 20.03 (6.77) % of individuals w. eq. fam. income<$20k 27.57 (8.49) 27.87 (8.24) 26.39 (8.53) 29.48 (8.60) % of individuals w. income<$15k 39.01 (6.25) 38.55 (6.66) 38.87 (5.94) 40.37 (5.79) % of individuals w. income<$20k 47.26 (7.06) 46.78 (7.27) 46.95 (6.90) 49.07 (6.66) Observations 240 241 241 722 Average size of each CZ 429,880 413,836 186,930 343,429 Notes: RTI is the routine task index defined in Subsection 1.2. CZs are weighted by their population in 1990. Open in new tab Table 1. CZ Characteristics by RTI Tercile, in 1990. . All . RTI low . RTI medium . RTI high . . Mean . SD . Mean . SD . Mean . SD . Mean . SD . Imports and RTI IPW (in $1,000) 0.30 (0.33) 0.21 (0.24) 0.32 (0.34) 0.45 (0.42) IPWOTH (in $1,000) 0.40 (0.34) 0.29 (0.21) 0.41 (0.32) 0.62 (0.47) RTI (mean) 1.27 (0.10) 1.24 (0.08) 1.29 (0.09) 1.28 (0.13) RTI (mean) in manufacturing 1.46 (0.14) 1.33 (0.09) 1.51 (0.04) 1.64 (0.09) Demographics % of male 49.33 (1.11) 49.88 (1.11) 48.99 (0.86) 48.84 (1.08) % of white individuals 81.23 (11.21) 79.02 (11.20) 83.22 (9.29) 81.90 (13.95) % of black individuals 11.51 (9.16) 10.49 (8.94) 12.28 (8.56) 12.14 (10.65) % of low-educated individuals 16.71 (5.40) 16.27 (5.17) 16.27 (4.95) 18.70 (6.36) % of individuals aged less than 25 19.42 (2.43) 19.39 (2.45) 19.43 (2.40) 19.47 (2.48) % of individuals aged 25–34 27.91 (1.94) 28.71 (2.06) 27.57 (1.63) 26.81 (1.46) % of individuals aged 35–44 23.26 (1.22) 23.56 (1.49) 23.12 (0.94) 22.88 (0.85) % of individuals aged 45–54 15.79 (1.10) 15.43 (1.12) 15.95 (0.96) 16.27 (1.08) % of individuals aged 55 and over 13.62 (2.14) 12.90 (2.48) 13.93 (1.73) 14.56 (1.54) Labour % of employed individuals 71.82 (4.58) 71.78 (5.11) 71.97 (4.12) 71.59 (4.26) % of unemployed individuals 4.57 (0.98) 4.56 (0.94) 4.60 (0.96) 4.51 (1.12) % of not in labour force 23.61 (3.91) 23.65 (4.45) 23.43 (3.52) 23.90 (3.35) % of individuals in manufacturing 12.92 (4.91) 10.95 (3.76) 14.00 (4.04) 15.02 (6.98) Income Income (mean, household equivalised) 38,738 (7,221) 39,251 (6,990) 39,075 (7,211) 36,814 (7,497) % of individuals w. eq. fam. income<$15k 18.82 (6.52) 19.12 (6.45) 17.96 (6.38) 20.03 (6.77) % of individuals w. eq. fam. income<$20k 27.57 (8.49) 27.87 (8.24) 26.39 (8.53) 29.48 (8.60) % of individuals w. income<$15k 39.01 (6.25) 38.55 (6.66) 38.87 (5.94) 40.37 (5.79) % of individuals w. income<$20k 47.26 (7.06) 46.78 (7.27) 46.95 (6.90) 49.07 (6.66) Observations 240 241 241 722 Average size of each CZ 429,880 413,836 186,930 343,429 . All . RTI low . RTI medium . RTI high . . Mean . SD . Mean . SD . Mean . SD . Mean . SD . Imports and RTI IPW (in $1,000) 0.30 (0.33) 0.21 (0.24) 0.32 (0.34) 0.45 (0.42) IPWOTH (in $1,000) 0.40 (0.34) 0.29 (0.21) 0.41 (0.32) 0.62 (0.47) RTI (mean) 1.27 (0.10) 1.24 (0.08) 1.29 (0.09) 1.28 (0.13) RTI (mean) in manufacturing 1.46 (0.14) 1.33 (0.09) 1.51 (0.04) 1.64 (0.09) Demographics % of male 49.33 (1.11) 49.88 (1.11) 48.99 (0.86) 48.84 (1.08) % of white individuals 81.23 (11.21) 79.02 (11.20) 83.22 (9.29) 81.90 (13.95) % of black individuals 11.51 (9.16) 10.49 (8.94) 12.28 (8.56) 12.14 (10.65) % of low-educated individuals 16.71 (5.40) 16.27 (5.17) 16.27 (4.95) 18.70 (6.36) % of individuals aged less than 25 19.42 (2.43) 19.39 (2.45) 19.43 (2.40) 19.47 (2.48) % of individuals aged 25–34 27.91 (1.94) 28.71 (2.06) 27.57 (1.63) 26.81 (1.46) % of individuals aged 35–44 23.26 (1.22) 23.56 (1.49) 23.12 (0.94) 22.88 (0.85) % of individuals aged 45–54 15.79 (1.10) 15.43 (1.12) 15.95 (0.96) 16.27 (1.08) % of individuals aged 55 and over 13.62 (2.14) 12.90 (2.48) 13.93 (1.73) 14.56 (1.54) Labour % of employed individuals 71.82 (4.58) 71.78 (5.11) 71.97 (4.12) 71.59 (4.26) % of unemployed individuals 4.57 (0.98) 4.56 (0.94) 4.60 (0.96) 4.51 (1.12) % of not in labour force 23.61 (3.91) 23.65 (4.45) 23.43 (3.52) 23.90 (3.35) % of individuals in manufacturing 12.92 (4.91) 10.95 (3.76) 14.00 (4.04) 15.02 (6.98) Income Income (mean, household equivalised) 38,738 (7,221) 39,251 (6,990) 39,075 (7,211) 36,814 (7,497) % of individuals w. eq. fam. income<$15k 18.82 (6.52) 19.12 (6.45) 17.96 (6.38) 20.03 (6.77) % of individuals w. eq. fam. income<$20k 27.57 (8.49) 27.87 (8.24) 26.39 (8.53) 29.48 (8.60) % of individuals w. income<$15k 39.01 (6.25) 38.55 (6.66) 38.87 (5.94) 40.37 (5.79) % of individuals w. income<$20k 47.26 (7.06) 46.78 (7.27) 46.95 (6.90) 49.07 (6.66) Observations 240 241 241 722 Average size of each CZ 429,880 413,836 186,930 343,429 Notes: RTI is the routine task index defined in Subsection 1.2. CZs are weighted by their population in 1990. Open in new tab The interplay between import competition and automatability. One important question is whether treating the IPW shock at the CZ level as exogenous to exposure to automation in the manufacturing sector at the CZ is reasonable. The concern would be that the industry composition that makes a CZ more exposed to import competition from China also contains more routine jobs that are prone to go through automation. If this were the case, and, provided that the two processes occur over the same period with the same adverse consequences in terms of employment, it would be hard to disentangle the impact of the import shock on local labour markets from that of automatability. Below we verify the extent of the overlap between the two phenomena. Autor et al. (2015) is centred on this very issue, i.e., juxtaposing and untangling import competition and technology effects on employment in US local labour markets, from 1980 to 2007. Their findings are threefold: first, technology (defined as the RTI measure) and import competition (defined as the IPW measure) have distinct effects on employment: while import competition leads to worse outcomes in terms of employment, unemployment and non-employment, technological change has only minor adverse effects on employment. Second, technological change gives rise to occupational polarisation, as losses in routine-intensive jobs are largely compensated by gains in jobs that are intensive in abstract or manual tasks. This compensation does not occur in the case of the import shock, which affects the whole manufacturing sector across all occupation groups, i.e., jobs intensive in manual and abstract tasks as well. Third, the timing of the two processes differ, as technological change has its greatest impact on employment in manufacturing (which is the technological change measure we focus on) in the 1980s, its smallest impact in the 2000s, when imports from China were skyrocketing. Those findings show that import competition and technology are separate phenomena in terms of the magnitude and timing of their effects. Since we use technology at one moment in time (in 1990) as a source of heterogeneity across the territory, the two phenomena should also be explored together at the geographical level. As described in Table 1, the IPW measure in 1990 increases across the RTI terciles, but the correlation between the two measures is quite low, i.e., less than 0.06 over the period. This is in line with Autor et al. (2013b), which explores the geographic overlap of trade and technology shocks in US local labour markets, and finds them to be largely uncorrelated across the territory. In the following analyses we will therefore interact the IPW measure with the three terciles of RTI as defined in 1990, i.e., after most of the technological change has occurred in the manufacturing sector but before the so-called China shock has hit the USA. 2. The Dynamic Impact of Import Competition on Local Labour Markets We first investigate the effect of import competition from China on the share of manufacturing employment among the working-age population (18–65 years old), replicating the work of Autor et al. (2013a) for the 1991–2011 period, i.e., adding the 2007–11 period to their two periods (1990–2000 and 2000–7). Both the dependent variable and the IPW shock are defined in differences with respect to the beginning of the period, all regressions include year and region fixed effects, and a set of CZ characteristics, such as the share of individuals in routine occupations at the start of the period (see Table 2 for all the controls). We define an occupation as a routine-intensive occupation if it belongs to the highest tercile of the RTI measure in 1980, so that 33% of employment in 1980 corresponds to those routine occupations. We aggregate this measure to the CZ level for every year, to obtain the share of routine-intensive occupations for every CZ and year. Both the outcome and the controls (except for the share of manufacturing workers among all workers at the start of the period, which comes from the CBP) are extracted from the IPUMS Census data for years 1990, 2000, 2007 and 2010. The key explanatory variable—i.e., the IPW shock—is computed as explained above using both CBP and trade data. This analysis is therefore at the CZ*year level (N=2,166, i.e., 722 CZs over three periods). Denote Yjct the outcome of interest in CZ c and in year t. We relate it to the IPW shock in the following way: $$\begin{eqnarray} \Delta Y_{c,t}=\alpha _{0}+\alpha _{1} \Delta \textit{IPW}_{c,t}+\alpha _{X} X_{c,t}+\delta _{r}+\delta _{t}+\epsilon _{c,t}, \end{eqnarray}$$(1) where δr are region fixed effects, δt year fixed effects, Xc,t are CZ characteristics. We cluster the standard errors at state level, to account for spatial correlation across CZs within states. The change in import exposure IPWc,t is instrumented by the change in exposure to Chinese imports in other countries |$\textit{IPW}_{c,t}^{\textit{OTH}}$|⁠. Autor et al. (2013a) enumerates three threats to identification: first, product-demand shocks may be correlated among high-income countries; second, US—rather than Chinese—productivity shocks may be driving the growth in imports from China; third, technology shocks common to high-income countries may affect negatively their labour-intensive industries. Autor et al. (2013a) addresses the first concern by estimating a gravity model and showing that the instrumental variable method and gravity model lead to similar conclusions. They also construct the IPW shock without considering the computer industry, in which demand does increase at the same time in all high-income countries. The robustness of the results allow us to be confident that the labour market and the resulting health effects of the IPW shock are not driven by positive demand shocks that would occur in all high-income countries at the same time. It is also worth mentioning that had it been the case, we would be estimating a lower bound of the effect of import competition on local labour markets and health outcomes. The second concern is very unlikely: that a surge in US productivity would drive the growth of US imports from China does not seem to reflect the reality. This is also supported by Brandt et al. (2012), which estimates that productivity in China increased by 8% over 1998 to 2007, i.e., more that twice that of the USA. The third concern is that automation could be the hidden force behind the growth in US imports from China, and that this process would be undermining employment in industries that are labour-intensive. We believe—along with Autor et al. (2013a)—that this story is unlikely, as the growth in Chinese exports seems to be mainly due to factors that are specific to China such as policy reforms and rapid productivity growth. Nevertheless we add a control for the share of routine occupations at the CZ level in all our specifications. We use the same definition of a routine occupation as Autor et al. (2013a), incorporating both white-collar jobs that are at risk of being computerised, suck as clerks and administrative support, and blue-collar production occupations, which involve repetitive tasks at risk of being replaced by machines. By including this control, we make sure that the adverse effects of a higher share of routine-intensive occupations in a CZ on labour and health outcomes—which are significant and negative, and similar whether we introduce RTI heterogeneity or not—are not captured by the IPW coefficient.6 Table 2 presents the estimation of equation (1) with the share of working-age individuals working in manufacturing as the outcome. In other words, it replicates and extends the well-established results of Autor et al. (2013a) on the effect of the IPW shock on the share of individuals working in manufacturing, adding a third period (2007–11) to it. Columns (1)–(5) show a significant and negative coefficient for the IPW measure across all specifications, but of lesser magnitude than in the two-period model (i.e., until 2007), as the start-of-period percentage of employment in manufacturing correlates more with the outcome than in the initial results. Table 2. Imports from China and Change of Manufacturing Employment in CZs. 2SLS Estimates—Stacked Differences, 1990–2011 (Three Periods). Dependent Variable: 10 x Annual Change in Manufacturing Emp./Working-Age Pop. (in %pts). . (1) . (2) . (3) . (4) . (5) . (6) . Δ IPWCHN −0.732*** −0.345*** −0.282*** −0.278*** −0.347*** (0.086) (0.096) (0.103) (0.102) (0.106) Δ IPWCHN X (Low RTI=1) −0.255** (0.129) Δ IPWCHN X (Medium RTI=1) −0.445*** (0.163) Δ IPWCHN X (High RTI=1) −0.577*** (0.130) % of manufacturing workers −0.101*** −0.110*** −0.111*** −0.095*** −0.083*** (0.018) (0.019) (0.019) (0.016) (0.017) % of college-educated individuals −0.000 0.018 0.011 (0.013) (0.013) (0.013) % of foreign born individuals 0.002 0.034*** 0.035*** (0.008) (0.011) (0.012) % of employed individuals among women −0.046** −0.016 −0.008 (0.022) (0.020) (0.022) % of individuals in routine occupations −0.273*** −0.254*** (0.046) (0.047) Task offshorability (mean) −0.000 −0.004 (0.011) (0.011) Constant −2.263*** −1.233*** −1.733*** 1.507 5.850*** 4.882** (0.272) (0.303) (0.320) (1.353) (1.927) (2.073) Census division dummies No No Yes Yes Yes Yes R2 . 0.151 0.210 0.220 0.235 0.193 . (1) . (2) . (3) . (4) . (5) . (6) . Δ IPWCHN −0.732*** −0.345*** −0.282*** −0.278*** −0.347*** (0.086) (0.096) (0.103) (0.102) (0.106) Δ IPWCHN X (Low RTI=1) −0.255** (0.129) Δ IPWCHN X (Medium RTI=1) −0.445*** (0.163) Δ IPWCHN X (High RTI=1) −0.577*** (0.130) % of manufacturing workers −0.101*** −0.110*** −0.111*** −0.095*** −0.083*** (0.018) (0.019) (0.019) (0.016) (0.017) % of college-educated individuals −0.000 0.018 0.011 (0.013) (0.013) (0.013) % of foreign born individuals 0.002 0.034*** 0.035*** (0.008) (0.011) (0.012) % of employed individuals among women −0.046** −0.016 −0.008 (0.022) (0.020) (0.022) % of individuals in routine occupations −0.273*** −0.254*** (0.046) (0.047) Task offshorability (mean) −0.000 −0.004 (0.011) (0.011) Constant −2.263*** −1.233*** −1.733*** 1.507 5.850*** 4.882** (0.272) (0.303) (0.320) (1.353) (1.927) (2.073) Census division dummies No No Yes Yes Yes Yes R2 . 0.151 0.210 0.220 0.235 0.193 Notes: N=2,166=722 CZs x three time periods (1990–2000, 2000–7, 2007–11). All regressions include a constant and a dummy for each time period. First stage estimates also include the control variables that are indicated in the corresponding columns (taken at the start of the period). Routine occupations are defined such that they account for one-third of US employment in 1980. The offshorability index variable is standardised to mean of 0 and SD of 10 in 1980. Robust SE in parentheses are clustered on state. Models are weighted by start of period CZ share of national population. *p < 0.10, **p < 0.05, ***p < 0.01. Open in new tab Table 2. Imports from China and Change of Manufacturing Employment in CZs. 2SLS Estimates—Stacked Differences, 1990–2011 (Three Periods). Dependent Variable: 10 x Annual Change in Manufacturing Emp./Working-Age Pop. (in %pts). . (1) . (2) . (3) . (4) . (5) . (6) . Δ IPWCHN −0.732*** −0.345*** −0.282*** −0.278*** −0.347*** (0.086) (0.096) (0.103) (0.102) (0.106) Δ IPWCHN X (Low RTI=1) −0.255** (0.129) Δ IPWCHN X (Medium RTI=1) −0.445*** (0.163) Δ IPWCHN X (High RTI=1) −0.577*** (0.130) % of manufacturing workers −0.101*** −0.110*** −0.111*** −0.095*** −0.083*** (0.018) (0.019) (0.019) (0.016) (0.017) % of college-educated individuals −0.000 0.018 0.011 (0.013) (0.013) (0.013) % of foreign born individuals 0.002 0.034*** 0.035*** (0.008) (0.011) (0.012) % of employed individuals among women −0.046** −0.016 −0.008 (0.022) (0.020) (0.022) % of individuals in routine occupations −0.273*** −0.254*** (0.046) (0.047) Task offshorability (mean) −0.000 −0.004 (0.011) (0.011) Constant −2.263*** −1.233*** −1.733*** 1.507 5.850*** 4.882** (0.272) (0.303) (0.320) (1.353) (1.927) (2.073) Census division dummies No No Yes Yes Yes Yes R2 . 0.151 0.210 0.220 0.235 0.193 . (1) . (2) . (3) . (4) . (5) . (6) . Δ IPWCHN −0.732*** −0.345*** −0.282*** −0.278*** −0.347*** (0.086) (0.096) (0.103) (0.102) (0.106) Δ IPWCHN X (Low RTI=1) −0.255** (0.129) Δ IPWCHN X (Medium RTI=1) −0.445*** (0.163) Δ IPWCHN X (High RTI=1) −0.577*** (0.130) % of manufacturing workers −0.101*** −0.110*** −0.111*** −0.095*** −0.083*** (0.018) (0.019) (0.019) (0.016) (0.017) % of college-educated individuals −0.000 0.018 0.011 (0.013) (0.013) (0.013) % of foreign born individuals 0.002 0.034*** 0.035*** (0.008) (0.011) (0.012) % of employed individuals among women −0.046** −0.016 −0.008 (0.022) (0.020) (0.022) % of individuals in routine occupations −0.273*** −0.254*** (0.046) (0.047) Task offshorability (mean) −0.000 −0.004 (0.011) (0.011) Constant −2.263*** −1.233*** −1.733*** 1.507 5.850*** 4.882** (0.272) (0.303) (0.320) (1.353) (1.927) (2.073) Census division dummies No No Yes Yes Yes Yes R2 . 0.151 0.210 0.220 0.235 0.193 Notes: N=2,166=722 CZs x three time periods (1990–2000, 2000–7, 2007–11). All regressions include a constant and a dummy for each time period. First stage estimates also include the control variables that are indicated in the corresponding columns (taken at the start of the period). Routine occupations are defined such that they account for one-third of US employment in 1980. The offshorability index variable is standardised to mean of 0 and SD of 10 in 1980. Robust SE in parentheses are clustered on state. Models are weighted by start of period CZ share of national population. *p < 0.10, **p < 0.05, ***p < 0.01. Open in new tab We then add to these established results by introducing the RTI as a spatial source of heterogeneity in the impact of exposure to import competition on local labour markets. Bernard et al. (2006) shows that import competition from low-wage countries leads US manufacturing to reallocate over time towards industries that are more capital and skill intensive. Firms that are hit the hardest—i.e., firms intense in low-skilled labour—by import competition either close down or react by upgrading their product mix. Low-skilled production workers are therefore likely to be more affected than high-skilled non-production workers. When hit by import competition, they may lose their jobs due to plant closure, or see their job automated away, precisely because low-skilled jobs in manufacturing are intense in tasks that require less human intelligence and are more prone to being robotised. Chinese import competition has also been shown to induce more technological change (R&D, patenting, IT and productivity) in the firms that were not driven out (Bloom et al., 2015). Going further, Jaimovich and Siu (2012) show that once routine jobs are destroyed during an economic downturn, they are less likely to rebound when recovery occurs than jobs in non-routine occupations. Manufacturing workers in areas where jobs are more routine intensive are then under the double pressure of plants closing down due to a shrinking domestic market, and an automation process threatening the existence of their jobs. We should therefore observe more dramatic consequences of the import competition shock in those areas. Areas where jobs are the least intense in routine tasks are still exposed to import competition from China, but these effects are not amplified by import-induced technological change. To investigate this issue, we introduce interactions between the IPW shock and the three RTI terciles in equation (1), which are now instrumented by the interactions of |$IPW_{c,t}^{OTH}$| and the three terciles of RTI. As shown in column (6), the IPW effect increases with the intensity of automatability across the territory: the higher the average RTI, the higher the impact of the import shock on manufacturing decline. All three coefficients are statistically different, with the estimate of the IPW coefficient in the highest RTI tercile being more than twice that in the lowest RTI tercile.7 We then investigate the effect of import competition from China on other labour market outcomes such as the share of individuals who are employed, unemployed or out of the labour force, and the average equivalised family income. In the left panel of Table 3, we estimate again equation (1) for the 1991–2011 period, but with annual differences, i.e., considering 20 one-year periods. All regressions control for the share of individuals in routine occupations at the start of the period. A comparison with Table 2 which used exactly the same set of controls as in Autor et al. (2013a) shows that results are unchanged. In Table 3 and for the remainder of the analyses we control for the share of routine occupations at the CZ level and in the health analysis section we add individual controls for the other characteristics such as race, education and gender. All the outcomes, and the share of routine occupations, are extracted from the IPUMS Census data for years 1990, 2000, 2007 and 2010. Years in between (and 2011) are interpolated (or extrapolated). The IPW shock is defined from 1991 to 2011 using the CBP and trade data for every year. This analysis is therefore at the CZ*year level (N=14,440, i.e., 722 CZs over 20 years.). We check that the previous results are not driven by one atypical year among the very few that were exploited in the literature before. By using 21 years of data instead of four, our estimates of the local labour market effects of the import shock will be more robust. This will be even more important for the health section of the paper as we will exploit annual data for the outcomes as well. Table 3. Imports from China and Change of Labour Market Outcomes in CZs, by RTI Tercile. 2SLS Estimates—Stacked One-year Differences, 1990–2011. Dependent Variables: Annual Change in Labour Market Outcome/Working-Age Pop. (in %pts) for the Left Panel. Level of Labour Force Outcome/Working-Age Pop. (in %pts) for the Right Panel. . Δ IPW interacted with . IPW (in levels) interacted with . . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Share employed −0.22*** −0.08 −0.33*** −0.40*** −0.31* −0.11 −0.44*** −0.50*** (0.05) (0.06) (0.09) (0.07) (0.16) (0.14) (0.16) (0.18) Share unemployed 0.06*** 0.05* 0.08** 0.07** 0.06 0.05 0.09 0.07 (0.02) (0.03) (0.04) (0.03) (0.05) (0.05) (0.07) (0.06) Share not in labour force 0.16*** 0.03 0.25*** 0.32*** 0.25* 0.07 0.35*** 0.43*** (0.05) (0.05) (0.06) (0.05) (0.14) (0.12) (0.12) (0.14) Share manufacturing −0.34*** −0.23*** −0.36*** −0.55*** −0.92*** −0.70*** −0.97*** −1.20*** (0.05) (0.05) (0.05) (0.07) (0.17) (0.14) (0.2) (0.22) Mean family income (eq.) −164.34** −71.66 −252.00** −252.97** −323.72 −57.67 −492.66* −569.98** (78.02) (70.67) (110.86) (105.54) (235.96) (201.69) (271.47) (230.44) Family income (eq.)<15k 0.2*** 0.11 0.27*** 0.3*** 0.25* 0.13 0.37*** 0.31** (0.05) (0.07) (0.09) (0.07) (0.14) (0.17) (0.14) (0.15) . Δ IPW interacted with . IPW (in levels) interacted with . . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Share employed −0.22*** −0.08 −0.33*** −0.40*** −0.31* −0.11 −0.44*** −0.50*** (0.05) (0.06) (0.09) (0.07) (0.16) (0.14) (0.16) (0.18) Share unemployed 0.06*** 0.05* 0.08** 0.07** 0.06 0.05 0.09 0.07 (0.02) (0.03) (0.04) (0.03) (0.05) (0.05) (0.07) (0.06) Share not in labour force 0.16*** 0.03 0.25*** 0.32*** 0.25* 0.07 0.35*** 0.43*** (0.05) (0.05) (0.06) (0.05) (0.14) (0.12) (0.12) (0.14) Share manufacturing −0.34*** −0.23*** −0.36*** −0.55*** −0.92*** −0.70*** −0.97*** −1.20*** (0.05) (0.05) (0.05) (0.07) (0.17) (0.14) (0.2) (0.22) Mean family income (eq.) −164.34** −71.66 −252.00** −252.97** −323.72 −57.67 −492.66* −569.98** (78.02) (70.67) (110.86) (105.54) (235.96) (201.69) (271.47) (230.44) Family income (eq.)<15k 0.2*** 0.11 0.27*** 0.3*** 0.25* 0.13 0.37*** 0.31** (0.05) (0.07) (0.09) (0.07) (0.14) (0.17) (0.14) (0.15) Notes: N=722 CZs x 20 years for the left panel, N=722 x 21 years for the right panel. Dependent variables are listed in each row. The left panel displays the results of two regressions: in columns (1)–(3) the IPW measure is interacted with three RTI terciles, in column (4) it is not. The right panel is similar to the left panel, with the dependent variable and IPW variable being defined in levels instead of as differences. All regressions include a constant and a dummy for each time period, percent of individuals in routine occupations, region fixed effects. The right panel also includes region-specific trends and CZ fixed effects. Routine occupations are defined such that they account for one-third of US employment in 1980. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered on state. Models are weighted by start of period CZ share of national population. *p < 0.10, **p < 0.05, ***p < 0.01. Open in new tab Table 3. Imports from China and Change of Labour Market Outcomes in CZs, by RTI Tercile. 2SLS Estimates—Stacked One-year Differences, 1990–2011. Dependent Variables: Annual Change in Labour Market Outcome/Working-Age Pop. (in %pts) for the Left Panel. Level of Labour Force Outcome/Working-Age Pop. (in %pts) for the Right Panel. . Δ IPW interacted with . IPW (in levels) interacted with . . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Share employed −0.22*** −0.08 −0.33*** −0.40*** −0.31* −0.11 −0.44*** −0.50*** (0.05) (0.06) (0.09) (0.07) (0.16) (0.14) (0.16) (0.18) Share unemployed 0.06*** 0.05* 0.08** 0.07** 0.06 0.05 0.09 0.07 (0.02) (0.03) (0.04) (0.03) (0.05) (0.05) (0.07) (0.06) Share not in labour force 0.16*** 0.03 0.25*** 0.32*** 0.25* 0.07 0.35*** 0.43*** (0.05) (0.05) (0.06) (0.05) (0.14) (0.12) (0.12) (0.14) Share manufacturing −0.34*** −0.23*** −0.36*** −0.55*** −0.92*** −0.70*** −0.97*** −1.20*** (0.05) (0.05) (0.05) (0.07) (0.17) (0.14) (0.2) (0.22) Mean family income (eq.) −164.34** −71.66 −252.00** −252.97** −323.72 −57.67 −492.66* −569.98** (78.02) (70.67) (110.86) (105.54) (235.96) (201.69) (271.47) (230.44) Family income (eq.)<15k 0.2*** 0.11 0.27*** 0.3*** 0.25* 0.13 0.37*** 0.31** (0.05) (0.07) (0.09) (0.07) (0.14) (0.17) (0.14) (0.15) . Δ IPW interacted with . IPW (in levels) interacted with . . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Share employed −0.22*** −0.08 −0.33*** −0.40*** −0.31* −0.11 −0.44*** −0.50*** (0.05) (0.06) (0.09) (0.07) (0.16) (0.14) (0.16) (0.18) Share unemployed 0.06*** 0.05* 0.08** 0.07** 0.06 0.05 0.09 0.07 (0.02) (0.03) (0.04) (0.03) (0.05) (0.05) (0.07) (0.06) Share not in labour force 0.16*** 0.03 0.25*** 0.32*** 0.25* 0.07 0.35*** 0.43*** (0.05) (0.05) (0.06) (0.05) (0.14) (0.12) (0.12) (0.14) Share manufacturing −0.34*** −0.23*** −0.36*** −0.55*** −0.92*** −0.70*** −0.97*** −1.20*** (0.05) (0.05) (0.05) (0.07) (0.17) (0.14) (0.2) (0.22) Mean family income (eq.) −164.34** −71.66 −252.00** −252.97** −323.72 −57.67 −492.66* −569.98** (78.02) (70.67) (110.86) (105.54) (235.96) (201.69) (271.47) (230.44) Family income (eq.)<15k 0.2*** 0.11 0.27*** 0.3*** 0.25* 0.13 0.37*** 0.31** (0.05) (0.07) (0.09) (0.07) (0.14) (0.17) (0.14) (0.15) Notes: N=722 CZs x 20 years for the left panel, N=722 x 21 years for the right panel. Dependent variables are listed in each row. The left panel displays the results of two regressions: in columns (1)–(3) the IPW measure is interacted with three RTI terciles, in column (4) it is not. The right panel is similar to the left panel, with the dependent variable and IPW variable being defined in levels instead of as differences. All regressions include a constant and a dummy for each time period, percent of individuals in routine occupations, region fixed effects. The right panel also includes region-specific trends and CZ fixed effects. Routine occupations are defined such that they account for one-third of US employment in 1980. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered on state. Models are weighted by start of period CZ share of national population. *p < 0.10, **p < 0.05, ***p < 0.01. Open in new tab In the right panel of Table 3, we move to a fixed effects model, which we adopt in the remainder of the text either because we estimate the model from repeated cross-sections at the individual level, or because of the unbalanced nature of our panel data. We estimate regressions of the corresponding outcome at the CZ-year level on the level of the IPW (instrumented by the level of |$\textit{IPW}_{c,t}^{\textit{OTH}}$|⁠), year and CZ fixed effects, region-specific trends and CZ characteristics. This model is therefore equivalent to the first differenced model: CZ and year fixed effects ensure we estimate within-CZ effects, and the region-specific trends allow us to control for any trend that would affect differentially local labour markets across regions. Results in the left panel (the first differenced model) column (4) suggest that a CZ going through a $1,000 IPW increase from one year to another will suffer a decline in the share of the working-age population employed across all sectors (0.22 percentage point), employed in manufacturing (0.34 percentage points), and an increase of the share of the working-age population who are unemployed (very small: 0.06 percentage points), out of the labour force (0.16 percentage points), or whose average family income is below $15,000 (0.2 percentage point). Columns (1)–(3) show that the negative impact of the import shock on local labour markets is mostly concentrated in the top-RTI-tercile CZs, and to a lesser extent in the medium tercile group. The shares of individuals who are employed or out of the labour force are impacted by exposure to import competition only in the medium and highest RTI terciles. It therefore seems that those who exit the manufacturing sector in the low RTI CZs do not exit employment or the labour force as a result of the import shock, but reallocate out of the manufacturing sector, and consequently do not suffer a drop in income, unlike those in the medium and highest RTI terciles. The corresponding estimates in the right panel are very similar. Last, we introduce lags in the IPW shock, so that we can look at how local labour markets are affected immediately and a few years after imports per worker have increased in a CZ. The fixed effects model we estimate now allows for lags and RTI heterogeneity. Table 4 displays the results for years 1997 to 2011—so that the sample is the same across all lags—for areas with a high RTI. All regressions point to an increasing effect of the IPW shock across lags, more so after four years. Again, import competition does not significantly increase the share of individuals who are unemployed, even though the coefficient is positive and of greater magnitude after four years. Column (1) also shows that the point estimates are higher when years 1991–6 are omitted (compared with column (8) of Table 3.), which suggests the import competition effects on local labour markets were lesser in the early 1990s than afterwards. Table 4. Imports from China and Labour Market Outcomes in CZs, in High-Routine-Task-Intensity Tercile, with Lags. 2SLS Estimates—Fixed-Effects Model, 1997−2011. Dependent Variable: Level of Labour Force Outcomes/Working-Age Pop. (in %pts). . IPW interacted with high RTI . . Lag0 . Lag1 . Lag2 . Lag3 . Lag4 . Lag5 . Lag6 . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . Share employed −0.41* −0.42** −0.44** −0.43** −0.50** −0.63*** −0.81*** (0.21) (0.21) (0.21) (0.21) (0.2) (0.22) (0.28) Share unemployed 0.03 0.04 0.04 0.01 0.03 0.04 0.07 (0.08) (0.08) (0.08) (0.09) (0.09) (0.1) (0.13) Share not in labour force 0.38** 0.39** 0.4** 0.41*** 0.47*** 0.59*** 0.74*** (0.17) (0.16) (0.16) (0.15) (0.15) (0.17) (0.21) Share manufacturing −1.22*** −1.20*** −1.16*** −1.16*** −1.19*** −1.31*** −1.60*** (0.21) (0.18) (0.17) (0.17) (0.18) (0.19) (0.23) Mean family income (eq.) −447.69* −430.04* −375.86 −279.13 −300.58 −385.56 −532.06 (258.18) (252.94) (246.20) (249.05) (256.40) (281.99) (340.93) Family income (eq.)<15k 0.45*** 0.48*** 0.46*** 0.43** 0.47** 0.56*** 0.68*** (0.17) (0.17) (0.18) (0.18) (0.18) (0.2) (0.25) . IPW interacted with high RTI . . Lag0 . Lag1 . Lag2 . Lag3 . Lag4 . Lag5 . Lag6 . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . Share employed −0.41* −0.42** −0.44** −0.43** −0.50** −0.63*** −0.81*** (0.21) (0.21) (0.21) (0.21) (0.2) (0.22) (0.28) Share unemployed 0.03 0.04 0.04 0.01 0.03 0.04 0.07 (0.08) (0.08) (0.08) (0.09) (0.09) (0.1) (0.13) Share not in labour force 0.38** 0.39** 0.4** 0.41*** 0.47*** 0.59*** 0.74*** (0.17) (0.16) (0.16) (0.15) (0.15) (0.17) (0.21) Share manufacturing −1.22*** −1.20*** −1.16*** −1.16*** −1.19*** −1.31*** −1.60*** (0.21) (0.18) (0.17) (0.17) (0.18) (0.19) (0.23) Mean family income (eq.) −447.69* −430.04* −375.86 −279.13 −300.58 −385.56 −532.06 (258.18) (252.94) (246.20) (249.05) (256.40) (281.99) (340.93) Family income (eq.)<15k 0.45*** 0.48*** 0.46*** 0.43** 0.47** 0.56*** 0.68*** (0.17) (0.17) (0.18) (0.18) (0.18) (0.2) (0.25) Notes: For all regressions, N=10,830=722 CZs x 15 years. Years 1991–6 are omitted in order to have the same set of observations for all lags. Dependent variables are listed in each row. Each column corresponds to a different lag of the IPW variable. Each cell displays the coefficient of the IPW variable interacted with the highest RTI tercile in the corresponding regression. All regressions include a constant and a dummy for each time period, percent of individuals in routine occupations, region-specific trends and CZ fixed effects. Routine occupations are defined such that they account for one-third of US employment in 1980. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered on state. Models are weighted by annual CZ share of national population. *p < 0.10, **p < 0.05, ***p < 0.01. Open in new tab Table 4. Imports from China and Labour Market Outcomes in CZs, in High-Routine-Task-Intensity Tercile, with Lags. 2SLS Estimates—Fixed-Effects Model, 1997−2011. Dependent Variable: Level of Labour Force Outcomes/Working-Age Pop. (in %pts). . IPW interacted with high RTI . . Lag0 . Lag1 . Lag2 . Lag3 . Lag4 . Lag5 . Lag6 . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . Share employed −0.41* −0.42** −0.44** −0.43** −0.50** −0.63*** −0.81*** (0.21) (0.21) (0.21) (0.21) (0.2) (0.22) (0.28) Share unemployed 0.03 0.04 0.04 0.01 0.03 0.04 0.07 (0.08) (0.08) (0.08) (0.09) (0.09) (0.1) (0.13) Share not in labour force 0.38** 0.39** 0.4** 0.41*** 0.47*** 0.59*** 0.74*** (0.17) (0.16) (0.16) (0.15) (0.15) (0.17) (0.21) Share manufacturing −1.22*** −1.20*** −1.16*** −1.16*** −1.19*** −1.31*** −1.60*** (0.21) (0.18) (0.17) (0.17) (0.18) (0.19) (0.23) Mean family income (eq.) −447.69* −430.04* −375.86 −279.13 −300.58 −385.56 −532.06 (258.18) (252.94) (246.20) (249.05) (256.40) (281.99) (340.93) Family income (eq.)<15k 0.45*** 0.48*** 0.46*** 0.43** 0.47** 0.56*** 0.68*** (0.17) (0.17) (0.18) (0.18) (0.18) (0.2) (0.25) . IPW interacted with high RTI . . Lag0 . Lag1 . Lag2 . Lag3 . Lag4 . Lag5 . Lag6 . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . Share employed −0.41* −0.42** −0.44** −0.43** −0.50** −0.63*** −0.81*** (0.21) (0.21) (0.21) (0.21) (0.2) (0.22) (0.28) Share unemployed 0.03 0.04 0.04 0.01 0.03 0.04 0.07 (0.08) (0.08) (0.08) (0.09) (0.09) (0.1) (0.13) Share not in labour force 0.38** 0.39** 0.4** 0.41*** 0.47*** 0.59*** 0.74*** (0.17) (0.16) (0.16) (0.15) (0.15) (0.17) (0.21) Share manufacturing −1.22*** −1.20*** −1.16*** −1.16*** −1.19*** −1.31*** −1.60*** (0.21) (0.18) (0.17) (0.17) (0.18) (0.19) (0.23) Mean family income (eq.) −447.69* −430.04* −375.86 −279.13 −300.58 −385.56 −532.06 (258.18) (252.94) (246.20) (249.05) (256.40) (281.99) (340.93) Family income (eq.)<15k 0.45*** 0.48*** 0.46*** 0.43** 0.47** 0.56*** 0.68*** (0.17) (0.17) (0.18) (0.18) (0.18) (0.2) (0.25) Notes: For all regressions, N=10,830=722 CZs x 15 years. Years 1991–6 are omitted in order to have the same set of observations for all lags. Dependent variables are listed in each row. Each column corresponds to a different lag of the IPW variable. Each cell displays the coefficient of the IPW variable interacted with the highest RTI tercile in the corresponding regression. All regressions include a constant and a dummy for each time period, percent of individuals in routine occupations, region-specific trends and CZ fixed effects. Routine occupations are defined such that they account for one-third of US employment in 1980. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered on state. Models are weighted by annual CZ share of national population. *p < 0.10, **p < 0.05, ***p < 0.01. Open in new tab The results so far point to a detrimental effect of import competition, with considerable heterogeneity across US CZs. If the effect of imports on health operates through a loss of income or through a loss of employer-sponsored healthcare plan, we expect to see a stark difference in terms of health outcomes across different CZs depending on their degree of exposure to import competition from China, differentially for low and high RTI areas. 3. Impact of Import Competition on Health and Mortality In this section we investigate the effects of import competition on health using three different data sets which bring new light on the many aspects of the relationship between import competition and health. We first exploit large survey data with information on self-assessed health, health behaviour and healthcare utilisation. We next draw on extensive data on hospitalisations to refine the analysis. Finally, we exploit longitudinal individual data where we can directly assign workers to a particular industry and where we can control for prior sorting based on health. We first review the different potential pathways that the literature has uncovered and we discuss whether import competition shocks may generate different effects. 3.1. Potential Pathways We have shown that import competition, in affected areas, leads to a loss of employment and a loss of income over many years. How changes in income and labour market status is related to health has been a topic of interest across disciplines. A large literature in social medicine has documented the relationship between income and health, emphasising the role of material deprivation (see for instance Marmot et al., 1991). In the field of economics, Smith (1999) provides an overview of the many aspects and channels through which income and health could be linked. Lindahl (2005) or Snyder and Evans (2006) use quasi-experimental settings to evaluate the causal pathway between income and health at the individual level and find that higher income leads to better health. Similarly, Lleras-Muney (2005) shows that higher education, possibly as a proxy for permanent income, causes better health. The evidence using aggregate income shocks is more mixed. Ruhm (2000) finds that mortality declines during economic recessions. Similar evidence is found by Adda et al. (2009) using permanent shocks to household income for different birth cohorts. However, more recent evidence points at recessions not being healthy anymore: Ruhm (2015) finds that over the 1976–2010 period, total mortality shifted from strongly procyclical to being weakly or unrelated to macroeconomic conditions, depending on which cause of death is looked at. While cardiovascular diseases and motor accidents are still procyclical, countercyclical patterns have emerged for mortality due to cancer and external causes. The results in Section 2 show that the import shock is much more sustained than recessions. While a recession lasts on average for about one to two years, we find effects lasting for many years. This is a reason why it is difficult to extrapolate the health effects from results based on aggregate shocks such as business cycle variations. Exploiting firm closures, Martikainen et al. (2007), Rege et al. (2009) and Sullivan and von Wachter (2009) investigate the mortality pattern of workers who have been laid off in Finland, Norway and the USA. They find a marked increase in mortality, which is consistent with the decrease in income for the individuals who lose their job (Huttunen et al., 2011). Eliason and Storrie (2009) and Browning and Heinesen (2012) find similar effects using administrative data in Sweden and Denmark. Their data allow them to look at the cause of mortality to infer the mechanism. They find an increased mortality due to suicides, alcohol abuse and circulatory diseases. Schaller and Stevens (2015) investigates the short-run effects of job loss and shows evidence of poor self-assessed health and poor mental health. In contrast, Kuhn et al. (2009) or Black et al. (2015) find little effects of job displacement. The health effects of the import shock could be amplified by the interplay between mental and physical health. Experiencing job-related distress, whether due to actual or potential future job loss, or to being unable to find a new job, is likely to trigger or worsen mental health issues. The epidemiology literature has long recognised the role of psychosocial factors on health (Bartley, 1994; Brunner, 1997). In the most extreme cases, this can translate into increased mortality due to suicide (in line with Ruhm,2000; Eliason and Storrie, 2009; Browning and Heinesen, 2012). More commonly, job loss has also been found to increase mental disorders (Ruhm, 2003) and the consumption of antidepressants and related drugs, as well as hospitalisations due to mental health problems (Kuhn et al., 2009). The consequences of mental stress go beyond mental health conditions. Deaton et al. (2006) reviews a number of experiments and analyses concluding that psychological stress is responsible for higher odds of developing a disease, particularly a cardiovascular one.8 Tawakol et al. (2017) confirmed a causal link between brain stress and heart stress, offering novel insights into the mechanism through which brain stress converts into subsequent cardiovascular disease events, such as heart diseases and strokes. Last, losing one’s job also leads to greater risk of social isolation, which is associated with higher mortality risk (see Steptoe et al., 2013). Another potential consequence of an import shock—through job loss—is the loss of the employer-provided health insurance, which—in the case of the US—is not replaced by public coverage in most cases (i.e., before the recent implementation of the Affordable Care Act, when workers are not old enough to be covered by Medicare or do not fulfil the Medicaid requirements). Kuka (2020) shows that variations in unemployment insurance affect healthcare coverage and health. Untreated or delayed treatment could lead to more serious conditions and more fatal ones. 3.2. Impact of Imports on Health, Health Behaviour and Healthcare Utilisation 3.2.1. Data and empirical strategy We pool annual cross-sections of the BRFSS from 1997 to 2011. After 2011, the data do not record the county of residence. As in the case of the CBP, we focus on the post-1997 period in order to be able to look at the impact of exposure to import competition on health with an up-to-six-year lag. Our sample is made of individuals aged between 18 and 65, who were interviewed at some point between 1997 and 2011. The data on county of residence are used to assign individuals to CZs.9 We rely on a similar specification as in Section 2, equation (1), but we define the outcome as Yi,c,t for individual i in CZ c and year t. Our variable of interest is the instrumented IPW measured in CZ c and in year t − k. We also interact this measure with the routine task index of the CZ c, categorised as above into low, medium or high (L, M, H). Contrasting the effect of import competition across those three areas is akin to a triple diff-in-diff design, given that we have shown in the previous section that areas with lower RTI appear to be much less affected by import shocks. The model includes year and CZ fixed effects, and state-specific trends instead of region-specific trends, in order to control for potential state healthcare policy changes across years. We also include controls at the CZ level, i.e., the share of routine occupations in manufacturing employment in a CZ and individual controls such as gender, age, race and education. We estimate the model by fixed effects rather than with a first difference method because the data set is cross-sectional with regard to the individual and because not all health variables are collected every year. Following Abadie et al. (2017), we cluster standard errors at the level of variation of the shock, i.e., the CZ level.10 We weight each observation by its weight in the CZ, based on observable characteristics.11 The BRFSS offers a wide variety of outcomes of interest regarding the individuals’ health. We focus on a subset of outcomes that is common to most years of observation. As the survey contains many measures of health and we want to explore the dynamic effects of import competition by exploring its effect over many years, we first reduce the dimensionality of the data. We construct three indices relating to health, health behaviour and healthcare utilisation, using principal-component analysis. The composite measure of health is constructed by including self-assessed health, indicators for diabetes, being obese (with a BMI that is superior to 30), and poor mental health (number of days with mental health problems in the past 30 days). We also build a composite measure of health behaviour, summarising drinking, smoking and exercise habits. The index of healthcare utilisation is composed of an indicator for having a health plan, for having had a flu shot, whether a doctor visit was forgone due to its cost, and the time since last medical check-up. By construction, the composite indices have mean zero and a standard deviation of 100 (see Table A2 in the Appendix for descriptive statistics). All indices are such that higher values mean better health outcomes. 3.2.2. Evidence on health and its dynamics We provide estimates of the effect of import competition in Table 5, columns (1)–(4) using our general health composite index for lags ranging from 0 to six years. At the aggregate level (column (1)), the impact of the import shock on individuals’ health peaks at lag 0 (driven largely by mental and self-assessed health), then decreases until it loses significance after two years. A $1,000 increase in the import competition measure reduces the health index by about 1.5 units at lag zero. This translates into a 1% reduction of a standard deviation of health for a one standard deviation change in imports. Table 5. Imports from China and Composite Measures of Health, Health Behaviour and Healthcare Utilisation, by RTI Tercile. Dependent Variables: Composite Measures of Health, Health Behaviour and Healthcare Utilisation. . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lag 0 −1.551** −1.289* −1.890 −2.468*** 0.944 0.904 1.621 0.8 −1.358 −1.188 −1.353 −2.158 (0.729) (0.693) (1.297) (0.744) (1.086) (0.981) (2.537) (1.167) (1.500) (1.389) (2.846) (1.461) Lag 1 −1.219 −1.207 −0.999 −1.715*** 0.77 0.711 0.996 0.721 −1.161 −0.947 −2.594 −2.148 (0.749) (0.865) (0.855) (0.557) (0.809) (0.69) (1.513) (0.731) (1.314) (1.210) (2.920) (1.423) Lag 2 −0.977* −0.874 −0.975 −1.704*** 0.181 0.121 0.257 0.3 −1.657* −1.175 −2.967* −2.625*** (0.572) (0.611) (0.735) (0.553) (0.513) (0.512) (0.878) (0.514) (0.962) (0.96) (1.549) (0.882) Lag 3 −0.418 −0.433 −0.143 −1.473** 0.49 0.453 0.608 0.238 −0.758 −0.413 −1.086 −2.615*** (0.598) (0.588) (0.704) (0.575) (0.524) (0.551) (0.647) (0.504) (0.811) (0.895) (1.059) (0.927) Lag 4 −0.669 −0.773 −0.324 −1.614*** 0.75* 0.897* 0.65 0.391 −0.354 −0.200 −0.234 −2.109*** (0.699) (0.65) (0.8) (0.575) (0.451) (0.534) (0.509) (0.455) (0.739) (0.902) (0.838) (0.657) Lag 5 −0.714 −0.948 −0.266 −1.808*** 0.831** 0.943* 0.813* 0.123 −0.540 −0.444 −0.333 −2.370*** (0.749) (0.709) (0.761) (0.549) (0.415) (0.524) (0.453) (0.427) (1.089) (1.167) (1.183) (0.774) Lag 6 −0.664 −0.839 −0.252 −2.236*** 0.901** 1.249* 0.722* 0.232 −0.063 0.124 0.122 −1.920** (0.695) (0.724) (0.637) (0.521) (0.452) (0.669) (0.408) (0.495) (1.122) (1.650) (0.971) (0.844) Obs 2,558,350 2,310,087 1,960,926 Upper bound of −0.515*** −0.446*** −0.762*** $1,000 loss (0.011) (0.023) (0.034) Obs 2,317,766 2,080,098 1,768,292 . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lag 0 −1.551** −1.289* −1.890 −2.468*** 0.944 0.904 1.621 0.8 −1.358 −1.188 −1.353 −2.158 (0.729) (0.693) (1.297) (0.744) (1.086) (0.981) (2.537) (1.167) (1.500) (1.389) (2.846) (1.461) Lag 1 −1.219 −1.207 −0.999 −1.715*** 0.77 0.711 0.996 0.721 −1.161 −0.947 −2.594 −2.148 (0.749) (0.865) (0.855) (0.557) (0.809) (0.69) (1.513) (0.731) (1.314) (1.210) (2.920) (1.423) Lag 2 −0.977* −0.874 −0.975 −1.704*** 0.181 0.121 0.257 0.3 −1.657* −1.175 −2.967* −2.625*** (0.572) (0.611) (0.735) (0.553) (0.513) (0.512) (0.878) (0.514) (0.962) (0.96) (1.549) (0.882) Lag 3 −0.418 −0.433 −0.143 −1.473** 0.49 0.453 0.608 0.238 −0.758 −0.413 −1.086 −2.615*** (0.598) (0.588) (0.704) (0.575) (0.524) (0.551) (0.647) (0.504) (0.811) (0.895) (1.059) (0.927) Lag 4 −0.669 −0.773 −0.324 −1.614*** 0.75* 0.897* 0.65 0.391 −0.354 −0.200 −0.234 −2.109*** (0.699) (0.65) (0.8) (0.575) (0.451) (0.534) (0.509) (0.455) (0.739) (0.902) (0.838) (0.657) Lag 5 −0.714 −0.948 −0.266 −1.808*** 0.831** 0.943* 0.813* 0.123 −0.540 −0.444 −0.333 −2.370*** (0.749) (0.709) (0.761) (0.549) (0.415) (0.524) (0.453) (0.427) (1.089) (1.167) (1.183) (0.774) Lag 6 −0.664 −0.839 −0.252 −2.236*** 0.901** 1.249* 0.722* 0.232 −0.063 0.124 0.122 −1.920** (0.695) (0.724) (0.637) (0.521) (0.452) (0.669) (0.408) (0.495) (1.122) (1.650) (0.971) (0.844) Obs 2,558,350 2,310,087 1,960,926 Upper bound of −0.515*** −0.446*** −0.762*** $1,000 loss (0.011) (0.023) (0.034) Obs 2,317,766 2,080,098 1,768,292 Notes: Data from BRFSS, years 1997−2011. Good health is the first factor from a principal-component factor analysis including self-assessed health, indicators for diabetes, obesity and poor mental health. Healthcare utilisation is the first factor from a principal-component factor analysis including an indicator for having a health plan, for having had a flu shot, a medical check-up and whether a doctor visit is too expensive. Health behaviour is the first factor from a principal-component factor analysis including smoking, alcohol consumption and exercise. All regressions include age dummies, sex, race, education and year and CZ fixed effects as well as state linear trends. We also include the percent of individuals in routine occupations. The bottom panel displays the regression of the different health measures on individual log income and controls. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered at CZ level. Models are weighted in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age group–race–sex cell in the IPUMS Census 2000 data. Open in new tab Table 5. Imports from China and Composite Measures of Health, Health Behaviour and Healthcare Utilisation, by RTI Tercile. Dependent Variables: Composite Measures of Health, Health Behaviour and Healthcare Utilisation. . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lag 0 −1.551** −1.289* −1.890 −2.468*** 0.944 0.904 1.621 0.8 −1.358 −1.188 −1.353 −2.158 (0.729) (0.693) (1.297) (0.744) (1.086) (0.981) (2.537) (1.167) (1.500) (1.389) (2.846) (1.461) Lag 1 −1.219 −1.207 −0.999 −1.715*** 0.77 0.711 0.996 0.721 −1.161 −0.947 −2.594 −2.148 (0.749) (0.865) (0.855) (0.557) (0.809) (0.69) (1.513) (0.731) (1.314) (1.210) (2.920) (1.423) Lag 2 −0.977* −0.874 −0.975 −1.704*** 0.181 0.121 0.257 0.3 −1.657* −1.175 −2.967* −2.625*** (0.572) (0.611) (0.735) (0.553) (0.513) (0.512) (0.878) (0.514) (0.962) (0.96) (1.549) (0.882) Lag 3 −0.418 −0.433 −0.143 −1.473** 0.49 0.453 0.608 0.238 −0.758 −0.413 −1.086 −2.615*** (0.598) (0.588) (0.704) (0.575) (0.524) (0.551) (0.647) (0.504) (0.811) (0.895) (1.059) (0.927) Lag 4 −0.669 −0.773 −0.324 −1.614*** 0.75* 0.897* 0.65 0.391 −0.354 −0.200 −0.234 −2.109*** (0.699) (0.65) (0.8) (0.575) (0.451) (0.534) (0.509) (0.455) (0.739) (0.902) (0.838) (0.657) Lag 5 −0.714 −0.948 −0.266 −1.808*** 0.831** 0.943* 0.813* 0.123 −0.540 −0.444 −0.333 −2.370*** (0.749) (0.709) (0.761) (0.549) (0.415) (0.524) (0.453) (0.427) (1.089) (1.167) (1.183) (0.774) Lag 6 −0.664 −0.839 −0.252 −2.236*** 0.901** 1.249* 0.722* 0.232 −0.063 0.124 0.122 −1.920** (0.695) (0.724) (0.637) (0.521) (0.452) (0.669) (0.408) (0.495) (1.122) (1.650) (0.971) (0.844) Obs 2,558,350 2,310,087 1,960,926 Upper bound of −0.515*** −0.446*** −0.762*** $1,000 loss (0.011) (0.023) (0.034) Obs 2,317,766 2,080,098 1,768,292 . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lag 0 −1.551** −1.289* −1.890 −2.468*** 0.944 0.904 1.621 0.8 −1.358 −1.188 −1.353 −2.158 (0.729) (0.693) (1.297) (0.744) (1.086) (0.981) (2.537) (1.167) (1.500) (1.389) (2.846) (1.461) Lag 1 −1.219 −1.207 −0.999 −1.715*** 0.77 0.711 0.996 0.721 −1.161 −0.947 −2.594 −2.148 (0.749) (0.865) (0.855) (0.557) (0.809) (0.69) (1.513) (0.731) (1.314) (1.210) (2.920) (1.423) Lag 2 −0.977* −0.874 −0.975 −1.704*** 0.181 0.121 0.257 0.3 −1.657* −1.175 −2.967* −2.625*** (0.572) (0.611) (0.735) (0.553) (0.513) (0.512) (0.878) (0.514) (0.962) (0.96) (1.549) (0.882) Lag 3 −0.418 −0.433 −0.143 −1.473** 0.49 0.453 0.608 0.238 −0.758 −0.413 −1.086 −2.615*** (0.598) (0.588) (0.704) (0.575) (0.524) (0.551) (0.647) (0.504) (0.811) (0.895) (1.059) (0.927) Lag 4 −0.669 −0.773 −0.324 −1.614*** 0.75* 0.897* 0.65 0.391 −0.354 −0.200 −0.234 −2.109*** (0.699) (0.65) (0.8) (0.575) (0.451) (0.534) (0.509) (0.455) (0.739) (0.902) (0.838) (0.657) Lag 5 −0.714 −0.948 −0.266 −1.808*** 0.831** 0.943* 0.813* 0.123 −0.540 −0.444 −0.333 −2.370*** (0.749) (0.709) (0.761) (0.549) (0.415) (0.524) (0.453) (0.427) (1.089) (1.167) (1.183) (0.774) Lag 6 −0.664 −0.839 −0.252 −2.236*** 0.901** 1.249* 0.722* 0.232 −0.063 0.124 0.122 −1.920** (0.695) (0.724) (0.637) (0.521) (0.452) (0.669) (0.408) (0.495) (1.122) (1.650) (0.971) (0.844) Obs 2,558,350 2,310,087 1,960,926 Upper bound of −0.515*** −0.446*** −0.762*** $1,000 loss (0.011) (0.023) (0.034) Obs 2,317,766 2,080,098 1,768,292 Notes: Data from BRFSS, years 1997−2011. Good health is the first factor from a principal-component factor analysis including self-assessed health, indicators for diabetes, obesity and poor mental health. Healthcare utilisation is the first factor from a principal-component factor analysis including an indicator for having a health plan, for having had a flu shot, a medical check-up and whether a doctor visit is too expensive. Health behaviour is the first factor from a principal-component factor analysis including smoking, alcohol consumption and exercise. All regressions include age dummies, sex, race, education and year and CZ fixed effects as well as state linear trends. We also include the percent of individuals in routine occupations. The bottom panel displays the regression of the different health measures on individual log income and controls. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered at CZ level. Models are weighted in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age group–race–sex cell in the IPUMS Census 2000 data. Open in new tab When looking at the differential effect of import competition across areas with different propensity to automate (columns (2)–(4)), most of the negative effect of exposure to imports is concentrated in the high RTI areas, where it shows a U-shaped pattern with the time lag. The areas in the low or middle-RTI terciles show insignificant and much smaller effects on this general health measure. These health results align well with the patterns we uncovered in Section 2 both in terms of geography and in terms of the dynamic effects of import shocks on the labour market. Table 6, panel A disaggregates the health index into its different components allowing for a lag of four years for the import shock to have an effect. We find that import competition affects negatively a range of health measures and almost only in areas with high RTI. Those health measures include worse cardiovascular diseases (strokes), endocrine diseases (diabetes), respiratory diseases (asthma) and diet (obesity). We also find a worsening of mental health in high RTI areas, although this effect is not statistically significant at a four-year lag, but results show that mental health problems peak at earlier lags. We now explore possible mechanisms to this general deterioration in health. We focus first on proximal causes such as changes in health behaviour or healthcare utilisation. We then look at more distal causes such as income effects and job loss. Table 6. Health Effects of Imports from China—with a Four-Year Lag, by RTI Tercile Dependent Variables: Health and Labour Outcomes (No Composite Measures). . All . Low . Medium . High . . . Areas . RTI . RTI . RTI . . . (1) . (2) . (3) . (4) . Obs . Panel A: Health measures Health good −0.141 −0.188 −0.042 −0.271 2,802,175 (0.21) (0.221) (0.246) (0.224) Ever had a stroke 0.091 0.121** 0.057 0.135** 2,013,389 (0.059) (0.059) (0.058) (0.056) Ever diagnosed with diabetes 0.292** 0.316** 0.244* 0.352*** 2,798,653 (0.137) (0.148) (0.146) (0.109) Has asthma now 0.125 0.104 0.116 0.289*** 2,561,978 (0.103) (0.117) (0.127) (0.103) Overweight −0.092 −0.100 −0.104 0.016 2,680,234 (0.187) (0.257) (0.172) (0.165) Obese 0.242 0.193 0.264 0.484** 2,680,234 (0.212) (0.231) (0.239) (0.207) Underweight −0.044 −0.070 −0.015 0.003 2,680,234 (0.056) (0.066) (0.055) (0.054) Mental health problems −0.151 −0.165 −0.192 0.147 2,675,623 (0.14) (0.167) (0.14) (0.107) Panel B: Health behaviour Days had alcohol past 30 days 0.073* 0.081** 0.083* −0.022 2,449,825 (0.039) (0.037) (0.047) (0.036) Smokes now 0.064 0.15 −0.064 0.068 2,792,750 (0.155) (0.177) (0.205) (0.148) Exercise in past 30 days 0.181 0.284 0.093 −0.055 2,645,923 (0.228) (0.307) (0.28) (0.18) Panel C: Healthcare utilisation No doctor because of cost 0.085 0.057 0.036 0.544*** 2,521,971 (0.23) (0.243) (0.244) (0.164) Has any health plan −0.183 −0.099 −0.244 −0.473** 2,795,626 (0.248) (0.38) (0.288) (0.197) Flu shot 0.269 0.536 0.105 −0.676** 2,623,346 (0.312) (0.345) (0.392) (0.267) Time since check-up 0.011 0.019 −0.0007 0.002 2,182,957 (0.011) (0.014) (0.013) (0.013) Panel D: Labour and Income Currently working −0.409 −0.583 −0.045 −0.883*** 2,796,782 (0.333) (0.495) (0.293) (0.245) Income < $20k 0.399 0.592 0.078 0.555** 2,802,175 (0.379) (0.504) (0.346) (0.268) . All . Low . Medium . High . . . Areas . RTI . RTI . RTI . . . (1) . (2) . (3) . (4) . Obs . Panel A: Health measures Health good −0.141 −0.188 −0.042 −0.271 2,802,175 (0.21) (0.221) (0.246) (0.224) Ever had a stroke 0.091 0.121** 0.057 0.135** 2,013,389 (0.059) (0.059) (0.058) (0.056) Ever diagnosed with diabetes 0.292** 0.316** 0.244* 0.352*** 2,798,653 (0.137) (0.148) (0.146) (0.109) Has asthma now 0.125 0.104 0.116 0.289*** 2,561,978 (0.103) (0.117) (0.127) (0.103) Overweight −0.092 −0.100 −0.104 0.016 2,680,234 (0.187) (0.257) (0.172) (0.165) Obese 0.242 0.193 0.264 0.484** 2,680,234 (0.212) (0.231) (0.239) (0.207) Underweight −0.044 −0.070 −0.015 0.003 2,680,234 (0.056) (0.066) (0.055) (0.054) Mental health problems −0.151 −0.165 −0.192 0.147 2,675,623 (0.14) (0.167) (0.14) (0.107) Panel B: Health behaviour Days had alcohol past 30 days 0.073* 0.081** 0.083* −0.022 2,449,825 (0.039) (0.037) (0.047) (0.036) Smokes now 0.064 0.15 −0.064 0.068 2,792,750 (0.155) (0.177) (0.205) (0.148) Exercise in past 30 days 0.181 0.284 0.093 −0.055 2,645,923 (0.228) (0.307) (0.28) (0.18) Panel C: Healthcare utilisation No doctor because of cost 0.085 0.057 0.036 0.544*** 2,521,971 (0.23) (0.243) (0.244) (0.164) Has any health plan −0.183 −0.099 −0.244 −0.473** 2,795,626 (0.248) (0.38) (0.288) (0.197) Flu shot 0.269 0.536 0.105 −0.676** 2,623,346 (0.312) (0.345) (0.392) (0.267) Time since check-up 0.011 0.019 −0.0007 0.002 2,182,957 (0.011) (0.014) (0.013) (0.013) Panel D: Labour and Income Currently working −0.409 −0.583 −0.045 −0.883*** 2,796,782 (0.333) (0.495) (0.293) (0.245) Income < $20k 0.399 0.592 0.078 0.555** 2,802,175 (0.379) (0.504) (0.346) (0.268) Notes: Data from BRFSS, years 1997−2011. Dependent variables are listed in each row. All regressions include age dummies, sex, race, education and year and CZ fixed effects as well as state linear trends. We also include the percent of individuals in routine occupations. SE clustered at CZ level. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Models are weighted in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age group−race−sex cell in the IPUMS Census 2000 data. Open in new tab Table 6. Health Effects of Imports from China—with a Four-Year Lag, by RTI Tercile Dependent Variables: Health and Labour Outcomes (No Composite Measures). . All . Low . Medium . High . . . Areas . RTI . RTI . RTI . . . (1) . (2) . (3) . (4) . Obs . Panel A: Health measures Health good −0.141 −0.188 −0.042 −0.271 2,802,175 (0.21) (0.221) (0.246) (0.224) Ever had a stroke 0.091 0.121** 0.057 0.135** 2,013,389 (0.059) (0.059) (0.058) (0.056) Ever diagnosed with diabetes 0.292** 0.316** 0.244* 0.352*** 2,798,653 (0.137) (0.148) (0.146) (0.109) Has asthma now 0.125 0.104 0.116 0.289*** 2,561,978 (0.103) (0.117) (0.127) (0.103) Overweight −0.092 −0.100 −0.104 0.016 2,680,234 (0.187) (0.257) (0.172) (0.165) Obese 0.242 0.193 0.264 0.484** 2,680,234 (0.212) (0.231) (0.239) (0.207) Underweight −0.044 −0.070 −0.015 0.003 2,680,234 (0.056) (0.066) (0.055) (0.054) Mental health problems −0.151 −0.165 −0.192 0.147 2,675,623 (0.14) (0.167) (0.14) (0.107) Panel B: Health behaviour Days had alcohol past 30 days 0.073* 0.081** 0.083* −0.022 2,449,825 (0.039) (0.037) (0.047) (0.036) Smokes now 0.064 0.15 −0.064 0.068 2,792,750 (0.155) (0.177) (0.205) (0.148) Exercise in past 30 days 0.181 0.284 0.093 −0.055 2,645,923 (0.228) (0.307) (0.28) (0.18) Panel C: Healthcare utilisation No doctor because of cost 0.085 0.057 0.036 0.544*** 2,521,971 (0.23) (0.243) (0.244) (0.164) Has any health plan −0.183 −0.099 −0.244 −0.473** 2,795,626 (0.248) (0.38) (0.288) (0.197) Flu shot 0.269 0.536 0.105 −0.676** 2,623,346 (0.312) (0.345) (0.392) (0.267) Time since check-up 0.011 0.019 −0.0007 0.002 2,182,957 (0.011) (0.014) (0.013) (0.013) Panel D: Labour and Income Currently working −0.409 −0.583 −0.045 −0.883*** 2,796,782 (0.333) (0.495) (0.293) (0.245) Income < $20k 0.399 0.592 0.078 0.555** 2,802,175 (0.379) (0.504) (0.346) (0.268) . All . Low . Medium . High . . . Areas . RTI . RTI . RTI . . . (1) . (2) . (3) . (4) . Obs . Panel A: Health measures Health good −0.141 −0.188 −0.042 −0.271 2,802,175 (0.21) (0.221) (0.246) (0.224) Ever had a stroke 0.091 0.121** 0.057 0.135** 2,013,389 (0.059) (0.059) (0.058) (0.056) Ever diagnosed with diabetes 0.292** 0.316** 0.244* 0.352*** 2,798,653 (0.137) (0.148) (0.146) (0.109) Has asthma now 0.125 0.104 0.116 0.289*** 2,561,978 (0.103) (0.117) (0.127) (0.103) Overweight −0.092 −0.100 −0.104 0.016 2,680,234 (0.187) (0.257) (0.172) (0.165) Obese 0.242 0.193 0.264 0.484** 2,680,234 (0.212) (0.231) (0.239) (0.207) Underweight −0.044 −0.070 −0.015 0.003 2,680,234 (0.056) (0.066) (0.055) (0.054) Mental health problems −0.151 −0.165 −0.192 0.147 2,675,623 (0.14) (0.167) (0.14) (0.107) Panel B: Health behaviour Days had alcohol past 30 days 0.073* 0.081** 0.083* −0.022 2,449,825 (0.039) (0.037) (0.047) (0.036) Smokes now 0.064 0.15 −0.064 0.068 2,792,750 (0.155) (0.177) (0.205) (0.148) Exercise in past 30 days 0.181 0.284 0.093 −0.055 2,645,923 (0.228) (0.307) (0.28) (0.18) Panel C: Healthcare utilisation No doctor because of cost 0.085 0.057 0.036 0.544*** 2,521,971 (0.23) (0.243) (0.244) (0.164) Has any health plan −0.183 −0.099 −0.244 −0.473** 2,795,626 (0.248) (0.38) (0.288) (0.197) Flu shot 0.269 0.536 0.105 −0.676** 2,623,346 (0.312) (0.345) (0.392) (0.267) Time since check-up 0.011 0.019 −0.0007 0.002 2,182,957 (0.011) (0.014) (0.013) (0.013) Panel D: Labour and Income Currently working −0.409 −0.583 −0.045 −0.883*** 2,796,782 (0.333) (0.495) (0.293) (0.245) Income < $20k 0.399 0.592 0.078 0.555** 2,802,175 (0.379) (0.504) (0.346) (0.268) Notes: Data from BRFSS, years 1997−2011. Dependent variables are listed in each row. All regressions include age dummies, sex, race, education and year and CZ fixed effects as well as state linear trends. We also include the percent of individuals in routine occupations. SE clustered at CZ level. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Models are weighted in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age group−race−sex cell in the IPUMS Census 2000 data. Open in new tab 3.2.3. Health behaviour and healthcare utilisation Some of the health deterioration described above may originate in changes in health behaviour. For instance, smoking has strong links with cardiovascular health and exercise affects obesity. Table 5, columns (5)−(8) show the effect of import competition on the health behaviour score. We find that import competition induces people to adopt a healthier lifestyle, but this is the case only in areas that are less prone to automation in the manufacturing sector, where the China import shock consequences exist but are less acute. It therefore seems that changes in health behaviour resulting from increased exposure to import competition cannot explain the adverse health effects of the import shock, as those changes are small in the highest RTI area, and beneficial in the low and medium-RTI areas. We find that the effect of import competition on health behaviour is rather similar to the effect of recessions. Ruhm and Black (2002) and Ruhm (2005) show that part of the business cycle effect operates through changes in health behaviour, as lower income leads to less alcohol or tobacco consumption, a better diet and more physical exercise (also due to an increase in leisure time).12 The literature on health behaviour has found mixed evidence on the effect of income. While smokers are found to be price sensitive (see the review by Chaloupka and Warner, 2000; DeCicca et al., 2002), Adda and Cornaglia (2006) find that compensation through a change in smoking intensity offsets the decrease in the number of cigarettes smoked. That change in behaviour can have detrimental effects and lead to more severe lung cancers. Alcohol consumption is generally income sensitive, leading to less drinking when income decreases (Chaloupka et al., 2002; Nelson, 2013). Another possibility to the lack of an effect on health behaviour is that the BRFSS is not large enough as a survey to pick up changes in health behaviour of a smaller population affected by the import shock. To identify effects on subgroups or on rarer conditions, we rely on the very large samples available from the hospitalisation discharge data presented in Subsection 3.3. Another channel through which health could deteriorate is the lack of access to treatment. We explore the consequences of the import shock on a composite measure that summarises both healthcare access (whether the individual has ‘any kind of healthcare’) and healthcare utilisation (whether the individual has received a flu shot in the past 12 months, whether he/she had to forgo a doctor visit due to cost).13 Results displayed in columns (9)−(12) of Table 5 show that healthcare access/utilisation has been significantly undermined by the import shock in those areas where jobs were more likely to be automated away in manufacturing. The coefficients appear both significant and big (compared with the estimated effects of the IPW measure on the ‘good health’ and ‘good health behaviour’ factors). Those effects are again concentrated in the highest RTI tercile. Looking at individual measures in Table 6, the effects are driven by those who could not see a doctor because of the cost, and fewer individuals taking preventive measures such as flu shots, or not having any health plan. Delayed treatment, discontinuing the treatment of pre-existing conditions or delaying the diagnosis and treatment of new conditions is likely to lead to more severe health issues later on. The information in the BRFSS does not allow us to check this mechanism directly, and we use the information in hospitalisation discharges in Subsection 3.3 to explore the issue further. In the USA, health insurance is often employer-provided and the increased proportion of individuals without a health plan is therefore a consequence of the rise in individuals out of the labour market documented in Section 2. 3.2.4. Is income loss enough to explain the decline in health? In addition to loss of healthcare, income variation is also a likely mechanism behind the health effects of the China shock. The extant literature has pointed to contrasted effects of the import shock itself: access to cheaper goods increases purchasing power and acts as an increase in income for those consuming those goods. This effect is presumably diffuse and difficult to measure directly.14 On the negative side, individuals working in industries that were the most exposed to increased competition with China have been faced with higher unemployment and income loss (due to job loss and lower wages), which could both affect their health. As pointed out in Table 3, increasing exposure to import competition leads to lower income, except for the low RTI areas, in line with the absence of effect on the share of individuals being employed or out of the labour force. Evidence from the BRFSS confirms these findings, with less people working, and more people with low income, as a consequence of the import shock in high RTI CZs (a $1,000 increase in IPW leads to a 0.9 percentage point decrease in the probability of working, and a 0.54 percentage point increase in the probability of earning less than $20,000 a year. See Table 6, panel D). As the import shock leads to potentially a loss of income, a higher likelihood of not working and a loss of health insurance, it is difficult to separate each effect in a precise and causal way. Estimating the causal effect of income on health in general is beyond the scope of this paper. We approach the issue of the effect of income loss through a bounding method. We compare the causal effect of increased exposure to import competition from China with the non-causal association between income and health. The estimate of the effect of income on health we get can be considered as an upper bound, due to reverse causality and omitted variables.15 We regress our health composite measure on adjusted income (reported in the BRFSS and then adjusted for inflation by the CPI) and the same set of controls as in the IPW regressions (age, sex, race, education, year and CZ effects, state-specific time trends, share of routine occupations), and display the results in the bottom panel of Table 5. We find that for this population, a $1,000 decrease in income is associated with a decrease of at most 0.5 units of the health factor. The effect of a $1,000 increase in IPW is therefore equivalent to (at least) three to five times a $1,000 loss of income in terms of the associated health deterioration. Taking the highest estimate of the income loss triggered by import competition in Table 3, i.e., a $570 loss, a $1,000 increase in IPW would lead to at most a 0.29 decrease in the ‘good health’ factor, which is much less than the estimates displayed in Table 5. In other terms, we observe a deterioration in health that is much larger than what the loss of income alone would imply.16 In a similar way, Table 5 reports the association between income and healthcare utilisation. We find that a $1,000 decrease in income associated with a decrease of −0.8 units of the healthcare utilisation index. This effect is much smaller than the (causal) effect of import competition on utilisation. This confirms that part of the lack of interaction with the healthcare system operates through a loss of access rather than a lack of resources alone. We explore further this issue in the next section. 3.3. Evidence from Hospital Discharges In this section we look at the impact of import competition on hospital discharges, which provides further insight on the role of import competition in shaping health, health behaviour and healthcare utilisation. The advantage of hospital data compared to health surveys such as the BRFSS is twofold. First, it consists of ‘hard’ outcomes, established by doctors, whereas health surveys rely mostly on self-declaration. Second, sample sizes are of a larger order of magnitude and allow to detect rarer outcomes as well as changes in health behaviour, not just on average but at the right tail of the distribution. 3.3.1. Data We use data from the Healthcare Cost and Utilization Project (HCUP) and more specifically from the National Inpatient Sample (NIS). The NIS is the largest publicly available all-payer inpatient healthcare database in the United States, covering the years 1993 to 2011. It consists of a 20% stratified sample of all discharges from US community hospitals. In each of those years, 20% of the hospitals were sampled and all discharges within those hospitals were recorded. After 2011, the design of the survey changed and hospital identifiers are no longer available. The data we analyse record the identity of the hospital and its zip code, which allows us to match it to a CZ. For each patient, the data contain basic demographics (sex, age, race, the quartile of income within the zip code of living), but does not record the sector of occupation of the patient nor education. Hence, these data do not allow direct evaluation of the effect of import shocks on individuals employed in the manufacturing sector (nor did the BRFSS analysis, but the mortality analysis in Subsection 3.4 will). To overcome this issue, we proceed in a similar way as we did in Section 2 and Subsection 3.2. We use information on the composition in terms of industry for each of the CZs and we look at areas where routine tasks are more or less abundant. The data contain information on up to 15 diagnostic codes (coded using the ICD 9 classification) as well as information on the length of stay, total charges incurred and how charges were covered. We restrict the sample to look at individuals who are between the ages of 18 to 65, and excluded all discharges related to births. The resulting sample contains close to 40 million observations. We grouped the diagnostic codes into 18 categories, not mutually exclusive. We consider discharges where at least one of the diagnostic codes mention heart problems, infectious, respiratory, skin, digestive or endocrine diseases, cancers (we also distinguish tobacco and non-tobacco-related cancers), the occurrence of pain, mental disorders, suicide attempts, injuries, homicides, alcohol abuse, substance abuse and opioid abuse. We also define two categories which may be relevant for the shock we consider. The first is related to stress and groups various conditions like mental disorders but also skin problems, ulcers or backache. The second is related to diet.17 We partition the discharges into ten groups defined by birth year and gender. We define five birth year groups for years before 1940 to after 1970. For each hospital, we then compute the number of diagnoses of a given type within those birth year–gender groups and by year. We restrict the sample to the years 1997 to 2011 to be consistent with the analysis in the previous sections. We follow 1,990 hospitals over time, totalling 91,229 hospital year–group observations. Table A4 in the Appendix provides descriptive statistics on the number of diagnosis and proportion of patients by age, sex and race. In the following, we provide evidence at hospital level with import shocks matched at CZ levels. 3.3.2. Empirical strategy The design of the data is different from the one in the BRFSS and the CBP. As we do not observe the universe of hospitals in a CZ, we estimate the effect of imports within a CZ at hospital level instead. Our specification is similar to the one we used before (see equation (1)), but we now define the outcome as Yh,g,c,t, observed in hospital h, for group g, belonging to CZ c, in year t. We relate this outcome to the IPW in the CZ c, k years prior. We control for time and hospital fixed effects as well as birth year–gender fixed effects. In addition, the regressions include county and CZ time-varying characteristics (e.g., the share of routine occupations in manufacturing employment, the racial and gender composition of the CZ or the number of hospital beds in the county) and state-specific trends.18 The variable measuring the IPW is instrumented as explained in Section 1. We cluster the error term at CZ level. To probe the role of import shocks further, we interact it with terciles of average RTI, computed for manufacturing jobs in each CZ in 1990 as we have done above. 3.3.3. Results using hospitalisation data The outcome variable is the log number of one plus admissions for a particular cause.19 We measure import competition in $1,000 per worker. On average during the period we consider, its mean is 1.3 with a standard deviation of 1.6 (see also Table 1). Table 7 presents the results. We first look at the global effect of the import shock, without introducing any heterogeneity linked to RTI. The results displayed in the first column show the effect of import competition across all CZs on the health measures we consider. In general, the effects are positive but not always significant at the 5% level. For instance, a $1,000 increase in import competition raises the number of admissions for suicide attempts by about 0.02 log points, the latter translating into a 1.2% increase for a one standard deviation shock in imports. We find significant import competition effects for admissions for pain motives, although modest in size. The results using hospital discharge are thus in line with those found using the BRFSS in the previous section. At an aggregate level, import competition has a small (mostly non-significant) impact on most health measures. Table 7. Imports from China and Hospitalisation: Discharges by Cause—with a Four-Year Lag, by RTI Tercile. . All areas . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms −0.012 −0.015 0.02 0.152** (0.042) (0.033) (0.027) (0.065) Mental health problems −0.012 −0.028 0.047 0.159** (0.047) (0.036) (0.032) (0.07) Suicides attempts 0.021 0.014 0.042 0.129** (0.036) (0.028) (0.036) (0.055) Alcohol abuse −0.014 −0.020 0.016 0.084 (0.037) (0.034) (0.028) (0.059) Substance abuse −0.066 −0.046 −0.032 0.154** (0.056) (0.045) (0.037) (0.078) Opioid abuse −0.058 −0.017 −0.056 0.166** (0.055) (0.044) (0.042) (0.069) Injuries 0.046 0.054** 0.014 0.174** (0.031) (0.025) (0.03) (0.078) Homicide injuries 0.024 0.027 0.014 0.229** (0.035) (0.026) (0.036) (0.091) Driving accidents 0.009 0.017 −0.047 0.05 (0.04) (0.034) (0.056) (0.073) Pain 0.067** 0.069*** 0.014 0.132** (0.029) (0.025) (0.039) (0.062) Skin disease −0.020 −0.015 0.02 0.171*** (0.045) (0.033) (0.036) (0.056) Heart problems 0.025 0.031 0.015 0.116*** (0.026) (0.021) (0.021) (0.043) Infectious diseases −0.007 −0.011 0.026 0.14*** (0.039) (0.029) (0.03) (0.049) Respiratory diseases 0.022 0.026 0.014 0.105** (0.028) (0.023) (0.024) (0.047) Disease of digestive system 0.014 0.015 0.016 0.126** (0.029) (0.023) (0.028) (0.058) Endocrine diseases 0.042 0.05** 0.007 0.09** (0.027) (0.023) (0.026) (0.04) Diet-related diseases 0.027 0.04 0.001 0.131*** (0.033) (0.027) (0.03) (0.05) Cancers 0.019 0.022 0.018 0.16*** (0.026) (0.017) (0.022) (0.053) Tobacco-related cancers 0.006 0.014 0.019 0.171*** (0.023) (0.016) (0.018) (0.051) Non-tobacco-related cancers 0.022 0.023 0.02 0.153*** (0.026) (0.017) (0.023) (0.052) . All areas . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms −0.012 −0.015 0.02 0.152** (0.042) (0.033) (0.027) (0.065) Mental health problems −0.012 −0.028 0.047 0.159** (0.047) (0.036) (0.032) (0.07) Suicides attempts 0.021 0.014 0.042 0.129** (0.036) (0.028) (0.036) (0.055) Alcohol abuse −0.014 −0.020 0.016 0.084 (0.037) (0.034) (0.028) (0.059) Substance abuse −0.066 −0.046 −0.032 0.154** (0.056) (0.045) (0.037) (0.078) Opioid abuse −0.058 −0.017 −0.056 0.166** (0.055) (0.044) (0.042) (0.069) Injuries 0.046 0.054** 0.014 0.174** (0.031) (0.025) (0.03) (0.078) Homicide injuries 0.024 0.027 0.014 0.229** (0.035) (0.026) (0.036) (0.091) Driving accidents 0.009 0.017 −0.047 0.05 (0.04) (0.034) (0.056) (0.073) Pain 0.067** 0.069*** 0.014 0.132** (0.029) (0.025) (0.039) (0.062) Skin disease −0.020 −0.015 0.02 0.171*** (0.045) (0.033) (0.036) (0.056) Heart problems 0.025 0.031 0.015 0.116*** (0.026) (0.021) (0.021) (0.043) Infectious diseases −0.007 −0.011 0.026 0.14*** (0.039) (0.029) (0.03) (0.049) Respiratory diseases 0.022 0.026 0.014 0.105** (0.028) (0.023) (0.024) (0.047) Disease of digestive system 0.014 0.015 0.016 0.126** (0.029) (0.023) (0.028) (0.058) Endocrine diseases 0.042 0.05** 0.007 0.09** (0.027) (0.023) (0.026) (0.04) Diet-related diseases 0.027 0.04 0.001 0.131*** (0.033) (0.027) (0.03) (0.05) Cancers 0.019 0.022 0.018 0.16*** (0.026) (0.017) (0.022) (0.053) Tobacco-related cancers 0.006 0.014 0.019 0.171*** (0.023) (0.016) (0.018) (0.051) Non-tobacco-related cancers 0.022 0.023 0.02 0.153*** (0.026) (0.017) (0.023) (0.052) Notes: Data from NIS for the years 1997−2011. Instrumental variable estimates using the sum of Chinese imports to the other countries as instruments for US imports. The table reports the effect of a $1,000 import shock on the log of 1 + the number of admissions of patients with a certain condition. All regressions include year fixed effects, state trends, hospital fixed effects, birth year–gender fixed effects of patients, CZ time-varying characteristics (demographic composition of the CZ in terms of gender, race, education, age composition and share of routine occupations). Weighted by hospital weights and population weights. SE clustered at CZ level. Open in new tab Table 7. Imports from China and Hospitalisation: Discharges by Cause—with a Four-Year Lag, by RTI Tercile. . All areas . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms −0.012 −0.015 0.02 0.152** (0.042) (0.033) (0.027) (0.065) Mental health problems −0.012 −0.028 0.047 0.159** (0.047) (0.036) (0.032) (0.07) Suicides attempts 0.021 0.014 0.042 0.129** (0.036) (0.028) (0.036) (0.055) Alcohol abuse −0.014 −0.020 0.016 0.084 (0.037) (0.034) (0.028) (0.059) Substance abuse −0.066 −0.046 −0.032 0.154** (0.056) (0.045) (0.037) (0.078) Opioid abuse −0.058 −0.017 −0.056 0.166** (0.055) (0.044) (0.042) (0.069) Injuries 0.046 0.054** 0.014 0.174** (0.031) (0.025) (0.03) (0.078) Homicide injuries 0.024 0.027 0.014 0.229** (0.035) (0.026) (0.036) (0.091) Driving accidents 0.009 0.017 −0.047 0.05 (0.04) (0.034) (0.056) (0.073) Pain 0.067** 0.069*** 0.014 0.132** (0.029) (0.025) (0.039) (0.062) Skin disease −0.020 −0.015 0.02 0.171*** (0.045) (0.033) (0.036) (0.056) Heart problems 0.025 0.031 0.015 0.116*** (0.026) (0.021) (0.021) (0.043) Infectious diseases −0.007 −0.011 0.026 0.14*** (0.039) (0.029) (0.03) (0.049) Respiratory diseases 0.022 0.026 0.014 0.105** (0.028) (0.023) (0.024) (0.047) Disease of digestive system 0.014 0.015 0.016 0.126** (0.029) (0.023) (0.028) (0.058) Endocrine diseases 0.042 0.05** 0.007 0.09** (0.027) (0.023) (0.026) (0.04) Diet-related diseases 0.027 0.04 0.001 0.131*** (0.033) (0.027) (0.03) (0.05) Cancers 0.019 0.022 0.018 0.16*** (0.026) (0.017) (0.022) (0.053) Tobacco-related cancers 0.006 0.014 0.019 0.171*** (0.023) (0.016) (0.018) (0.051) Non-tobacco-related cancers 0.022 0.023 0.02 0.153*** (0.026) (0.017) (0.023) (0.052) . All areas . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms −0.012 −0.015 0.02 0.152** (0.042) (0.033) (0.027) (0.065) Mental health problems −0.012 −0.028 0.047 0.159** (0.047) (0.036) (0.032) (0.07) Suicides attempts 0.021 0.014 0.042 0.129** (0.036) (0.028) (0.036) (0.055) Alcohol abuse −0.014 −0.020 0.016 0.084 (0.037) (0.034) (0.028) (0.059) Substance abuse −0.066 −0.046 −0.032 0.154** (0.056) (0.045) (0.037) (0.078) Opioid abuse −0.058 −0.017 −0.056 0.166** (0.055) (0.044) (0.042) (0.069) Injuries 0.046 0.054** 0.014 0.174** (0.031) (0.025) (0.03) (0.078) Homicide injuries 0.024 0.027 0.014 0.229** (0.035) (0.026) (0.036) (0.091) Driving accidents 0.009 0.017 −0.047 0.05 (0.04) (0.034) (0.056) (0.073) Pain 0.067** 0.069*** 0.014 0.132** (0.029) (0.025) (0.039) (0.062) Skin disease −0.020 −0.015 0.02 0.171*** (0.045) (0.033) (0.036) (0.056) Heart problems 0.025 0.031 0.015 0.116*** (0.026) (0.021) (0.021) (0.043) Infectious diseases −0.007 −0.011 0.026 0.14*** (0.039) (0.029) (0.03) (0.049) Respiratory diseases 0.022 0.026 0.014 0.105** (0.028) (0.023) (0.024) (0.047) Disease of digestive system 0.014 0.015 0.016 0.126** (0.029) (0.023) (0.028) (0.058) Endocrine diseases 0.042 0.05** 0.007 0.09** (0.027) (0.023) (0.026) (0.04) Diet-related diseases 0.027 0.04 0.001 0.131*** (0.033) (0.027) (0.03) (0.05) Cancers 0.019 0.022 0.018 0.16*** (0.026) (0.017) (0.022) (0.053) Tobacco-related cancers 0.006 0.014 0.019 0.171*** (0.023) (0.016) (0.018) (0.051) Non-tobacco-related cancers 0.022 0.023 0.02 0.153*** (0.026) (0.017) (0.023) (0.052) Notes: Data from NIS for the years 1997−2011. Instrumental variable estimates using the sum of Chinese imports to the other countries as instruments for US imports. The table reports the effect of a $1,000 import shock on the log of 1 + the number of admissions of patients with a certain condition. All regressions include year fixed effects, state trends, hospital fixed effects, birth year–gender fixed effects of patients, CZ time-varying characteristics (demographic composition of the CZ in terms of gender, race, education, age composition and share of routine occupations). Weighted by hospital weights and population weights. SE clustered at CZ level. Open in new tab The next three columns display the effects of import competition across areas with low, medium or high RTI. As in previous sections, the detrimental effects of import competition are concentrated in areas with high RTI. In those regions, a $1,000 increase in imports per worker leads to an increase of about 0.1 to 0.2 log points for most outcomes we consider. The effect of import competition is particularly strong for mental health problems, substance abuse and especially substance abuse linked to opioid abuse. Case and Deaton (2015) have documented the recent rise of ‘deaths of despair’ in the USA. Recent literature has linked opioid abuse to local levels of unemployment (Hollingsworth et al., 2017) or to import competition (Pierce and Schott, 2020, using data on mortality by cause). We also document a rise in injuries. While it is possible that import competition may lead to more work accidents through increased stress at work or pressure to increase work productivity, it is well known that a number of injuries reported in hospitals are in fact mislabelled suicide attempts (Phillips and Ruth, 1993). We find a significant increase in suicide attempts as well in high RTI areas, following an increase in import competition. We also find an even greater increase in homicide injuries. This finding corroborates those of Deiana (2018) that documents an increase in crime in areas with higher import competition. In Subsection 3.2, we did not find a significant increase in alcohol consumption. The hospitalisation results differ from the results using the BRFSS for alcohol consumption. The BRFSS captures day-to-day consumption, but the hospitalisation records relates to alcohol abuse. Although not significant, the results suggest that areas hit by an import shock see a decrease in overall alcohol consumption, perhaps through an income effect, but also an increase in the upper tail of the distribution of alcohol consumption that health surveys such as the BRFSS miss. Table 7 next displays results on physical health, as opposed to the first set of results that relate to mental health and its consequences. We first document a rise in the occurrence of pain in high RTI areas. The most frequent issues related to pain are chronic pain, backaches and chest pain. These are often manifestations of other medical problems, but constitute also a pathway to substance abuse, distinct from a deterioration in mental health. Consumption of painkillers can lead to addictive behaviour which are picked up in our analysis as opioid abuse. The results in Subsection 3.2 showed an effect of import competition on general health, cardiovascular diseases, endocrine diseases such as diabetes, or respiratory diseases. The results using hospitalisation data confirm those results and shows increased rates of hospitalisations due to heart problems, infectious diseases or respiratory diseases. The most common respiratory diseases include asthma and pneumonia. These conditions are linked to stress and lack of preventive care, among others factors. We find a large effect on skin diseases, where a leading cause are skin infections, often linked to diabetes or obesity. The effect is lower but still significant for endocrine diseases. The most common endocrine diseases in our data are diabetes and hypercholesterolemia, two conditions related to poorer health behaviour. In addition, we find an increased rate of admissions related to cancers driven both by tobacco-related causes as well as non-tobacco-related ones. The effect of import competition is considerably lower in areas with low or medium RTI and often not significant. We present in Table 8 the effect of import competition on the types of admissions and the composition of patients. We find evidence of a small increase in the number of admissions overall, mainly driven by high RTI areas. We find evidence that in those areas, admissions are more likely to be categorised as emergency ones. This could be due to the nature of some of the causes of hospitalisation, such as suicides. To investigate this further we also compute the number of emergency admissions, excluding admissions due to suicides, homicides and injuries. We still find a significant and large effect of import shocks on emergency admissions for all other causes. This could be due to an increase in life-threatening conditions such as acute cardiovascular diseases, and generally to the fact that some pathologies may have gone untreated for too long. By the time these patients show up in hospital, they could be more likely to have acute conditions. This is also in line with the increased mortality within hospitals as shown in the table. Looking at diagnostics for each individual, the occurrence of hospital deaths are far more prevalent for cardiovascular, endocrine and respiratory diseases than for causes linked to mental health issues such as suicides or drug abuse. Table 8. Imports from China and Hospitalisation: Composition of Discharges—with a Four-Year Lag, by RTI Tercile. . All areas . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Total admissions 0.029 0.03* 0.023 0.117*** (0.019) (0.016) (0.017) (0.036) Admissions emergency −0.024 −0.032 −0.002 0.139** (0.039) (0.063) (0.031) (0.065) Admissions emergency excluding −0.014 −0.008 0.005 0.125* (0.04) (0.061) (0.031) (0.067) Average charge 0.037 0.032 0.024 0.066 (0.03) (0.024) (0.025) (0.059) Admissions length 0.008 0.002 0.026 0.097*** (0.025) (0.02) (0.019) (0.037) Admissions length>7 −0.008 −0.021 0.037 0.125** (0.035) (0.025) (0.023) (0.051) Admissions Medicaid −0.019 −0.025 0.036 0.088* (0.035) (0.03) (0.03) (0.051) Admissions Medicare 0.023 0.025 0.038 0.137*** (0.031) (0.025) (0.024) (0.05) Admissions white 0.079* 0.034 0.081 0.091 (0.041) (0.027) (0.05) (0.062) Admissions males 0.036 0.038** 0.03* 0.127*** (0.023) (0.019) (0.018) (0.041) Admissions aged 51–65 0.017 0.015 0.019 0.106*** (0.023) (0.02) (0.021) (0.038) Died in hospital 0.039* 0.029* 0.043** 0.096*** (0.021) (0.017) (0.02) (0.037) . All areas . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Total admissions 0.029 0.03* 0.023 0.117*** (0.019) (0.016) (0.017) (0.036) Admissions emergency −0.024 −0.032 −0.002 0.139** (0.039) (0.063) (0.031) (0.065) Admissions emergency excluding −0.014 −0.008 0.005 0.125* (0.04) (0.061) (0.031) (0.067) Average charge 0.037 0.032 0.024 0.066 (0.03) (0.024) (0.025) (0.059) Admissions length 0.008 0.002 0.026 0.097*** (0.025) (0.02) (0.019) (0.037) Admissions length>7 −0.008 −0.021 0.037 0.125** (0.035) (0.025) (0.023) (0.051) Admissions Medicaid −0.019 −0.025 0.036 0.088* (0.035) (0.03) (0.03) (0.051) Admissions Medicare 0.023 0.025 0.038 0.137*** (0.031) (0.025) (0.024) (0.05) Admissions white 0.079* 0.034 0.081 0.091 (0.041) (0.027) (0.05) (0.062) Admissions males 0.036 0.038** 0.03* 0.127*** (0.023) (0.019) (0.018) (0.041) Admissions aged 51–65 0.017 0.015 0.019 0.106*** (0.023) (0.02) (0.021) (0.038) Died in hospital 0.039* 0.029* 0.043** 0.096*** (0.021) (0.017) (0.02) (0.037) Notes: Data from NIS for the years 1997−2011. Instrumental variable estimates using the sum of Chinese imports to the other countries as instruments for US imports. Effect of a $1,000 import shock. The outcome variable is the log of 1 + the number of admissions of patients with a certain condition. All regressions include year fixed effects, state trends, hospital fixed effects, birth year–gender fixed effects of patients, CZ time-varying characteristics (demographic composition of the CZ in terms of gender, race, education, age composition and share of routine occupations). Weighted by hospital weights and population weights. SE clustered at CZ level. Open in new tab Table 8. Imports from China and Hospitalisation: Composition of Discharges—with a Four-Year Lag, by RTI Tercile. . All areas . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Total admissions 0.029 0.03* 0.023 0.117*** (0.019) (0.016) (0.017) (0.036) Admissions emergency −0.024 −0.032 −0.002 0.139** (0.039) (0.063) (0.031) (0.065) Admissions emergency excluding −0.014 −0.008 0.005 0.125* (0.04) (0.061) (0.031) (0.067) Average charge 0.037 0.032 0.024 0.066 (0.03) (0.024) (0.025) (0.059) Admissions length 0.008 0.002 0.026 0.097*** (0.025) (0.02) (0.019) (0.037) Admissions length>7 −0.008 −0.021 0.037 0.125** (0.035) (0.025) (0.023) (0.051) Admissions Medicaid −0.019 −0.025 0.036 0.088* (0.035) (0.03) (0.03) (0.051) Admissions Medicare 0.023 0.025 0.038 0.137*** (0.031) (0.025) (0.024) (0.05) Admissions white 0.079* 0.034 0.081 0.091 (0.041) (0.027) (0.05) (0.062) Admissions males 0.036 0.038** 0.03* 0.127*** (0.023) (0.019) (0.018) (0.041) Admissions aged 51–65 0.017 0.015 0.019 0.106*** (0.023) (0.02) (0.021) (0.038) Died in hospital 0.039* 0.029* 0.043** 0.096*** (0.021) (0.017) (0.02) (0.037) . All areas . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Total admissions 0.029 0.03* 0.023 0.117*** (0.019) (0.016) (0.017) (0.036) Admissions emergency −0.024 −0.032 −0.002 0.139** (0.039) (0.063) (0.031) (0.065) Admissions emergency excluding −0.014 −0.008 0.005 0.125* (0.04) (0.061) (0.031) (0.067) Average charge 0.037 0.032 0.024 0.066 (0.03) (0.024) (0.025) (0.059) Admissions length 0.008 0.002 0.026 0.097*** (0.025) (0.02) (0.019) (0.037) Admissions length>7 −0.008 −0.021 0.037 0.125** (0.035) (0.025) (0.023) (0.051) Admissions Medicaid −0.019 −0.025 0.036 0.088* (0.035) (0.03) (0.03) (0.051) Admissions Medicare 0.023 0.025 0.038 0.137*** (0.031) (0.025) (0.024) (0.05) Admissions white 0.079* 0.034 0.081 0.091 (0.041) (0.027) (0.05) (0.062) Admissions males 0.036 0.038** 0.03* 0.127*** (0.023) (0.019) (0.018) (0.041) Admissions aged 51–65 0.017 0.015 0.019 0.106*** (0.023) (0.02) (0.021) (0.038) Died in hospital 0.039* 0.029* 0.043** 0.096*** (0.021) (0.017) (0.02) (0.037) Notes: Data from NIS for the years 1997−2011. Instrumental variable estimates using the sum of Chinese imports to the other countries as instruments for US imports. Effect of a $1,000 import shock. The outcome variable is the log of 1 + the number of admissions of patients with a certain condition. All regressions include year fixed effects, state trends, hospital fixed effects, birth year–gender fixed effects of patients, CZ time-varying characteristics (demographic composition of the CZ in terms of gender, race, education, age composition and share of routine occupations). Weighted by hospital weights and population weights. SE clustered at CZ level. Open in new tab Another sign of the increased complexity of cases is shown in the rise in the length of admissions, which is significantly higher in areas with a high RTI. The distribution for the length of admission is skewed and we also find an increase for admissions lasting for more than a week. In those areas, hospital charges tend to be higher, although we do not find a significant effect. Table 8 next shows the effect of import competition on number of patients covered by Medicaid, with a significant increase of 0.09 log points as well as those covered by Medicare (0.14 log point increase) in high RTI areas. The latter ones are individuals under 65 that are recipients of social security disability benefits or have end-stage renal disease. We also find that admitted individuals are more likely to be white, and to some extent males in their late forties to mid fifties. These results align well with those of Case and Deaton (2015), who found rising mortality among non-Hispanic middle-aged whites, due to suicides, drug and alcohol abuse, along with self-reported declines in health and mental health, with most of the toll borne by the low educated. Our results point to import shocks as a possible factor explaining those results. However, ascribing all of those results to mental health is not warranted, as we show that import competition also leads to the deterioration of a range of health conditions. 3.3.4. Dynamic effects of import competition Figure 4 displays the effect of import competition at various leads and lags for a subset of the outcomes. Given that we find strong and significant effects of import competition in high RTI areas, we limit the analysis to those areas. The figure displays the coefficients on import competition obtained from regressions similar to those in Table 7, that control for hospital, time, socio-demographic fixed effects, as well as state trends, and time-varying characteristics at CZ or county level. We find that the effect of import competition gets stronger over time and become significant at the 5% level after one or two years. Remarkably, the effect of future import shocks is much smaller and statistically insignificant. This shows that pre-trends or prior sorting into industries that will be hit by import competition are not causing a spurious effect. Fig. 4. Open in new tabDownload slide Import Shocks and Hospital Admissions in High RTI Areas. Notes: The figures displays the coefficients and 95% confidence intervals for the effect of import competition on different hospitalisation outcomes. The data are drawn from NIS. All regressions are done separately for outcomes and for lags or leads of the import shock. All regressions include hospital, year, socio-demographic fixed effects, and control for state trends, time-varying CZ and county characteristics. Fig. 4. Open in new tabDownload slide Import Shocks and Hospital Admissions in High RTI Areas. Notes: The figures displays the coefficients and 95% confidence intervals for the effect of import competition on different hospitalisation outcomes. The data are drawn from NIS. All regressions are done separately for outcomes and for lags or leads of the import shock. All regressions include hospital, year, socio-demographic fixed effects, and control for state trends, time-varying CZ and county characteristics. 3.4. Impact of Import Competition on Mortality In this section we look at the impact of exposure to import competition from China. While some studies have analysed mortality in relation to import competition (Pierce and Schott, 2020), they rely on aggregate mortality patterns at CZ level matched to imports in that area. In contrast, we rely on restricted-use individual data following individuals over time. This design has two advantages. First, as the data record three-digit occupations, we can match the individual to a precise measure of imports of that industry as opposed to an import mix at CZ level. Second, as the data comes from a health survey, we are able to control for health when we first observe the individual, which allows us to control for potential sorting into particular industries based on health. 3.4.1. Data We use data from the National Health Interview Survey (NHIS), over the period from 1988 to 2009. The NHIS is the principal source of information on the health of the civilian non-institutionalised population of the United States. The NHIS offers a rich set of individuals characteristics, including gender, race, education, self-assessed health, occupation and, most importantly, industry, at a very disaggregated level (three-digit Census 1990 based on three-digit SIC, four-digit Census 2002 based on four-digit NAICS); and county of residence.20 All our estimations include these socio-demographic variables as baseline controls. Our sample is made of 126,625 workers in the manufacturing industry, aged 18–65 at baseline, i.e., when they are surveyed.21 The NHIS provides a linkage to death certificate records from the National Death Index. Individuals who are surveyed at any point between 1988 and 2009 are observed again when they die, if they do before 31 December 2011.22 We can therefore construct a panel, in which each respondent is observed from the year they are surveyed until the year they die, or up to 2011 if they survive until then. For instance, a person entering the survey in 1990 and dying in 2002 is observed for 13 years. In principle, we can observe individuals until they die if they do before December 2011, but because the focus of our study is on how exposure to import competition in one’s own industry affects one’s chances of dying, we restrict the sample in the following way. First, an individual remains at most 15 years in the sample, so that the assumption that the worker will still be affected by a shock in the industry at baseline is more reasonable; second, since most workers retire at about 65, individuals exit the sample once they are 70, allowing for lags in the effect of imports. This way, we focus on the impact of import competition at the industry level on premature deaths, of individuals who are more likely to be still working. Of the 126,625 manufacturing workers we observe at baseline, 12,302 die before December 2011, but only 5,569 of those deaths are considered in our analysis, for the restrictions mentioned above. Trade data: in this section, data on imports are aggregated from four to three digits, so that it can match worker’s industry from the NHIS. The import shock is now defined as Importj,t−k, the imports from China in industry j and year t − k, where k is a lag varying between 0 and six years, in order to leave time for the import shock to potentially impact the worker’s mortality. It is now assigned to worker i working in industry j at year t, rather than to a CZ. We use imports series from 1988 to 2011 for both the USA and the four high-income countries that are used to construct the instrument.23 3.4.2. Empirical strategy We estimate the impact of import competition on all-cause mortality using a Cox survival model, as described in the following equation: $$\begin{eqnarray} h(\textit{age}_{\textit{it}}|\textit{Import}_{j,t-k},X_{i,j,c,t})=h_{0}(\textit{age}_{\textit{it}}|X_{i,j,c})\,\, \textit{exp}(\alpha \textit{Import}_{j,t-k} +\delta _t), \end{eqnarray}$$(2) where the baseline hazard h0 is stratified by industry j, CZ c and individual characteristics such as education, race, gender and health when interviewed. A Cox model allows us to specify only a functional form for the influence of import competition while leaving the shape of the hazard rates as unspecified as possible. In this case, each group of individuals defined by a combination of education, race, gender, industry and CZ, has a specific shape for the baseline hazard function. The model also includes a yearly trend δt, which—like our key explanatory variables—shifts the baseline hazard upwards or downwards. Note that the stratification by three-digit industry and CZ is equivalent to consider (interacted) industry and area fixed effects. The identification of import shocks comes from the differential mortality over time, areas and industries. We instrument the imports from China using the instrument presented in Subsection 1.1. Given that our Cox model is non-linear, we implement the instrumentation through a control-function approach, i.e., by including the first-stage residuals in the estimating equation. 3.4.3. Results As the first column of Table 9 shows, the import shock moves the mortality hazard upwards by around 1% at first, with an increasing impact as we allow more time for the shock to impact mortality. The effect increases to 6% with a seven-year lag. These results brings additional weight to the one we have using health surveys and administrative data from hospitals. The contemporaneous effect is in line with an immediate worsening in mental health found in Subsection 3.2, potentially leading to suicides. As the time lag increases, the rise in mortality comes increasingly from other causes, as we found effects of import competition on cardiovascular, endocrine or respiratory diseases at longer lags in Subsection 3.3. Table 9. Imports from China and All-Cause Mortality. . Coeff. . SE . Obs. . Imports, Lag 0 0.015** (0.007) 1,561,678 Imports, Lag 1 0.021*** (0.006) 1,534,308 Imports, Lag 2 0.022*** (0.006) 1,496,911 Imports, Lag 3 0.018*** (0.005) 1,449,259 Imports, Lag 4 0.021*** (0.006) 1,392,098 Imports, Lag 5 0.024*** (0.009) 1,325,529 Imports, Lag 6 0.036** (0.012) 1,250,632 Imports, Lag 7 0.059*** (0.015) 1,167,249 . Coeff. . SE . Obs. . Imports, Lag 0 0.015** (0.007) 1,561,678 Imports, Lag 1 0.021*** (0.006) 1,534,308 Imports, Lag 2 0.022*** (0.006) 1,496,911 Imports, Lag 3 0.018*** (0.005) 1,449,259 Imports, Lag 4 0.021*** (0.006) 1,392,098 Imports, Lag 5 0.024*** (0.009) 1,325,529 Imports, Lag 6 0.036** (0.012) 1,250,632 Imports, Lag 7 0.059*** (0.015) 1,167,249 Notes: NHIS data 1988–2009 (mortality up to 2011) for lag 0, 1989–2009 for lag 1, ..., 1995–2009 for lag 7. Imports are instrumented using a control-function approach, where the instrument is the imports from from China of four other high-income countries (Australia, Finland, Japan, Switzerland) for which we have comparable imports data over all the period. Baseline hazard stratified by three-digit industry codes, CZs, gender, race, education and self-assessed health. Regressions control for a yearly trend. Each entry corresponds to a separate regression. SE clustered at industry three-digit sector. * p < 0.10, ** p < 0.05, *** p < 0.01. Open in new tab Table 9. Imports from China and All-Cause Mortality. . Coeff. . SE . Obs. . Imports, Lag 0 0.015** (0.007) 1,561,678 Imports, Lag 1 0.021*** (0.006) 1,534,308 Imports, Lag 2 0.022*** (0.006) 1,496,911 Imports, Lag 3 0.018*** (0.005) 1,449,259 Imports, Lag 4 0.021*** (0.006) 1,392,098 Imports, Lag 5 0.024*** (0.009) 1,325,529 Imports, Lag 6 0.036** (0.012) 1,250,632 Imports, Lag 7 0.059*** (0.015) 1,167,249 . Coeff. . SE . Obs. . Imports, Lag 0 0.015** (0.007) 1,561,678 Imports, Lag 1 0.021*** (0.006) 1,534,308 Imports, Lag 2 0.022*** (0.006) 1,496,911 Imports, Lag 3 0.018*** (0.005) 1,449,259 Imports, Lag 4 0.021*** (0.006) 1,392,098 Imports, Lag 5 0.024*** (0.009) 1,325,529 Imports, Lag 6 0.036** (0.012) 1,250,632 Imports, Lag 7 0.059*** (0.015) 1,167,249 Notes: NHIS data 1988–2009 (mortality up to 2011) for lag 0, 1989–2009 for lag 1, ..., 1995–2009 for lag 7. Imports are instrumented using a control-function approach, where the instrument is the imports from from China of four other high-income countries (Australia, Finland, Japan, Switzerland) for which we have comparable imports data over all the period. Baseline hazard stratified by three-digit industry codes, CZs, gender, race, education and self-assessed health. Regressions control for a yearly trend. Each entry corresponds to a separate regression. SE clustered at industry three-digit sector. * p < 0.10, ** p < 0.05, *** p < 0.01. Open in new tab 4. Conclusion In this paper we make three main contributions to the literature on trade and health. We first show how import competition effects on the labour market are mediated by the composition of tasks in the industry. We show that import competition effects are concentrated in areas in the USA where routine tasks are the most prevalent, and largely absent elsewhere. Our results therefore complement and extend the work by Autor et al. (2013a), Autor et al. (2014) and Autor et al. (2016) by emphasising the role of technology and tasks in understanding the effect of import competition on the economy. This heterogeneous effect is a new finding. The task content of occupations has been mainly studied in the context of the effect of technological progress on labour markets pioneered by Autor et al. (2003). Second, we investigate the dynamic effects of import shocks and show that they display considerable inertia. Their effects are growing with time, at least over a span of six years. Third, exploiting multiple and large data sets covering about two decades, we show that the geographical and temporal patterns of labour market effects are also found for a very large array of health measures. Import competition has led to a significant deterioration of health in areas where jobs are the most intense in routine tasks but it has not in areas with the lowest RTI. We find a worsening in mental health and associated outcomes such as suicides or substance abuse. Those results align well with those of Case and Deaton (2015) and show that import competition is one of the determinants of this unprecedented decline in health. However, import competition is also related to many aspects of physical health. Those include cardiovascular problems and endocrine diseases which can be linked to stress and poorer health habits, but also other problems such as infectious diseases or skin problems, which are often the consequences of distinct diseases such as diabetes. We investigate the pathways to this deterioration in health and find mixed evidence on health behaviour as an explanation. We also show that income loss alone cannot explain this worsening in health, so that part of the effects is attributable to a lack of access to healthcare. This in turn can lead to worse health outcomes later on. Indeed we also find that hospitalisations are more likely to be classified as emergencies and that patients stay longer in hospital following an import shock. We show that the effects we find are not due to sorting of individuals into areas or industries prone to face import competition. Our results suggest that the effect of import competition is more pronounced than other studies investigating this same shock but also other aggregate shocks. One reason that economic recessions seem to be less harmful than import shocks is due to the persistence of those shocks. The literature has also pointed to the large cost of moving from one sector to the other, and an import shock could be a large and permanent shock for a subset of older workers with lower human capital. Further research should take into account the effect of import competition on health and mortality when assessing the welfare effects of trade. Appendix A. Robustness of Results In this section we further probe the robustness of our results. We first present falsification tests, looking at the effect of future import shocks on health and hospitalisation. Table A6 presents the results for the health scores defined in Subsection 3.2 with data from the BRFSS, for leads of import varying from 1 to 4. We find few effects that are significant, apart for healthcare utilisation at leads 1 and 2. Table A7 displays the results for a shock four years ahead. For effects at different leads, we refer the reader to Figure 4 in the main text. The table shows that contrary to Table 7—where the effects for the high RTI areas were mainly positive and significant—the effects at lead 4 are mostly insignificant, or significant and negative. Those results suggest either no sorting of workers across CZ or a negative selection that would imply that our results in the text are even stronger. As our sample contains the financial crisis of 2007–8, some of the effects we find may be due to the recession rather than import competition. Our regressions control for time fixed effects which would control for that event, but it is still possible that CZs with a mix of industries in competition with foreign imports were more susceptible to the recession. We therefore display in Tables A8 and A9 results similar to those presented in Tables 5 and 7, but where we discarded two years of data, 2009 and 2010, leaving one year for the 2008–9 recession to have an effect on health outcomes. The exclusion of that time period does not change the results. This could be due to the fact that either the recession had a general negative effect across the whole of the USA, or that recessions do not affect the health of working-age adults substantially, a phenomenon described in Ruhm (2000). Table A1. Occupation and Industry Composition of CZs by RTI Terciles. Five most important occupations . . Five most important industries . . Occupation . Share . Industry . Share . RTI: Low Assemblers of electrical equipment 6.7% Printing, publishing and allied industries, except newspapers 5.8% Managers and administrators, n.e.c 6.5% Electrical machinery, equipment and supplies, n.e.c 5.1% Machine operators, n.e.c 5.8% Apparel and accessories, except knitting 4.9% Production supervisors or foremen 4.8% Sawmills, planing mills, and mill work 4.4% Textile sewing machine operators 3.5% Machinery, except electrical, n.e.c 4% RTI: Medium Assemblers of electrical equipment 8.7% Motor vehicles and motor vehicle equipment 7.6% Machine operators, n.e.c 6.7% Printing, publishing and allied industries, except newspapers 6.1% Managers and administrators, n.e.c 5.2% Apparel and accessories, except knit 5.9% Production supervisors or foremen 4.8% Machinery, except electrical, n.e.c 5.5% Textile sewing machine operators 4.6% Electrical machinery, equipment and supplies, n.e.c 4.4% RTI: High Assemblers of electrical equipment 8.8% Apparel and accessories, except knitting 7.5% Textile sewing machine operators 6.6% Yarn, thread and fabric mills 6.2% Machine operators, n.e.c 6.6% Printing, publishing and allied industries, except newspapers 5.5% Managers and administrators, n.e.c 4.4% Meat products 5.1% Production supervisors or foremen 4.9% Motor vehicles and motor vehicle equipment 5.1% Five most important occupations . . Five most important industries . . Occupation . Share . Industry . Share . RTI: Low Assemblers of electrical equipment 6.7% Printing, publishing and allied industries, except newspapers 5.8% Managers and administrators, n.e.c 6.5% Electrical machinery, equipment and supplies, n.e.c 5.1% Machine operators, n.e.c 5.8% Apparel and accessories, except knitting 4.9% Production supervisors or foremen 4.8% Sawmills, planing mills, and mill work 4.4% Textile sewing machine operators 3.5% Machinery, except electrical, n.e.c 4% RTI: Medium Assemblers of electrical equipment 8.7% Motor vehicles and motor vehicle equipment 7.6% Machine operators, n.e.c 6.7% Printing, publishing and allied industries, except newspapers 6.1% Managers and administrators, n.e.c 5.2% Apparel and accessories, except knit 5.9% Production supervisors or foremen 4.8% Machinery, except electrical, n.e.c 5.5% Textile sewing machine operators 4.6% Electrical machinery, equipment and supplies, n.e.c 4.4% RTI: High Assemblers of electrical equipment 8.8% Apparel and accessories, except knitting 7.5% Textile sewing machine operators 6.6% Yarn, thread and fabric mills 6.2% Machine operators, n.e.c 6.6% Printing, publishing and allied industries, except newspapers 5.5% Managers and administrators, n.e.c 4.4% Meat products 5.1% Production supervisors or foremen 4.9% Motor vehicles and motor vehicle equipment 5.1% Notes: Sample: manufacturing workers in 1990 IPUMS census. Weighted by person weights. N=589,720 individuals in low RTI CZs; 814,761 individuals in Medium RTI CZs; 486,382 individuals in High RTI CZs. ‘Share’ refers to the share of manufacturing employment represented by those occupations and industries in each RTI group of CZs. Open in new tab Table A1. Occupation and Industry Composition of CZs by RTI Terciles. Five most important occupations . . Five most important industries . . Occupation . Share . Industry . Share . RTI: Low Assemblers of electrical equipment 6.7% Printing, publishing and allied industries, except newspapers 5.8% Managers and administrators, n.e.c 6.5% Electrical machinery, equipment and supplies, n.e.c 5.1% Machine operators, n.e.c 5.8% Apparel and accessories, except knitting 4.9% Production supervisors or foremen 4.8% Sawmills, planing mills, and mill work 4.4% Textile sewing machine operators 3.5% Machinery, except electrical, n.e.c 4% RTI: Medium Assemblers of electrical equipment 8.7% Motor vehicles and motor vehicle equipment 7.6% Machine operators, n.e.c 6.7% Printing, publishing and allied industries, except newspapers 6.1% Managers and administrators, n.e.c 5.2% Apparel and accessories, except knit 5.9% Production supervisors or foremen 4.8% Machinery, except electrical, n.e.c 5.5% Textile sewing machine operators 4.6% Electrical machinery, equipment and supplies, n.e.c 4.4% RTI: High Assemblers of electrical equipment 8.8% Apparel and accessories, except knitting 7.5% Textile sewing machine operators 6.6% Yarn, thread and fabric mills 6.2% Machine operators, n.e.c 6.6% Printing, publishing and allied industries, except newspapers 5.5% Managers and administrators, n.e.c 4.4% Meat products 5.1% Production supervisors or foremen 4.9% Motor vehicles and motor vehicle equipment 5.1% Five most important occupations . . Five most important industries . . Occupation . Share . Industry . Share . RTI: Low Assemblers of electrical equipment 6.7% Printing, publishing and allied industries, except newspapers 5.8% Managers and administrators, n.e.c 6.5% Electrical machinery, equipment and supplies, n.e.c 5.1% Machine operators, n.e.c 5.8% Apparel and accessories, except knitting 4.9% Production supervisors or foremen 4.8% Sawmills, planing mills, and mill work 4.4% Textile sewing machine operators 3.5% Machinery, except electrical, n.e.c 4% RTI: Medium Assemblers of electrical equipment 8.7% Motor vehicles and motor vehicle equipment 7.6% Machine operators, n.e.c 6.7% Printing, publishing and allied industries, except newspapers 6.1% Managers and administrators, n.e.c 5.2% Apparel and accessories, except knit 5.9% Production supervisors or foremen 4.8% Machinery, except electrical, n.e.c 5.5% Textile sewing machine operators 4.6% Electrical machinery, equipment and supplies, n.e.c 4.4% RTI: High Assemblers of electrical equipment 8.8% Apparel and accessories, except knitting 7.5% Textile sewing machine operators 6.6% Yarn, thread and fabric mills 6.2% Machine operators, n.e.c 6.6% Printing, publishing and allied industries, except newspapers 5.5% Managers and administrators, n.e.c 4.4% Meat products 5.1% Production supervisors or foremen 4.9% Motor vehicles and motor vehicle equipment 5.1% Notes: Sample: manufacturing workers in 1990 IPUMS census. Weighted by person weights. N=589,720 individuals in low RTI CZs; 814,761 individuals in Medium RTI CZs; 486,382 individuals in High RTI CZs. ‘Share’ refers to the share of manufacturing employment represented by those occupations and industries in each RTI group of CZs. Open in new tab Table A2. Descriptive Statistics, BRFSS 1997–2011. . Mean . SD . Min. . Max. . Count . Demographics Ref. Age 40.08 12.54 18 65 2,810,752 Male 0.49 0.50 0 1 2,810,752 Race: white 0.73 0.45 0 1 2,805,798 Race: black 0.13 0.33 0 1 2,805,798 Education: high school or less 0.32 0.47 0 1 2,807,113 Education: some college 0.26 0.44 0 1 2,807,113 Education: college graduate 0.41 0.49 0 1 2,807,113 Health Ref. Index of good health 0.00 100.00 −465 61 2,564,920 (Very) good health 87.97 32.53 0 100 2,810,752 Ever told blood pressure high 21.16 40.85 0 100 1,592,224 Ever diagnosed with a stroke 1.34 11.49 0 100 2,019,757 Ever diagnosed with diabetes 6.95 25.42 0 100 2,807,176 Still has asthma 8.65 28.11 0 100 2,569,959 Overweight 34.83 47.64 0 100 2,687,250 Obese 22.06 41.47 0 100 2,687,250 Mental health problems 10.11 30.14 0 100 2,683,631 Satisfaction with life 93.77 24.17 0 100 1,442,919 Health behaviour Ref. Index of good health behaviour 0.00 100.00 −271 70 2,316,894 How many days with alcohol in past 30 days 4.84 7.50 0 31 2,456,971 More than 14 days with alcohol in past 30 days 11.93 32.41 0 100 2,456,971 Currently smoking 20.56 40.41 0 100 2,801,199 Exercise in past 30 days 78.85 40.84 0 100 2,654,080 Healthcare utilisation Ref. Index of healthcare utilisation 0.00 100.00 −361 92 1,966,660 Could not see doctor because of cost 13.58 34.26 0 100 2,529,740 Has any healthcare coverage 85.28 35.43 0 100 2,804,080 Seasonal flu shot past 12 months 27.76 44.78 0 100 2,631,076 Ever had blood-stool test 36.69 48.20 0 100 624,499 Last check-up more than 5 years ago 8.92 28.50 0 100 2,189,677 Last dentist visit more than 5 years ago 7.64 26.56 0 100 1,323,363 Labour and Income Ref. Currently working 72.04 44.88 0 100 2,804,625 Annual household income less than $20k 10.28 30.36 0 100 2,810,752 . Mean . SD . Min. . Max. . Count . Demographics Ref. Age 40.08 12.54 18 65 2,810,752 Male 0.49 0.50 0 1 2,810,752 Race: white 0.73 0.45 0 1 2,805,798 Race: black 0.13 0.33 0 1 2,805,798 Education: high school or less 0.32 0.47 0 1 2,807,113 Education: some college 0.26 0.44 0 1 2,807,113 Education: college graduate 0.41 0.49 0 1 2,807,113 Health Ref. Index of good health 0.00 100.00 −465 61 2,564,920 (Very) good health 87.97 32.53 0 100 2,810,752 Ever told blood pressure high 21.16 40.85 0 100 1,592,224 Ever diagnosed with a stroke 1.34 11.49 0 100 2,019,757 Ever diagnosed with diabetes 6.95 25.42 0 100 2,807,176 Still has asthma 8.65 28.11 0 100 2,569,959 Overweight 34.83 47.64 0 100 2,687,250 Obese 22.06 41.47 0 100 2,687,250 Mental health problems 10.11 30.14 0 100 2,683,631 Satisfaction with life 93.77 24.17 0 100 1,442,919 Health behaviour Ref. Index of good health behaviour 0.00 100.00 −271 70 2,316,894 How many days with alcohol in past 30 days 4.84 7.50 0 31 2,456,971 More than 14 days with alcohol in past 30 days 11.93 32.41 0 100 2,456,971 Currently smoking 20.56 40.41 0 100 2,801,199 Exercise in past 30 days 78.85 40.84 0 100 2,654,080 Healthcare utilisation Ref. Index of healthcare utilisation 0.00 100.00 −361 92 1,966,660 Could not see doctor because of cost 13.58 34.26 0 100 2,529,740 Has any healthcare coverage 85.28 35.43 0 100 2,804,080 Seasonal flu shot past 12 months 27.76 44.78 0 100 2,631,076 Ever had blood-stool test 36.69 48.20 0 100 624,499 Last check-up more than 5 years ago 8.92 28.50 0 100 2,189,677 Last dentist visit more than 5 years ago 7.64 26.56 0 100 1,323,363 Labour and Income Ref. Currently working 72.04 44.88 0 100 2,804,625 Annual household income less than $20k 10.28 30.36 0 100 2,810,752 Notes: Weights are computed in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age–race–sex cell in the IPUMS Census 2000 data. Open in new tab Table A2. Descriptive Statistics, BRFSS 1997–2011. . Mean . SD . Min. . Max. . Count . Demographics Ref. Age 40.08 12.54 18 65 2,810,752 Male 0.49 0.50 0 1 2,810,752 Race: white 0.73 0.45 0 1 2,805,798 Race: black 0.13 0.33 0 1 2,805,798 Education: high school or less 0.32 0.47 0 1 2,807,113 Education: some college 0.26 0.44 0 1 2,807,113 Education: college graduate 0.41 0.49 0 1 2,807,113 Health Ref. Index of good health 0.00 100.00 −465 61 2,564,920 (Very) good health 87.97 32.53 0 100 2,810,752 Ever told blood pressure high 21.16 40.85 0 100 1,592,224 Ever diagnosed with a stroke 1.34 11.49 0 100 2,019,757 Ever diagnosed with diabetes 6.95 25.42 0 100 2,807,176 Still has asthma 8.65 28.11 0 100 2,569,959 Overweight 34.83 47.64 0 100 2,687,250 Obese 22.06 41.47 0 100 2,687,250 Mental health problems 10.11 30.14 0 100 2,683,631 Satisfaction with life 93.77 24.17 0 100 1,442,919 Health behaviour Ref. Index of good health behaviour 0.00 100.00 −271 70 2,316,894 How many days with alcohol in past 30 days 4.84 7.50 0 31 2,456,971 More than 14 days with alcohol in past 30 days 11.93 32.41 0 100 2,456,971 Currently smoking 20.56 40.41 0 100 2,801,199 Exercise in past 30 days 78.85 40.84 0 100 2,654,080 Healthcare utilisation Ref. Index of healthcare utilisation 0.00 100.00 −361 92 1,966,660 Could not see doctor because of cost 13.58 34.26 0 100 2,529,740 Has any healthcare coverage 85.28 35.43 0 100 2,804,080 Seasonal flu shot past 12 months 27.76 44.78 0 100 2,631,076 Ever had blood-stool test 36.69 48.20 0 100 624,499 Last check-up more than 5 years ago 8.92 28.50 0 100 2,189,677 Last dentist visit more than 5 years ago 7.64 26.56 0 100 1,323,363 Labour and Income Ref. Currently working 72.04 44.88 0 100 2,804,625 Annual household income less than $20k 10.28 30.36 0 100 2,810,752 . Mean . SD . Min. . Max. . Count . Demographics Ref. Age 40.08 12.54 18 65 2,810,752 Male 0.49 0.50 0 1 2,810,752 Race: white 0.73 0.45 0 1 2,805,798 Race: black 0.13 0.33 0 1 2,805,798 Education: high school or less 0.32 0.47 0 1 2,807,113 Education: some college 0.26 0.44 0 1 2,807,113 Education: college graduate 0.41 0.49 0 1 2,807,113 Health Ref. Index of good health 0.00 100.00 −465 61 2,564,920 (Very) good health 87.97 32.53 0 100 2,810,752 Ever told blood pressure high 21.16 40.85 0 100 1,592,224 Ever diagnosed with a stroke 1.34 11.49 0 100 2,019,757 Ever diagnosed with diabetes 6.95 25.42 0 100 2,807,176 Still has asthma 8.65 28.11 0 100 2,569,959 Overweight 34.83 47.64 0 100 2,687,250 Obese 22.06 41.47 0 100 2,687,250 Mental health problems 10.11 30.14 0 100 2,683,631 Satisfaction with life 93.77 24.17 0 100 1,442,919 Health behaviour Ref. Index of good health behaviour 0.00 100.00 −271 70 2,316,894 How many days with alcohol in past 30 days 4.84 7.50 0 31 2,456,971 More than 14 days with alcohol in past 30 days 11.93 32.41 0 100 2,456,971 Currently smoking 20.56 40.41 0 100 2,801,199 Exercise in past 30 days 78.85 40.84 0 100 2,654,080 Healthcare utilisation Ref. Index of healthcare utilisation 0.00 100.00 −361 92 1,966,660 Could not see doctor because of cost 13.58 34.26 0 100 2,529,740 Has any healthcare coverage 85.28 35.43 0 100 2,804,080 Seasonal flu shot past 12 months 27.76 44.78 0 100 2,631,076 Ever had blood-stool test 36.69 48.20 0 100 624,499 Last check-up more than 5 years ago 8.92 28.50 0 100 2,189,677 Last dentist visit more than 5 years ago 7.64 26.56 0 100 1,323,363 Labour and Income Ref. Currently working 72.04 44.88 0 100 2,804,625 Annual household income less than $20k 10.28 30.36 0 100 2,810,752 Notes: Weights are computed in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age–race–sex cell in the IPUMS Census 2000 data. Open in new tab Table A3. Category Definition, NIS. Condition . ICD-9 codes . Suicide E850–E859 E868.2 E950–E960 Homicides and crime E960–E979 Heart problems 410–438 Infectious diseases 001–139 Respiratory diseases 460–519 Mental disorders 290–311 Injury 800–869 Alcohol abuse 305, 291–292, 303, 571.0−571.4, E860.0 Substance abuse 304 292.0 305.2/305.95 E850.0 E850.1 970.8 Opioid abuse 304.00 304.01 304.02 304.03 304.70 304.71 304.72 304.73 305.50 305.51 305.52 305.53 965.00 965.09 E850.2 E935.2 Endocrine, nutritional and metabolic diseases 240–280 Neoplasm (all) 140–239 Neoplasm (tobacco related) 162, 140–151, 153–154, 157, 160–161 179–180, 183, 188–189, 205 Stress: Mental disorder 300–311, 316 Tachycardia 427.2 Asthma 493.00 Ulcers 531–533 Colitis 556 Functional disorders of intestine 564 Dermatitis, eczema, urticaria 691–692, 708 Backache 724.0/724.99 Diet related: Diabetes 250 Nutritional deficiencies 260–269, 280.1 Anaemia 285.9 Eating disorder 307.1,307.5 Calculus of kidney 592 Chronic kidney disease 585.3−583.5 Hyper cholesterolemia, glyceridemia, lipidemia 272 Abnormal weight change 783 Obesity V85.3–V85.45, 278 Inappropriate diet V69.1 Condition . ICD-9 codes . Suicide E850–E859 E868.2 E950–E960 Homicides and crime E960–E979 Heart problems 410–438 Infectious diseases 001–139 Respiratory diseases 460–519 Mental disorders 290–311 Injury 800–869 Alcohol abuse 305, 291–292, 303, 571.0−571.4, E860.0 Substance abuse 304 292.0 305.2/305.95 E850.0 E850.1 970.8 Opioid abuse 304.00 304.01 304.02 304.03 304.70 304.71 304.72 304.73 305.50 305.51 305.52 305.53 965.00 965.09 E850.2 E935.2 Endocrine, nutritional and metabolic diseases 240–280 Neoplasm (all) 140–239 Neoplasm (tobacco related) 162, 140–151, 153–154, 157, 160–161 179–180, 183, 188–189, 205 Stress: Mental disorder 300–311, 316 Tachycardia 427.2 Asthma 493.00 Ulcers 531–533 Colitis 556 Functional disorders of intestine 564 Dermatitis, eczema, urticaria 691–692, 708 Backache 724.0/724.99 Diet related: Diabetes 250 Nutritional deficiencies 260–269, 280.1 Anaemia 285.9 Eating disorder 307.1,307.5 Calculus of kidney 592 Chronic kidney disease 585.3−583.5 Hyper cholesterolemia, glyceridemia, lipidemia 272 Abnormal weight change 783 Obesity V85.3–V85.45, 278 Inappropriate diet V69.1 Open in new tab Table A3. Category Definition, NIS. Condition . ICD-9 codes . Suicide E850–E859 E868.2 E950–E960 Homicides and crime E960–E979 Heart problems 410–438 Infectious diseases 001–139 Respiratory diseases 460–519 Mental disorders 290–311 Injury 800–869 Alcohol abuse 305, 291–292, 303, 571.0−571.4, E860.0 Substance abuse 304 292.0 305.2/305.95 E850.0 E850.1 970.8 Opioid abuse 304.00 304.01 304.02 304.03 304.70 304.71 304.72 304.73 305.50 305.51 305.52 305.53 965.00 965.09 E850.2 E935.2 Endocrine, nutritional and metabolic diseases 240–280 Neoplasm (all) 140–239 Neoplasm (tobacco related) 162, 140–151, 153–154, 157, 160–161 179–180, 183, 188–189, 205 Stress: Mental disorder 300–311, 316 Tachycardia 427.2 Asthma 493.00 Ulcers 531–533 Colitis 556 Functional disorders of intestine 564 Dermatitis, eczema, urticaria 691–692, 708 Backache 724.0/724.99 Diet related: Diabetes 250 Nutritional deficiencies 260–269, 280.1 Anaemia 285.9 Eating disorder 307.1,307.5 Calculus of kidney 592 Chronic kidney disease 585.3−583.5 Hyper cholesterolemia, glyceridemia, lipidemia 272 Abnormal weight change 783 Obesity V85.3–V85.45, 278 Inappropriate diet V69.1 Condition . ICD-9 codes . Suicide E850–E859 E868.2 E950–E960 Homicides and crime E960–E979 Heart problems 410–438 Infectious diseases 001–139 Respiratory diseases 460–519 Mental disorders 290–311 Injury 800–869 Alcohol abuse 305, 291–292, 303, 571.0−571.4, E860.0 Substance abuse 304 292.0 305.2/305.95 E850.0 E850.1 970.8 Opioid abuse 304.00 304.01 304.02 304.03 304.70 304.71 304.72 304.73 305.50 305.51 305.52 305.53 965.00 965.09 E850.2 E935.2 Endocrine, nutritional and metabolic diseases 240–280 Neoplasm (all) 140–239 Neoplasm (tobacco related) 162, 140–151, 153–154, 157, 160–161 179–180, 183, 188–189, 205 Stress: Mental disorder 300–311, 316 Tachycardia 427.2 Asthma 493.00 Ulcers 531–533 Colitis 556 Functional disorders of intestine 564 Dermatitis, eczema, urticaria 691–692, 708 Backache 724.0/724.99 Diet related: Diabetes 250 Nutritional deficiencies 260–269, 280.1 Anaemia 285.9 Eating disorder 307.1,307.5 Calculus of kidney 592 Chronic kidney disease 585.3−583.5 Hyper cholesterolemia, glyceridemia, lipidemia 272 Abnormal weight change 783 Obesity V85.3–V85.45, 278 Inappropriate diet V69.1 Open in new tab Table A4. Descriptive Statistics, Hospital Discharges (NIS). . Number or mean . SD . Total discharges 38,979,165 Stress-related discharges 13,503,978 Mental disorders-related diagnostics 12,226,730 Suicides-related discharges 544,223 Alcohol abuse-related discharges 3,229,212 Substance abuse-related discharges 2,450,524 Opioid abuse 908,743 Injuries-related diagnostics 1,457,970 Homicides-related discharges 200,142 Driving accidents 418,766 Pain 3,393,051 Skin disease 2,170,968 Heart-related diagnostics 8,238,972 Infectious diseases-related diagnostics 4,308,504 Respiratory diseases 7,971,887 Disease of digestive system 14,755,025 Endocrine diseases 8,896,102 Diet-related diseases 11,113,310 Cancers 3,855,483 Tobacco-related cancers 983,787 Non-tobacco-related cancers 3,367,591 Total deaths in hospital 435,405 Average age 43.47 (5.04) Proportion males 0.38 (0.10) Proportion white 0.54 (0.35) Proportion African-American 0.09 (0.15) Proportion urgent 0.24 (0.26) Proportion emergency 0.34 (0.26) Proportion length of stay (days) 4.66 (4.94) Proportion stay > 7 days 0.12 (0.16) Average charges (2016 $) 19,249 (22,863) Proportion self-pay 0.08 (0.07) Proportion Medicaid 0.22 (0.13) Proportion Medicare 0.17 (0.11) Number of hospitals in sample 2,877 Hospital–year–group observations 91,535 Average number of years per hospital 3.48 (1.97) Average annual number of discharges per hospital 4,087 (5,086) Number of CZs 386 . Number or mean . SD . Total discharges 38,979,165 Stress-related discharges 13,503,978 Mental disorders-related diagnostics 12,226,730 Suicides-related discharges 544,223 Alcohol abuse-related discharges 3,229,212 Substance abuse-related discharges 2,450,524 Opioid abuse 908,743 Injuries-related diagnostics 1,457,970 Homicides-related discharges 200,142 Driving accidents 418,766 Pain 3,393,051 Skin disease 2,170,968 Heart-related diagnostics 8,238,972 Infectious diseases-related diagnostics 4,308,504 Respiratory diseases 7,971,887 Disease of digestive system 14,755,025 Endocrine diseases 8,896,102 Diet-related diseases 11,113,310 Cancers 3,855,483 Tobacco-related cancers 983,787 Non-tobacco-related cancers 3,367,591 Total deaths in hospital 435,405 Average age 43.47 (5.04) Proportion males 0.38 (0.10) Proportion white 0.54 (0.35) Proportion African-American 0.09 (0.15) Proportion urgent 0.24 (0.26) Proportion emergency 0.34 (0.26) Proportion length of stay (days) 4.66 (4.94) Proportion stay > 7 days 0.12 (0.16) Average charges (2016 $) 19,249 (22,863) Proportion self-pay 0.08 (0.07) Proportion Medicaid 0.22 (0.13) Proportion Medicare 0.17 (0.11) Number of hospitals in sample 2,877 Hospital–year–group observations 91,535 Average number of years per hospital 3.48 (1.97) Average annual number of discharges per hospital 4,087 (5,086) Number of CZs 386 Notes: For definitions of the morbidity categories, see Table A3. Open in new tab Table A4. Descriptive Statistics, Hospital Discharges (NIS). . Number or mean . SD . Total discharges 38,979,165 Stress-related discharges 13,503,978 Mental disorders-related diagnostics 12,226,730 Suicides-related discharges 544,223 Alcohol abuse-related discharges 3,229,212 Substance abuse-related discharges 2,450,524 Opioid abuse 908,743 Injuries-related diagnostics 1,457,970 Homicides-related discharges 200,142 Driving accidents 418,766 Pain 3,393,051 Skin disease 2,170,968 Heart-related diagnostics 8,238,972 Infectious diseases-related diagnostics 4,308,504 Respiratory diseases 7,971,887 Disease of digestive system 14,755,025 Endocrine diseases 8,896,102 Diet-related diseases 11,113,310 Cancers 3,855,483 Tobacco-related cancers 983,787 Non-tobacco-related cancers 3,367,591 Total deaths in hospital 435,405 Average age 43.47 (5.04) Proportion males 0.38 (0.10) Proportion white 0.54 (0.35) Proportion African-American 0.09 (0.15) Proportion urgent 0.24 (0.26) Proportion emergency 0.34 (0.26) Proportion length of stay (days) 4.66 (4.94) Proportion stay > 7 days 0.12 (0.16) Average charges (2016 $) 19,249 (22,863) Proportion self-pay 0.08 (0.07) Proportion Medicaid 0.22 (0.13) Proportion Medicare 0.17 (0.11) Number of hospitals in sample 2,877 Hospital–year–group observations 91,535 Average number of years per hospital 3.48 (1.97) Average annual number of discharges per hospital 4,087 (5,086) Number of CZs 386 . Number or mean . SD . Total discharges 38,979,165 Stress-related discharges 13,503,978 Mental disorders-related diagnostics 12,226,730 Suicides-related discharges 544,223 Alcohol abuse-related discharges 3,229,212 Substance abuse-related discharges 2,450,524 Opioid abuse 908,743 Injuries-related diagnostics 1,457,970 Homicides-related discharges 200,142 Driving accidents 418,766 Pain 3,393,051 Skin disease 2,170,968 Heart-related diagnostics 8,238,972 Infectious diseases-related diagnostics 4,308,504 Respiratory diseases 7,971,887 Disease of digestive system 14,755,025 Endocrine diseases 8,896,102 Diet-related diseases 11,113,310 Cancers 3,855,483 Tobacco-related cancers 983,787 Non-tobacco-related cancers 3,367,591 Total deaths in hospital 435,405 Average age 43.47 (5.04) Proportion males 0.38 (0.10) Proportion white 0.54 (0.35) Proportion African-American 0.09 (0.15) Proportion urgent 0.24 (0.26) Proportion emergency 0.34 (0.26) Proportion length of stay (days) 4.66 (4.94) Proportion stay > 7 days 0.12 (0.16) Average charges (2016 $) 19,249 (22,863) Proportion self-pay 0.08 (0.07) Proportion Medicaid 0.22 (0.13) Proportion Medicare 0.17 (0.11) Number of hospitals in sample 2,877 Hospital–year–group observations 91,535 Average number of years per hospital 3.48 (1.97) Average annual number of discharges per hospital 4,087 (5,086) Number of CZs 386 Notes: For definitions of the morbidity categories, see Table A3. Open in new tab Table A5. Descriptive Statistics, NHIS. Sample characteristics . NHIS 1988−2009 . . Manufacturing workers, aged 18−65 at baseline . Observations 1,591,587 Subjects 126,625 Average age at baseline 39 Average health at baseline (1−5) 2.04 (SD=0.96) Birth cohorts 1921−91 Male 66% White 81% Low education 62% Number of deaths 5,569 Sample characteristics . NHIS 1988−2009 . . Manufacturing workers, aged 18−65 at baseline . Observations 1,591,587 Subjects 126,625 Average age at baseline 39 Average health at baseline (1−5) 2.04 (SD=0.96) Birth cohorts 1921−91 Male 66% White 81% Low education 62% Number of deaths 5,569 Open in new tab Table A5. Descriptive Statistics, NHIS. Sample characteristics . NHIS 1988−2009 . . Manufacturing workers, aged 18−65 at baseline . Observations 1,591,587 Subjects 126,625 Average age at baseline 39 Average health at baseline (1−5) 2.04 (SD=0.96) Birth cohorts 1921−91 Male 66% White 81% Low education 62% Number of deaths 5,569 Sample characteristics . NHIS 1988−2009 . . Manufacturing workers, aged 18−65 at baseline . Observations 1,591,587 Subjects 126,625 Average age at baseline 39 Average health at baseline (1−5) 2.04 (SD=0.96) Birth cohorts 1921−91 Male 66% White 81% Low education 62% Number of deaths 5,569 Open in new tab Table A6. Future Imports from China and Health, Health Behaviour and Healthcare Utilisation, by RTI Terciles. . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lead 1 −0.725 −0.488 −0.984 −1.159* −1.395 −1.202 −2.463 −1.097 −2.127*** −1.750** −3.005** −2.155** (0.686) (0.708) (1.069) (0.605) (1.160) (0.955) (2.373) (1.212) (0.806) (0.774) (1.340) (0.993) Lead 2 −0.470 −0.361 −0.422 −0.859 −2.025 −2.137 −5.773 −2.127 −2.385** −2.307** −2.964* −1.936* (0.955) (1.046) (1.404) (0.751) (1.574) (2.371) (7.425) (3.097) (1.022) (1.044) (1.640) (1.023) Lead 3 0.993 1.450 0.415 −0.151 −1.321 −8.530 −29.735 −15.143 0.343 0.726 −0.852 −0.168 (1.292) (1.360) (2.165) (1.198) (3.253) (112.104) (375.046) (204.729) (1.020) (1.031) (1.554) (1.040) Lead 4 0.027 0.253 0.213 −0.643 −1.211 −1.756 −4.361 −1.219 −0.526 −0.347 −1.161 −0.922 (1.225) (1.176) (2.235) (1.202) (2.901) (3.852) (10.629) (7.362) (1.929) (1.707) (3.742) (2.225) Obs. 1,531,603 1,318,554 914,648 . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lead 1 −0.725 −0.488 −0.984 −1.159* −1.395 −1.202 −2.463 −1.097 −2.127*** −1.750** −3.005** −2.155** (0.686) (0.708) (1.069) (0.605) (1.160) (0.955) (2.373) (1.212) (0.806) (0.774) (1.340) (0.993) Lead 2 −0.470 −0.361 −0.422 −0.859 −2.025 −2.137 −5.773 −2.127 −2.385** −2.307** −2.964* −1.936* (0.955) (1.046) (1.404) (0.751) (1.574) (2.371) (7.425) (3.097) (1.022) (1.044) (1.640) (1.023) Lead 3 0.993 1.450 0.415 −0.151 −1.321 −8.530 −29.735 −15.143 0.343 0.726 −0.852 −0.168 (1.292) (1.360) (2.165) (1.198) (3.253) (112.104) (375.046) (204.729) (1.020) (1.031) (1.554) (1.040) Lead 4 0.027 0.253 0.213 −0.643 −1.211 −1.756 −4.361 −1.219 −0.526 −0.347 −1.161 −0.922 (1.225) (1.176) (2.235) (1.202) (2.901) (3.852) (10.629) (7.362) (1.929) (1.707) (3.742) (2.225) Obs. 1,531,603 1,318,554 914,648 Notes: Data from BRFSS, years 1997−2007. Good health is the first factor from a principal-component factor analysis including self-assessed health, and indicators for diabetes, obesity and poor mental health. Healthcare utilisation is the first factor from a principal-component factor analysis including an indicator for having a health plan, for having had a flu shot, a medical check-up and whether a doctor visit is too expensive. Health behaviour is the first factor from a principal-component factor analysis including smoking, alcohol consumption and exercise. All regressions include age dummies, sex, race, education and year and CZ fixed effects as well as state linear trends. We also include the percent of individuals in routine occupations. The second panel displays the regression of the different health measures on individual log income and controls. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered at CZ level. Models are weighted in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age group−race−sex cell in the IPUMS Census 2000 data. Open in new tab Table A6. Future Imports from China and Health, Health Behaviour and Healthcare Utilisation, by RTI Terciles. . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lead 1 −0.725 −0.488 −0.984 −1.159* −1.395 −1.202 −2.463 −1.097 −2.127*** −1.750** −3.005** −2.155** (0.686) (0.708) (1.069) (0.605) (1.160) (0.955) (2.373) (1.212) (0.806) (0.774) (1.340) (0.993) Lead 2 −0.470 −0.361 −0.422 −0.859 −2.025 −2.137 −5.773 −2.127 −2.385** −2.307** −2.964* −1.936* (0.955) (1.046) (1.404) (0.751) (1.574) (2.371) (7.425) (3.097) (1.022) (1.044) (1.640) (1.023) Lead 3 0.993 1.450 0.415 −0.151 −1.321 −8.530 −29.735 −15.143 0.343 0.726 −0.852 −0.168 (1.292) (1.360) (2.165) (1.198) (3.253) (112.104) (375.046) (204.729) (1.020) (1.031) (1.554) (1.040) Lead 4 0.027 0.253 0.213 −0.643 −1.211 −1.756 −4.361 −1.219 −0.526 −0.347 −1.161 −0.922 (1.225) (1.176) (2.235) (1.202) (2.901) (3.852) (10.629) (7.362) (1.929) (1.707) (3.742) (2.225) Obs. 1,531,603 1,318,554 914,648 . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lead 1 −0.725 −0.488 −0.984 −1.159* −1.395 −1.202 −2.463 −1.097 −2.127*** −1.750** −3.005** −2.155** (0.686) (0.708) (1.069) (0.605) (1.160) (0.955) (2.373) (1.212) (0.806) (0.774) (1.340) (0.993) Lead 2 −0.470 −0.361 −0.422 −0.859 −2.025 −2.137 −5.773 −2.127 −2.385** −2.307** −2.964* −1.936* (0.955) (1.046) (1.404) (0.751) (1.574) (2.371) (7.425) (3.097) (1.022) (1.044) (1.640) (1.023) Lead 3 0.993 1.450 0.415 −0.151 −1.321 −8.530 −29.735 −15.143 0.343 0.726 −0.852 −0.168 (1.292) (1.360) (2.165) (1.198) (3.253) (112.104) (375.046) (204.729) (1.020) (1.031) (1.554) (1.040) Lead 4 0.027 0.253 0.213 −0.643 −1.211 −1.756 −4.361 −1.219 −0.526 −0.347 −1.161 −0.922 (1.225) (1.176) (2.235) (1.202) (2.901) (3.852) (10.629) (7.362) (1.929) (1.707) (3.742) (2.225) Obs. 1,531,603 1,318,554 914,648 Notes: Data from BRFSS, years 1997−2007. Good health is the first factor from a principal-component factor analysis including self-assessed health, and indicators for diabetes, obesity and poor mental health. Healthcare utilisation is the first factor from a principal-component factor analysis including an indicator for having a health plan, for having had a flu shot, a medical check-up and whether a doctor visit is too expensive. Health behaviour is the first factor from a principal-component factor analysis including smoking, alcohol consumption and exercise. All regressions include age dummies, sex, race, education and year and CZ fixed effects as well as state linear trends. We also include the percent of individuals in routine occupations. The second panel displays the regression of the different health measures on individual log income and controls. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered at CZ level. Models are weighted in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age group−race−sex cell in the IPUMS Census 2000 data. Open in new tab Table A7. Future Imports from China (Four Years Ahead) and Hospitalisation: Discharges by Cause. . All . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms 0.006 0.008 0.035* −0.104* (0.026) (0.026) (0.02) (0.059) Mental health problems −0.015 −0.006 0.018 −0.126** (0.019) (0.02) (0.015) (0.059) Suicides attempts 0.017 0.033 0.03 −0.144*** (0.034) (0.036) (0.025) (0.048) Alcohol abuse −0.019 −0.007 −0.020 −0.016 (0.024) (0.021) (0.032) (0.018) Substance abuse −0.0001 0.01 0.007 −0.074* (0.033) (0.025) (0.038) (0.043) Opioid abuse −0.035 −0.015 −0.031 −0.057 (0.042) (0.032) (0.044) (0.041) Injuries 0.017 0.02 0.033 −0.069 (0.024) (0.021) (0.026) (0.053) Homicide injuries 0.007 0.013 0.037 −0.114*** (0.027) (0.023) (0.023) (0.039) Pain 0.023 −0.005 0.084** −0.068* (0.044) (0.032) (0.034) (0.041) Skin disease 0.014 0.006 0.042** −0.061** (0.026) (0.024) (0.018) (0.031) Heart problems 0.032 0.009 0.068*** −0.024 (0.03) (0.024) (0.019) (0.031) Infectious diseases 0.021 0.004 0.04* −0.006 (0.023) (0.019) (0.021) (0.017) Respiratory diseases 0.013 −0.005 0.053*** −0.039 (0.026) (0.02) (0.018) (0.031) Disease of digestive system 0.024 0.002 0.07*** −0.037 (0.031) (0.025) (0.023) (0.038) Endocrine diseases 0.032 0.01 0.064*** −0.027 (0.037) (0.032) (0.023) (0.024) Diet-related diseases 0.04 0.026 0.062** −0.055 (0.035) (0.032) (0.025) (0.039) Cancers 0.006 −0.011 0.053** −0.033 (0.018) (0.012) (0.023) (0.025) Tobacco-related cancers 0.003 −0.004 0.037 −0.026 (0.023) (0.019) (0.024) (0.019) Non-tobacco-related cancers 0.006 −0.014 0.055** −0.031 (0.02) (0.014) (0.025) (0.025) Died in hospital 0.017 −0.010 0.034 0.072 (0.029) (0.025) (0.023) (0.055) . All . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms 0.006 0.008 0.035* −0.104* (0.026) (0.026) (0.02) (0.059) Mental health problems −0.015 −0.006 0.018 −0.126** (0.019) (0.02) (0.015) (0.059) Suicides attempts 0.017 0.033 0.03 −0.144*** (0.034) (0.036) (0.025) (0.048) Alcohol abuse −0.019 −0.007 −0.020 −0.016 (0.024) (0.021) (0.032) (0.018) Substance abuse −0.0001 0.01 0.007 −0.074* (0.033) (0.025) (0.038) (0.043) Opioid abuse −0.035 −0.015 −0.031 −0.057 (0.042) (0.032) (0.044) (0.041) Injuries 0.017 0.02 0.033 −0.069 (0.024) (0.021) (0.026) (0.053) Homicide injuries 0.007 0.013 0.037 −0.114*** (0.027) (0.023) (0.023) (0.039) Pain 0.023 −0.005 0.084** −0.068* (0.044) (0.032) (0.034) (0.041) Skin disease 0.014 0.006 0.042** −0.061** (0.026) (0.024) (0.018) (0.031) Heart problems 0.032 0.009 0.068*** −0.024 (0.03) (0.024) (0.019) (0.031) Infectious diseases 0.021 0.004 0.04* −0.006 (0.023) (0.019) (0.021) (0.017) Respiratory diseases 0.013 −0.005 0.053*** −0.039 (0.026) (0.02) (0.018) (0.031) Disease of digestive system 0.024 0.002 0.07*** −0.037 (0.031) (0.025) (0.023) (0.038) Endocrine diseases 0.032 0.01 0.064*** −0.027 (0.037) (0.032) (0.023) (0.024) Diet-related diseases 0.04 0.026 0.062** −0.055 (0.035) (0.032) (0.025) (0.039) Cancers 0.006 −0.011 0.053** −0.033 (0.018) (0.012) (0.023) (0.025) Tobacco-related cancers 0.003 −0.004 0.037 −0.026 (0.023) (0.019) (0.024) (0.019) Non-tobacco-related cancers 0.006 −0.014 0.055** −0.031 (0.02) (0.014) (0.025) (0.025) Died in hospital 0.017 −0.010 0.034 0.072 (0.029) (0.025) (0.023) (0.055) Notes: Data from NIS for the years 1997−2007. Instrumental variable estimates using the sum of Chinese imports to the other countries as instruments for US imports. Instrumented imports are leaded four years. The table reports the effect of a $1,000 import shock on the log of 1 + the number of admissions of patients with a certain condition. All regressions include year fixed effects, state trends, hospital fixed effects, birth year–gender fixed effects of patients, CZ time-varying characteristics (demographic composition of the CZ in terms of gender, race, education, age composition and share of routine occupations). Weighted by hospital weights and population weights. SE clustered at CZ level. Open in new tab Table A7. Future Imports from China (Four Years Ahead) and Hospitalisation: Discharges by Cause. . All . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms 0.006 0.008 0.035* −0.104* (0.026) (0.026) (0.02) (0.059) Mental health problems −0.015 −0.006 0.018 −0.126** (0.019) (0.02) (0.015) (0.059) Suicides attempts 0.017 0.033 0.03 −0.144*** (0.034) (0.036) (0.025) (0.048) Alcohol abuse −0.019 −0.007 −0.020 −0.016 (0.024) (0.021) (0.032) (0.018) Substance abuse −0.0001 0.01 0.007 −0.074* (0.033) (0.025) (0.038) (0.043) Opioid abuse −0.035 −0.015 −0.031 −0.057 (0.042) (0.032) (0.044) (0.041) Injuries 0.017 0.02 0.033 −0.069 (0.024) (0.021) (0.026) (0.053) Homicide injuries 0.007 0.013 0.037 −0.114*** (0.027) (0.023) (0.023) (0.039) Pain 0.023 −0.005 0.084** −0.068* (0.044) (0.032) (0.034) (0.041) Skin disease 0.014 0.006 0.042** −0.061** (0.026) (0.024) (0.018) (0.031) Heart problems 0.032 0.009 0.068*** −0.024 (0.03) (0.024) (0.019) (0.031) Infectious diseases 0.021 0.004 0.04* −0.006 (0.023) (0.019) (0.021) (0.017) Respiratory diseases 0.013 −0.005 0.053*** −0.039 (0.026) (0.02) (0.018) (0.031) Disease of digestive system 0.024 0.002 0.07*** −0.037 (0.031) (0.025) (0.023) (0.038) Endocrine diseases 0.032 0.01 0.064*** −0.027 (0.037) (0.032) (0.023) (0.024) Diet-related diseases 0.04 0.026 0.062** −0.055 (0.035) (0.032) (0.025) (0.039) Cancers 0.006 −0.011 0.053** −0.033 (0.018) (0.012) (0.023) (0.025) Tobacco-related cancers 0.003 −0.004 0.037 −0.026 (0.023) (0.019) (0.024) (0.019) Non-tobacco-related cancers 0.006 −0.014 0.055** −0.031 (0.02) (0.014) (0.025) (0.025) Died in hospital 0.017 −0.010 0.034 0.072 (0.029) (0.025) (0.023) (0.055) . All . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms 0.006 0.008 0.035* −0.104* (0.026) (0.026) (0.02) (0.059) Mental health problems −0.015 −0.006 0.018 −0.126** (0.019) (0.02) (0.015) (0.059) Suicides attempts 0.017 0.033 0.03 −0.144*** (0.034) (0.036) (0.025) (0.048) Alcohol abuse −0.019 −0.007 −0.020 −0.016 (0.024) (0.021) (0.032) (0.018) Substance abuse −0.0001 0.01 0.007 −0.074* (0.033) (0.025) (0.038) (0.043) Opioid abuse −0.035 −0.015 −0.031 −0.057 (0.042) (0.032) (0.044) (0.041) Injuries 0.017 0.02 0.033 −0.069 (0.024) (0.021) (0.026) (0.053) Homicide injuries 0.007 0.013 0.037 −0.114*** (0.027) (0.023) (0.023) (0.039) Pain 0.023 −0.005 0.084** −0.068* (0.044) (0.032) (0.034) (0.041) Skin disease 0.014 0.006 0.042** −0.061** (0.026) (0.024) (0.018) (0.031) Heart problems 0.032 0.009 0.068*** −0.024 (0.03) (0.024) (0.019) (0.031) Infectious diseases 0.021 0.004 0.04* −0.006 (0.023) (0.019) (0.021) (0.017) Respiratory diseases 0.013 −0.005 0.053*** −0.039 (0.026) (0.02) (0.018) (0.031) Disease of digestive system 0.024 0.002 0.07*** −0.037 (0.031) (0.025) (0.023) (0.038) Endocrine diseases 0.032 0.01 0.064*** −0.027 (0.037) (0.032) (0.023) (0.024) Diet-related diseases 0.04 0.026 0.062** −0.055 (0.035) (0.032) (0.025) (0.039) Cancers 0.006 −0.011 0.053** −0.033 (0.018) (0.012) (0.023) (0.025) Tobacco-related cancers 0.003 −0.004 0.037 −0.026 (0.023) (0.019) (0.024) (0.019) Non-tobacco-related cancers 0.006 −0.014 0.055** −0.031 (0.02) (0.014) (0.025) (0.025) Died in hospital 0.017 −0.010 0.034 0.072 (0.029) (0.025) (0.023) (0.055) Notes: Data from NIS for the years 1997−2007. Instrumental variable estimates using the sum of Chinese imports to the other countries as instruments for US imports. Instrumented imports are leaded four years. The table reports the effect of a $1,000 import shock on the log of 1 + the number of admissions of patients with a certain condition. All regressions include year fixed effects, state trends, hospital fixed effects, birth year–gender fixed effects of patients, CZ time-varying characteristics (demographic composition of the CZ in terms of gender, race, education, age composition and share of routine occupations). Weighted by hospital weights and population weights. SE clustered at CZ level. Open in new tab Table A8. Imports from China and Health, Healthcare Utilisation and Health Behaviour, by RTI—Excluding the Great Recession. . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lag 0 −1.627** −1.466* −1.716 −2.133*** 1.252 0.97 2.398 1.107 −1.555 −1.400 −1.388 −2.276* (0.769) (0.781) (1.113) (0.685) (1.137) (0.879) (2.412) (1.077) (1.375) (1.232) (2.750) (1.304) Lag 1 −0.973 −0.831 −1.114 −1.469** 0.991 0.631 1.657 1.203 −0.658 −0.550 −0.255 −1.339 (0.715) (0.779) (0.846) (0.585) (0.838) (0.715) (1.307) (0.735) (1.447) (1.365) (3.486) (1.519) Lag 2 −0.791 −0.627 −0.981 −1.287** 0.492 0.069 1.020 0.888 −0.442 −0.196 −0.681 −1.787** (0.663) (0.766) (0.667) (0.603) (0.586) (0.685) (0.778) (0.556) (0.872) (0.854) (1.285) (0.761) Lag 3 −0.520 −0.582 −0.300 −1.225** 0.842* 0.475 1.306** 0.807 0.407 0.442 0.641 −2.016** (0.58) (0.695) (0.54) (0.598) (0.494) (0.569) (0.508) (0.574) (0.897) (1.024) (0.908) (0.894) Lag 4 −0.652 −0.689 −0.269 −1.291** 1.272* 1.064 1.771* 0.985 0.667 0.76 1.527 −1.685* (0.655) (0.686) (0.808) (0.599) (0.752) (0.724) (0.945) (0.655) (1.246) (1.228) (1.524) (0.971) Lag 5 −0.419 −0.559 0.185 −1.219* 1.532 1.281 2.320* 0.742 0.486 0.579 1.165 −2.171* (0.846) (0.832) (1.028) (0.69) (1.001) (0.823) (1.337) (0.752) (1.743) (1.464) (2.442) (1.258) Lag 6 −0.236 −0.632 0.194 −1.630*** 1.193** 1.266* 1.164** 0.519 0.571 0.799 0.638 −2.143** (0.663) (0.93) (0.477) (0.611) (0.489) (0.737) (0.457) (0.675) (1.079) (1.505) (0.933) (0.998) Obs. 2,058,380 1,822,949 1,449,127 . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lag 0 −1.627** −1.466* −1.716 −2.133*** 1.252 0.97 2.398 1.107 −1.555 −1.400 −1.388 −2.276* (0.769) (0.781) (1.113) (0.685) (1.137) (0.879) (2.412) (1.077) (1.375) (1.232) (2.750) (1.304) Lag 1 −0.973 −0.831 −1.114 −1.469** 0.991 0.631 1.657 1.203 −0.658 −0.550 −0.255 −1.339 (0.715) (0.779) (0.846) (0.585) (0.838) (0.715) (1.307) (0.735) (1.447) (1.365) (3.486) (1.519) Lag 2 −0.791 −0.627 −0.981 −1.287** 0.492 0.069 1.020 0.888 −0.442 −0.196 −0.681 −1.787** (0.663) (0.766) (0.667) (0.603) (0.586) (0.685) (0.778) (0.556) (0.872) (0.854) (1.285) (0.761) Lag 3 −0.520 −0.582 −0.300 −1.225** 0.842* 0.475 1.306** 0.807 0.407 0.442 0.641 −2.016** (0.58) (0.695) (0.54) (0.598) (0.494) (0.569) (0.508) (0.574) (0.897) (1.024) (0.908) (0.894) Lag 4 −0.652 −0.689 −0.269 −1.291** 1.272* 1.064 1.771* 0.985 0.667 0.76 1.527 −1.685* (0.655) (0.686) (0.808) (0.599) (0.752) (0.724) (0.945) (0.655) (1.246) (1.228) (1.524) (0.971) Lag 5 −0.419 −0.559 0.185 −1.219* 1.532 1.281 2.320* 0.742 0.486 0.579 1.165 −2.171* (0.846) (0.832) (1.028) (0.69) (1.001) (0.823) (1.337) (0.752) (1.743) (1.464) (2.442) (1.258) Lag 6 −0.236 −0.632 0.194 −1.630*** 1.193** 1.266* 1.164** 0.519 0.571 0.799 0.638 −2.143** (0.663) (0.93) (0.477) (0.611) (0.489) (0.737) (0.457) (0.675) (1.079) (1.505) (0.933) (0.998) Obs. 2,058,380 1,822,949 1,449,127 Notes: Data from BRFSS, years 1997−2011, excluding 2009−10. Good health is the first factor from a principal-component factor analysis including self-assessed health, and indicators for diabetes, obesity and poor mental health. Healthcare utilisation is the first factor from a principal-component factor analysis including an indicator for having a health plan, for having had a flu shot, a medical check-up and whether a doctor visit is too expensive. Health behaviour is the first factor from a principal-component factor analysis including smoking, alcohol consumption and exercise. All regressions include age dummies, sex, race, education and year and CZ fixed effects as well as state linear trends. We also include the percent of individuals in routine occupations. The second panel displays the regression of the different health measures on individual log income and controls. SE clustered at CZ level. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered at CZ level. Models are weighted in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age group−race−sex cell in the IPUMS Census 2000 data. Open in new tab Table A8. Imports from China and Health, Healthcare Utilisation and Health Behaviour, by RTI—Excluding the Great Recession. . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lag 0 −1.627** −1.466* −1.716 −2.133*** 1.252 0.97 2.398 1.107 −1.555 −1.400 −1.388 −2.276* (0.769) (0.781) (1.113) (0.685) (1.137) (0.879) (2.412) (1.077) (1.375) (1.232) (2.750) (1.304) Lag 1 −0.973 −0.831 −1.114 −1.469** 0.991 0.631 1.657 1.203 −0.658 −0.550 −0.255 −1.339 (0.715) (0.779) (0.846) (0.585) (0.838) (0.715) (1.307) (0.735) (1.447) (1.365) (3.486) (1.519) Lag 2 −0.791 −0.627 −0.981 −1.287** 0.492 0.069 1.020 0.888 −0.442 −0.196 −0.681 −1.787** (0.663) (0.766) (0.667) (0.603) (0.586) (0.685) (0.778) (0.556) (0.872) (0.854) (1.285) (0.761) Lag 3 −0.520 −0.582 −0.300 −1.225** 0.842* 0.475 1.306** 0.807 0.407 0.442 0.641 −2.016** (0.58) (0.695) (0.54) (0.598) (0.494) (0.569) (0.508) (0.574) (0.897) (1.024) (0.908) (0.894) Lag 4 −0.652 −0.689 −0.269 −1.291** 1.272* 1.064 1.771* 0.985 0.667 0.76 1.527 −1.685* (0.655) (0.686) (0.808) (0.599) (0.752) (0.724) (0.945) (0.655) (1.246) (1.228) (1.524) (0.971) Lag 5 −0.419 −0.559 0.185 −1.219* 1.532 1.281 2.320* 0.742 0.486 0.579 1.165 −2.171* (0.846) (0.832) (1.028) (0.69) (1.001) (0.823) (1.337) (0.752) (1.743) (1.464) (2.442) (1.258) Lag 6 −0.236 −0.632 0.194 −1.630*** 1.193** 1.266* 1.164** 0.519 0.571 0.799 0.638 −2.143** (0.663) (0.93) (0.477) (0.611) (0.489) (0.737) (0.457) (0.675) (1.079) (1.505) (0.933) (0.998) Obs. 2,058,380 1,822,949 1,449,127 . Good health . Good health behaviour . Healthcare utilisation . . . Low . Medium . High . . Low . Medium . High . . Low . Medium . High . . All . RTI . RTI . RTI . All . RTI . RTI . RTI . All . RTI . RTI . RTI . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . Lag 0 −1.627** −1.466* −1.716 −2.133*** 1.252 0.97 2.398 1.107 −1.555 −1.400 −1.388 −2.276* (0.769) (0.781) (1.113) (0.685) (1.137) (0.879) (2.412) (1.077) (1.375) (1.232) (2.750) (1.304) Lag 1 −0.973 −0.831 −1.114 −1.469** 0.991 0.631 1.657 1.203 −0.658 −0.550 −0.255 −1.339 (0.715) (0.779) (0.846) (0.585) (0.838) (0.715) (1.307) (0.735) (1.447) (1.365) (3.486) (1.519) Lag 2 −0.791 −0.627 −0.981 −1.287** 0.492 0.069 1.020 0.888 −0.442 −0.196 −0.681 −1.787** (0.663) (0.766) (0.667) (0.603) (0.586) (0.685) (0.778) (0.556) (0.872) (0.854) (1.285) (0.761) Lag 3 −0.520 −0.582 −0.300 −1.225** 0.842* 0.475 1.306** 0.807 0.407 0.442 0.641 −2.016** (0.58) (0.695) (0.54) (0.598) (0.494) (0.569) (0.508) (0.574) (0.897) (1.024) (0.908) (0.894) Lag 4 −0.652 −0.689 −0.269 −1.291** 1.272* 1.064 1.771* 0.985 0.667 0.76 1.527 −1.685* (0.655) (0.686) (0.808) (0.599) (0.752) (0.724) (0.945) (0.655) (1.246) (1.228) (1.524) (0.971) Lag 5 −0.419 −0.559 0.185 −1.219* 1.532 1.281 2.320* 0.742 0.486 0.579 1.165 −2.171* (0.846) (0.832) (1.028) (0.69) (1.001) (0.823) (1.337) (0.752) (1.743) (1.464) (2.442) (1.258) Lag 6 −0.236 −0.632 0.194 −1.630*** 1.193** 1.266* 1.164** 0.519 0.571 0.799 0.638 −2.143** (0.663) (0.93) (0.477) (0.611) (0.489) (0.737) (0.457) (0.675) (1.079) (1.505) (0.933) (0.998) Obs. 2,058,380 1,822,949 1,449,127 Notes: Data from BRFSS, years 1997−2011, excluding 2009−10. Good health is the first factor from a principal-component factor analysis including self-assessed health, and indicators for diabetes, obesity and poor mental health. Healthcare utilisation is the first factor from a principal-component factor analysis including an indicator for having a health plan, for having had a flu shot, a medical check-up and whether a doctor visit is too expensive. Health behaviour is the first factor from a principal-component factor analysis including smoking, alcohol consumption and exercise. All regressions include age dummies, sex, race, education and year and CZ fixed effects as well as state linear trends. We also include the percent of individuals in routine occupations. The second panel displays the regression of the different health measures on individual log income and controls. SE clustered at CZ level. RTI terciles are defined using the RTI measure for the manufacturing sector in 1990. Robust SE in parentheses are clustered at CZ level. Models are weighted in a way that the BRFSS population at the CZ level reflects the proportions of individuals from a certain age group−race−sex cell in the IPUMS Census 2000 data. Open in new tab Table A9. Effect of Import Shocks on Hospitalisation by Cause, Excluding the Great Recession. . All . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms −0.041 −0.036 0.017 0.224** (0.056) (0.039) (0.036) (0.09) Mental health problems −0.044 −0.038 0.022 0.251*** (0.061) (0.041) (0.04) (0.097) Suicides attempts 0.019 0.011 0.072 0.182** (0.05) (0.036) (0.056) (0.081) Alcohol abuse −0.042 −0.046 0.023 0.077 (0.042) (0.036) (0.037) (0.075) Substance abuse −0.084 −0.048 −0.081* 0.132 (0.063) (0.049) (0.049) (0.087) Opioid abuse −0.059 −0.006 −0.114** 0.147* (0.066) (0.052) (0.056) (0.081) Injuries 0.018 0.036 0.002 0.224** (0.04) (0.029) (0.04) (0.105) Homicide injuries 0.038 0.033 0.015 0.183* (0.059) (0.043) (0.051) (0.103) Driving accidents 0.011 0.023 −0.073 0.074 (0.055) (0.046) (0.065) (0.11) Pain 0.064* 0.068** 0.01 0.183** (0.036) (0.029) (0.045) (0.088) Skin disease −0.061 −0.046 −0.009 0.212*** (0.052) (0.035) (0.036) (0.073) Heart problems −0.007 0.005 −0.0005 0.144** (0.034) (0.025) (0.027) (0.056) Infectious diseases −0.044 −0.036 −0.004 0.194*** (0.05) (0.033) (0.037) (0.067) Respiratory diseases 0.004 0.015 −0.002 0.158** (0.034) (0.025) (0.028) (0.069) Disease of digestive system 0.002 0.01 0.006 0.171** (0.033) (0.024) (0.028) (0.074) Endocrine diseases 0.028 0.038 −0.016 0.108* (0.032) (0.025) (0.033) (0.057) Diet-related diseases 0.023 0.037 −0.018 0.174** (0.042) (0.031) (0.037) (0.069) Cancers 0.017 0.026 −0.007 0.151** (0.031) (0.02) (0.033) (0.059) Tobacco-related cancers 0.028 0.044** 0.01 0.161** (0.025) (0.021) (0.027) (0.065) Non-tobacco-related cancers 0.028 0.033 −0.002 0.139** (0.031) (0.02) (0.035) (0.059) Died in hospital −0.009 −0.005 0.022 0.118** (0.03) (0.023) (0.028) (0.051) . All . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms −0.041 −0.036 0.017 0.224** (0.056) (0.039) (0.036) (0.09) Mental health problems −0.044 −0.038 0.022 0.251*** (0.061) (0.041) (0.04) (0.097) Suicides attempts 0.019 0.011 0.072 0.182** (0.05) (0.036) (0.056) (0.081) Alcohol abuse −0.042 −0.046 0.023 0.077 (0.042) (0.036) (0.037) (0.075) Substance abuse −0.084 −0.048 −0.081* 0.132 (0.063) (0.049) (0.049) (0.087) Opioid abuse −0.059 −0.006 −0.114** 0.147* (0.066) (0.052) (0.056) (0.081) Injuries 0.018 0.036 0.002 0.224** (0.04) (0.029) (0.04) (0.105) Homicide injuries 0.038 0.033 0.015 0.183* (0.059) (0.043) (0.051) (0.103) Driving accidents 0.011 0.023 −0.073 0.074 (0.055) (0.046) (0.065) (0.11) Pain 0.064* 0.068** 0.01 0.183** (0.036) (0.029) (0.045) (0.088) Skin disease −0.061 −0.046 −0.009 0.212*** (0.052) (0.035) (0.036) (0.073) Heart problems −0.007 0.005 −0.0005 0.144** (0.034) (0.025) (0.027) (0.056) Infectious diseases −0.044 −0.036 −0.004 0.194*** (0.05) (0.033) (0.037) (0.067) Respiratory diseases 0.004 0.015 −0.002 0.158** (0.034) (0.025) (0.028) (0.069) Disease of digestive system 0.002 0.01 0.006 0.171** (0.033) (0.024) (0.028) (0.074) Endocrine diseases 0.028 0.038 −0.016 0.108* (0.032) (0.025) (0.033) (0.057) Diet-related diseases 0.023 0.037 −0.018 0.174** (0.042) (0.031) (0.037) (0.069) Cancers 0.017 0.026 −0.007 0.151** (0.031) (0.02) (0.033) (0.059) Tobacco-related cancers 0.028 0.044** 0.01 0.161** (0.025) (0.021) (0.027) (0.065) Non-tobacco-related cancers 0.028 0.033 −0.002 0.139** (0.031) (0.02) (0.035) (0.059) Died in hospital −0.009 −0.005 0.022 0.118** (0.03) (0.023) (0.028) (0.051) Notes: Data from NIS for the years 1997−2011, excluding 2009−10. Instrumental variable estimates using the sum of Chinese imports to the other countries as instruments for US imports. Instrumented imports are leaded four years. The table reports the effect of a $1,000 import shock on the log of 1 + the number of admissions of patients with a certain condition. All regressions include year fixed effects, state trends, hospital fixed effects, birth year−gender fixed effects of patients, CZ time-varying characteristics (demographic composition of the CZ in terms of gender, race, education, age composition and share of routine occupations). Weighted by hospital weights and population weights. SE clustered at CZ level. Open in new tab Table A9. Effect of Import Shocks on Hospitalisation by Cause, Excluding the Great Recession. . All . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms −0.041 −0.036 0.017 0.224** (0.056) (0.039) (0.036) (0.09) Mental health problems −0.044 −0.038 0.022 0.251*** (0.061) (0.041) (0.04) (0.097) Suicides attempts 0.019 0.011 0.072 0.182** (0.05) (0.036) (0.056) (0.081) Alcohol abuse −0.042 −0.046 0.023 0.077 (0.042) (0.036) (0.037) (0.075) Substance abuse −0.084 −0.048 −0.081* 0.132 (0.063) (0.049) (0.049) (0.087) Opioid abuse −0.059 −0.006 −0.114** 0.147* (0.066) (0.052) (0.056) (0.081) Injuries 0.018 0.036 0.002 0.224** (0.04) (0.029) (0.04) (0.105) Homicide injuries 0.038 0.033 0.015 0.183* (0.059) (0.043) (0.051) (0.103) Driving accidents 0.011 0.023 −0.073 0.074 (0.055) (0.046) (0.065) (0.11) Pain 0.064* 0.068** 0.01 0.183** (0.036) (0.029) (0.045) (0.088) Skin disease −0.061 −0.046 −0.009 0.212*** (0.052) (0.035) (0.036) (0.073) Heart problems −0.007 0.005 −0.0005 0.144** (0.034) (0.025) (0.027) (0.056) Infectious diseases −0.044 −0.036 −0.004 0.194*** (0.05) (0.033) (0.037) (0.067) Respiratory diseases 0.004 0.015 −0.002 0.158** (0.034) (0.025) (0.028) (0.069) Disease of digestive system 0.002 0.01 0.006 0.171** (0.033) (0.024) (0.028) (0.074) Endocrine diseases 0.028 0.038 −0.016 0.108* (0.032) (0.025) (0.033) (0.057) Diet-related diseases 0.023 0.037 −0.018 0.174** (0.042) (0.031) (0.037) (0.069) Cancers 0.017 0.026 −0.007 0.151** (0.031) (0.02) (0.033) (0.059) Tobacco-related cancers 0.028 0.044** 0.01 0.161** (0.025) (0.021) (0.027) (0.065) Non-tobacco-related cancers 0.028 0.033 −0.002 0.139** (0.031) (0.02) (0.035) (0.059) Died in hospital −0.009 −0.005 0.022 0.118** (0.03) (0.023) (0.028) (0.051) . All . Low RTI . Medium RTI . High RTI . . (1) . (2) . (3) . (4) . Stress-related symptoms −0.041 −0.036 0.017 0.224** (0.056) (0.039) (0.036) (0.09) Mental health problems −0.044 −0.038 0.022 0.251*** (0.061) (0.041) (0.04) (0.097) Suicides attempts 0.019 0.011 0.072 0.182** (0.05) (0.036) (0.056) (0.081) Alcohol abuse −0.042 −0.046 0.023 0.077 (0.042) (0.036) (0.037) (0.075) Substance abuse −0.084 −0.048 −0.081* 0.132 (0.063) (0.049) (0.049) (0.087) Opioid abuse −0.059 −0.006 −0.114** 0.147* (0.066) (0.052) (0.056) (0.081) Injuries 0.018 0.036 0.002 0.224** (0.04) (0.029) (0.04) (0.105) Homicide injuries 0.038 0.033 0.015 0.183* (0.059) (0.043) (0.051) (0.103) Driving accidents 0.011 0.023 −0.073 0.074 (0.055) (0.046) (0.065) (0.11) Pain 0.064* 0.068** 0.01 0.183** (0.036) (0.029) (0.045) (0.088) Skin disease −0.061 −0.046 −0.009 0.212*** (0.052) (0.035) (0.036) (0.073) Heart problems −0.007 0.005 −0.0005 0.144** (0.034) (0.025) (0.027) (0.056) Infectious diseases −0.044 −0.036 −0.004 0.194*** (0.05) (0.033) (0.037) (0.067) Respiratory diseases 0.004 0.015 −0.002 0.158** (0.034) (0.025) (0.028) (0.069) Disease of digestive system 0.002 0.01 0.006 0.171** (0.033) (0.024) (0.028) (0.074) Endocrine diseases 0.028 0.038 −0.016 0.108* (0.032) (0.025) (0.033) (0.057) Diet-related diseases 0.023 0.037 −0.018 0.174** (0.042) (0.031) (0.037) (0.069) Cancers 0.017 0.026 −0.007 0.151** (0.031) (0.02) (0.033) (0.059) Tobacco-related cancers 0.028 0.044** 0.01 0.161** (0.025) (0.021) (0.027) (0.065) Non-tobacco-related cancers 0.028 0.033 −0.002 0.139** (0.031) (0.02) (0.035) (0.059) Died in hospital −0.009 −0.005 0.022 0.118** (0.03) (0.023) (0.028) (0.051) Notes: Data from NIS for the years 1997−2011, excluding 2009−10. Instrumental variable estimates using the sum of Chinese imports to the other countries as instruments for US imports. Instrumented imports are leaded four years. The table reports the effect of a $1,000 import shock on the log of 1 + the number of admissions of patients with a certain condition. All regressions include year fixed effects, state trends, hospital fixed effects, birth year−gender fixed effects of patients, CZ time-varying characteristics (demographic composition of the CZ in terms of gender, race, education, age composition and share of routine occupations). Weighted by hospital weights and population weights. SE clustered at CZ level. Open in new tab Additional Supporting Information may be found in the online version of this article: Replication Package Notes The data and codes for this paper are available on the Journal website. They were checked for their ability to reproduce the results presented in the paper. The authors were granted an exemption to publish parts of their data because access to these data is restricted. However, the authors provided the Journal with temporary access to some of the data, and a simulated or synthetic dataset for the others, which allowed the Journal to run their codes. The synthetic/simulated data and the codes for the parts subject to exemption are also available on the Journal website. They were checked for their ability to generate the tables and figures presented in the paper, but the synthetic/simulated data are not designed to reproduce the same results. We are grateful to David Dorn and Gordon Hanson for sharing data with us, to Tito Boeri, Italo Colantone, Rosario Crino, Jonathan Dingel, Simone Ferro, Teresa Fort and participants in seminars at many universities and conferences for helpful comments and discussion as well as constructive comments of the referees and the editor. Footnotes 1 These eight countries are Australia, Denmark, Finland, Germany, Japan, New Zealand, Spain and Switzerland, all high-income countries that have comparable trade data over the period 1991–2011. Costa et al. (2016) improve on this procedure to deal with the possibility of correlated world-level shocks by using auxiliary regressions. 2 The data is available at http://www.census.gov/econ/cbp/download/ from 1986 onwards, and via ICPSR before 1986. Industries are coded in 1972 SIC up to 1987, then in 1987 SIC for 1988 to 1997, in NAICS 1997 for 1998 to 2002, in NAICS 2002 for 2003 to 2007, in NAICS 2007 for 2008 to 2011. We construct weighted crosswalks from these classification into 1987 SIC, using the bridges made available by the Census Bureau from NAICS 2007 to NAICS 2002, and from NAICS 2002 to NAICS 1997. For each year with a change of classification, we find the redistribution of employment from the new classification into the old one. The crosswalk from NAICS 1997 to SIC 1987 was found on David Dorn’s web page. The CBP sometimes reports brackets instead of exact values for employment or number of establishments in one of the nine categories of firm size. We impute employment at the four-digit SIC*county level by using the method proposed in Autor et al. (2013a) for years 1980, 1990 and 2000, and generalise it to the entire period. 3 Following Autor–Dorn–Hanson, when an occupation has a zero value for one of those task contents, we replace zero by the minimum non-zero value of the variable for the other occupations. 4 IPW data correspond to year 1991, the remaining CZ characteristics correspond to year 1990. CZ characteristics are derived from IPUMS Census data. We compute the average equivalised family income (including losses), reported as the total pre-tax money income earned by one’s family from all sources for the previous year, divided by the square root of the family size 5 Table A1 in the Appendix lists the most important occupations and industries in each tercile of RTI, for the manufacturing sector. Although the shares of each industry and occupation vary across terciles, the most important industries and occupations are very similar. 6 Autor (2017) addresses a more recent discussion about the growth in housing prices potentially driving the effects of the IPW shock: controlling for housing prices does not affect the initial findings about the impact of import competition from China on local labour markets. 7 The increasing effect of the IPW shock across RTI terciles is robust to restricting the model to the first two periods, and to other definitions of the RTI terciles such as one using the RTI of all jobs within a CZ in 1980 instead of 1990 to divide the territory into three terciles, one based on the share of routine occupations instead of the average RTI of a CZ, or to a definition of RTI that incorporates all sectors instead of only manufacturing. In the latter case, there is no statistical difference between the coefficients of IPW in the medium and high RTI areas, but their effect is still much larger than in the lowest RTI area. 8 This argument is sometimes used to explain part of the life expectancy gradient between low-income and high-income individuals: the ‘low-status’ group is more likely to suffer from ‘psychosocial stress’, which leads to a higher probability of death. 9 In the BRFSS data, 649 CZs (out of 722) are present. Alaska and Hawaii are excluded from all analyses, due to many changes of counties over time in these two states. 10 Section 2 used state-level clustering to follow closely the ADH approach. In practice, the two clusterings deliver very similar results. 11 We construct the weighting in the following way: for each individual we compute the share of his/her group in the corresponding CZ in terms of gender, race and age group, in the BRFSS for all years, and in the Census for 2000, then the Census share is divided by the corresponding share in the BRFSS, and this ratio is multiplied by the share of the CZ in the population for each year. Our BRFSS estimates therefore reflect the proportions of individuals from a certain age group–race–sex cell in the IPUMS Census 2000 data. 12 Adda (2016) finds evidence of an alternative mechanism in which viral infections are more prevalent during economic expansions. Stevens et al. (2015) show that the cyclicality in mortality is mainly due to the cyclicality of healthcare in nursing homes affecting the death of elderly individuals. 13 Although the BRFSS includes many other items that are related to healthcare utilisation such as blood-stool test, mammograms and dentist visits, those are not asked every year, so that incorporating them would lead to a much smaller sample for the main factor of healthcare utilisation. 14 di Giovanni et al. (2014) calculates that mean welfare gain from adding China to world trade is 0.13% and about the same for the USA. Caliendo et al. (2015) also finds an overall positive effect, which is higher in the long run. 15 Causal estimates of the effect of income on health can be found in Lindahl (2005), Snyder and Evans (2006) or Adda et al. (2009) for instance, using different identification schemes. 16 In addition, results in Table 5 are robust to the inclusion of income as a control in the regressions of the composite health measure on the IPW shock (at all lags). This suggests that income is not the only pathways to poor health. 17 Table A3 in the Appendix provides a classification of the categories with the ICD 9 codes we use. The two latter groupings were defined based on discussions with medical doctors. 18 Given that our panel is unbalanced—not all hospitals are observed in each year—we estimate the model using a fixed effect estimator. 19 In smaller hospitals there are years where we do not observe any discharge for a particular cause and a particular age–gender group. 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Aldashev,, Gani;Marini,, Marco;Verdier,, Thierry

doi: 10.1093/ej/ueaa031pmid: N/A

ABSTRACT This article provides a theoretical framework to understand the tendency of non-governmental organisations (NGOs) to cluster and the circumstances under which such clustering is socially undesirable. NGOs compete through fundraising for donations and choose issues to focus their projects on. Donors have latent willingness-to-give that may differ across issues, but they need to be ‘awakened' to give. Raising funds focusing on the same issue creates positive informational spillovers across NGOs. Each NGO chooses whether to compete in the same market (clustering) with spillovers, or to face weaker competition under issue specialisation. We show that equilibrium clustering is more likely to occur when the share of multiple-issue donors is relatively large, and when the fundraising technology is sufficiently efficient. Moreover, this situation is socially inefficient when the cost of fundraising takes intermediate values and the motivation for donors’ giving is relatively high. We illustrate the mechanisms of the model with several case studies. ‘The greatest tension for the thoughtful Northern NGO today lies in the attempt to balance fundraising messages for a public most easily moved by short-term disaster appeals, with recognition that longer-term development depends on the willingness of that same public to support difficult and costly structural change.' (Smillie, 1995, p.137) ‘The “humanitarian Gresham’s Law” is derived from the decoupling of aid agencies’ hard and soft interests (their institutional interests versus their stated aims). It states: in a situation of unregulated private humanitarian activity, “debased” humanitarianism will drive out the “authentic version.”' (De Waal, 1997, p.138) Non-governmental organisations (NGOs) have become key actors in development assistance over the last decades (Robinson and Riddell, 1995; Riddell, 2007; Werker and Ahmed, 2008). Currently, they represent a major channel through which aid projects are implemented in developing countries, in several main sectors of public good provision (health, education, poverty relief, environment, human rights, gender equality, etc.).1 To finance their projects, NGOs rely on a mix of sources, the main ones being public funds (typically in the form of grants) and private voluntary donations. The development NGO sector has two key features. The first is the non-spontaneous nature of private donations: NGOs have to engage in (often large-scale) fundraising campaigns to mobilise private donations from a multitude of donors which have a rather limited awareness about the issues at which the NGO projects are aimed. The second is the diversity: as entry into the NGO sector is relatively easy, the sector is a plethora of organisations working towards numerous causes and in a multitude of different ways. Hence, the provision of public goods through NGOs based (at least in part) on voluntary donations faces the following fundamental problem: there are multiple deserving causes or issues, but donors are often unaware of them. The NGOs thus act as intermediaries, and have to play a double role. On the one hand, they collect donations and produce the good or deliver the service to the beneficiaries of projects. On the other, they raise the awareness of potential donors about the various issues. Economists have studied extensively the first dimension (Besley and Ghatak, 2003, and François and Vlassopoulos, 2008, are excellent reviews of this literature). The second dimension remains relatively understudied, despite being a very interesting and important economic phenomenon, as it implies costly investments and is often subject to externalities across NGOs. For instance, the awareness-raising effort of one NGO working towards a given cause might increase the donations to other NGOs working towards the same cause. The existing empirical literature, albeit limited, documents several interesting patterns. Researchers find that on many occasions NGOs allocate their resources in a collectively distorted fashion. Koch et al. (2009) analyse the international allocation of NGO aid, using data on 61 large NGOs from various OECD countries, and find that NGOs mostly follow other NGOs in their choices of where to carry out their projects. In other words, NGO aid is highly ‘clustered’. They also find that NGOs tend, in general, to select recipient countries with traits common to the headquarter countries of NGOs (for instance, headquarter and beneficiary countries usually have the same religion, share common colonial history, etc.). How does this phenomenon of NGO clustering look, in the aggregate and over time? Despite the relative scarcity of data on NGOs, we can identify certain patterns by relying on the best existing sources. The AidData 2.0 (aiddata.org) initiative systematises the data on virtually all the development aid projects with at least some involvement of public funds from the OECD countries. By relying on their core data set and restricting our attention to projects where NGOs are the project implementation channel, we obtain a data set covering the period from 1993 to 2013 (the latest year for which systematised project data are available) which contains over 250,000 aid projects. Table 1 decomposes this data by year of project implementation and by broad aid sector. Looking at Panel A, we observe a strong increase in the number of NGO projects over the two decades. Focusing on the cross-sector distribution of projects (Panel B), we notice that the largest category (almost one-fifth of all NGO projects) falls into the category ‘Government and civil society' (this category includes government aid projects with NGO involvement; thus, it is not surprising that many projects with public aid fall into this group). However, beyond this category, we observe quite an uneven distribution of NGO projects across sectors. For instance, health, education, and agriculture/rural development each account for more than 10% of projects, whereas, for instance, environment-related NGO projects account for barely 3% of the total. Table 1. Distribution of NGO Aid Projects, by Year and Sector. A. Distribution of NGO aid projects by year . Year of implementation of NGO aid project . Number of projects . Percent of total projects . 1993 11 0.00 1994 209 0.08 1995 615 0.24 1996 773 0.31 1997 770 0.30 1998 876 0.35 1999 30 0.01 2000 26 0.01 2001 114 0.05 2002 913 0.36 2003 848 0.33 2004 7,859 3.10 2005 10,894 4.30 2006 12,769 5.04 2007 17,790 7.02 2008 24,920 9.84 2009 30,981 12.23 2010 36,413 14.38 2011 33,732 13.32 2012 42,175 16.65 2013 30,533 12.06 Total 253,251 100.00 B. Distribution of NGO aid projects by sector Sector (type) of aid project Number of projects Percent of total projects Government & civil society 49,511 19.76 Agriculture, forestry, fishing & rural development 34,924 13.94 Health 33,411 13.34 Education 25,462 10.16 Emergency response, reconstruction, and disaster prevention 23,963 9.56 Social infrastructure & welfare 17,514 6.99 General/unspecified 15,779 6.30 Food aid, food security & commodity assistance 11,507 4.59 Conflict prevention & peace 10,086 4.03 Water supply & sanitation 7,679 3.06 Environment 7,611 3.04 Transport, communications & energy 4,349 1.74 Industry, mining & construction 3,407 1.36 Banking, financial, business services & debt-related 2,779 1.11 Trade & tourism 1,775 0.71 Refugees in donor countries 790 0.32 Total 250,547 100.00 A. Distribution of NGO aid projects by year . Year of implementation of NGO aid project . Number of projects . Percent of total projects . 1993 11 0.00 1994 209 0.08 1995 615 0.24 1996 773 0.31 1997 770 0.30 1998 876 0.35 1999 30 0.01 2000 26 0.01 2001 114 0.05 2002 913 0.36 2003 848 0.33 2004 7,859 3.10 2005 10,894 4.30 2006 12,769 5.04 2007 17,790 7.02 2008 24,920 9.84 2009 30,981 12.23 2010 36,413 14.38 2011 33,732 13.32 2012 42,175 16.65 2013 30,533 12.06 Total 253,251 100.00 B. Distribution of NGO aid projects by sector Sector (type) of aid project Number of projects Percent of total projects Government & civil society 49,511 19.76 Agriculture, forestry, fishing & rural development 34,924 13.94 Health 33,411 13.34 Education 25,462 10.16 Emergency response, reconstruction, and disaster prevention 23,963 9.56 Social infrastructure & welfare 17,514 6.99 General/unspecified 15,779 6.30 Food aid, food security & commodity assistance 11,507 4.59 Conflict prevention & peace 10,086 4.03 Water supply & sanitation 7,679 3.06 Environment 7,611 3.04 Transport, communications & energy 4,349 1.74 Industry, mining & construction 3,407 1.36 Banking, financial, business services & debt-related 2,779 1.11 Trade & tourism 1,775 0.71 Refugees in donor countries 790 0.32 Total 250,547 100.00 Source. Authors’ calculations using AidData Core Research Release, Version 3.1. Open in new tab Table 1. Distribution of NGO Aid Projects, by Year and Sector. A. Distribution of NGO aid projects by year . Year of implementation of NGO aid project . Number of projects . Percent of total projects . 1993 11 0.00 1994 209 0.08 1995 615 0.24 1996 773 0.31 1997 770 0.30 1998 876 0.35 1999 30 0.01 2000 26 0.01 2001 114 0.05 2002 913 0.36 2003 848 0.33 2004 7,859 3.10 2005 10,894 4.30 2006 12,769 5.04 2007 17,790 7.02 2008 24,920 9.84 2009 30,981 12.23 2010 36,413 14.38 2011 33,732 13.32 2012 42,175 16.65 2013 30,533 12.06 Total 253,251 100.00 B. Distribution of NGO aid projects by sector Sector (type) of aid project Number of projects Percent of total projects Government & civil society 49,511 19.76 Agriculture, forestry, fishing & rural development 34,924 13.94 Health 33,411 13.34 Education 25,462 10.16 Emergency response, reconstruction, and disaster prevention 23,963 9.56 Social infrastructure & welfare 17,514 6.99 General/unspecified 15,779 6.30 Food aid, food security & commodity assistance 11,507 4.59 Conflict prevention & peace 10,086 4.03 Water supply & sanitation 7,679 3.06 Environment 7,611 3.04 Transport, communications & energy 4,349 1.74 Industry, mining & construction 3,407 1.36 Banking, financial, business services & debt-related 2,779 1.11 Trade & tourism 1,775 0.71 Refugees in donor countries 790 0.32 Total 250,547 100.00 A. Distribution of NGO aid projects by year . Year of implementation of NGO aid project . Number of projects . Percent of total projects . 1993 11 0.00 1994 209 0.08 1995 615 0.24 1996 773 0.31 1997 770 0.30 1998 876 0.35 1999 30 0.01 2000 26 0.01 2001 114 0.05 2002 913 0.36 2003 848 0.33 2004 7,859 3.10 2005 10,894 4.30 2006 12,769 5.04 2007 17,790 7.02 2008 24,920 9.84 2009 30,981 12.23 2010 36,413 14.38 2011 33,732 13.32 2012 42,175 16.65 2013 30,533 12.06 Total 253,251 100.00 B. Distribution of NGO aid projects by sector Sector (type) of aid project Number of projects Percent of total projects Government & civil society 49,511 19.76 Agriculture, forestry, fishing & rural development 34,924 13.94 Health 33,411 13.34 Education 25,462 10.16 Emergency response, reconstruction, and disaster prevention 23,963 9.56 Social infrastructure & welfare 17,514 6.99 General/unspecified 15,779 6.30 Food aid, food security & commodity assistance 11,507 4.59 Conflict prevention & peace 10,086 4.03 Water supply & sanitation 7,679 3.06 Environment 7,611 3.04 Transport, communications & energy 4,349 1.74 Industry, mining & construction 3,407 1.36 Banking, financial, business services & debt-related 2,779 1.11 Trade & tourism 1,775 0.71 Refugees in donor countries 790 0.32 Total 250,547 100.00 Source. Authors’ calculations using AidData Core Research Release, Version 3.1. Open in new tab Next, let’s focus on the geographic distribution of projects. Koch (2009, Figure 1.4) presented the distribution of NGO aid for the 61 largest organisations in 2005, in per capita terms, across the world. This distribution is highly unbalanced: six developing countries received more than 9 euro per capita of NGO aid, whereas 28 countries received less than 0.5 euros per capita. Fig. 1. Open in new tabDownload slide Equilibrium Issue Choice. Fig. 1. Open in new tabDownload slide Equilibrium Issue Choice. Relying on AidData 2.0 data set, we can also see a similar pattern, which is surprisingly stable over time. Table 2 presents the ‘top ten' beneficiary countries of NGO aid projects, over a five-year period. One can easily see that certain countries (such as, for instance, Ethiopia and India) always appear among the top ten beneficiaries. However, there are also some interesting dynamics, if one looks across time. For example, Sri Lanka was particularly ‘attractive' for NGOs during the 1993–2002 decade, but then disappeared from the top ten list. On the other hand, Bolivia appeared in this list only in the 2003–12 decade. Table 2. Top Ten Beneficiary Countries of NGO Aid Projects, Over a Five-Year Period. . Country . Number of projects . Percent of total projects . 1993–7 1 Nicaragua 84 3.53 2 India 77 3.24 3 Sri Lanka 75 3.15 4 Zimbabwe 67 2.82 5 Botswana 65 2.73 6 Guatemala 63 2.65 7 Uganda 62 2.61 8 Ethiopia 60 2.52 9 Bangladesh 59 2.48 10 Mozambique 59 2.48 1998–2002 1 Sri Lanka 68 3.47 2 Zimbabwe 61 3.11 3 Ethiopia 54 2.76 4 Nicaragua 50 2.55 5 Mozambique 42 2.14 6 Tanzania 42 2.14 7 Zambia 42 2.14 8 India 41 2.09 9 Kenya 38 1.94 10 DRC 36 1.84 2003–7 1 DRC 1,491 2.97 2 Ethiopia 1,257 2.51 3 India 1,257 2.51 4 Bolivia 1,226 2.44 5 Kenya 1,184 2.36 6 Uganda 1,105 2.20 7 Nicaragua 974 1.94 8 Sudan 922 1.84 9 Brazil 911 1.82 10 Guatemala 909 1.81 2008–12 1 Ethiopia 3,935 2.34 2 India 3,795 2.26 3 DRC 3,564 2.12 4 Kenya 3,466 2.06 5 Peru 3,361 2.00 6 Tanzania 2,899 1.72 7 Bolivia 2,891 1.72 8 Uganda 2,820 1.68 9 Guatemala 2,805 1.67 10 Haiti 2,703 1.61 . Country . Number of projects . Percent of total projects . 1993–7 1 Nicaragua 84 3.53 2 India 77 3.24 3 Sri Lanka 75 3.15 4 Zimbabwe 67 2.82 5 Botswana 65 2.73 6 Guatemala 63 2.65 7 Uganda 62 2.61 8 Ethiopia 60 2.52 9 Bangladesh 59 2.48 10 Mozambique 59 2.48 1998–2002 1 Sri Lanka 68 3.47 2 Zimbabwe 61 3.11 3 Ethiopia 54 2.76 4 Nicaragua 50 2.55 5 Mozambique 42 2.14 6 Tanzania 42 2.14 7 Zambia 42 2.14 8 India 41 2.09 9 Kenya 38 1.94 10 DRC 36 1.84 2003–7 1 DRC 1,491 2.97 2 Ethiopia 1,257 2.51 3 India 1,257 2.51 4 Bolivia 1,226 2.44 5 Kenya 1,184 2.36 6 Uganda 1,105 2.20 7 Nicaragua 974 1.94 8 Sudan 922 1.84 9 Brazil 911 1.82 10 Guatemala 909 1.81 2008–12 1 Ethiopia 3,935 2.34 2 India 3,795 2.26 3 DRC 3,564 2.12 4 Kenya 3,466 2.06 5 Peru 3,361 2.00 6 Tanzania 2,899 1.72 7 Bolivia 2,891 1.72 8 Uganda 2,820 1.68 9 Guatemala 2,805 1.67 10 Haiti 2,703 1.61 Source. Authors’ calculations using AidData Core Research Release, Version 3.1. Open in new tab Table 2. Top Ten Beneficiary Countries of NGO Aid Projects, Over a Five-Year Period. . Country . Number of projects . Percent of total projects . 1993–7 1 Nicaragua 84 3.53 2 India 77 3.24 3 Sri Lanka 75 3.15 4 Zimbabwe 67 2.82 5 Botswana 65 2.73 6 Guatemala 63 2.65 7 Uganda 62 2.61 8 Ethiopia 60 2.52 9 Bangladesh 59 2.48 10 Mozambique 59 2.48 1998–2002 1 Sri Lanka 68 3.47 2 Zimbabwe 61 3.11 3 Ethiopia 54 2.76 4 Nicaragua 50 2.55 5 Mozambique 42 2.14 6 Tanzania 42 2.14 7 Zambia 42 2.14 8 India 41 2.09 9 Kenya 38 1.94 10 DRC 36 1.84 2003–7 1 DRC 1,491 2.97 2 Ethiopia 1,257 2.51 3 India 1,257 2.51 4 Bolivia 1,226 2.44 5 Kenya 1,184 2.36 6 Uganda 1,105 2.20 7 Nicaragua 974 1.94 8 Sudan 922 1.84 9 Brazil 911 1.82 10 Guatemala 909 1.81 2008–12 1 Ethiopia 3,935 2.34 2 India 3,795 2.26 3 DRC 3,564 2.12 4 Kenya 3,466 2.06 5 Peru 3,361 2.00 6 Tanzania 2,899 1.72 7 Bolivia 2,891 1.72 8 Uganda 2,820 1.68 9 Guatemala 2,805 1.67 10 Haiti 2,703 1.61 . Country . Number of projects . Percent of total projects . 1993–7 1 Nicaragua 84 3.53 2 India 77 3.24 3 Sri Lanka 75 3.15 4 Zimbabwe 67 2.82 5 Botswana 65 2.73 6 Guatemala 63 2.65 7 Uganda 62 2.61 8 Ethiopia 60 2.52 9 Bangladesh 59 2.48 10 Mozambique 59 2.48 1998–2002 1 Sri Lanka 68 3.47 2 Zimbabwe 61 3.11 3 Ethiopia 54 2.76 4 Nicaragua 50 2.55 5 Mozambique 42 2.14 6 Tanzania 42 2.14 7 Zambia 42 2.14 8 India 41 2.09 9 Kenya 38 1.94 10 DRC 36 1.84 2003–7 1 DRC 1,491 2.97 2 Ethiopia 1,257 2.51 3 India 1,257 2.51 4 Bolivia 1,226 2.44 5 Kenya 1,184 2.36 6 Uganda 1,105 2.20 7 Nicaragua 974 1.94 8 Sudan 922 1.84 9 Brazil 911 1.82 10 Guatemala 909 1.81 2008–12 1 Ethiopia 3,935 2.34 2 India 3,795 2.26 3 DRC 3,564 2.12 4 Kenya 3,466 2.06 5 Peru 3,361 2.00 6 Tanzania 2,899 1.72 7 Bolivia 2,891 1.72 8 Uganda 2,820 1.68 9 Guatemala 2,805 1.67 10 Haiti 2,703 1.61 Source. Authors’ calculations using AidData Core Research Release, Version 3.1. Open in new tab Similar patterns of NGO aid clustering occur also at the sub-national level. Fruttero and Gauri (2005) document that NGOs in Bangladesh (especially those focusing on microfinance) tend to cluster geographically within the country. Barr and Fafchamps (2006) find evidence for strong geographic clustering of NGOs within Uganda, whereas Öhler (2013) documents such clustering of NGO projects in regions within Cambodia. Koch (2009, Figure A9.1) illustrates the distribution of NGO office density across Tanzanian regions, against the poverty levels for these regions. Two regions (Arusha and Dar-es-Salaam) have more than 30 NGO offices; however, these regions have the lowest relative poverty rates within the country. On the other hand, the poorest areas of the country exhibit the lowest density of NGO offices. A similar picture emerges when one looks at the location of projects (and not just offices) across a sub-set of regions for which data are available. Clustering occurs not only in geographic terms, but also in the type of projects. Smillie (1995, p. 136) describes that in the early 1980s, one of most successful types of projects in which numerous NGOs engaged was child sponsorship. Gauri and Galef (2005) document that in mid-2000s, most NGOs in Bangladesh were (at least in part) engaged in micro-credit services. Similar clustering patterns have been extensively documented in the inter-temporal dimension (e.g., Mattei, 2005): often, during large humanitarian crises, too many NGOs rush to carry out emergency activities whereas too few take care of the crucial post-emergency reconstruction work. On the contrary, during certain other crises (especially when the attention of the international community is turned to other events), extremely few NGOs act sufficiently early, which aggravates the crisis, and a large number of NGOs start acting with considerable delay. We see a similar picture when analysing the AidData 2.0 data set. Table 3 presents the decomposition of NGO projects in three large sectors, by sub-sector (using the Country Reporting System purpose code). Within the ‘Emergency response, reconstruction, and disaster prevention' sector, the lion’s share (almost two-third of projects) is taken up by material relief assistance and services. On the other hand, the reconstruction projects (which, arguably, are also extremely important) account for a mere 6.73% of the total. Within the health sector, one out of every five projects has to do with HIV/AIDS, while malaria- and tuberculosis-related projects jointly fail to reach even 5% of projects. Finally, within the environment-related projects, more than 38% of projects are devoted to biodiversity; on the other hand, site preservation projects account only for 2.86% of the total. Table 3. Distribution of NGO Aid Projects, by Sub-Sector, for Selected Sectors. Sub-sector (type) of aid project . Number of projects . Percent of total projects . A. Emergency response, reconstruction, and disaster prevention projects Material relief assistance and services 15,027 62.71 Emergency food aid 4,010 16.73 Disaster prevention and preparedness 2,236 9.33 Reconstruction relief and rehabilitation 1,612 6.73 Relief co-ordination; protection and support services 1,078 4.50 Total 23,963 100.00 B. Health, population policies/programmes reproductive health projects STD control including HIV/AIDS 6,872 20.57 Basic health care 4,692 14.04 Reproductive health care 4,400 13.17 Medical services 2,521 7.55 Health policy and administrative management 2,383 7.13 Basic health infrastructure 1,987 5.95 Population policy and administrative management 1,881 5.63 Family planning 1,440 4.31 Health education 1,372 4.11 Basic nutrition 1,311 3.92 Infectious disease control 1,311 3.92 Malaria control 940 2.81 Tuberculosis control 651 1.95 Health personnel development 598 1.79 Medical education/training 570 1.71 Medical research 300 0.90 Personnel development for population and reproductive health 182 0.54 Total 33,411 100.00 C. Environment-related projects Bio-diversity 2,924 38.42 Environmental policy and administrative management 2,792 36.68 Environmental education/training 862 11.33 Biosphere protection 584 7.67 Site preservation 218 2.86 Environmental research 155 2.04 Flood prevention/control 76 1.00 Total 7,611 100.00 Sub-sector (type) of aid project . Number of projects . Percent of total projects . A. Emergency response, reconstruction, and disaster prevention projects Material relief assistance and services 15,027 62.71 Emergency food aid 4,010 16.73 Disaster prevention and preparedness 2,236 9.33 Reconstruction relief and rehabilitation 1,612 6.73 Relief co-ordination; protection and support services 1,078 4.50 Total 23,963 100.00 B. Health, population policies/programmes reproductive health projects STD control including HIV/AIDS 6,872 20.57 Basic health care 4,692 14.04 Reproductive health care 4,400 13.17 Medical services 2,521 7.55 Health policy and administrative management 2,383 7.13 Basic health infrastructure 1,987 5.95 Population policy and administrative management 1,881 5.63 Family planning 1,440 4.31 Health education 1,372 4.11 Basic nutrition 1,311 3.92 Infectious disease control 1,311 3.92 Malaria control 940 2.81 Tuberculosis control 651 1.95 Health personnel development 598 1.79 Medical education/training 570 1.71 Medical research 300 0.90 Personnel development for population and reproductive health 182 0.54 Total 33,411 100.00 C. Environment-related projects Bio-diversity 2,924 38.42 Environmental policy and administrative management 2,792 36.68 Environmental education/training 862 11.33 Biosphere protection 584 7.67 Site preservation 218 2.86 Environmental research 155 2.04 Flood prevention/control 76 1.00 Total 7,611 100.00 Source. Authors’ calculations using AidData Core Research Release, Version 3.1. Open in new tab Table 3. Distribution of NGO Aid Projects, by Sub-Sector, for Selected Sectors. Sub-sector (type) of aid project . Number of projects . Percent of total projects . A. Emergency response, reconstruction, and disaster prevention projects Material relief assistance and services 15,027 62.71 Emergency food aid 4,010 16.73 Disaster prevention and preparedness 2,236 9.33 Reconstruction relief and rehabilitation 1,612 6.73 Relief co-ordination; protection and support services 1,078 4.50 Total 23,963 100.00 B. Health, population policies/programmes reproductive health projects STD control including HIV/AIDS 6,872 20.57 Basic health care 4,692 14.04 Reproductive health care 4,400 13.17 Medical services 2,521 7.55 Health policy and administrative management 2,383 7.13 Basic health infrastructure 1,987 5.95 Population policy and administrative management 1,881 5.63 Family planning 1,440 4.31 Health education 1,372 4.11 Basic nutrition 1,311 3.92 Infectious disease control 1,311 3.92 Malaria control 940 2.81 Tuberculosis control 651 1.95 Health personnel development 598 1.79 Medical education/training 570 1.71 Medical research 300 0.90 Personnel development for population and reproductive health 182 0.54 Total 33,411 100.00 C. Environment-related projects Bio-diversity 2,924 38.42 Environmental policy and administrative management 2,792 36.68 Environmental education/training 862 11.33 Biosphere protection 584 7.67 Site preservation 218 2.86 Environmental research 155 2.04 Flood prevention/control 76 1.00 Total 7,611 100.00 Sub-sector (type) of aid project . Number of projects . Percent of total projects . A. Emergency response, reconstruction, and disaster prevention projects Material relief assistance and services 15,027 62.71 Emergency food aid 4,010 16.73 Disaster prevention and preparedness 2,236 9.33 Reconstruction relief and rehabilitation 1,612 6.73 Relief co-ordination; protection and support services 1,078 4.50 Total 23,963 100.00 B. Health, population policies/programmes reproductive health projects STD control including HIV/AIDS 6,872 20.57 Basic health care 4,692 14.04 Reproductive health care 4,400 13.17 Medical services 2,521 7.55 Health policy and administrative management 2,383 7.13 Basic health infrastructure 1,987 5.95 Population policy and administrative management 1,881 5.63 Family planning 1,440 4.31 Health education 1,372 4.11 Basic nutrition 1,311 3.92 Infectious disease control 1,311 3.92 Malaria control 940 2.81 Tuberculosis control 651 1.95 Health personnel development 598 1.79 Medical education/training 570 1.71 Medical research 300 0.90 Personnel development for population and reproductive health 182 0.54 Total 33,411 100.00 C. Environment-related projects Bio-diversity 2,924 38.42 Environmental policy and administrative management 2,792 36.68 Environmental education/training 862 11.33 Biosphere protection 584 7.67 Site preservation 218 2.86 Environmental research 155 2.04 Flood prevention/control 76 1.00 Total 7,611 100.00 Source. Authors’ calculations using AidData Core Research Release, Version 3.1. Open in new tab These findings confirm the numerous ethnographic accounts of NGO practitioners and investigative journalists that decry such patterns inside the international NGO sector (see Smillie, 1995; De Waal, 1997; Dichter, 2003; Mattei, 2005; Werly, 2005; Polman, 2010; among others). For instance, Smillie (1995) writes: The ‘pornography of poverty' [is] the use of starving babies and other emotive imagery to coax, cajole, and bludgeon donations from a guilt-ridden Northern public … [The problem is] not that starving babies don’t exist, but that such pictures, repeated year after year, create an image of horror and helplessness that far outweigh reality. This is generally recognised by most NGOs to be counter-productive in terms of creating understanding and awareness for longer-term development assistance. (p. 136) Why does such clustering of NGO projects occurs so often? Why do some issues get neglected and certain others often command disproportionate attention? Is the decentralised allocation of NGOs across issues socially efficient? This article builds a simple model of NGO fundraising competition and issue choice that provides an analytical framework to address the above questions. In our model, two NGOs strategically choose issues to focus their projects on and then compete through fundraising for donations, to finance their projects. Donors have latent willingness-to-give, but need to be ‘awakened' by fundraising campaigns to effectively give (Donkers et al., 2017). They also differ in terms of their motivation to give across issues. Some donors are interested in giving only to one type of issue (single issue donors), while others have a warm-glow to give to any issue they get sensibilised to (multiple issue donors). Raising funds focusing on the same issue creates positive spillovers across NGOs. Starting with a baseline model with a symmetric distribution of single issue donors, our first contribution is to characterise the resulting equilibrium NGO issue choice configuration, highlighting the tension between three forces. First, when choosing whether to compete in the same market as its rival (i.e., clustering), an NGO benefits from awareness-raising spillovers, as donors are activated through the strength of a common NGO voice on a single issue (i.e., a positive activation effect). Second, clustering however potentially reduces the share of each NGO on the market of activated donors on that same issue (i.e., a direct donation–competition effect). Third, by clustering on the same issue, NGOs strategically soften the fundraising competition they undertake in the second stage to activate donors on their own project (i.e., an implicit fundraising–coordination effect). The positive activation effect and the implicit fundraising–coordination effect favour the emergence of issue clustering, while on the opposite, the direct donation–competition effect favours issue specialisation. We highlight the conditions under which the first two effects jointly outweigh the latter effect. Specifically, two fundamental parameters matter to determine whether NGOs cluster or specialise in issues: the degree of issue specificity of donors’ warm-glow motivation (i.e., the share of donors attached to a single issue) and the cost of fundraising. Equilibrium clustering is more likely to occur when the share of multiple-issue donors is relatively large, and when the fundraising technology is sufficiently efficient. Our second contribution is to discuss the normative properties of the decentralised NGO issue choice equilibrium. As is well known, defining an appropriate social welfare function in models with warm-glow altruism is notoriously tricky (Andreoni, 2006). Our analysis takes therefore an ‘agnostic' approach listing several options (from the most narrow definition of welfare to the broadest one), and we analyse the welfare properties of the decentralised equilibrium under each option.2 Interestingly, taking as a normative criterion the aggregate NGOs surplus and the aggregate welfare of donors, we show that equilibrium clustering may be welfare dominated by issue specialisation when the cost of fundraising is in some intermediate range, and the motivation for donors’ giving is relatively high. The essence for this inefficiency of issue clustering comes from two features. First, by clustering on the same issue, NGOs implicitly restrict their competition for fundraising. This, in turn, effectively reduces the share of activated donors who might have contributed positively to social welfare. Second, when NGOs cluster on one issue, they do not internalise the fact that donors who are attached to the other issue will not be activated. At the source of these features is the lack of credible coordination that NGOs face when competing for fundraising once their issue choice is made. As a matter of fact, assuming that projects are perfect substitutes from the beneficiaries’ point of view, we show that equilibrium clustering is always efficient whenever NGO coordination at the fundraising stage is feasible. Our analysis therefore emphasises the fundamental importance of fundraising coordination between NGOs for the optimality of issue clustering. The article then explores the extension of the baseline model to asymmetric distributions of single issue donors. Additional to the three forces identified in the baseline model, this brings an additional donor demand effect determining the equilibrium NGO choice of issues, namely the relative size of the ‘captive' specific issue donation markets. Not surprisingly, the larger the share of potential donors specifically attached to give to one single issue, the more likely do we have equilibrium NGO clustering on that issue. However, the basic inefficiency features associated to fundraising competition are still present in this extended context, and there are parameters’ configurations such that equilibrium clustering is welfare dominated by issue specialisation. We also apply our model to study settings with inter-temporal issue choices of NGOs and the question of ‘rushing to emergency' (i.e., NGO clustering on first period immediate issues) as opposed to ‘intertemporal project specialisation'. There, we show that the conditions for ‘rushing to emergency' are more likely to hold than in the simultaneous non-timing game structure. The reason is that in the intertemporal setting, on top of time discounting, there is a sequential strategic advantage in fundraising competition to be the first NGO to sensibilise non-specific donors to one’s project. Finally, throughout the article, we illustrate the mechanisms of the different versions of our model with several case studies drawn from the empirical and NGO development policy literature. Case study 1 deals with the Ethiopian Famine of 1984; case study 2 considers the Biafra Famine episode of 1968, case study 3 discusses the situation of Sierra Leone at the End of the 1991–2002 Civil War; finally case study 4 illustrates the case of the 2004 Indian Ocean tsunami. We contribute to the growing literature on the economics of development NGOs that engage in providing public goods. Besley and Ghatak (2001) present a general model of optimal ownership of public goods (government versus NGO), focusing on the key role of incompleteness of contracts in foreign aid and the non-excludable nature of project benefits. Fruttero and Gauri (2005) are the first to model the rational decision of geographic location of NGOs under alternative assumptions about their motivations. Aldashev and Verdier (2009; 2010) build models of horizontally-differentiated NGO competition on the markets for donations, while Aldashev et al. (2014) show the conditions under which NGOs are able to overcome the excessive competition and coordinate their fundraising activities in a stable fashion. Burger et al. (2015) focus on the optimal regulatory policies of NGOs under asymmetric information concerning the level of altruism of NGO founders. Heyes and Martin (2015) study the equilibrium breadth of NGO missions in a model where NGOs compete for donations through the choice of mission statements. Auriol and Brilon (2014) and Aldashev et al. (2018) study the self-selection of motivated agents into the NGO sector. Scharf (2014) studies the relative efficiency of the equilibrium entry/selection of NGOs into the competitive market under alternative financing schemes, whereas Krasteva and Yildirim (2016) analyse how the adverse selection into NGO sector depends on the sector size and the donors’ information costs about NGO quality. Aldashev and Vallino (2019) show that the concerns about losing donors might induce environmental NGOs to allocate their resources sub-optimally. Our article contributes to this literature by providing a simple but flexible model of NGO choice of issues to focus on, which can encompass a rich set of choices that NGOs competing for donations undertake in real-life contexts. The plan of the article is the following. Section 1 presents the baseline model and analyses the NGO equilibrium in fundraising and issue choice. Section 2 provides a normative discussion of the decentralised equilibria. In Section 3, we consider the possibility of coordination for fundraising and/or issue choice for NGOs. Section 4 extends the model to asymmetric distributions of donors’ motivation, while Section 5 proceeds with the intertemporal application. Finally Section 6 concludes. Proofs of propositions are relegated to the Appendix. 1. Model 1.1. Setup Actors and preferences. Consider a setting with two NGOs, denoted by k ∈ {1, 2}, which undertake projects targeting two charitable or development issues, i ∈ {A, B}. The examples of these issues are education and health, humanitarian emergencies in two countries, or poverty in two locations of a specific country. Each NGO is run by an impurely altruistic (à la Andreoni, 1989) social entrepreneur who enjoys a warm-glow utility increasing with the output of her organisation. This implies that an NGO aims at maximising the output of its project. Each NGO can undertake only one project (for instance, because social entrepreneurs’ time is in fixed supply), and each project targets only one issue. For simplicity, we assume that the beneficiaries of these projects are passive; however, their well-being is affected by the size (measured by the output) of the projects. Hence, NGOs act as intermediaries between donors and beneficiaries. The economy has a continuum of atomistic donors of mass one. Each donor has one (indivisible) unit of resource. Similar to the social entrepreneurs, donors are impurely altruistic: they receive a warm-glow utility from giving to the NGO projects. However, we assume that donors do not seek out the projects to donate to, because they are initially unaware of the issues and NGO projects that target them, and become ‘activated' by NGO fundraising activities, as explained below. Moreover, donors are heterogeneous in their motivation towards the two issues, as well as in their ease of mobilisation to donate. Formally, each donor is characterised by four parameters (UA, UB, θA, θB). The first two parameters Ui describe the potential warm-glow utility of giving to issue i. The remaining two parameters, θi, describe the degree of (un)awareness of each donor about issue i, which reflects the effort needed to ‘activate' her, i.e., making her willing to give to issue i. Once ‘activated', a donor decides whether to give to that issue given her warm-glow utility from giving to that issue and, eventually, towards which NGO to give if she has the choice. We assume that the pairs of (un)awareness levels (θA, θB) are distributed i.i.d. (independent and identically distributed) uniformly on [0, 1]2 across all donors. To simplify the analysis, we assume that there are three different types of donors in terms of the nature of their warm-glow utility pairs (UA, UB) on issues A and B. Share α ∈ [0, 1|$/$|2] of donors only cares about issue A (i.e., their warm-glow utilities are UA = U and UB = 0). Similarly, share α of donors only cares about issue B (i.e., their warm-glow utilities are UA = 0 and UB = U). The remaining share 1 − 2α of donors cares equally about the two issues A and B (i.e., their warm-glow utilities are UA = UB = U). To guarantee that donations are non-trivially positive, we assume that the value of the warm-glow utility U is larger than the resource cost of giving (i.e., U > 1). Let yik denote the fundraising effort of NGO k targeting issue i, and Yi the total fundraising effort spent on issue i by all NGOs. We assume that the donor with parameters (UA, UB, θA, θB) becomes aware on issue i ∈ {A, B} if the NGOs’ total ‘voice' Yi is ‘loud' enough, i.e., if θi ≤ Yi. Technology. An NGO project transforms funds collected (net of fundraising expenditures) into output. The output of NGO k targeting issue i is: $$\begin{align*} Q_{ik}=F_{ik}-\phi \frac{y_{ik}^{2}}{2}, \end{align*}$$ where Fik is the amount of funds raised by the NGO, whereas the second term denotes the fundraising (quadratic) effort cost borne by the NGO to raise donors’ awareness on issue i, with ϕ > 0 parameterising the efficiency of the fundraising technology. Timing. The model has two stages. At stage 1, each NGO (simultaneously and non-cooperatively) chooses the issue on which to carry out its project. At stage 2, the NGOs (simultaneously and non-cooperatively) set their fundraising efforts yik. Some donors are activated and decide the project(s) to donate to. NGOs collect donations, cover fundraising costs, and produce. The equilibrium concept we adopt is the subgame perfect Nash equilibrium in issue choice and fundraising efforts. Issue Choice. Importantly, at the first stage NGOs decide simultaneously whether (i) to cluster, i.e., choose the same issue, or (ii) to specialise in two different issues. For each case, we need to specify the output levels of NGO projects. Case 1: Clustering Let both NGOs decide to carry out their projects targeting issue A. Then, their fundraising effort is spent only on this issue; hence, YA = y1 + y2. Donors are only made aware of issue A. Hence, the total amount of donations given toward this issue, exploiting the assumption of uniform i.i.d. distribution of θA on [0, 1], equals: $$\begin{align*} F_{A}=\Pr (\theta _{A}\le y_{1}+y_{2})=y_{1}+y_{2}.\end{align*}$$ Only activated donors among those who care about issue A (share α) and those who are indifferent between the two issues (share 1 − 2α) will give to the NGOs. These donors will split themselves equally across the two NGOs. Given the symmetry of the problem, the output of each NGO is: $$\begin{eqnarray} Q_{k}^{AA}(y_{1},y_{2})=\frac{\alpha +(1-2\alpha )}{2}(y_{1}+y_{2})-\phi \frac{y_{k}^{2}}{2}=\frac{1-\alpha }{2}(y_{1}+y_{2})-\phi \frac{y_{k}^{2}}{2} . \end{eqnarray}$$(1) Similarly, if both NGO choose to focus their projects on issue B, the output of each NGO is: $$\begin{eqnarray} Q_{k}^{BB}(y_{1},y_{2})=\frac{1-\alpha }{2}(y_{1}+y_{2})-\phi \frac{y_{k}^{2} }{2}. \end{eqnarray}$$(2)Case 2: Specialisation Suppose now that the NGOs choose their projects focusing on two distinct issues i, j ∈ {A, B}, with i ≠ j. Let, for instance, NGO 1’s project focus on issue A, and NGO 2’s project on issue B. Then, using the assumption of uniform i.i.d. distribution of θi on [0, 1], the mass of activated donors aware about issue i (and the total donations towards that issue) becomes: $$\begin{align*} F_{A}=\Pr (\theta _{A}\le y_{1})=y_{1}\quad \text{and}\quad F_{B}=\Pr (\theta _{B}\le y_{2})=y_{2}. \end{align*}$$ Note that each donor is made aware of issue A with probability y1(1 − y2), of issue B with probability y2(1 − y1), of both issues with probability y1y2, and remains unaware with the residual probability (1 − y1)(1 − y2). A donor aware of only one issue will give to the NGO working on that issue if and only if she cares about this issue (i.e., has a positive warm-glow utility of giving to that issue). In case a donor is aware of both issues, two cases are possible. Either she cares only about one issue and therefore gives to the NGO having a project on that issue, or she cares equally about both issues and, therefore, she randomly chooses between the two NGOs to give. Then, the output level for NGO 1 becomes: $$\begin{eqnarray} Q_{1}^{AB}(y_{1},y_{2})=\alpha y_{1}+(1-2\alpha )\left[ y_{1}(1-y_{2})+y_{1}y_{2}\tfrac{1}{2}\right] -\phi \tfrac{y_{1}^{2}}{2}. \end{eqnarray}$$(3) The first term represents donors aware of issue A who only care about this issue. The second term reflects the donors who equally care about the two issues and are only aware of issue A (the share (1 − 2α)y1(1 − y2)) , as well as those aware of both issues, with half of those them giving to NGO 1 (the share |$(1-2\alpha )y_{1}y_{2}\tfrac{1}{2}$|⁠). Similarly, the output level for NGO 2 is: $$\begin{eqnarray} Q_{2}^{AB}(y_{1},y_{2})=\alpha y_{2}+(1-2\alpha )\left[ y_{2}(1-y_{1})+y_{1}y_{2}\tfrac{1}{2}\right] -\phi \tfrac{y_{2}^{2}}{2}. \end{eqnarray}$$(4) Hereafter, we assume that ϕ ∈ [1, ∞), which guarantees that the probabilities of donors’ awareness on any issue i resulting from the fundraising efforts of NGOs yi ∈ [0, 1] are always well-defined and below 1. 1.2. Equilibrium Analysis 1.2.1. Equilibrium fundraising efforts Let’s first focus on the second stage of the model, and characterise the Nash equilibrium levels of fundraising in the two possible configurations of issue choice emerging from the first stage. Case 1: Clustering The analysis of NGO behaviour under clustering on issue A or B is symmetric and, hence, rather easy to solve. The strict concavity of NGOs’ output functions (1)–(2) in their own fundraising efforts guarantees a unique Nash equilibrium fundraising effort equal to: $$\begin{eqnarray} y_{1}^{c}=y_{2}^{c}=y^{c}=\frac{1-\alpha }{2\phi }, \end{eqnarray}$$(5) where superscript c stands for clustering. Case 2: Specialisation Let NGOs specialise on issues, with NGO 1 focusing on A and NGO 2 on issue B. Given the output functions (3) and (4), the first-order conditions of NGOs’ optimisation problems write as: $$\begin{eqnarray} 1-\alpha -(1-2\alpha )\tfrac{y_{2}}{2}=\phi y_{1}, \end{eqnarray}$$(6) $$\begin{eqnarray} 1-\alpha -(1-2\alpha )\tfrac{y_{1}}{2}=\phi y_{2}. \end{eqnarray}$$(7) These best-response functions yield the following unique symmetric level of effort for both NGOs (denoted by superscript s, for specialisation): $$\begin{eqnarray} y_{1}^{s}=y_{2}^{s}=y^{s}=\frac{1-\alpha }{\phi +\tfrac{1}{2}-\alpha }. \end{eqnarray}$$(8) Thus, we immediately get the following result: Proposition 1. (i) Each NGO’s equilibrium fundraising effort under issue clustering is: $$\begin{align*} y_{1}^{c}=y_{2}^{c}=y^{c}=\frac{1-\alpha }{2\phi }; \end{align*}$$ (ii) each NGO’s equilibrium fundraising effort under issue specialisation is: $$\begin{align*} y_{1}^{s}=y_{2}^{s}=y^{s}=\frac{1-\alpha }{\phi +\tfrac{1}{2}-\alpha }\text{; } \end{align*}$$ (iii) fundraising efforts under issue specialisation are (weakly) higher than under issue clustering: $$\begin{align*} y^{s}\ge y^{c}. \end{align*}$$ The intuition for the last part of the proposition is as follows. Under issue clustering, the NGOs target the same pool of donors: those who care only about the issue on which clustering occurs plus those who potentially care about both issues. Although the NGOs have to compete for these donors, given the issue clustering, the fundraising activities of one NGO create substantial positive externalities on the other NGO’s output through raising donors’ awareness (and hence awakening certain donors) towards their common cause. The existence of these positive externalities induces NGOs to free-ride, to a certain extent, on each other’s fundraising efforts. The situation is completely different under issue specialisation. Under such configuration, each NGO has a ‘captive' share of potential donors α, those who only care about this NGO’s issue. Hence, an NGO competes with the rival only for the residual share of donors 1 − 2α (i.e., those who care about both issues). However, these donors can be activated towards either one or both issues, and, moreover, NGOs do not have a common cause. Therefore, each NGO has an incentive to undertake more fundraising to induce donors’ awareness towards her issue. The absence of positive externalities in fundraising thus eliminates any free-riding among NGOs and the equilibrium fundraising efforts result to be larger than those under clustering. Consequently, and as we show below, this key feature enhances the NGOs’ relative incentives to cluster (rather than to specialise), as a way of mitigating the intensity of costly fundraising competition for donors. 1.2.2. Equilibrium issue choice Moving to the analysis of the first stage, we easily obtain the equilibrium NGO output levels in the two issue configurations, by substituting the second-stage Nash equilibrium fundraising efforts into the NGO output functions (respectively, (5) into (1)–(2), and (8) into (3)–(4)): $$\begin{eqnarray} Q_{k}^{AA}(y_{1}^{c},y_{2}^{c})=Q_{k}^{BB}(y_{1}^{c},y_{2}^{c})=Q^{c}=\frac{3 }{4}\frac{(1-\alpha )^{2}}{2\phi }\text{ for }k=1,2, \end{eqnarray}$$(9) and $$\begin{eqnarray} Q_{1}^{AB}(y_{1}^{s},y_{2}^{s})=Q_{2}^{BA}(y_{1}^{s},y_{2}^{s})=Q^{s}=\frac{ \phi }{2}\frac{(1-\alpha )^{2}}{\left[ \phi +\tfrac{1}{2}-\alpha \right] ^{2} }. \end{eqnarray}$$(10) These expressions allow us to characterise the first-stage equilibrium issue configurations. Proposition 2. The equilibrium in issue choice is: (i) for|$1\le \phi \lt \frac{\sqrt{3}}{2-\sqrt{3}}\left( \frac{1}{2}-\alpha \right)$|⁠, the NGOs cluster on the same issue (either A or B); (ii) for|$\frac{\sqrt{3}}{2-\sqrt{3}}\left( \frac{1}{2}-\alpha \right) \lt \phi$|⁠, the NGOs specialise, with one NGO choosing issue A and the other issueB. Proof. See the Appendix. Intuitively, the equilibrium issue choice by NGOs reflects the tension between different forces. The two NGOs interact strategically at three different levels: (i) in issue choice, (ii) in awakening (activating) the donors through fundraising efforts, and (iii) in competing for awakened donors (again by fundraising). Under issue clustering, NGOs operate towards the same cause, but also have to compete with each other for funding. As explained above, given that donors are activated through the strength of the common voice by the NGOs on this single issue, fundraising generates a positive informational spillover between the two NGOs at the donor activation level. Let us call this the positive activation effect. On the other hand, clustering potentially reduces the share of each NGO on the market consisting of these activated donors. Let us denote this the direct donation–competition effect. Under specialisation, NGOs compete for donors’ attention, given that under this configuration donors have to be awakened to different issues. Thus, the activation effect between NGOs turns negative. However, once donors are activated, the competition for their donations is softened, as some donors care about only one issue, for which the NGO targeting that issue enjoys a monopoly position. Consequently, issue specialisation reduces the direct donation–competition effect. At the issue choice stage, NGOs anticipate the fundraising competition to raise donors’ awareness that will occur in the second stage. As highlighted in Proposition 1, issue clustering induces lower equilibrium fundraising efforts, as compared to issue specialisation (ys ≥ yc). Thus, by choosing to cluster, NGOs strategically soften the fundraising competition in the second stage. We call this implicit fundraising–coordination effect. The positive activation effect and the implicit fundraising–coordination effect favour the emergence of issue clustering. On the other hand, the direct donation–competition effect favours issue specialisation. Proposition 2 provides the conditions under which the first two effects jointly outweigh the latter effect and thus determine whether NGOs cluster or specialise in issues. Figure 1 depicts the equilibrium configurations of issue choice in the space (ϕ, α). It shows that the state of the fundraising technology (in particular, the cost of fundraising, ϕ) and the structure of donors’ motivation (the degree of issue specificity of donors, α) are the key drivers behind the equilibrium of the model. If the share of single-issue donors α is (symmetrically) large enough (i.e., |$\alpha \gt \alpha _{\min }=\frac{1}{2}-\frac{2-\sqrt{3}}{\sqrt{3}}$|⁠), the direct donation–competition effect (associated with the advantage of having a captive donation market of size α, through issue specialisation) outweighs the positive activation effect and implicit fundraising–coordination effect. Hence, the NGOs choose to specialise in issues, for all values of ϕ ≥ 1 (which is the relevant range for this parameter). When, contrarily, α < αmin , the choice between issue clustering and issue specialisation depends on the cost parameter ϕ of the technology of fundraising. When the fundraising technology is sufficiently efficient (i.e., ϕ is low enough), the equilibrium fundraising efforts undertaken by the NGOs are relatively high. Consequently, the positive activation effect (the positive informational spillover between the NGOs under clustering) and the implicit fundraising–coordination effect (the incentive to reduce fundraising competition) are sufficiently strong to jointly outweigh the direct donation–competition effect. Hence, in this parameter region, issue clustering emerges in equilibrium. Conversely, when the technology of fundraising is relatively costly, the direct donation–competition effect outweighs the sum of the two other effects and the NGOs choose to specialise on different issues. The above analysis and Figure 1 indicate that the clustering of NGOs on the same issue is relatively more likely to occur when the cost of fundraising is rather low and when the large majority of potential donors do not have strong intrinsic preferences towards one particular issue. In addition, our analysis suggests that if the mass of these neutral donors is large, a sudden drop in the cost of fundraising can move the equilibrium from issue specialisation to issue clustering. The two case studies presented below highlight this possibility in practice. 1.3. Case 1: Ethiopian Famine of 1984 A key example of the behavioural change of NGOs in the context where our model seems to apply comes from the 1984 Ethiopian case. It was a complex political situation in which the combination of the drought and political problems created a severe famine. The political manipulation of the situation by the Ethiopian dictator induced the official donors to be wary of sending aid and, consequently, the private donors’ willingness to give was also muted. However, as images of starving children reached the press, this changed dramatically: Until early 1984, international donors were justifiably sceptical about the Ethiopian Government’s appeals for relief. There was evidence of both diversion of food aid and the strategic abuse of relief to support counter-insurgency efforts in the south-east. … In October 1984 the famine suddenly became international news … (De Waal, 1997, p.121) What led to this rapid change and the consequent massive inflows of aid? De Waal points out that it was a combination of the mediatisation of the famine during the fall of 1984 and the fact that such attention reached its maximum close to Christmas: It is interesting to chart the way in which the famine progressed from its niche as a news item and a campaign by relief agencies into an unprecedented international media event with political repercussions in leading Western democracies. BandAid played a key role in this: while not the first, it was the definitive media-charitable event. The timing was crucial: Christmas is the fund-raising season for relief agencies and a time of particular sensitivity in the public conscience. (De Waal, 1997, p.122) Hancock (1989) also describes how this shock suddenly increased the attention of the donors to give to humanitarian causes, and, importantly, how this induced one of the largest NGOs, the World Vision, to enter into competition for funds with the religious organisations during the Christmas time: On 21 December 1984, unable to resist the allure of Ethiopian famine pictures, World Vision ran an Australia-wide Christmas Special television show calling on the public in that country to give it funds. In so doing it broke an explicit understanding with the Australian Council of Churches that it would not run such television spectaculars in competition with the ACC’s traditional Christmas Bowl appeal … (Hancock, 1989, p.17) In terms of our model, this last statement seems to suggest that the initial equilibrium was that of specialisation. The cost of fundraising (ϕ) was relatively high; the World Vision and the ACC conducted their fundraising campaigns in different moments of the year, to avoid the direct donation–competition effect. However, as the famine became suddenly mediatised, the cost of fundraising fell, and the positive activation effect grew larger. Hence, the equilibrium issue choice configuration became that of clustering, with both World Vision and the ACC conducting the fundraising campaigns at the same moment of the year. 1.4. Case 2: Biafra Famine of 1968 The Biafra famine broke out in 1968 in the aftermath of the civil war between the Federal Military Government of Nigeria and the secessionist Eastern region’s militants, mostly because of the blockade by the former. The international community initially showed little interest in the famine, and the international media covered it only marginally. As Alex de Waal (1997) writes: The famine first became news, almost wholly by accident, in June 1968, when the war was already decided in military terms. … The press had [initially] shown little interest in the ‘famine story’. In fact, the first journalist to take famine pictures never got them published because his paper considered them of no news value … (De Waal, 1997, pp.73–74) Only after some journalists took pictures of malnourished children in Biafran hospitals and diffused them in the UK, the attention of the international public turned to the crises. Then, rapidly, this interest became massive: For relief agencies, the impact of the first African famine to become world news was electric. … Immediately the press coverage began, Oxfam swung into action, breaking ranks with the other members of the Disasters Emergency Committee (a club of leading British relief NGOs formed to co-ordinate television fund-raising for disasters) and the ICRC [International Committee of the Red Cross], with whom it had previously made an agreement not to act unilaterally. [Oxfam] became operational in the field for only the second time in its history. (De Waal, 1997, pp.74–75) The above description of the behavioural change of Oxfam, one of the largest international NGOs, is illustrative of the key prediction of our model. As in the first case study, this last statement indicates that the initial equilibrium implied issue specialisation: Oxfam specialised in operating outside the field, while the ICRC was operational in the field. This way, the two NGOs avoided the direct donation–competition effect. However, as the cost of fundraising ϕ fell and the informational spillovers became stronger because of the sudden increase in the attention of international public, the equilibrium issue choice configuration became that of clustering, with both Oxfam and the ICRC being operational in the field. The study by Sogge and Zadek (1996) suggests that such sudden rise in media attention regularly turns the equilibria of the game into clustering: The siege of Biafra of 1968–9, the Sahelian drought of 1974–5, and the Ethiopian famine of 1984–6 proved financial watersheds for a number of private agencies [i.e., NGOs] whose prior involvement in those parts of the world had been minimal or non-existent. (Sogge and Zadek, 1996, p.80) Several observers, including Smillie (1995), argue that this kind of rush by international NGOs led to a highly inefficient outcome. This occurred in particular because the sheer mass of aid and humanitarian relief allowed the local political power holders to exploit it for their means, which prolonged the conflict: 'The airlift and the broader relief efforts was … an act of unfortunate and profound folly. It prolonged the war by 18 months' (Smillie, 1995, p.104). Such conclusions raise the key questions whether the decentralised equilibrium in issue choice deviate from social optimum. We turn to this question next. 2. Welfare What are the normative properties of the decentralised issue choice equilibrium of the model? In particular, when is the NGO equilibrium clustering inefficient? Understanding the answers to these questions is crucial for the formulation of optimal public policies towards the NGO sector (for example, in terms of direct and matching grants, tax deductions for charitable giving, subsidising fundraising costs, etc.). Defining an appropriate social welfare function in models with warm-glow altruism is known to be tricky (see, for instance, the discussion in Section 5 of Andreoni, 2006). In our setting, there are two key reasons for this difficulty: donors’ preferences include unawareness about the issues (e.g., is the unaware donor less happy than the aware donor deciding not to give?) and whether/how to weigh the well-being of the social entrepreneurs that found NGOs (e.g., are they to be considered as representing the interests of project beneficiaries, or should the beneficiaries’ well-being be counted separately?). Our approach in solving these problems is to list several options (from the most narrow definition of welfare to the broadest one) and analysing the welfare properties of the decentralised equilibrium under each option. 2.1. Aggregate NGO Surplus We start by considering the point of view of NGOs alone. Is the aggregate NGO surplus (i.e., the joint output of their projects) maximised in equilibrium? Let us compare the two NGO issue choice configurations, assuming that the NGOs behave as decentralised competitors in the subsequent fundraising competition process (we analyse the coordination in fundraising in a later subsection). Obviously, given the symmetry at each equilibrium, the aggregate NGO surplus with non-cooperative fundraising competition is given by 2Qc under clustering and 2Qs under specialisation. This directly implies that the Nash equilibrium issue choice outcomes (clustering or specialisation) is also the one that provides the higher aggregate surplus as compared to the other configuration. In other words, if one only considers the joint interests of the NGOs and coordinating them in terms of fundraising efforts is prohibitively costly, there seems to be no scope for improving the decentralised issue choice equilibrium emerging in our model. 2.2. General Welfare (NGOs and Donors) Consider next a broader social welfare function that includes both the aggregate NGOs surplus and the aggregate welfare of the donors. Let’s assume that a donor (either aware or unaware) that does not give enjoys the resource cost of her endowment, i.e., 1. When a donor decides to give to an issue on which she has a positive warm-glow, she enjoys a net utility gain of u ≡ U − 1 > 0. Given this assumption, we can compare the two issue choice configurations, again assuming a non-cooperative fundraising competition in the subsequent stage. The general welfare under issue clustering (for example, on issue A) writes as: $$\begin{eqnarray} W^{c} &=&\underset{\text{NGO surplus}}{\underbrace{ 2Q^{AA}(y_{1}^{c},y_{2}^{c})}}+\underset{\text{aggregate welfare of activated donors}}{\underbrace{2\cdot \frac{\left( \alpha +(1-2\alpha )\right) }{2}(y_{1}^{c}+y_{2}^{c})\cdot u}} \\ &=&2Q^{AA}(y^{c},y^{c})+(1-\alpha )(2y^{c})\cdot u=\frac{(1-\alpha )^{2}}{ 2\phi }\cdot \left[ \frac{3}{2}+2u\right] . \end{eqnarray}$$ Similarly, the general welfare under issue specialisation writes as: $$\begin{eqnarray} W^{s} &=&\underset{\text{NGO surplus}}{\underbrace{2Q^{AB}(y^{s},y^{s})}}+ \underset{\text{aggregate welfare of activated donors}}{\underbrace{2\cdot \left\lbrace \alpha y^{s}+(1-2\alpha )y^{s}\left[ 1-y^{s}\tfrac{1}{2}\right] \right\rbrace \cdot u}} \\ &=&\phi \frac{(1-\alpha )^{2}}{\left[ \phi +\tfrac{1}{2}-\alpha \right] ^{2}} (1+2u). \end{eqnarray}$$ Thus, the issue clustering configuration is welfare-dominated by the issue specialisation configuration when Ws > Wc or: $$\begin{align*} \frac{\phi }{2}\frac{(1-\alpha )^{2}}{\left[ \phi +\tfrac{1}{2}-\alpha \right] ^{2}}(2+4u)\gt \frac{(1-\alpha )^{2}}{2\phi }\cdot \frac{3}{4}\left[ 2+ \frac{8}{3}u\right] . \end{align*}$$ This condition can be rewritten as: $$\begin{align*} \phi \gt \Gamma (u)\left( \frac{1}{2}-\alpha \right) , \end{align*}$$ where $$\begin{eqnarray} \Gamma (u)=\frac{\sqrt{3}}{2\sqrt{\frac{2+4u}{2+\frac{8}{3}u}}-\sqrt{3}}. \end{eqnarray}$$(11) Note that Γ(u) is a decreasing function of each donor’s net surplus u, with |$\Gamma (0)=\frac{\sqrt{3}}{2-\sqrt{3}}$| and |$\lim _{u\rightarrow \infty }\Gamma (u)=\frac{1}{\sqrt{2}-1}\gt 1$|⁠. As we have shown above, the condition under which the issue clustering configuration is the equilibrium outcome, is |$\phi \lt \frac{\sqrt{3}}{2-\sqrt{3}}\left( \frac{1}{2}-\alpha \right)$|⁠. Therefore, issue clustering is a decentralised equilibrium choice that is welfare-dominated by the issue specialisation configuration, when: $$\begin{align*} \Gamma (u)\left( \frac{1}{2}-\alpha \right) \lt \phi \lt \frac{\sqrt{3}}{2-\sqrt{3} }\left( \frac{1}{2}-\alpha \right). \end{align*}$$ We can summarise our findings in the following proposition. Proposition 3. (i) Issue clustering is the decentralised equilibrium and is efficient (welfare-dominates issue specialisation) when the cost of fundraising is relatively low (i.e., when|$1\le \phi \lt \Gamma (u)\left( \frac{1}{2}-\alpha \right)$|). (ii) Issue clustering is the decentralised equilibrium and is inefficient (welfare-dominated by issue specialisation) when the cost of fundraising is in some intermediate range (i.e., when|$\Gamma (u)\left( \frac{1}{2}-\alpha \right) \lt \phi \lt \frac{\sqrt{3}}{2-\sqrt{3}}\left( \frac{1}{2}-\alpha \right)$|). (iii) Issue specialisation is the decentralised equilibrium and is efficient (welfare-dominates issue clustering) when the cost of fundraising is relatively high (i.e., when|$\phi \gt \frac{\sqrt{3}}{2-\sqrt{3}}\left( \frac{1}{ 2}-\alpha \right)$|). (iv) Equilibrium issue clustering is more likely to be inefficient (welfare-dominated by specialisation), the larger the individual donor warm-glow utility U. Note that since |$\lim _{u\rightarrow \infty }\Gamma (u)=\frac{1}{\sqrt{2}-1}\gt 1$|⁠, the region in which the decentralised equilibrium issue clustering is welfare-dominated by specialisation is never empty. The efficiency comparison of the two configurations are shown in Figure 2. It shows the two lines, |$\phi =\frac{\sqrt{3}}{2-\sqrt{3}}\left( \frac{1}{2}-\alpha \right)$| and |$\phi =\Gamma (u)\left( \frac{1}{2}-\alpha \right)$|⁠. The first line delimits the parameter regions in which issue clustering versus issue specialisation is a decentralised equilibrium outcome. The second line delimits the parameter regions in which a given issue choice configuration welfare-dominates the other configuration. Fig. 2. Open in new tabDownload slide Welfare: Clustering vs Specialisation. Fig. 2. Open in new tabDownload slide Welfare: Clustering vs Specialisation. Figure 2 shows that, in the dashed region, issue clustering is a decentralised equilibrium outcome and is welfare-dominated by the issue specialisation configuration. This is the sense in which equilibrium NGO clustering is inefficient. The intuition for this inefficiency of issue clustering comes from the interaction between two elements on activated donors who contribute positively to social welfare (they obtain 1 whereas they could have obtained U > 1). First, by clustering on the same issue NGOs implicitly restrict their competition for fundraising. This effectively reduces the share of single-issue activated donors compared to the specialisation regime.3 At the same time; however, clustering also generates awareness spillovers on multiple issue donors that specialisation does not provide.4 When the technology of fundraising is relatively inefficient (i.e., ϕ large enough) the second effect is weak and specialisation results in more donors being activated in total in equilibrium. In such a case, the donor welfare under clustering ends up being smaller than under specialisation. Moreover when the share α of single-issue donors is sufficiently high but still compatible with the existence of a decentralised issue clustering equilibrium, these donor welfare losses outweigh the larger aggregate NGO surplus that prevails in the equilibrium clustering configuration, hence causing an inefficiency. 2.3. Welfare of Beneficiaries Note that our approach to social welfare did not take into account the welfare of project beneficiaries. Integrating the beneficiaries’ welfare into our analysis would reinforce the possibility of inefficiency of issue clustering. First, and obviously, if the two issues are complementary in the beneficiaries’ welfare function, clustering on a single issue is definitively sub-optimal from their point of view. Now suppose that the two issues are perfect substitutes. The beneficiaries’ welfare depends on the total amount of resources raised by the NGOs, which in our model is proportional to the equilibrium share of activated donors, under clustering or specialisation. Hence, in our welfare analysis developed above, adding beneficiaries’ welfare would be equivalent to increase the warm-glow surplus u of an activated donor by the additional marginal utility that this donation provides to the beneficiaries. From the last part of Proposition 3 (that depends on the function Γ(u) decreasing in u), integrating the beneficiaries’ welfare is thus equivalent to expanding the parameter region in which equilibrium issue clustering is welfare-dominated by the issue specialisation configuration. 3. Coordination between NGOs So far, we have assumed away the possibility that NGOs design voluntary coordination agreements. This might be excessively pessimistic, as there exist several real-life examples of successful coordination among NGOs. For instance, on multiple occasions, understanding the downsides of excessive fundraising competition, NGOs united their forces into umbrella organisations that conduct joint fundraising appeals. The most well-known example is, perhaps, the American United Way (see Brilliant, 1990, for a detailed history), but such examples exist also in other countries, for instance, the Disaster Relief Agency created by Dutch NGOs in 1993, Disasters Emergency Committee (DEC) in Britain, and Belgian National Center for Development Cooperation (see Similon, 2015, for a detailed discussion). Understanding the welfare properties of the equilibrium when coordination between NGOs (either in fundraising or in issue choice) arises is also important from the public policy viewpoint. If NGOs can reduce or eliminate the inefficiency discussed above through their voluntary coordination activities, there is less scope for public intervention. If, on the contrary, voluntary coordination is insufficient to overcome the inefficiencies, public policies aimed at the competitive NGO sector are still needed. In this subsection, we analyse the equilibrium outcomes of the model when (i) the NGOs jointly decide the level of their fundraising efforts, and can or cannot also coordinate in their issue choice, (ii) they coordinate their actions only at the first stage (in issue choice), but are unable to coordinate their choices of the second stage. We also study the welfare properties of the equilibria emerging in these two cases. Hereafter, we assume that when NGOs can coordinate, they have a common objective function, i.e., maximising the sum of the outputs of their projects.5 3.1. Coordination in Fundraising Activities Let’s suppose that NGOs are able to construct coordination agreements, so as to jointly choose their levels of fundraising, but their choice of issues remains decentralised (non-coordinated). This assumption applies well to settings where NGOs create umbrella fundraising organisations, but do not consider coordinating on the choice of issues feasible or desirable. What kind of issue configuration will emerge in equilibrium? And how does it differ from the fully non-coordinated case? It is straightforward to see that when the two NGOs coordinate their fundraising efforts, the problem of the two NGOs at the second stage becomes maximising their joint output. If the two NGOs operate towards the same issue (AA or BB), this would imply selecting a pair of fundraising effort levels to maximise: $$\begin{align*} \mathcal {Q}^{CF}=2Q_{k}^{AA}=2Q_{k}^{BB}=\left( 1-\alpha \right) (y_{1}+y_{2})-\frac{\phi }{2}\left( y_{1}^{2}+y_{2}^{2}\right) , \end{align*}$$ where the superscript CF denotescoordination in fundraising. Then, the optimal fundraising effort levels obtained by solving the system of first-order conditions are simply given by: $$\begin{align*} y_{1}^{CF}=y_{2}^{CF}=y^{CF}=\frac{1-\alpha }{\phi }. \end{align*}$$ Clearly, |$y^{CF}\gt y^{c}=\frac{1-\alpha }{2\phi }$|⁠, as NGOs now internalise the positive activation effect that each of them generates on the other through fundraising. The coordinated output of each NGO’s project under clustering would, therefore, be: $$\begin{align*} Q_{1}^{CF}=Q_{2}^{CF}=\frac{1}{2}\mathcal {Q}^{CF}=\frac{\left( 1-\alpha \right) ^{2}}{2\phi }. \end{align*}$$ Conversely, under issue specialisation (AB or BA), a coordinated fundraising agreement would aim at maximising: $$\begin{align*} \mathcal {Q}^{S}=Q_{1}^{AB}+Q_{2}^{AB}=\alpha (y_{1}+y_{2})+(1-2\alpha )\left[ y_{1}+y_{2}-y_{1}y_{2}\right] -\frac{\phi }{2}\left( y_{1}^{2}+y_{2}^{2}\right) . \end{align*}$$ The optimal coordinated fundraising efforts obtained from the system of first-order conditions are: $$\begin{align*} y_{1}^{SF}=y_{2}^{SF}=y^{SF}=\frac{1-\alpha }{\phi +1-2\alpha }, \end{align*}$$ where the superscript SF denotes here coordination in fundraising under specialisation, with NGO projects’ output levels equal to: $$\begin{align*} Q_{1}^{SF}=Q_{2}^{SF}=\frac{1}{2}\mathcal {Q}^{SF}=\frac{\left( 1-\alpha \right) ^{2}}{2\left( \phi +1-2\alpha \right) }. \end{align*}$$ Again, it is easy to see that ys > ySF, as the NGOs internalise the direct donation–competition effect of fundraising on the ‘neutral' donors they compete for under specialisation. From the above expressions, two features are worth mentioning. First, given that output levels are the same across NGOs in the clustering and in the specialisation configurations, full coordination on both fundraising and issue choice will generate the same equilibrium pattern as under fundraising coordination and uncoordinated issue choice.6 Second, in both cases, issue clustering (AA or BB) will occur if and only if QCF ≥ QSF, namely for: $$\begin{eqnarray} \frac{\left( 1-\alpha \right) ^{2}}{2\phi }\ge \frac{\left( 1-\alpha \right) ^{2}}{2\left( \phi +1-2\alpha \right) }, \end{eqnarray}$$(12) or $$\begin{align*} \left( \phi +1-2\alpha \right) \ge \phi , \end{align*}$$ and this condition is always satisfied for all the relevant values of α (i.e., α ≤ 1|$/$|2). We can then sum up our analysis above in the following proposition. Proposition 4. NGOs always choose issue clustering when they can coordinate on their fundraising efforts (regardless whether they can or cannot coordinate on their issue choice). Hence, NGO coordination in fundraising only or full coordination agreement (both in fundraising and issue choice) yields a much higher incentive to cluster on the same issue than when they act in uncoordinated fashion. As we discuss below, and differently from this case, when NGOs can coordinate only in their issue choice (but not in fundraising activities), this clustering effect is mitigated, and NGOs select the issue to focus on exactly as when playing in uncoordinated fashion in both stages. 3.2. Issue Choice Coordination Only Let’s now briefly consider the outcome that occurs when NGOs choose their fundraising efforts in a decentralised way but can decide jointly the issues to focus on. Given the symmetry between NGOs, it immediately follows that the outcome in this case replicates the equilibrium outcome of Proposition 2. Indeed, from (5) and (8), we see that under issue clustering (respectively, issue specialisation) the equilibrium fundraising effort levels are, respectively, yc and ys, and hence the individual NGO output levels are Qc and Qs as in (9) and (10). Hence, we obtain the following. Proposition 5. The equilibrium issue choice when NGOs can coordinate on issues but choose their fundraising efforts independently replicates the equilibrium issue choice of the fully decentralised equilibrium. Proof. Follows immediately from the proof of Proposition 2. From the above analysis, it emerges that issue clustering is much more likely to occur when NGOs coordinate their fundraising activities than when they can only coordinate on their choices of issues (but not their fundraising efforts). The main reason is that issue clustering potentially yields an output advantage at the fundraising stage that can only be exploited when NGOs are allowed to coordinate their fundraising activity. Indeed, when fundraising coordination is not possible, in equilibrium the positive spillover effect from increasing awareness among unaffiliated donors results in free-riding incentives and underinvestment under clustering relative to the case with fundraising coordination (i.e., yc < yCF). At the same time, project specialisation corrects for this problem (i.e., ys > ySF) but at the expense of losing the positive spillover effect of clustering. Clustering will then be preferred only when the free-riding problem is not too severe (the technology of fundraising is sufficiently efficient, i.e., ϕ low enough) and the spillover effect strong enough (the fraction 1 − 2α of unaffiliated donors large enough). Because the two NGOs are facing symmetric donation markets for the two issues, these conditions replicate the conditions for equilibrium choice of the fully decentralised equilibrium.7 This result suggests that leaving the fundraising coordination activities to the voluntary agreement of NGOs may potentially be counterproductive for their incentive to cluster. Consequently, the third-party independent agencies (or public policies) could be better suited to coordinate the excessive fundraising competition by NGOs. 3.3. Welfare Under Coordination Let’s analyse the decentralised equilibrium that emerges when coordination is (at least in part) feasible, from the social welfare perspective. The general welfare under clustering (e.g., on issue A) writes as: $$\begin{eqnarray} W^{c} &=&\underset{\text{NGO surplus}}{\underbrace{\mathcal {Q}^{CF}}}+ \underset{\text{aggregate welfare of activated donors}}{\underbrace{2\cdot \frac{\left( \alpha +(1-2\alpha )\right) }{2}(y_{1}^{CF}+y_{2}^{CF})\cdot u}}\\ &=&Q^{CF}+(1-\alpha )(2y_{1}^{CF})\cdot u=\frac{\left( 1-\alpha \right) ^{2} }{\phi }+\frac{2\left( 1-\alpha \right) ^{2}}{\phi }u \\ &=&\frac{(1-\alpha )^{2}}{\phi }\cdot \left[ 1+2u\right] . \end{eqnarray}$$ Similarly, the general welfare under issue specialisation writes as: $$\begin{eqnarray} W^{s} &=&\underset{\text{NGO surplus}}{\underbrace{\mathcal {Q}^{SF}}}+ \underset{\text{aggregate welfare of activated donors}}{\underbrace{2\cdot \left\lbrace \alpha y^{SF}+(1-2\alpha )y^{SF}\left[ 1-y^{SF}\tfrac{1}{2}\right] \right\rbrace \cdot u}} \\ &=&\frac{\left( 1-\alpha \right) ^{2}}{\left( \phi +1-2\alpha \right) } +2\phi \left( \frac{1-\alpha }{\phi +1-2\alpha }\right) ^{2}u \\ &=&\frac{\left( 1-\alpha \right) ^{2}}{\left( \phi +1-2\alpha \right) }\left[ 1+\frac{2\phi }{\phi +1-2\alpha }\cdot u\right] . \end{eqnarray}$$ We can show the following: Proposition 6. The issue clustering configuration always welfare-dominates issue specialisation when NGOs can coordinate on their fundraising efforts. Proof. See the Appendix. Thus, differently from the analysis in the uncoordinated case, if projects are perfect substitutes from the beneficiaries’ point of view and NGOs can coordinate their fundraising, clustering is always efficient. The intuition for this result is as follows. Nash equilibrium clustering generates an inefficiency, as we showed in Proposition 3, because of the lack of coordination at the non-cooperative fundraising equilibrium stage. Indeed, under specialisation, NGOs tend to engage in excessive uncoordinated fundraising competition (from the perspective of the NGOs). Through the implicit fundraising–coordination effect, clustering on the same issue mitigates this excessive competition. At the same time, though, when clustering, NGOs exert suboptimal (uncoordinated) fundraising effort in equilibrium, because they do not internalise the informational spillovers that this configuration induces on raising donors’ awareness. From the general welfare point of view, this creates the following trade-off. On the one hand, issue clustering is an indirect way to reduce excessive fundraising competition, as compared to issue specialisation. This increases the aggregate NGO surplus. On the other hand, issue clustering leads to a less than optimal level of donors’ awareness. This reduces the donors’ welfare component. The issue clustering configuration can be welfare-dominated by issue specialisation when the importance of donors is large enough as compared to the aggregate NGO surplus (i.e., when the warm-glow net utility u is large enough, see Proposition 3, part (iv)). When NGO coordination at the fundraising stage is feasible, the NGOs exert the (larger) jointly optimal fundraising effort under issue clustering (as they now internalise the informational spillovers donors’ awareness). They also exert the (lower) jointly optimal fundraising effort under specialisation, since they NGOs now internalise the excessive competition effect of fundraising. Both effects tend to create larger donors’ awareness under issue clustering, as compared to issue specialisation. Similarly, from the aggregate NGO surplus point of view, the internalisation of the spillovers of fundraising under clustering generates a higher surplus than the internalisation of excessive fundraising competition under specialisation. Therefore, for both reasons, clustering tends to dominate specialisation when NGOs are allowed to fully coordinate their choices. This analysis emphasises the fundamental importance of fundraising coordination between NGOs for the optimality of issue clustering. Indeed, as we saw in the previous section, when NGOs cannot credibly coordinate their fundraising efforts, then equilibrium issue clustering can be welfare-dominated by issue specialisation in such second-best situation, and thus excessive issue clustering might arise. In such situations, issue clustering should be considered as a negative phenomenon. Contrarily, when fundraising coordination is feasible (i.e., when NGOs can create credible fundraising–coordination agreements), issue clustering is actually a positive phenomenon, from the normative perspective. Finally, let us note that this normative analysis does not account for the beneficiaries’ welfare. If the two issues are close enough substitutes from the beneficiaries’ point of view, the above analysis carries through fully. Contrarily, issue specialisation will obviously welfare-dominate issue clustering if the issues are strong enough complements for the project beneficiaries. 4. Extension: Asymmetric Donor Motivation Our basic model assumed symmetry between the shares of single-issue donors for both issues. In numerous real-life situations, however, it is clear that one of the two issues is substantially more attractive, from the potential donors’ point of view. In such cases, the share of potential donors for this more attractive issue is likely to be considerably larger than the share of donors for the second issue. In this section, we study the implications of such asymmetry on the strategic behaviour of NGOs and the resulting equilibrium outcomes. Let us modify the setup of our basic model by assuming that a share αA ∈ [0, 1|$/$|2] of donors cares only about issue A (i.e., have warm-glow utilities UA = U and UB = 0). Similarly, a share αB ∈ [0, 1|$/$|2] of donors care only about issue B (i.e., have warm-glow utilities UA = 0 and UB = U). The remaining share 1 − αA − αB ≥ 0 of donors care equally about the two issues A and B (i.e., have warm-glow utilities UA = UB = U). As before, we assume that the value of the warm-glow utility U is larger that the resource cost of giving (i.e., U > 1). 4.1. Equilibrium Analysis Clustering. If both NGOs decide to focus their projects on issue A, their outputs can now be written as: $$\begin{eqnarray} Q_{k}^{AA}(y_{1},y_{2}) &=&\frac{\left( \alpha _{A}+1-\alpha _{A}-\alpha _{B}\right) }{2}(y_{1}+y_{2})-\phi \frac{y_{k}^{2}}{2} \\ &=&\frac{\left( 1-\alpha _{B}\right) }{2}(y_{1}+y_{2})-\phi \frac{y_{k}^{2}}{ 2}. \end{eqnarray}$$(13) Similarly, if both NGOs choose to focus their projects on issue B, the output of each NGO is simply: $$\begin{align*} Q_{k}^{BB}(y_{1},y_{2})=\frac{\left( 1-\alpha _{A}\right) }{2} (y_{1}+y_{2})-\phi \frac{y_{k}^{2}}{2}. \end{align*}$$ Again, the analysis of NGOs’ behaviour under issue clustering is symmetric and the Nash equilibrium fundraising efforts are given by: $$\begin{eqnarray} y_{1}^{AA} &=&y_{2}^{AA}=y_{A}^{c}=\frac{\left( 1-\alpha _{B}\right) }{2\phi }, \\ y_{1}^{BB} &=&y_{2}^{BB}=y_{B}^{c}=\frac{\left( 1-\alpha _{A}\right) }{2\phi }, \end{eqnarray}$$(14) where superscript c stands for clustering and subscript A or B denotes the issue on which NGOs cluster. In this case, the equilibrium NGO payoffs can be easily obtained as: $$\begin{eqnarray} Q_{k}^{AA}(y_{A}^{c},y_{A}^{c}) &=&Q_{A}^{c}=\frac{3}{4}\frac{(1-\alpha _{B})^{2}}{2\phi }\text{ for }k=1,2, \\ Q_{k}^{BB}(y_{B}^{c},y_{B}^{c}) &=&Q_{B}^{c}=\frac{3}{4}\frac{(1-\alpha _{A})^{2}}{2\phi }\text{ for }k=1,2. \end{eqnarray}$$ Specialisation. Suppose now that NGOs decide to specialise, with NGO 1 choosing issue A and NGO 2 choosing issue B. Their output functions simply write as: $$\begin{eqnarray} Q_{1}^{AB}(y_{1},y_{2}) &=&\alpha _{A}y_{1}+(1-\alpha _{A}-\alpha _{B})\left[ y_{1}(1-y_{2})+y_{1}y_{2}\tfrac{1}{2}\right] -\phi \tfrac{y_{1}^{2}}{2}, \\ Q_{2}^{AB}(y_{1},y_{2}) &=&\alpha _{B}y_{2}+(1-\alpha _{A}-\alpha _{B})\left[ y_{2}(1-y_{1})+y_{1}y_{2}\tfrac{1}{2}\right] -\phi \tfrac{y_{2}^{2}}{2}. \end{eqnarray}$$ We obtain the best-response functions of the NGOs from the first-order conditions of their optimisation problems: $$\begin{eqnarray} 1-\alpha _{B}-(1-\alpha _{A}-\alpha _{B})\tfrac{y_{2}}{2} &=&\phi y_{1} \\ 1-\alpha _{A}-(1-\alpha _{A}-\alpha _{B})\tfrac{y_{1}}{2} &=&\phi y_{2}. \end{eqnarray}$$ These best responses jointly give the Nash equilibrium fundraising effort levels: $$\begin{eqnarray} y_{1}^{AB} &=&y_{2}^{BA}=y_{AB}^{s}=\frac{\phi \left( 1-\alpha _{B}\right) - \frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{A})}{\phi ^{2}-\frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}}, \\ y_{2}^{AB} &=&y_{1}^{BA}=y_{BA}^{s}=\frac{\phi \left( 1-\alpha _{A}\right) - \frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{B})}{\phi ^{2}-\frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}}, \end{eqnarray}$$ with equilibrium NGO output levels: $$\begin{eqnarray} Q_{1}\left( y_{1}^{AB},y_{2}^{AB}\right) &=&Q_{AB}^{s}=\phi \frac{\left( y_{AB}^{s}\right) ^{2}}{2}=\frac{\phi }{2}\left[ \frac{\phi \left( 1-\alpha _{B}\right) -\frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{A})}{\phi ^{2}-\frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}} \right] ^{2}, \\ Q_{2}\left( y_{1}^{AB},y_{2}^{AB}\right) &=&Q_{BA}^{s}=\phi \frac{\left( y_{BA}^{s}\right) ^{2}}{2}=\frac{\phi }{2}\left[ \frac{\phi \left( 1-\alpha _{A}\right) -\frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{B})}{\phi ^{2}-\frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}} \right] ^{2}. \end{eqnarray}$$ To characterise the NGO equilibrium issue choices, let us conveniently reparameterise the distribution of donors (αA, αB) by introducing the following auxiliary variables: $$\begin{align*} X=\frac{1-\alpha _{A}-\alpha _{B}}{2}\in \left[ 0,\frac{1}{2}\right] \rm{ ,\qquad \ }Z=\frac{1-\alpha _{A}}{1-\alpha _{B}}. \end{align*}$$ The variable X stands for the (half of the) share of non-specific donors, whereas Z denotes the relative maximum size of the B-issue donor market as compared to the A-issue donor market.8 Then, the following proposition characterises the Nash equilibria in issue choice under asymmetric donor motivation: Proposition 7. (1) If the cost of fundraising ϕ is relatively high: (i) NGOs cluster on issue A when the maximum size of theA-issue donor market is sufficiently large, (ii) on issue B when the maximum size of theB-issue donor market is sufficiently large and (iii) NGOs specialise when the sizes of the two potential donor markets are relatively similar. (2) If the cost of fundraising ϕ is relatively low: (i) NGOs cluster on issue A when the maximum size of the A-issue donor market is sufficiently large, (ii) they cluster on issue B when the maximum size of the B-issue donor market is sufficiently large, (iii) NGOs cluster either on A or on B, when the sizesof the two potential specific donor markets are relatively similar and the share of non-specific donors X is high enough and (iv) NGOs specialise when the sizes of the two potential specific donor markets are relatively similar and the share of non-specific donors X is low enough. Proof. See the Appendix. Figure 3 illustrates the above proposition. It depicts the space of donors’ distributions (αA, αB) ∈ [0, 1]2, with the three regions in which the following issue choice equilibria arise: region CA defines the set of parameters for the clustering equilibrium on issue A; region CB defines the set of parameters for the clustering equilibrium on issue B; region S defines the set of parameters for the issue specialisation NGO equilibrium. Fig. 3. Open in new tabDownload slide (A). Equilibrium Issue Choice with Asymmetric Donor Motivation (High Cost of Fundraising) (B). Equilibrium Issue Choice With Asymmetric Donor Motivation (Low Cost of Fundraising). Fig. 3. Open in new tabDownload slide (A). Equilibrium Issue Choice with Asymmetric Donor Motivation (High Cost of Fundraising) (B). Equilibrium Issue Choice With Asymmetric Donor Motivation (Low Cost of Fundraising). The shape of these regions and the boundary curves DA (respectively, DB) defining the boundary between regions CA (respectively, CB ) and S, is explicitly characterised in the Online Appendix. Panel A of Figure 3 shows the case of a relatively inefficient technology of fundraising. It corresponds to case (1) of the above proposition. In the relevant set of donor distributions (i.e., below the line αA + αB = 1), clustering equilibria on issue A (respectively, B) appear for distributions of donors mostly composed of single-issue donors focusing on that issue. Contrarily, specialisation equilibria are sustained by more balanced distributions of donors (relatively close to the diagonal αA = αB) across the two issues. Panel B shows the case of a more efficient technology of fundraising. This picture covers case (2) of the proposition (corresponding to the condition ϕ · β < X < 1|$/$|2 in the Appendix), and to some extent case (1), corresponding to the condition X < ϕ · β in the Appendix. Once again, clustering equilibria on a given issue are sustained by distributions of donors biased (in the aggregate) towards that issue. More interestingly, the central region of issue specialisation equilibria disappears for distributions of donors with a large enough fraction of neutral donors, namely when 1 − αA − αB = 2X > 2ϕ · β. In such a case, there is a region of distribution of donors giving rise to equilibrium clustering either on issue A or on issue B. Clearly, regardless of the state of the fundraising technology, when the share of single-issue donors is large enough (i.e., αA or αB sufficiently large), there is a unique equilibrium, with NGOs clustering on that specific issue. However, when the shares of single-issue donors caring about each issue are relatively balanced (we are close to the diagonal in Figure 3), the equilibrium depends on the technology of fundraising. Under a rather inefficient technology (i.e., ϕ > ϕmax ), the positive activation effect and the implicit fundraising–coordination effect that favour the emergence of clustering are weaker than the direct donation–competition effect (which favours issue specialisation). Therefore, in that case issue specialisation arises in equilibrium for balanced distributions of single-issue donors (and any range of neutral donors). On the other hand, when the technology of fundraising is relatively efficient (i.e., ϕ < ϕmax ), then the positive activation effect and the implicit fundraising–coordination effect may jointly outweigh the direct donation–competition effect, especially when there is a relatively large share of non-specific donors. In such case, the size of this mass of non-specific donors enhances the forces towards issue clustering. This is why for a value of X = ϕ · β large enough (i.e., the fraction 1 − αA − αB of non-specific donors sufficiently large), one only obtains the issue clustering equilibria. In addition, when the remaining shares of the single-issue donors are relatively balanced (i.e., αA and αB are close to the diagonal on the graph), multiple clustering equilibria are possible. In particular, clustering on one issue (say A) can be an equilibrium even if the fraction αA of single-issue donors caring about that issue is smaller than the fraction αB. 4.2. Welfare 4.2.1. Aggregate NGO surplus We are now ready to study the equilibrium issue choice outcomes, in terms of aggregate NGO surplus and social welfare that includes the donors’ utility. Let us start first with the aggregate NGO surplus. We can show the following: Proposition 8. From the point of view of the aggregate NGO surplus: There always exists a region of donor distribution such that the equilibrium issue clustering configuration is dominated by the issue specialisation configuration; Issue specialisation configuration dominates issue clustering, whenever specialisation is the equilibrium outcome; With a relatively efficient fundraising technology and for donor distributions with sufficiently many non-specific donors, equilibrium issue clustering always dominates issue specialisation. Proof. See the Appendix. Figure 4 depicts the parameter regions for equilibrium issue-choice configurations and for surplus-maximising configurations. The parameter regions for surplus-maximising configurations are delimited by the curves |$D_{A}^{S}$| and |$D_{B}^{S}$|⁠. Panel A illustrates the case of a relatively inefficient fundraising technology (i.e., ϕ > ϕmax ), whereas Panel B depicts the case of a relatively efficient fundraising technology (i.e., ϕ < ϕmax ). In both cases, there exists parameter regions (dashed on the figure), one per issue, such that equilibrium clustering on that issue is surplus-dominated by the issue specialisation configuration. In particular, we show (in the Appendix) that the boundary DA separating regions CA and S always falls inside the region of donor distributions such that issue specialisation surplus-dominates clustering on issue A. Fig. 4. Open in new tabDownload slide (A). Welfare Comparisons with Asymmetric Donor Motivation (High Cost of Fundraising) (B). Welfare Comparisons with Asymmetric Donor Motivation (Low Cost of Fundraising). Fig. 4. Open in new tabDownload slide (A). Welfare Comparisons with Asymmetric Donor Motivation (High Cost of Fundraising) (B). Welfare Comparisons with Asymmetric Donor Motivation (Low Cost of Fundraising). Interestingly, whereas under symmetry of the donor distribution (i.e., αA = αB = α), the Nash equilibrium issue choice always surplus-dominated the alternative configuration, this is no longer the case with asymmetric donor motivation (i.e., when αA ≠ αB). The intuition is as follows. Suppose the cost of fundraising is relatively high and the share of single-issue donors caring about A is about the same as the share of single-issue donors caring about B (i.e., we are on or close to the main diagonal of Figure 4, Panel A). Issue clustering in this case is not sustainable (NGOs prefer to specialise), because clustering would leave out a large segment of the donation market unserved, and one of the two NGOs would be tempted to switch to the other issue. At the same time, specialisation is also the surplus-maximising configuration, because inducing NGOs to cluster in a situation where fundraising is rather costly would depress aggregate NGO surplus. Now let the relative sizes of the two segments of the market diverge; for instance, αA > αB (on Figure 4, Panel A, we are moving away from the main diagonal towards the lower right corner). At some point, the A-issue segment of the market becomes sufficiently large so as the NGO focused on issue B decides to switch, giving rise to the issue clustering equilibrium. Consequently, the B-issue segment of the market stops being served. Moreover, in the A-issue segment, the positive spillovers generated by the fundraising activities of the two NGOs induce them to free-ride, which leads to under-investment in fundraising. This situation is inefficient (even from NGO surplus maximisation point of view): inducing one of the NGOs to switch back to the other issue would raise aggregate NGO surplus, but this does not occur in equilibrium. Now, Let us move even further away from the diagonal. At some point the aggregate fundraising in the large A-issue segment of the donation market is, despite the free riding, large enough to generate an aggregate NGO surplus that cannot be increased by switching back one of the NGOs to issue B. In this situation, issue clustering is both the equilibrium and surplus-maximising configuration. 4.2.2. General welfare (NGOs and donors) Next, we can compare the issue choices configurations in this asymmetric-motivation version of the model from a welfare perspective that accounts for donors’ warm-glow utility of giving. In particular, we can show that the following result holds. Proposition 9. The set of parameter values under which the issue clustering equilibrium is inefficient from the welfare point of view is broader than the set under which clustering equilibrium is inefficient from the point of view of aggregate NGO surplus. Proof. See the Appendix. What is the intuition for this result? To understand it, let us refer again to Panel A in Figure 4. Let us again start with the point at the intersection of the two diagonals of the graph, i.e., located exactly in the middle of the figure, and let us move towards the south-east direction staying on the line αA + αB = 1, up to the point where this line intersects with the curve |$D_{A}^{S}$|⁠. Just before we reach this point, as explained above, the two NGOs cluster on issue A, free-ride (to some extent) on each other’s fundraising, and forcing one of the NGOs to switch to issue B would still increase the aggregate NGO surplus. However, from the donors’ perspective, at this point there is still a substantial segment (that only cares about issue B) that is not activated at all, and every unactivated donor in that segment forgoes warm-glow utility u. Consider now a point just below the intersection. At this point, inducing one NGO to switch to issue B would slightly decrease aggregate NGO surplus. It would also reduce a little bit the share of A-issue donors that become activated (because there would remain only one NGO that operates on issue A). However, because the free-riding on fundraising would now be eliminated, each NGO would conduct considerably more fundraising, each one serving a different issue; and this would activate substantially more donors in the aggregate. This would definitely increase donors’ welfare enough to over-compensate the small loss in the aggregate NGO surplus. Hence, the parameter ranges in which the equilibrium NGO clustering is inefficient from the general welfare point of view (i.e., taking into account both the aggregate NGO surplus and donors’ well-being) are wider than the dashed areas in the two panels of Figure 4. Obviously, this gap increases with u: the likelihood of inefficient clustering increases when donors have a higher warm-glow valuation. 4.3. Case 3: Sierra Leone at the End of the 1991–2002 Civil War Our third case concerns the clustering of international NGOs in Sierra Leone, towards the end of the 1991–2002 civil war. The numerous brutalities of the civil war led to a large number of amputees, many of which lived in camps built and organised by international agencies. In her book The Crisis Caravan, Linda Polman describes in detail one of such camps: Murray Town Camp, that hosted ‘226 amputees, some with a couple of close relatives, 560 people in total. … In front of the gate was a small forest of notice boards … bearing the logos of aid organisations: Médecins sans Frontières, CAUSE Canada, World Hope International, UNICEF, [and more] …' (Polman, 2010, p.63). Initially a ‘forgotten' crisis, Sierra Leone got the international media attention because of the amputees’ camps. However, then this attention led to some unexpected dynamics. ‘Partly as a result of media attention, Sierra Leone became the beneficiary of the largest UN peace mission and—in terms of dollars per head of population—the largest humanitarian aid operation anywhere in the world at the time. Around three hundred INGOs rushed to the little country. Even organisations that were not there specifically to help amputees used photos of people in Murray Town Camp in their fund-raising campaigns. “It’s never been so easy to collect money as it is with the pictures of these poor devils,” said an INGO staff member in Freetown' (Polman, 2010, p.66) The detailed description by Polman clearly indicates that while other types of projects were highly needed in Sierra Leone, the massive willingness-to-give by donors (moved by media images, especially those of children) to amputee projects implied that an inefficiently high number of NGO activities and projects concentrated on this type, whereas other kinds of activities were underfunded. This huge media attention and private aid inflows earmarked to this type of projects created deeply perverse incentives: One [international] NGO had already offered to build a whole new neighbourhood for them at the edge of the city … [But] the amputees refused to leave … because in Murray Town Camp it was easy for foreign journalists, donors, and aid organisations to find them. Nor that such visitors could steer clear of the camp even if they wanted to. The amputees were the icons of Sierra Leone’s civil war. Of all the war victims in West Africa, foreign aid workers tried hardest to be associated with them. (Polman, 2010, p. 64) Our asymmetric potential market model provides one explanation for the above pattern. Sierra Leone initially was a forgotten crisis. In other words, the share of potential donors caring about this issue was rather small: hence, (almost) all the NGOs focused on other issues. The concentrated media attention on the amputees suddenly moved the donor preferences in such a way that now the majority of donors started to care about the amputees (and more broadly about Sierra Leone) issue. Consequently, (almost) all the NGOs rushed to carry out their projects on this issue. This new issue clustering equilibrium was—according to Polman—highly inefficient: it would have been much better if some NGOs focused on this issue, whereas others devoted their resources on other equally deserving humanitarian problems. In terms of Figure 4, the new equilibrium seems to be located in the dashed area. 5. Application: Intertemporal Issue Choice In this section, we develop an application of our baseline model to the problem of endogenous timing of projects and fundraising campaigns by humanitarian NGOs. We focus on explaining some of the key patterns discussed in the introduction section. Consider a setting with a large-scale humanitarian crisis. The choice between two ‘issues' by NGOs in this context can be interpreted as the choice between (i) intervening early/immediately (e.g., engaging in emergency care projects), or (ii) intervening later (e.g., carrying out reconstruction projects). Our principal objective in this section is to analyse the conditions under which NGOs decide to cluster temporally, i.e., both NGOs rush to do emergency care, or both wait to intervene later. The quotations in the introduction of this paper seems to suggest that the key reason for early inter-temporal clustering and the lack of NGOs conducting post-emergency reconstruction is that reconstruction projects, while being fundamentally important, are much less attractive from the perspective of fundraising. We adapt our basic model to formalise this argument and to verify its validity and limits. 5.1. Setup Assume there are two periods, t = 1, 2. The NGOs have two projects which can be implemented sequentially: project A gets implemented in period 1 while project B is implemented in period 2. The structure of the game is now somewhat different from the baseline model. Specifically, as before, the fixed pool of donors is characterised by three different types of donors in terms of the nature of their warm-glow utility pairs (UA, UB) on the issues A and B. Share α ≤ 1|$/$|2 of donors only care about period 1 (i.e., have warm-glow utilities UA = U and UB = 0). These donors consider that saving lives in the humanitarian emergency situation is the only imperative. Symmetrically, a share α ≤ 1|$/$|2 of donors only care about period 2 (i.e., have warm-glow utilities UA = 0 and UB = U). These donors consider that long-run projects are fundamental (for example, because they might ensure that the emergency would not arise in the future). Finally, the remaining fraction 1 − 2α of donors care equally about the projects in the two periods 1 and 2 (i.e., they have warm-glow utilities UA = UB = U). As before, we assume that the value of the warm-glow utility U is larger that the resource cost of giving (i.e., U > 1). Donors may be now activated sequentially by one or the other NGO. The timing is as follows: Stage 1. NGOs decide simultaneously whether to activate donors in period 1 (conducting project A) or in period 2 (conducting project B); Stage 2. NGOs decide on their fundraising efforts. This, in turn, occurs simultaneously if the NGO have chosen to activate donors in the same period, or sequentially if they have chosen to activate them in different periods. Furthermore, we assume that both NGOs discount the payoffs from delaying project implementation from period 1 to period 2 by a factor δ ∈ (0, 1). To insure that the (simultaneous or sequential) equilibrium values of yi are below 1, we assume again that ϕ > 1. When both NGOs activate donors in period 1 or in period 2, the fundraising competition game (the second stage) is a simultaneous-move one, and the NGOs compete for funds as in the benchmark model under clustering. Hence, their output functions are: $$\begin{eqnarray} Q_{k}^{11} &=&(y_{1}^{11}+y_{2}^{11})\frac{(1-\alpha )}{2}-\phi \frac{\left( y_{k}^{11}\right) ^{2}}{2}, \\ Q_{k}^{22} &=&(y_{1}^{22}+y_{2}^{22})\frac{\left( 1-\alpha \right) }{2}-\phi \frac{\left( y_{k}^{22}\right) ^{2}}{2}. \end{eqnarray}$$ Optimisation by NGOs gives the following equilibrium fundraising efforts and output levels: $$\begin{align*} y^{11}=y^{22}=y^{tc}=\frac{1-\alpha }{2\phi }, \end{align*}$$ $$\begin{eqnarray} Q^{11}=Q^{22}=Q^{tc}=\frac{3}{4}\frac{(1-\alpha )^{2}}{2\phi }, \end{eqnarray}$$(15) where the superscript tc stands for time clustering. If, conversely, one NGO chooses to conduct its project (and thus to raise funds) in period 1 while its rival does so in period 2, then the first-period NGO obtains an output level equal to: $$\begin{align*} Q_{1}^{12}=y_{1}^{12}(\alpha +1-2\alpha )-\phi \frac{\left( y_{1}^{12}\right) ^{2}}{2}=y_{1}^{12}(1-\alpha )-\phi \frac{\left( y_{1}^{12}\right) ^{2}}{2}, \end{align*}$$ while the output level of the second NGO equals: $$\begin{align*} Q_{2}^{12}=y_{2}^{12}\left( 1-y_{1}^{12}\right) \left( 1-2\alpha \right) +y_{2}^{12}\alpha -\phi \frac{\left( y_{2}^{12}\right) ^{2}}{2}. \end{align*}$$ In this version of the model, the importance of the temporal dimension comes from the fact that the NGO acting in the first period obtains donations from the donors activated by its own campaign (i.e., the donors with the ‘deafness' level θA below |$y_{1}^{12}$|⁠). Hence, given the uniform distribution, the fraction |$y_{1}^{12}$| of the α (emergency-motivated) donors and of 1 − 2α donors that are equally motivated about period 1 or period 2 projects, are activated. The second NGO, which conducts its campaign with a delay, gets access to donors who were not activated by NGO 1 (which equals to the share |$\left( 1-y_{1}^{12}\right)$|⁠), who get activated by NGO 2’s campaign (i.e., the fraction |$y_{2}^{12}$| of those), and who are equally ready to give to period 1 or period 2 projects (who are a fraction 1 − 2α). In addition, NGO 2 gets donations from activated donors who only care about period 2 projects (a fraction |$y_{2}^{12}\alpha$|⁠). The first-order conditions of the corresponding optimisation problems of the two NGOs give the equilibrium fundraising efforts in this case as: $$\begin{align*} y_{1}^{12}=\frac{1-\alpha }{\phi }, \end{align*}$$ and: $$\begin{align*} y_{2}^{12}=\left( \frac{1-\alpha }{\phi }\right) \left[ 1-\frac{\left( 1-2\alpha \right) }{\phi }\right] . \end{align*}$$ The equilibrium output levels are then: $$\begin{eqnarray} Q_{1}^{12} &=&\phi \frac{\left( y_{1}^{12}\right) ^{2}}{2}=\frac{\left( 1-\alpha \right) ^{2}}{2\phi }\,\, \\ Q_{2}^{12} &=&\phi \frac{\left( y_{2}^{12}\right) ^{2}}{2}=\frac{\left( 1-\alpha \right) ^{2}}{2\phi }\left[ 1-\frac{\left( 1-2\alpha \right) }{\phi }\right] ^{2}. \end{eqnarray}$$ 5.2. Equilibrium Analysis We can show the following proposition. Proposition 10. The equilibrium in intertemporal issue choice is unique. It is: (i)‘Rushing to emergency' (i.e., clustering in period 1), if (a) the NGOs are relatively impatient (i.e., δ < 3|$/$|4) or (b) NGOs are relatively patient (i.e., |$\delta \in \left( \frac{3}{4},1\right)$|) and the cost of fundraising is relatively low (i.e., |$1\le \phi \lt \frac{2}{1-\frac{\sqrt{3}}{2\sqrt{ \delta }}}\left( \frac{1}{2}-\alpha \right)$|); (ii)Intertemporal specialisation (i.e., one NGO carries out its project in period 1, whereas the second—in period 2), if NGOs are relatively patient (i.e., |$\delta \in \left( \frac{3}{4},1\right)$|) and the cost of fundraising is sufficiently high (i.e., |$\phi \gt \frac{2}{1-\frac{\sqrt{ 3}}{2\sqrt{\delta }}}\left( \frac{1}{2}-\alpha \right)$|). Proof. See the Appendix. The intuition for this result is the following. First, (i) says that clustering in period 1 is obviously the equilibrium outcome when the NGOs are impatient and discount significantly future outcomes. In this set-up this happens when the discount factor δ is below 3|$/$|4. When however NGOs are sufficiently patient (namely with δ > 3|$/$|4), the equilibrium project choices involves the three typical effects as highlighted in Proposition 2. As before, clustering on period 1 generates some informational fundraising spillovers, and a positive activation effect across NGOs. While rushing to emergency, NGOs face as well a direct donation–competition effect because they both compete for fundraising in this same period. Finally, the third effect (implicit fundraising-coordination) also kicks in, with however a slight different twist due to the asymmetry generated by the sequential timing nature of the intertemporal game. Indeed, and contrary to the simultaneous issue choice game of the baseline model, the first period NGO under intertemporal specialisation is now in a monopoly position to ‘awaken' non-specific donors. The second period NGO only gets the residual share of these donors not activated during the first period. This confers in the intertemporal specialisation regime a strong strategic advantage to the first period NGO.9 This strategic advantage to play first on fundraising creates a strong incentive to ‘rush to emergency' and therefore to cluster on the first period issue. As a consequence, equilibrium clustering occurs for a larger set of parameter configurations than in Proposition 2.10 5.3. Welfare 5.3.1. Aggregate NGO surplus Also in this intertemporal extension one may undertake an efficiency and welfare comparison of the ‘rush to emergency' and ‘intertemporal specialisation' regimes. Proposition 11. (i) The ‘rush to emergency' regime is the equilibrium outcome and maximises the aggregate NGO surplus when (a) The NGOs are sufficiently impatient (i.e., δ < 1|$/$|2), (b) the NGOs are sufficiently patient (i.e., δ > 3|$/$|4) and the cost of fundraising is sufficiently low (i.e., |$\phi \lt \frac{2\left( \frac{1}{2}-\alpha \right) }{1- \sqrt{\frac{1}{2\delta }}}$|); (ii) The ‘rush to emergency' is an equilibrium outcome and is NGO surplus-dominated by intertemporal specialisation, when the NGOs are relatively impatient (i.e., 1|$/$|2 < δ < 3|$/$|4) and the cost of fundraising is relatively high (i.e., |$\frac{2}{1-\frac{\sqrt{3}}{2\sqrt{ \delta }}}\left( \frac{1}{2}-\alpha \right) \lt \phi$|). Proof. See the Appendix. Two conditions need to be satisfied for rush to emergency to be dominated by intertemporal specialisation. First, the discount factor has to be large enough (i.e., δ > 1|$/$|2), for otherwise NGOs will obviously only be concerned by their first period payoffs. Second, the fundraising technology should not be too efficient (i.e., |$2/\left( 1-\sqrt{3 }/2\sqrt{\delta }\right) \left( \frac{1}{2}-\alpha \right) \lt \phi$|⁠). In this case, the informational spillover effect that NGOs have on each other in the ‘rush to emergency' regime is not too strong. The crowding out effect of first period NGO fundraising on second period NGO fundraising effort under intertemporal specialisation is also not too strong. In such a case, the positive aspect for NGO surplus of increased market power on specific donors under intertemporal specialisation outweighs the costs of crowding out of first period NGO fundraising on second period NGO fundraising effort on non-specific donors, as well as the benefit of informational spillovers of clustering on the first period project. 5.3.2. General welfare (NGOs and donors) Finally, we can evaluate the equilibria of this modified model from the general welfare point of view, i.e., taking into account also donors’ welfare. In particular, we can show that the following result holds. Proposition 12. The set of parameter values under which the ‘rush to emergency' equilibrium is inefficient from the welfare point of view is broader than the set under which the ‘rush to emergency' equilibrium is inefficient from the point of view of the aggregate NGO surplus. Proof. See the Appendix. The intuition is as follows. When one NGO rushes to emergency, it does not internalise the negative effects of its fundraising effort on the other NGO, if the other NGO chooses to act in the second period. At the same time, it does not internalise the informational spillovers that it provides to the other NGO, if also the second NGO chooses to act in the first period. The second NGO may decide to avoid the first negative effect on its surplus by rushing to emergency as well. This prevents donors that have a warm-glow for the second-period project to be activated. Moreover, under rush to emergency, both NGOs also tend to reduce their equilibrium fundraising efforts on the first-period donors. This, again, reduces the number of first-period donors that are awakened. For these reasons, when the donors’ warm-glow utility is large enough, rush to emergency is welfare-dominated by intertemporal specialisation. 5.4. Case 4: The 2004 Indian Ocean Tsunami On December 26, 2004, a tsunami of unprecedented power, triggered by the Sumatra-Andaman undersea earthquake, hit the coastal areas of 14 countries in Asia and Africa (with Indonesia and Sri Lanka receiving the strongest impact). It was one of the deadliest natural disasters in recent history, killing close to 230,000 people and displacing over 1.75 million people. The scale of the disaster, coinciding with it happening right after Christmas and fed by a large-scale international media coverage, led to a massive humanitarian response, both through public and private channels. The amount of private donations to international NGOs was huge: for example, Save the Children USA received over US$6 million in just four days, whereas Catholic Relief Services collected over US$1 million in three days. In total, US-based charities raised about US$1.6 billion for tsunami relief (Wallace and Wilhelm, 2005), whereas total international response (both public and private) amounted to US$17 billion (Jayasuriya and McCawley, 2010). This massive drive to give at the early stages of the disaster led an excessive focus on emergency projects, where too many NGOs engaged in projects early on but rather few wanted to carry out the post-crisis reconstruction and development projects. The report by the Joint Evaluation Report of the Tsunami Evaluation Coalition states: Exceptional international funding provided the opportunity for an exceptional international response. However, the pressure to spend money quickly and visibly worked against making the best use of local and national capacities. … Many efforts and capacities of locals and nationals were marginalised by an overwhelming flood of well-funded international agencies (as well as hundreds of private individuals and organisations), which controlled immense resources. (Telford et al., 2006, pp.18–19) Why the dynamics of NGO aid led to such an inefficiency? The then head of the French Red Cross, Jean-François Mattei notes that: ‘The particularity [of the tsunami donor appeals] resided in this unique combination of democratisation of information technologies, the ability of witnesses to become vectors of immediately available images, the underlying violence of the phenomenon, and its tragic evolution' (Mattei, 2005, p.41). He then suggests that the inefficiency had to do with the fact that NGOs found it difficult to explain to the donor public the complexity of the situation and the need to finance also the long-run projects, going beyond the emergency needs: ‘Few observers were aware of the complexity of this kind of engagement, that escapes the immediate perceptions of the expectations of the public. This implies a feeling of disconnection between the image that one has of the humanitarian [sector] and the reality found on the ground' (Mattei, 2005, p.12). In the context of our model of intertemporal issue choice, the above quotations suggest that the donors’ willingness to give was quite high, while the technological cost of raising funds was relatively low. Hence, even for relatively patient NGOs (e.g., those with long history and established reputation), the incentives to cluster in the first period were rather strong. Obviously, for less patient ones, the high willingness to give was alone a sufficient driving force for clustering in emergency-type projects. Interestingly, the tsunami case illustrates both the inter-temporal and spatial clustering problem, as the concentration of emergency projects in tsunami-hit areas went along with the relative lack of attention to other areas of the world that were facing large needs: ‘There are also neighbouring countries that are touched by the same problem, sometimes even more that the country on which the projectors are focused. One has to look also in the shadows cast by the projector lights. The mobilisation of public opinion can create terrible paradoxes: because of the emotions and emergency feelings, the concentrated flow of international aid can worsen the sentiment of neglect in the non-beneficiary areas. Thus, Darfour was erased by the tsunami, and then Niger by the Katrina hurricane …’ (Werly, 2005, p. 136). 6. Conclusion Reflecting over the deep problems of the international NGO sector, Alex De Waal writes: Specific NGO successes mask strategic failures. NGOs tend to focus their efforts on areas in which they have specialist skills, on which can make for good publicity, such as feeding centres and orphanages. Crucial areas such as sanitation and public health are relatively neglected. The charitable market is unable to fill the full spectrum of relief needs. (De Waal, 1997, p. 80) This article provided a simple economic framework for studying this and related problems. Our analysis provides interesting implications for the decentralised competitive organisation of the foreign aid industry. It highlights the importance of donors’ perceptions as a major source of difficulty of optimal fundraising coordination and efficient division of tasks between development NGOs. This is particularly salient for NGOs operating during humanitarian crises, where a strong asymmetry in donors’ awareness across different types of projects and the resulting willingness-to-give aggravates this difficulty. There are three promising avenues for future work. The first consists in testing empirically the main predictions of our model, using either the information on the geographic clustering of NGO projects or the intertemporal aspects developed in the timing-game version. Ideally, this requires having information on the baseline willingness-to-give or awareness of donors about the different causes, an exogenous (and asymmetric) variation in such willingness-to-give (for example, coming from a sudden natural shock or a large-scale outbreak of a disease), and measures of NGO project type choice before and after the shock. Given the relative scarcity of empirical work on the functioning of the development NGO sector, such analysis seems to have very high potential. Secondly, in this article we have not explored explicitly the effects of various policy instruments on the decentralised outcomes. Several instruments (tax deductions for donations, direct government grants to NGOs, registration fees, etc.) can affect both the behaviour of donors as well as the incentives of NGOs to conduct fundraising and thus indirectly to choose the type of projects. A natural next step would be to extend the analysis of our model to studying the effects of such instruments, so as to help in formulating welfare-enhancing public policies. Finally, our model disregarded the actions of NGO project beneficiaries. Enriching the model by integrating the beneficiaries as active players (as, for instance, in the models by Platteau et al., 2014 or by Aldashev and Vallino, 2019) can provide additional insights, especially concerning the potential inefficiencies of the decentralised development NGO sector. Appendix A A.1. Proof of Proposition 2 Consider the equilibrium NGO payoffs under clustering: $$\begin{align*} Q_{k}^{AA}(y_{1}^{c},y_{2}^{c})=Q_{k}^{BB}(y_{1}^{c},y_{2}^{c})=Q^{c}=\frac{3 }{4}\frac{(1-\alpha )^{2}}{2\phi }\rm{ \ for }k=1,2\rm{,} \end{align*}$$ and under specialisation: $$\begin{align*} Q_{1}^{AB}(y_{1}^{s},y_{2}^{s})=Q_{2}^{BA}(y_{1}^{s},y_{2}^{s})=Q^{s}=\frac{ \phi }{2}\frac{(1-\alpha )^{2}}{\left[ \phi +\tfrac{1}{2}-\alpha \right] ^{2} }. \end{align*}$$ Given the symmetry across NGOs, at the first stage NGOs are playing a symmetric simultaneous-move 2×2 game, where the payoffs are (Qc, Qc ) on the main diagonal of the payoff matrix, and (Qs, Qs) off the main diagonal. Hence, the necessary and sufficient condition for issue clustering equilibrium on issue A (or issue B) is Qc > Qs. This translates into the condition: $$\begin{align*} \frac{3}{4}\frac{(1-\alpha )^{2}}{2\phi }\gt \frac{\phi }{2}\frac{(1-\alpha )^{2}}{\left[ \phi +\tfrac{1}{2}-\alpha \right] ^{2}}, \end{align*}$$ or: $$\begin{align*} \phi \lt \frac{\sqrt{3}}{2-\sqrt{3}}\left[ \tfrac{1}{2}-\alpha \right] . \end{align*}$$ Hence, when |$1\le \phi \lt \frac{\sqrt{3}}{2-\sqrt{3}}\left( \frac{1}{2} -\alpha \right)$|⁠, the Nash equilibria of the first-stage game are issue clustering (on issue A or issue B). Contrarily, when |$\frac{\sqrt{3}}{2- \sqrt{3}}\left( \frac{1}{2}-\alpha \right) \lt \phi$|⁠, the Nash equilibria of the first-stage game are issue specialisation (i.e., one NGO chooses issue A and the other NGO issue B).☐ A.2. Proof of Proposition 6 Wc > Ws is equivalent to: $$\begin{align*} \frac{(1-\alpha )^{2}}{\phi }\cdot \left[ 1+2u\right] \gt \frac{\left( 1-\alpha \right) ^{2}}{\left( \phi +1-2\alpha \right) }\left[ 1+\frac{2\phi }{\phi +1-2\alpha }\cdot u\right] , \end{align*}$$ or: $$\begin{align*} \frac{\phi +1-2\alpha }{\phi }\gt \frac{1+\frac{2\phi }{\phi +1-2\alpha }\cdot u }{1+2u}, \end{align*}$$ which is always satisfied when: $$\begin{align*} \left( \phi +1-2\alpha \right) \left(\frac{1}{2}-\alpha\right )\gt u\left[ \phi ^{2}-\left[ \phi +1-2\alpha \right] ^{2}\right] . \end{align*}$$ This condition always holds since 1 − 2α > 0, thus implying: $$\begin{align*} \left( \phi +1-2\alpha \right) \left(\frac{1}{2}-\alpha\right )\gt 0\gt u\left[ \phi ^{2}- \left[ \phi +1-2\alpha \right] ^{2}\right] . \end{align*}$$ ☐ A.3. Proof of Proposition 7 Let’s introduce the following auxiliary function: $$\begin{align*} \chi \left( \phi ,X\right) =\frac{\frac{\sqrt{3}}{2}\left[ \phi ^{2}-X^{2} \right] +X\phi }{\phi ^{2}}. \end{align*}$$ We prove that there exists a constant β < 1 such that for all ϕ ≥ 1 we have: (1) when X < ϕ · β (i.e., χ(ϕ, X) < 1), we have the following NGO Nash equilibria: (i) clustering on issue A when Z < χ(ϕ, X), (ii) clustering on issue B when Z > 1|$/$|χ(ϕ, X), and (iii) NGO specialisation when χ(ϕ, X) < Z < 1|$/$|χ(ϕ, X); (2) when ϕ · β < X < ϕ (i.e., χ(ϕ, X) > 1), we only have NGO Nash equilibria with issue clustering with: (i) clustering on issue A when Z < χ(ϕ, X), (ii) clustering on issue B when Z > 1|$/$|χ(ϕ, X), and (iii) clustering on issue A and clustering on issue B are both NGO Nash equilibria when 1|$/$|χ(ϕ, X) < Z < χ(ϕ, X) (i.e., multiple clustering choice equilibria). Equilibrium NGO payoffs under the different issue choice regimes write as follows. For issue clustering, they are: $$\begin{eqnarray} Q_{k}^{AA}(y_{1}^{BB},y_{2}^{BB}) &=&\frac{3}{4}\frac{(1-\alpha _{B})^{2}}{ 2\phi }\rm{ for }k=1,2, \\ Q_{k}^{BB}(y_{1}^{BB},y_{2}^{BB}) &=&\frac{3}{4}\frac{(1-\alpha _{A})^{2}}{ 2\phi }\rm{ for }k=1,2. \end{eqnarray}$$ For issue specialisation, they are: $$\begin{eqnarray} Q_{1}^{AB} &=&Q_{AB}^{s}=\phi \frac{\left( y_{AB}^{s}\right) ^{2}}{2}=\frac{ \phi }{2}\left[ \frac{\phi \left( 1-\alpha _{B}\right) -\frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{A})}{\phi ^{2}-\frac{1}{4} \left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}}\right] ^{2}, \\ Q_{2}^{AB} &=&Q_{BA}^{s}=\phi \frac{\left( y_{BA}^{s}\right) ^{2}}{2}=\frac{ \phi }{2}\left[ \frac{\phi \left( 1-\alpha _{A}\right) -\frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{B})}{\phi ^{2}-\frac{1}{4} \left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}}\right] ^{2}. \end{eqnarray}$$ Now the equilibrium condition for NGO clustering on issue A writes as |$Q^{AA}\gt Q_{BA}^{s},$| or: $$\begin{align*} \frac{3}{4}\frac{(1-\alpha _{B})^{2}}{2\phi }\gt \frac{\phi }{2}\left[ \frac{ \phi \left( 1-\alpha _{A}\right) -\frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{B})}{\phi ^{2}-\frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}}\right] ^{2}, \end{align*}$$ which rewrites as: $$\begin{align*} \frac{1-\alpha _{A}}{1-\alpha _{B}}\lt \frac{\frac{\sqrt{3}}{2}\left[ \phi ^{2}- \frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}\right] +\left( \frac{ 1-\alpha _{A}-\alpha _{B}}{2}\right) \phi }{\phi ^{2}}. \end{align*}$$ Similarly, the equilibrium condition for NGO clustering on issue B is |$Q_{k}^{BB}\gt Q_{AB}^{s},$|or: $$\begin{align*} \frac{1-\alpha _{B}}{1-\alpha _{A}}\lt \frac{\frac{\sqrt{3}}{2}\left[ \phi ^{2}- \frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}\right] +\left( \frac{ 1-\alpha _{A}-\alpha _{B}}{2}\right) \phi }{\phi ^{2}}. \end{align*}$$ Therefore, using our auxiliary notation for X, Z, and χ(ϕ, X), the conditions for clustering on issue A and B write, respectively, as: $$\begin{eqnarray} Z &\lt &\chi \left( \phi ,X\right) \rm{ for clustering on issue }A, \\ Z &\gt &1/\chi \left( \phi ,X\right) \rm{ for clustering on issue }B\rm{.} \end{eqnarray}$$(A1) Finally, we have to check that χ(ϕ, X) > 1 if and only if: $$\begin{align*} \Omega (X)=\frac{\sqrt{3}}{2}\left[ \phi ^{2}-X^{2}\right] +X\phi -\phi ^{2}\gt 0. \end{align*}$$ The polynomial Ω(X) has two roots in terms of X :  X+ = ϕ and X− = ϕ · β with |$\beta =\frac{2-\sqrt{3}}{\sqrt{3}}\lt 1.$| Hence χ(ϕ, X) > 1 if and only if ϕ · β < X < 1|$/$|2 < ϕ and χ(ϕ, X) < 1 when X < ϕ · β . From this and (A1) it follows that: (1) when X < ϕ · β, then χ(ϕ, X) < 1 < 1|$/$|χ(ϕ, X). Hence, we have the following equilibria: (i) NGOs cluster on issue A when Z < χ(ϕ, X), (ii) they cluster on issue B when Z > 1|$/$|χ(ϕ, X), and (iii) NGOs specialise in the intermediate region χ(ϕ, X) < Z < 1|$/$|χ(ϕ, X). (2) when ϕ · β < X < 1|$/$|2 < ϕ, then χ(ϕ, X) > 1 > 1|$/$|χ(ϕ, X). Hence: (i) NGOs cluster on issue A when Z < 1|$/$|χ(ϕ, X), (ii) they cluster on issue B when Z > χ(ϕ, X), and (iii) they clustering either on issue A or issue B in the intermediate region 1|$/$|χ(ϕ, X) < Z < χ(ϕ, X) (i.e., there are multiple issue-choice equilibria). ☐ A.4. Proof of Proposition 8 Under issue clustering (respectively, on issue A and B) and non-cooperative fundraising competition at the second stage, the aggregate surplus writes as: $$\begin{align*} 2Q_{A}^{c}=\frac{3}{4}\frac{(1-\alpha _{B})^{2}}{\phi }\rm{ and } 2Q_{B}^{c}=\frac{3}{4}\frac{(1-\alpha _{A})^{2}}{\phi }. \end{align*}$$ On the other hand, under issue specialisation and non-cooperative fundraising competition at the second stage, the surplus equals: $$\begin{eqnarray} Q_{BA}^{s}+Q_{AB}^{s} &=&\frac{\phi }{2}\left[ \frac{\phi \left( 1-\alpha _{A}\right) -\frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{B})}{\phi ^{2}-\frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}} \right] ^{2} \\ &&+\,\frac{\phi }{2}\left[ \frac{\phi \left( 1-\alpha _{B}\right) -\frac{1}{2} \left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{A})}{\phi ^{2}-\frac{1}{4 }\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}}\right] ^{2}. \end{eqnarray}$$ Compare clustering on issue A to issue specialisation. The specialisation configuration dominates clustering on issue A when the following condition holds: $$\begin{eqnarray} \frac{(1-\alpha _{B})^{2}}{\phi }\cdot \frac{3}{4} &\lt &\frac{\phi }{2}\left[ \frac{\phi \left( 1-\alpha _{A}\right) -\frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{B})}{\phi ^{2}-\frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}}\right] ^{2} \\ &&+\,\frac{\phi }{2}\left[ \frac{\phi \left( 1-\alpha _{B}\right) -\frac{1}{2} \left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{A})}{\phi ^{2}-\frac{1}{4 }\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}}\right] ^{2}, \end{eqnarray}$$ which can be rewritten compactly as: $$\begin{align*} \frac{3}{4}\left( \frac{\phi ^{2}-X^{2}}{\phi }\right) ^{2}\lt \frac{\left[ \phi Z-X\right] ^{2}+\left[ \phi -XZ\right] ^{2}}{2}. \end{align*}$$ At the same time, the condition for clustering on issue A to be the Nash equilibrium writes as |$Z\phi ^{2}-X\phi \lt \frac{\sqrt{3}}{2}\left[ \phi ^{2}-X^{2}\right] ,$| which can also be rewritten as: $$\begin{align*} \left( Z\phi -X\right) ^{2}\lt \frac{3}{4}\left( \frac{\phi ^{2}-X^{2}}{\phi } \right) ^{2}. \end{align*}$$ Clearly, as in the symmetric case αA = αB = α, the two conditions do not coincide. In particular, the equilibrium clustering on issue A is surplus dominated by the specialisation configuration if: $$\begin{align*} \left( Z\phi -X\right) ^{2}\lt \frac{3}{4}\left( \frac{\phi ^{2}-X^{2}}{\phi } \right) ^{2}\lt \frac{\left[ \phi Z-X\right] ^{2}+\left[ \phi -XZ\right] ^{2}}{2 }. \end{align*}$$ ☐ A.5. Proof of Proposition 9 The general welfare levels under issue clustering (on issues A or B) and issue specialisation write, respectively, as: $$\begin{eqnarray} W_{A}^{c} &=&2Q_{A}^{c}+2\left( 1-\alpha _{B}\right) y_{A}^{c}\cdot u, \\ W_{B}^{c} &=&2Q_{B}^{c}+2\left( 1-\alpha _{A}\right) y_{B}^{c}\cdot u, \\ W_{AB}^{s} &=&Q_{BA}^{s}+Q_{AB}^{s}+\phi \left[ \left( y_{AB}^{s}\right) ^{2}+\left( y_{BA}^{s}\right) ^{2}\right] \cdot u. \end{eqnarray}$$ These expressions can be rewritten as: $$\begin{eqnarray} W_{A}^{c} &=&\frac{\left( 1-\alpha _{B}\right) ^{2}}{2\phi }\left[ \frac{3}{2 }+2u\right] =2Q_{A}^{c}\left[ 1+\frac{4}{3}u\right] , \\ W_{B}^{c} &=&\frac{\left( 1-\alpha _{A}\right) ^{2}}{2\phi }\left[ \frac{3}{2 }+2u\right] =2Q_{B}^{c}\left[ 1+\frac{4}{3}u\right] , \\ W_{AB}^{s} &=&2\left[ Q_{BA}^{s}+Q_{AB}^{s}\right] \left[ \frac{1}{2}+u \right] . \end{eqnarray}$$ Given that: $$\begin{eqnarray} 2Q_{A}^{c}=\frac{3}{4}\frac{(1-\alpha _{B})^{2}}{\phi }\rm{,}\quad 2Q_{B}^{c}=\frac{3}{4}\frac{(1-\alpha _{A})^{2}}{\phi }, \end{eqnarray}$$(A2) and: $$\begin{eqnarray} Q_{BA}^{s}+Q_{AB}^{s} &=&\frac{\phi }{2}\left[ \frac{\phi \left( 1-\alpha _{A}\right) -\frac{1}{2}\left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{B})}{\phi ^{2}-\frac{1}{4}\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}} \right] ^{2} \\ &&+\frac{\phi }{2}\left[ \frac{\phi \left( 1-\alpha _{B}\right) -\frac{1}{2} \left( 1-\alpha _{A}-\alpha _{B}\right) (1-\alpha _{A})}{\phi ^{2}-\frac{1}{4 }\left( 1-\alpha _{A}-\alpha _{B}\right) ^{2}}\right] ^{2}, \end{eqnarray}$$ the comparison between, say, clustering on issue A and issue specialisation shows immediately that specialisation welfare-dominates clustering if and only if: $$\begin{align*} 2Q_{A}^{c}\left[ 1+\frac{4}{3}u\right] \lt 2\left[ Q_{BA}^{s}+Q_{AB}^{s}\right] \left[ \frac{1}{2}+u\right] , \end{align*}$$ or: $$\begin{align*} \theta \left( u\right) \equiv \frac{1+\frac{4}{3}u}{1+2u}\lt \frac{ Q_{BA}^{s}+Q_{AB}^{s}}{2Q_{A}^{c}}. \end{align*}$$ Given that θ(u) <1, when there is inefficient clustering equilibrium on issue A from the point of view of total NGO surplus, there is also inefficient issue clustering equilibrium from the general welfare point of view. Also note that the function θ(u) is decreasing in u; therefore, the likelihood of inefficient NGO clustering is increased when donors have a higher warm-glow valuation, and the inefficient NGO clustering areas increases with u. The analysis for clustering on issue B is obtained in a symmetric way. ☐ A.6. Proof of Proposition 10 Clustering in period 1 (‘rushing' to conduct projects early) occurs at the equilibrium when: $$\begin{eqnarray} Q^{11}\gt \delta \cdot Q_{2}^{12}, \end{eqnarray}$$(A3) or when: $$\begin{align*} \frac{(1-\alpha )^{2}}{2\phi }\cdot \frac{3}{4}\gt \delta \cdot \frac{\left( 1-\alpha \right) ^{2}}{2\phi }\left[ 1-\frac{\left( 1-2\alpha \right) }{\phi }\right] ^{2}. \end{align*}$$ This condition always holds if |$\frac{3}{4\delta }\gt 1$|⁠, or if |$\delta \lt \frac{3 }{4}.$| Now when |$\delta \in \left( \frac{3}{4},1\right]$|⁠, the previous expression reduces to: $$\begin{align*} \phi \lt \frac{\left( 1-2\alpha \right) }{1-\frac{\sqrt{3}}{2\sqrt{\delta }}}= \frac{2}{1-\frac{\sqrt{3}}{2\sqrt{\delta }}}\left( \frac{1}{2}-\alpha \right) . \end{align*}$$ Similarly, clustering on period 2 (i.e., both NGOs strategically delay their interventions) would occur in equilibrium when: $$\begin{align*} \delta \cdot Q^{22}\gt Q_{1}^{12}, \end{align*}$$ which can be rewritten as: $$\begin{align*} \delta \cdot \frac{(1-\alpha )^{2}}{2\phi }\cdot \frac{3}{4}\gt \frac{\left( 1-\alpha \right) ^{2}}{2\phi }, \end{align*}$$ or: $$\begin{align*} \delta \cdot \frac{3}{4}\gt 1 \end{align*}$$ which is obviously unfeasible. In other words, each NGO always prefers to act early provided that the other NGO is entering later. Finally, intertemporal specialisation (non-clustering) by NGOs (i.e., one NGO conducts the emergency care project, whereas the second engages in post-reconstruction projects) is the equilibrium outcome when: $$\begin{align*} Q^{11}\lt \delta \cdot Q_{2}^{12}\rm{ and }\delta \cdot Q^{22}\lt Q_{1}^{12}. \end{align*}$$ The second inequality is always satisfied. The first inequality holds when |$\delta \in \left( \frac{3}{4},1\right]$| and: $$\begin{align*} \phi \gt \frac{\left( 1-2\alpha \right) }{1-\frac{\sqrt{3}}{2\sqrt{\delta }}}= \frac{2}{1-\frac{\sqrt{3}}{2\sqrt{\delta }}}\left( \frac{1}{2}-\alpha \right) . \end{align*}$$ ☐ A.7. Proof of Proposition 11 The aggregate NGO surplus under ‘rush to emergency' is: $$\begin{align*} 2Q^{11}=\frac{3}{4}\cdot \frac{(1-\alpha )^{2}}{\phi }. \end{align*}$$ Under intertemporal specialisation, the aggregate NGO surplus writes as: $$\begin{align*} Q_{1}^{12}+\delta \cdot Q_{2}^{12}=\frac{\left( 1-\alpha \right) ^{2}}{2\phi }+\delta \cdot \frac{\left( 1-\alpha \right) ^{2}}{2\phi }\left[ 1-\frac{ \left( 1-2\alpha \right) }{\phi }\right] ^{2}. \end{align*}$$ Thus, ‘rush to emergency' is surplus-dominant when the following relationship holds: $$\begin{align*} \frac{(1-\alpha )^{2}}{\phi }\cdot \frac{3}{4}\gt \frac{\left( 1-\alpha \right) ^{2}}{2\phi }+\delta \cdot \frac{\left( 1-\alpha \right) ^{2}}{2\phi }\left[ 1-\frac{\left( 1-2\alpha \right) }{\phi }\right] ^{2} \end{align*}$$ or: $$\begin{align*} \frac{3}{2}\gt 1+\delta \cdot \left[ 1-\frac{\left( 1-2\alpha \right) }{\phi } \right] ^{2}, \end{align*}$$ which always holds provided that δ ≤ 1|$/$|2. Conversely, when δ > 1|$/$|2, the condition rewrites as: $$\begin{align*} 1\le \phi \lt \frac{2}{1-\frac{\sqrt{3}}{2\sqrt{\delta }}}\left( \frac{1}{2} -\alpha \right) . \end{align*}$$ Note as well that the condition for ‘rush to emergency' to be an equilibrium writes as δ < 3|$/$|4, or |$\delta \in \left( \frac{3}{4},1\right)$| and: $$\begin{align*} \phi \lt \frac{2\left( \frac{1}{2}-\alpha \right) }{1-\sqrt{\frac{1}{2\delta }}} . \end{align*}$$ It can be easily seen that: $$\begin{align*} \frac{2}{1-\frac{\sqrt{3}}{2\sqrt{\delta }}}\left( \frac{1}{2}-\alpha \right) \gt \frac{2\left( \frac{1}{2}-\alpha \right) }{1-\sqrt{\frac{1}{2\delta }}}. \end{align*}$$ Thus, for δ > 3|$/$|4, ‘rush to emergency' is the equilibrium outcome and surplus-dominates intertemporal specialisation, when |$\phi \lt \frac{2\left( \frac{1}{2}-\alpha \right) }{1-\sqrt{\frac{1}{2\delta }}}$|⁠. For 1|$/$|2 < δ < 3|$/$|4, ‘rush to emergency' is always an equilibrium outcome but is surplus-dominated by intertemporal specialisation when: $$\begin{align*} \frac{2}{1-\frac{\sqrt{3}}{2\sqrt{\delta }}}\left( \frac{1}{2}-\alpha \right) \lt \phi . \end{align*}$$ Additional Supporting Information may be found in the online version of this article: Online Appendix Replication Package Notes The data and codes for this paper are available on the Journal website. They were checked for their ability to replicate the results presented in the paper. We thank Rachel Kranton (Editor), two anonymous referees, and audiences at CIRIEC International Conference (Antwerp), SITE (Stockholm), and NGO workshop (Frankfurt) for useful suggestions. Financial support from the Labex OSE, FNRS (FRFC grant 7106145 “Altruism and NGO performance”), and from CIRIEC International is gratefully acknowledged. Footnotes 1 See Aldashev and Navarra (2018) for a description of the major facts concerning the development NGO sector. 2 See our complete discussion in Sections 2 and 3. 3 Formally, we have |$\alpha (y_{1}^{c}+y_{2}^{c})\lt \alpha y_{1}^{s}+\alpha y_{2}^{s}$|⁠. 4 Formally, for a given total fundraising effort y1 + y2 = y the fraction of multiple issue donors awakened under clustering is (1 − 2α)(y1 + y2) while the fraction of multiple issue donors awakened under specialisation is (1 − 2α)[y1 + y2 − y1y2]. The latter expression is smaller than the former, reflecting the awareness spillover effect under clustering. 5 Alternatively, we could have considered a more complicated index function of these projects’ outputs, taking into account some degree of complementarity between the NGOs’ output levels. While this would significantly complicate the analysis, the basic feature that coordination allows NGOs to partly internalise the direct donation–competition effect of fundraising will still be present. 6 Indeed, under full coordination, the NGOs choose between the clustering and specialisation regime depending on 2QCF≷ 2QSF, while under fundraising coordination only, the choice between clustering and specialisation depends on QCF≷ QSF for each NGO. This provides the same equilibrium regime choice. 7 In the case of asymmetric distribution of donors across issues, the conditions will not coincide (see Section 4). 8 Note that the restrictions that αA ≥ 0, αB ≥ 0 and αA + αB ≤ 1 can be simply restated as |$Z\in \left[ 2X, \frac{1}{2X}\right]$| and |$X\in \left[ 0,\frac{1}{2}\right]$|⁠. 9 Indeed, the first period NGO is more aggressive in its fundraising effort than in the simultaneous issue choice game case of Proposition 1 (i.e., |$y_{1}^{12}\gt y_{1}^{s}=y^{s})$|⁠, while conversely the second period NGO is producing a weaker fundraising effort (ie |$y_{2}^{12}\lt $||$y_{2}^{s}=y^{s}$|⁠). Formally, this can be seen from: |$y_{1}^{12}=\frac{1-\alpha }{\phi }\gt \frac{ 1-\alpha }{\phi +\tfrac{1}{2}-\alpha }=y_{1}^{s}$| and |$y_{2}^{12}=\left( \frac{1-\alpha }{\phi }\right) \left[ 1-\frac{\left( 1-2\alpha \right) }{ \phi }\right] \lt \frac{1-\alpha }{\phi +\tfrac{1}{2}-\alpha }=y_{2}^{s}$|⁠. 10 This can be seen by the fact that in Proposition 10, equilibrium clustering occurs when the cost of fundraising ϕ is below the upper bound |$\frac{2 }{1-\frac{\sqrt{3}}{2\sqrt{\delta }}}\left( \frac{1}{2}-\alpha \right),$| which is larger than the corresponding upperbound |$\frac{\sqrt{3}}{2-\sqrt{3} }\left( \frac{1}{2}-\alpha \right)$| found in Proposition 1. References Aldashev G. , Marini M., Verdier T. ( 2014 ). ‘ Brothers in alms? Coordination between nonprofits on markets for donations ’, Journal of Public Economics , vol. 117 ( C ), pp. 182 – 200 . Google Scholar Crossref Search ADS WorldCat Aldashev G. , Navarra C. 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Attar,, Andrea;Mariotti,, Thomas;Salanié,, François

doi: 10.1093/ej/ueaa041pmid: N/A

Abstract We study resource allocation under private information when the planner cannot prevent bilateral side trading between consumers and firms. Adverse selection and side trading severely restrict feasible trades: each marginal quantity must be fairly priced given the consumer types who purchase it. The resulting social costs are twofold. First, second-best efficiency and robustness to side trading are in general irreconcilable requirements. Second, there actually exists only one budget-feasible allocation robust to side trading, which deprives the planner from any capacity to redistribute resources between different types of consumers. We discuss the relevance of our results for insurance and financial markets. The theory of incentives identifies the holding of private information by economic agents as a fundamental constraint on the allocation of resources (Hurwicz, 1973). Standard aggregate resource constraints must accordingly be supplemented by incentive-compatibility constraints that reflect the agents’ ability to conceal their private information (Myerson, 1979; 1982). The problem of the optimal allocation of resources then reduces to that of characterising informationally constrained efficient, or second-best, allocations (Harris and Townsend, 1981). The key finding is that a trade-off arises between redistribution and incentives (Mirrlees, 1971). A crucial assumption of theories of the second-best is that, although individual types are unobservable, individual trades can be perfectly monitored by the planning authority. Because few, if any, economic institutions have the required ability to monitor all individual trades, this calls for an explicit consideration of the role of side trading in the theory of resource allocation under private information, as first pointed out by Hammond (1979). To this end, we consider a general environment in which firms can provide a divisible good to privately informed consumers who may be of two types. Consumers’ preferences satisfy a single-crossing condition, and there is adverse selection in that consumers who are more willing to trade are also more costly to serve; private values arise as a limiting case when consumers’ types are not payoff-relevant for the firms selling to them. This framework encompasses many applications, including the standard Rothschild and Stiglitz (1976) insurance economy as a prominent example. In this setting, we characterise the allocations that can be achieved by a planner who observes neither consumers’ types nor the trades they may conduct with firms. To do so, we refine the standard notion of incentive-feasibility by focusing on allocations that are robust to side trading. This reflects two additional constraints on resource allocation. First, the planner cannot force consumers to trade with him; this is the case, for instance, when consumers can opt out of a publicly provided health-insurance plan, as in the current German system. Second, he cannot prevent them from engaging in mutually advantageous additional trades with a firm. We formalise these constraints by requiring the planner to offer a tariff such that no firm, acting as an entrant, can guarantee itself a positive profit by offering complementary side trades. This approach provides us with a modified criterion of incentive feasibility which is useful for evaluating the social costs of side trading. Focusing on two-type environments affords us a straightforward comparison with standard characterisations of the second-best efficiency frontier in both private-value (Bierbrauer and Boyer, 2014) and common-value (Prescott and Townsend, 1984; Crocker and Snow, 1985; Bisin and Gottardi, 2006) environments. We show that the social costs of side trading are twofold. First, second-best allocations are typically not robust to side trading, so that the planner’s inability to monitor consumers’ trades has significant welfare implications. Second, only one budget-feasible allocation is robust to side trading, so that the third-best efficiency frontier reduces to a point: the threat of side trading effectively deprives the planner from any capacity to redistribute resources between different types of consumers. The allocation we characterise is thus the natural candidate for a competitive equilibrium, but, being the only feasible one under side trading, little, if anything, can be argued about its desirability. A distinctive feature of our approach is that we model side trade as bilateral contracts between a consumer and a firm. This reflects our dissatisfaction with the standard way of representing unobservable side trades as transactions on Walrasian markets, which would call for a centralised market institution to ensure that all these trades take place at the same price. Bilateral trading plays a key role in our analysis. Our key Lemma 1, in particular, shows that budget-feasible allocations robust to side trading have a very peculiar price structure: each marginal quantity, or layer, is priced at the cost of serving the types who purchase it. This form of competitive pricing, reminiscent of Akerlof (1970), implies that there are no cross-subsidies between these layers, though there may be cross-subsidies between types. When the allocation is interior and separating, linear pricing can emerge only in the private-value limiting case. Lemma 1 has a simple but important implication that we state in Theorem 1: no second-best allocation in which only one incentive compatibility-constraint binds is robust to side trading. The reason is that, by the standard efficiency-at-the-top property, consumers for which this constraint binds must trade at the margin at the cost of serving them. As a result, the layer that connects the trades of the two types cannot be priced at the cost of serving the type who is the most willing to trade. But then, by Lemma 1, there always exists some side trade that a firm finds it profitable to conduct with at least one consumer type. For instance, in the Rothschild and Stiglitz (1976) insurance economy, any second-best allocation in which the high-risk type’s incentive-compatibility constraint binds can be exploited by an entrant offering complementary coverage at a premium rate slightly higher than the high-risk fair premium rate, which this type is willing to trade along with the coverage provided by the allocation for the low-risk type. Our second main result, Theorem 2, states that, among the allocations that feature no cross-subsidies between layers, only one is robust to side trading, namely, the Pareto-efficient one that maximises the utility of the consumer type who is the less willing to trade. This uniqueness result stands in stark contrast with the nondegenerate second-best efficiency frontier that emerges from the standard trade-off between redistribution and incentives. To complete our characterisation, we evaluate whether this allocation can be second-best, hence considering the situations not covered by Theorem 1. Theorem 3 shows that a second-best allocation robust to side trading must either feature pooling of the two consumers’ types, or each type purchasing her first-best quantity. We argue that these situations can only occur under very special assumptions on preferences and costs. Thus the unique third-best allocation typically does not belong to the second-best efficiency frontier. Related Literature While the constraints induced by private information on resource allocation are by now well understood, less is known about the impact of side trading on feasibility and redistribution. Starting with the early contributions of Hammond (1979; 1987), Allen (1985) and Jacklin (1987), several authors have attempted to identify the limits to risk sharing generated by consumers’ side trading in financial markets. Cole and Kocherlakota (2001), Golosov and Tsyvinski (2007) and Farhi et al. (2009) have analysed different private-value environments in which the planner is constrained by the existence of Walrasian markets on which privately informed consumers can complement their trades with the planner by trading linearly priced commodities. This raises two sets of questions, which we address in this paper. First, the existence of unobservable transactions is at odds with the idea that all trades take place in a centralised Walrasian market where a single market-clearing price is quoted—the issue is not so much that the quantities traded are unobservable, which is consistent with the functioning of a Walrasian market, but rather that side trades may take place at different prices and that bilateral contracting prevents the planner from monitoring the terms of these trades. Second, if one sticks to the Walrasian paradigm, extending the approach to incorporate common values and adverse selection presents severe conceptual difficulties (Prescott and Townsend, 1984; Rustichini and Siconolfi, 2008); a possible way out is to rely on an Akerlof-like (1970) equilibrium, which however only obtains under linear utilities and/or indivisibilities (Attar et al., 2011; Philippon and Skreta, 2012; Tirole, 2012). We hence depart from the above literature in two ways. First, we offer an alternative representation of side trading, which we essentially regard as a bilateral rather than a centralised process. Second, we focus on trade under common values; hence, in a bilateral relationship, a firm’s profit directly depends on the types of the consumers it trades with, arguably a prominent feature of insurance and financial markets. The constraints induced by private contracting on redistribution between workers who are privately informed of their productivities have also been investigated by Stantcheva (2014) in the context of optimal taxation. In her framework, however, the state retains full observability of workers’ total incomes, as in Mirrlees (1971), which severely limits their ability to engage in side trading. Our requirement that an allocation must be implementable by an entry-proof tariff to be robust to side trading is in line with the definition by Kahn and Mookherjee (1998) or Bisin and Guaitoli (2004) of third-best allocations in moral-hazard environments. In any such allocation, the planner’s tariff must prevent consumers from complementing it with an additional profit-making contract provided by a firm. We extend this notion to private-information environments, and, in addition, we put no restriction on the side trades a firm can make available. The unique third-best allocation that we characterise has been formerly derived by Glosten (1994) and Attar et al. (2020) as the outcome of competitive financial markets where market makers are restricted to post collections of limit orders and insiders thus face a convex aggregate tariff. In contrast with these authors, we adopt a fully normative perspective. This requires imposing no restriction on sides trades, which we assume to be fully bilateral. In line with this assumption, we allow firms to react to the planner’s tariff by posting arbitrary tariffs. Jaynes (1978), Hellwig (1988) and Stiglitz et al. (2018) show that this allocation can also be obtained in an equilibrium of a modified Rothschild and Stiglitz (1976) insurance economy in which insurance companies can exchange information about their customers. Although the allocation is the same, the logic of our approach is entirely different. First, these authors allow firms to react to the information disclosed by their competitors by possibly enforcing exclusivity clauses, which is at odds with the very notion of side trading that we emphasise. Second, as noticed above, we are interested in the normative implications of side trading and not in characterising the equilibrium of a given extensive-form game. We return to the issue of the decentralisation of the third-best allocation in Section 3. Our analysis shares with the common-agency literature (Martimort, 2007) the idea that what can be implemented by a principal—here, the planner—crucially depends on the trades made available by other principals—here, an entrant. Our normative approach, however, differs from the fully strategic approach adopted, in a similar environment, by Attar et al. (2014). The idea is that when a planner contemplates implementing an allocation by a tariff, he always anticipates that an entrant, acting as a follower, may complement this tariff by providing consumers with further trading opportunities. The requirement that the planner’s tariff be entry-proof then captures in a natural way the additional constraints that the possibility of side trades imposes on the planner. The paper is organised as follows. Section 1 describes the model. Section 2 defines our concept of robustness to side trading, fully characterises the only feasible allocation satisfying this requirement, and shows that it is typically not second-best. Section 3 discusses the relevance of our results for insurance and financial markets. Proofs not given in the text can be found in the Appendix. 1. The Economy Consumers: there is a continuum of consumers who can purchase a divisible good in exchange for monetary transfers. Each consumer is privately informed of her type i = 1, 2 and the proportion of type i among consumers is mi > 0. Type i’s preferences over quantity-transfer bundles |$(q,t) \in \mathbb {R}_+ \times \mathbb {R}$| are represented by a strictly quasiconcave and continuously differentiable utility function ui, with ∂tui < 0. Hence her marginal rate of substitution $$\begin{eqnarray} \tau _i \equiv -\, \frac{ \partial _q u_i }{ \partial _t u_i } \end{eqnarray}$$ is well defined and strictly decreasing along her indifference curves. We impose the Inada condition that τi(q, t) vanishes as q grows large along any such curve. Hence, whatever her endowment point, type i’s demand at any price p > 0 is finite. The following strict single-crossing condition is the key determinant of consumer demand: $$\begin{eqnarray} \mbox{For all $q$ and $t$, $\tau _2(q,t)\gt \tau _1(q,t)$.} \end{eqnarray}$$(1) Thus type 2 is more willing to increase her purchases than type 1. Firms: the supply side of the economy is described by a constant-return-to-scale technology, with unit cost ci > 0 of serving type i. Type 2 is weakly more costly to serve than type 1: $$\begin{eqnarray} c_2 \ge c_1. \end{eqnarray}$$(2) Together with (1), (2) typically generates adverse selection, whereas values are private in the limiting case c1 = c2. We let c ≡ m1c1 + m2c2 be the average cost of serving a consumer. These assumptions hold in the Rothschild and Stiglitz (1976) insurance economy: ci is type i’s riskiness, with c2 > c1, q is the amount of coverage she purchases, and t is the premium she pays in return. Our model encompasses many other specifications and is relevant for a broad spectrum of insurance, financial and labour markets. Incentive feasibility and efficiency: a contract is a pair (q, t) for some q ≥ 0, and with unit price t|$/$|q if q > 0. An allocation is a pair of contracts, one for each type. An allocation (qi, ti)i=1,2 is budget-feasible if $$\begin{eqnarray} m_1(t_1 - c_1 q_1)+ m_2(t_2-c_2 q_2) \ge 0. \end{eqnarray}$$ To this aggregate resource constraint, we must add, following Myerson (1979; 1982) and Harris and Townsend (1981), constraints reflecting that the allocation of resources takes place under asymmetric information. An allocation (qi, ti)i=1,2 is incentive-compatible if $$\begin{eqnarray} {u_1(q_1,t_1) \ge u_1(q_2,t_2) \text{ and } u_2(q_2,t_2) \ge u_2(q_1,t_1)}. \end{eqnarray}$$ We denote these constraints by IC1→2 and IC2→1, respectively. An allocation is incentive-feasible if it is budget-feasible and incentive-compatible. A second-best allocation is Pareto-efficient among incentive-feasible allocations. This is the relevant notion of efficiency for a planner who perfectly monitors trades, but does not observe consumer types (Prescott and Townsend, 1984). In the Rothschild and Stiglitz (1976) insurance economy, the second-best efficiency frontier consists of a continuum of allocations (Crocker and Snow, 1985; Bisin and Gottardi, 2006). Tariffs: a tariff T is a schedule specifying a transfer T(q) to be paid in return for a quantity q, with T(0) = 0 in case a consumer chooses not to trade along the tariff and T(q) = ∞ in case the tariff does not allow consumers to purchase the quantity q. A tariff T implements the allocation (qi, ti)i=1,2 if $$\begin{eqnarray} \mbox{For each}\, i, \, q_i \in \arg \max \, \lbrace u_i(q,T(q)): q \ge 0\rbrace \,\, {\rm and}\,\, t_i=T(q_i). \end{eqnarray}$$ To ensure that the various maximisation problems we will encounter have solutions, we impose the mild requirement that a tariff be lower semicontinuous, with T(q)|$/$|q bounded away from 0 as q grows large; this notably holds true if T has a compact domain. 2. Second-Best Allocations and Side Trading When side trading is feasible, the planner can no longer monitor trades between consumers and firms. This imposes two additional constraints on resource allocation. First, the planner cannot force consumers to trade with him, reflecting that they can opt out of any mechanism he could propose. To model this constraint, we require that the planner offer a tariff TP, the key restriction being TP(0) = 0. Second, the planner cannot prevent consumers from engaging in mutually advantageous additional trades with a firm. To model this constraint, we require that TP be such that no firm, acting as an entrant, can guarantee itself a positive profit by offering complementary side trades. Side trades are usually assumed to take place on Walrasian markets (Hammond, 1979; 1987; Allen, 1985; Jacklin, 1987; Cole and Kocherlakota, 2001; Golosov and Tsyvinski, 2007; Farhi et al., 2009); in our context, this would amount to impose that the entrant must post a linear tariff. We find this at odds with the idea that side trades cannot be monitored and instead allow the entrant to post an arbitrary tariff TE; the taxation principle (Hammond, 1979; Guesnerie, 1981; Rochet, 1985) ensures that this involves no loss of generality. Notice that we do not thereby prevent the entrant from offering a linear tariff; rather, the key idea is that the entrant can choose the terms of side trades and restrict the set of quantities consumers can choose from. This motivates the following definition. Definition 1. The planner’s tariff TPis entry-proof if, for any entrant’s tariff TE, there exists a solution|$(q^P_i,q^E_i)$|to each type i’s problem $$\begin{eqnarray} \max \, \lbrace U_i (q^P+q^E,T^P(q^P) + T^E(q^E)) : q^P\ge 0 \, \mbox{ and }\, q^E \ge 0 \rbrace \end{eqnarray}$$(3)such that entry is not profitable: $$\begin{eqnarray} m_1[T^E(q_1^E)-c_1 q_1^E] + m_2 [T^E(q_2^E)-c_2 q_2^E] \le 0. \end{eqnarray}$$(4)An allocation is robust to side trading if it can be implemented by an entry-proof tariff. It may at first be objected that we are tilting the odds in the planner’s favour by de facto assuming that he is able, in case consumers are indifferent, to coordinate their behaviour on an allocation in which the entrant does poorly. However, this assumption plays no role in the characterisation results we offer in Theorems 1–3: indeed, Theorem 2 shows that this arguably weak entry-proofness concept already singles out a unique budget-feasible allocation robust to side trading; moreover, the necessary conditions we derive are obtained using contracts that are profitable for the entrant no matter the consumers’ best responses. By contrast, strengthening our entry-proofness concept—for instance, by requiring that the planner’s tariff be robust to entry no matter the consumers’ best responses—would threaten the very existence of a budget-balanced allocation robust to side trading. This situation, however, is hardly specific to our model: indeed, when sustaining equilibria of competitive adverse-selection models, it is often necessary to assume that firms cannot sort out the least costly types at the deviation stage in case consumers are indifferent.1 Any allocation robust to side trading is incentive-compatible. The question we ask is whether such an allocation can also be second-best. Our argument is twofold. On the one hand, budget-feasible allocations robust to side trading have the following price structure. Lemma 1. In any budget-feasible allocation |$(q_i,t_i)_{i=1,2}$| robust to side trading, $$\begin{eqnarray} {t_1 = c q_1 \,\, and \,\, t_2 - t_1 = c_2(q_2-q_1)}. \end{eqnarray}$$(5) Proof. Because an allocation (qi, ti)i=1,2 robust to side trading is incentive-compatible, it satisfies q2 ≥ q1 by single crossing. Moreover, $$\begin{eqnarray} t_1 \le c q_1. \end{eqnarray}$$(6) Otherwise, an entrant can supply q1 at a price slightly above c: this profitably attracts type 1 as TP(0) = 0, and remains profitable even if type 2 is attracted. Similarly, $$\begin{eqnarray} t_2 - t_1 \le c_2(q_2-q_1). \end{eqnarray}$$(7) Otherwise, an entrant can supply q2 − q1 at a price slightly above c2: this profitably attracts type 2 along with the contract (q1, t1), and is even more profitable if type 1 is also attracted. Rewriting the resource constraint as $$\begin{eqnarray} t_1- c q_1 + m_2 [t_2 - t_1 - c_2(q_2 -q_1)] \ge 0 \end{eqnarray}$$ and taking advantage of (6)–(7) yields (5). The result follows. Hence pricing is competitive, in the sense that the prices of the layers q1 and q2 − q1 reflect the costs of serving the types who purchases them. However, if c2 > c1 and q1 > 0, then the quantities q1 and q2 are not priced competitively: as q1 is sold at the average cost c > c1, type 1 subsidises type 2. On the other hand, second-best allocations satisfy the following efficiency-at-the-top property. Lemma 2. In any second-best allocation |$(q_i,t_i)_{i=1,2}$|, If|$IC_{2 \to 1}$|is slack, then |$\tau_1(q_1,t_1)\leq c_1$|⁠, with equality if |$q_1>0$|. If|$IC_{1 \to 2}$|is slack, then|$\tau_2(q_2,t_2) = c_2$|⁠. Proof. If IC2→1 or IC1→2 is slack, then q2 > q1 by incentive compatibility and single crossing. If IC2→1 is slack and τ1(q1, t1) > c1, then ((q1 + ε, t1 + c1ε), (q2, t2)) is incentive-feasible for ε > 0 small enough and Pareto-dominates (qi, ti)i=1,2, a contradiction. Thus τ1(q1, t1) ≤ c1. Moreover, if q1 > 0 and τ1(q1, t1) < c1, then ((q1 − ε, t1 − c1ε), (q2, t2)) is incentive-feasible for ε > 0 small enough and Pareto-dominates (qi, ti)i=1,2, once again a contradiction. This proves (i). The proof of (ii) is similar, using q2 > 0, and is therefore omitted. The result follows. Combining Lemmas 1 and 2 yields our first main theorem. Theorem 1. A second-best allocation in which only one incentive-compatibility constraint binds is not robust to side trading. Proof. Suppose first that only IC1→2 binds. Then q2 > q1 by incentive compatibility and single crossing, and τ1(q1, t1) ≤ c1 by Lemma 2(i). Moreover, because type 1’s preferences are strictly convex and IC1→2 binds, we have t2 − t1 < c1(q2 − q1) ≤ c2(q2 − q1). By Lemma 1, (qi, ti)i=1,2 is not robust to side trading. Suppose next that only IC2→1 binds. Then q2 > q1 by incentive compatibility and single crossing, and τ2(q2, t2) = c2 by Lemma 2(ii). Moreover, because type 2’s preferences are strictly convex and IC2→1 binds, we have t2 − t1 > c2(q2 − q1). By Lemma 1, (qi, ti)i=1,2 is not robust to side trading. Hence the result. Theorem 1 covers most cases emphasised in the literature. For instance, in the Rothschild and Stiglitz (1976) insurance economy, either IC1→2 or IC2→1 bind in all but the pooling second-best allocation (Crocker and Snow, 1985), and Theorem 1 implies that none of these allocations is robust to side trading. This leaves only two cases in which a second-best allocation may be robust to side trading: when both IC1→2 and IC2→1 bind, which corresponds to a pooling allocation, or when both IC1→2 and IC2→1 are slack. Both cases can arise, as we show below, but only under very special assumptions on preferences and costs. To study these cases, we strengthen Lemma 1 by establishing that a unique allocation is budget-feasible and robust to side trading. In this allocation, the first layer is optimal for type 1 at price c, while the second layer is optimal for type 2 at price c2, conditional on her purchasing the first layer. This allocation is thus Pareto-efficient—maximising type 1’s utility—among those satisfying (5). Theorem 2. The third-best allocation defined by $$\begin{eqnarray} q_1^* \, & \equiv & \, \arg \max \lbrace u_1(q, cq): q \ge 0\rbrace , \end{eqnarray}$$(8) $$\begin{eqnarray} t_1^* \, & \equiv & \, cq_1^*, \end{eqnarray}$$(9) $$\begin{eqnarray} q_2^* \, & \equiv & \, q_1^* + \arg \max \, \lbrace u_2(q_1^*+q,t_1^*+c_2 q): q\ge 0\rbrace , \end{eqnarray}$$(10) $$\begin{eqnarray} t_2^* \, & \equiv & \, t_1^* + c_2(q_2^*-q_1^*), \end{eqnarray}$$(11)is the only budget-feasible allocation robust to side trading. Proof. (Uniqueness) Because an allocation (qi, ti)i=1,2 robust to side trading is incentive-compatible, it satisfies q2 ≥ q1 by single crossing. Moreover, $$\begin{eqnarray} u_1(q_1,t_1) \ge \max \lbrace u_1(q,cq):q \ge 0\rbrace . \end{eqnarray}$$(12) Otherwise, an entrant can offer a contract with unit price slightly above c that profitably attracts type 1 as TP(0) = 0, and remains profitable even if type 2 is attracted. Similarly, $$\begin{eqnarray} u_2(q_2,t_2) \ge \max \lbrace u_2(q_1+q,t_1+c_ 2q) : q \ge 0\rbrace . \end{eqnarray}$$(13) Otherwise, an entrant can offer a contract with unit price slightly above c2 that profitably attracts type 2 along with the contract (q1, t1), and is even more profitable if type 1 is also attracted. Finally, if (qi, ti)i=1,2 is budget-feasible, then (5) holds, so that (12)–(13) are equalities. Thus (qi, ti)i=1,2 is the third-best allocation defined by (8)–(11). (Existence) By (8)–(11), the piecewise-linear convex tariff $$\begin{eqnarray} T^P(q) \equiv 1_{\lbrace q\le Q_1^*\rbrace } c q +1_{\lbrace q\gt Q_1^*\rbrace } [ cq_1^* + c_2(q- q_1^*) ] \end{eqnarray}$$(14) implements the third-best allocation. Now, suppose that an entrant posts a tariff TE. The following monotonicity property is established in the Appendix. Lemma 3. There exists a solution|$((q_i^P,q_i^E))_{i=1,2}$|to (3) such that|$q_2^E \ge q_1^E$|⁠. Let us fix such a solution in what follows. As TP allows type 1 to purchase her optimal quantity |$q_1^*$| at price c, we must have $$\begin{eqnarray} T^E(q_1^E) \le cq_1^E . \end{eqnarray}$$(15) Moreover, because |$q_2 ^E\ge q_1^E$|⁠, type 2 could alternatively obtain the same aggregate quantity |$q_2^P + q^E_2$| as in her best response by purchasing |$q_1^E$| from the entrant and |$q^P_2+q^E_2 - q_1^E$| from the planner, paying overall |$T^P(q^P_2+q^E_2 - q_1^E) + T^E(q_1^E)$|⁠. As she chooses to pay |$T^P(q^P_2) + T^E(q_2^E)$| instead, we must have $$\begin{eqnarray} T^E(q_2^E) - T^E(q_1^E) \le T^P(q^P_2+q^E_2 - q_1^E) - T^P(q^P_2). \end{eqnarray}$$(16) Because TP is convex with slope at most c2 and |$q^E_2 \ge q_1^E$|⁠, $$\begin{eqnarray} T^P(q^P_2+q^E_2 - q_1^E) - T^P(q^P_2) \le c_2(q_2^E -q_1^E). \end{eqnarray}$$(17) Collecting (15) and (16)–(17) yields $$\begin{eqnarray} T^E(q_1^E)-c q_1^E + m_2 [T^E(q_2^E)-T^E(q_1^E)-c_2(q_2^E-q_1^E)] \le 0, \end{eqnarray}$$ which is (4). This shows that TP is entry-proof. Hence the result. ☐ The uniqueness of the third-best allocation contrasts with the multiplicity of second-best allocations, which form a nondegenerate frontier. The planner is thus severely constrained by his inability to monitor trades, which effectively prevents any kind of redistribution between different types of consumers. The existence of such an allocation for any binary distribution of types is also noteworthy. Non-exclusivity, or consumers’ ability to combine the contracts offered by an entrant with those offered by the planner, is key to this result. While this enlarges the set of contracts an entrant can use to attract consumers, this also gives the planner more instruments to deter entry. These take the form of latent contracts, which are not meant to be traded but only to make entry unprofitable. Of course, the planner must make sure that, by offering latent contracts, he does not create new profitable entry opportunities. The third-best tariff (14) strikes a balance between these two requirements. In the adverse-selection case c2 > c1, type 1’s and type 2’s marginal rates of substitution at the third-best allocation are strictly ordered, |$\tau _1(q_1^*,t_1^*) \lt \tau _2(q_2^*,t_2^*)$|⁠. In particular, we have |$\tau _1(q_1^*,t_1^*) =c \lt c_2= \tau _2(q_2^*,t_2^*)$| if the third-best allocation is interior and separating. This contrasts with private-value models where side trades take place on Walrasian markets, which calls for an equalisation of marginal rates of substitution (Hammond, 1979; 1987). Yet incentive-compatible gains from trade between types 1 and 2 are exhausted at the third-best allocation, subject to the side-trading constraint. Indeed, supposing that consumers have access to the same constant-return-to-scale technology as firms, the minimum price at which type 1 would be willing to sell a small additional quantity to type 2 is c2, and at this price type 2 is not willing to buy more. In that sense, the third-best allocation is the only candidate for a competitive equilibrium. Regarding the proof of Theorem 2, an interesting duality is that the third-best allocation is the only candidate for a budget-feasible allocation robust to side trading even if the entrant can only offer a single contract, while the third-best tariff is entry-proof even if the entrant can post an arbitrary tariff. This differs from Glosten (1994), who in his analysis of limit-order markets requires the entrant’s tariff to satisfy a property he dubs single crossing and that generalises convexity. Another important difference is that Theorem 2 does not require consumers’ preferences to be quasilinear, which makes it relevant for standard insurance economies. We are now ready to address the remaining cases not covered by Theorem 1. Theorem 3. If a second-best allocation is robust to side trading, then it coincides with the third-best allocation and one of the following conditions holds: The third-best allocation is pooling, that is, |$\tau _2(q_1^*, t_1^*) \le c_2$|. The third-best allocation is separating and first-best, that is, |$c_1=c_2$| or|$\tau_1(0,0) \leq c_1$|⁠. Proof. By Theorem 2, if a second-best allocation is robust to side trading, then it coincides with the third-best allocation. By Theorem 1, we only need to consider two cases. If IC1→2 and IC2→1 bind, then |$q^*_2 = q^*_1$| by incentive compatibility and single crossing. Hence the third-best allocation is pooling, which amounts to |$\tau _2(q_1^*, t_1^*) \le c_2$| by (10)–(11). If IC1→2 and IC2→1 are slack, then |$q^*_2 \gt q^*_1$| by incentive compatibility and single crossing. Hence the third-best allocation is separating. Two cases can arise. If |$q_1^* \gt 0$|⁠, then |$\tau _1(q_1^*,t_1^*) = c_1$| by Lemma 2(i) and |$\tau _1(q_1^*,t_1^*) = c$| by (8)–(9), so that c1 = c2. If |$q_1^* =0$|⁠, then τ1(0, 0) ≤ c1 by Lemma 2(i). In either case, each type i trades efficiently at cost ci, so that the third-best allocation is first-best. Hence the result. Condition (i) is clearly extreme. It cannot hold in a Rothschild and Stiglitz (1976) insurance economy, because the optimal coverage of type 1 at the average premium rate c is only partial, while type 2 is willing to purchase additional coverage at the fair premium rate c2 until she reaches full insurance. In the case of quasilinear preferences, condition (i) together with the condition |$\tau _1(q_1^*, t_1^*) \le c$| implied by (8)–(9) entails that type 1’s first-best quantity is at least as large as type 2’s, and strictly larger if |$q_1^*\gt 0$|⁠, a case of non-responsiveness (Caillaud et al., 1988). Condition (ii) is also extreme. Indeed, the third-best allocation is then first-best, and the third-best tariff is linear with slope c2. In the private-value case c1 = c2, each type trades efficiently at marginal cost. In the adverse-selection case c2 > c1, a separating second-best allocation is robust to side trading only if type 1 is not willing to trade at cost c1 and hence is in some sense irrelevant. This answers the question we raised in this section: second-best efficiency and robustness to side trading are irreconcilable requirements, except in very special cases. Overall, our results suggest that the threat of side trading constitutes a serious obstacle to efficiency and redistribution in private-information economies. In the limiting case of private values, side trading poses no threat to efficiency, as it leads to a first-best allocation; yet the requirement that there be no cross-subsidies between layers precludes the planner from redistributing resources between different consumer types. By contrast, under adverse selection, the social costs of side trading are twofold: first, the threat of side trading moves the economy away from the second-best efficiency frontier; second, it precludes redistribution. 3. Decentralisation and Market Intervention The decentralisation problem: determining whether constrained-efficient allocations can be supported in an equilibrium of an adverse-selection economy is a central issue for welfare economics. Bisin and Gottardi (2006) provide a positive answer to this question in the case of fully observable trades: for any second-best allocation, there exists a system of transfers ensuring that this allocation obtains in an equilibrium of a decentralised economy in which firms compete by offering exclusive contracts. However, in the polar case where firms can only observe their own trades with consumers, decentralising a third-best allocation is a more delicate task. To perform it, one needs to explicitly model firms’ behaviour when no information on consumers’ aggregate trades is available to them. In perfectly competitive markets, it is standard to assume, following Bisin and Gottardi (1999), that non-exclusive competition forces prices to be linear. Yet, as Theorem 3 shows, this is consistent with third-best efficiency only in the special private-value case. A natural alternative is to consider strategic models in which firms compete through menus of bilateral contracts. Side trading is then captured by letting consumers be free to trade with any subset of firms, in contrast with the exclusivity assumption made in standard competitive screening models following Rothschild and Stiglitz (1976). Attar et al. (2014) provide a general analysis of this non-exclusive-competition scenario. Their main result is that a positive level of trade for type 2 can be supported in a pure-strategy equilibrium only if type 1 is left out of the market. Indeed, equilibrium requires that type 1 not be willing to consume at price c, and type 2 purchasing her optimal quantity at price c2. Given (8)–(11), the resulting equilibrium allocation is a degenerate third-best one in which |$(q^*_1, t^*_1) = (0,0)$|⁠. A necessary and sufficient condition for decentralisation is τ1(0, 0) ≤ c, that is, Akerlof’s (1970) condition for a market breakdown in which only the worse-quality goods are traded. In all other cases, a pure-strategy equilibrium fails to exist altogether. An alternative strategy that has been pursued in the literature consists in designing extensive-form games that incorporate inter-firm communication. This approach, initiated by Jaynes (1978) and Hellwig (1988), and further developed by Stiglitz et al. (2018), allows each firm to dynamically react to the information about its customers’ trades disclosed by its competitors. This may induce a firm to withdraw its initial offers or to enforce exclusivity clauses, which suggests that these models are better interpreted as models of endogenous exclusivity than of side trading. In addition, enforcing any such mode of communication would require a very sophisticated institutional setting to properly take into account firms’ incentives to reveal information over time. By contrast, we suggest below some simple market interventions that decentralise the third-best allocation. The novelty of our proposal consists in the explicit consideration of public programmes that the agents can complement by resorting to the private sector, therefore endogenously determining the aggregate level of trade. Their simplicity lies in the fact that little information is required for public authorities. We develop our discussion in the context of insurance and financial markets. Insurance markets: in modern health-insurance systems, public insurance schemes for the provision of basic coverage do not prevent an active role for the private sector. In Germany, consumers can opt out from the public-insurance scheme to buy basic coverage designed and priced by private insurance companies. Consumers also often have the option to complement basic coverage with additional privately provided coverage, such as mutuelles in France. Finally, different forms of mandatory health insurance, whereby consumers are not allowed to remain uninsured, are in place in several systems, as in France, Germany, Japan, the Netherlands and Switzerland.2 Our analysis suggests a simple intervention that achieves a mix of public and private insurance, with no need for observability requirements. It consists in letting the state offer any amount of basic coverage up to |$q_1^*$| at the average premium rate c. As private insurance companies are willing to provide any amount of complementary coverage at the high premium rate c2, the state together with any insurance company make the third-best tariff available. Because this tariff is entry-proof, no insurance company has an incentive to deviate and entry is impossible. Implementing the third-best allocation is therefore compatible with letting consumers be free to choose their preferred level of coverage. This is reminiscent of the universal healthcare vouchers advocated by Emanuel and Fuchs (2005; 2007), whereby universal coverage is provided while letting consumers be free to purchase additional services or amenities on private insurance markets. Financial markets: in the aftermath of the recent financial crisis, the opportunity for agents to opt out of a public programme and trade in private markets has been acknowledged as a key constraint for the design of financial institutions in the presence of adverse selection. In this respect, recent works have suggested a rationale for liquidity-injection programmes that provide a credible signal to uninformed lenders by rejuvenating the relevant markets. An optimal intervention then typically consists in attracting only the least profitable borrowers, either through direct lending (Philippon and Skreta, 2012), or by repurchasing low-quality assets (Tirole, 2012). By participating in a bailout programme, a borrower may however end up signalling her financial weakness to the market, creating a stigma effect with potentially perverse implications (Gorton, 2015). While bailout policies are derived under the assumption that public and private liquidity are mutually exclusive, our approach offers a general theoretical framework for evaluating public interventions in situations where privately informed borrowers may complement a public programme with additional funds raised on private markets. A possible intervention would require public liquidity provision to involve a price sufficiently low, c, so as to attract all borrowers, and a borrowing limit |$q_1^*$| such that no overborrowing by the least profitable ones is possible. Further borrowing may then take place on private markets at price c2. Overall, such an intervention would implement the third-best allocation, thereby achieving budget balance, unlike those proposed by Philippon and Skreta (2012) and Tirole (2012), and inducing all types of borrowers to participate. This in turn would make it harder to infer their individual financial conditions, mitigating the impact of the stigma effect. Finally, the corresponding allocation of funds is the only one that can be reached under a budget-balanced programme under the threat of side trading. 4. Concluding Remarks We would like to conclude by mentioning two avenues for future research. First, we have followed Rothschild and Stiglitz (1976) and many authors since in assuming that there are only two types of consumers. This, in particular, enabled us to directly compare our results to the characterisation of the second-best efficiency frontier in Crocker and Snow (1985). Yet the question naturally arises to which extent our results are robust to this assumption. Attar et al. (2020) show that, in general, there exists a unique convex tariff for the planner that is entry-proof and implements a budget-feasible allocation. However, it is not straightforward to extend this uniqueness result to more than two types when the planner’s tariff is nonconvex.3 Preliminary work suggests that imposing more structure on the consumers’ preferences, as arises for instance in a Rothschild and Stiglitz (1976) economy, might be instrumental for such an extension. Second, we have throughout the analysis postulated that, given the planner’s tariff, an entrant can make a take-it-or-leave-it tariff offer to consumers. In that sense, bilateral trading is frictionless in our model. An alternative to this assumption, and to the standard Walrasian approach to side trading, would be to assume that bilateral trades are the outcome of a dynamic matching and bargaining game between firms and consumers searching for trade partners, in the spirit of Gale (2000). The planner may then be able to manipulate the outcome of this game by making search more costly, possibly enabling him to enlarge the set of implementable allocations and to achieve redistribution. More generally, the optimal manipulation of the market for side trades, which we have by assumption ruled out from our analysis, is an important topic for future investigation. Appendix Proof of Lemma 3. Each type i evaluates any contract (qE, tE) she can trade with the entrant through the indirect utility function $$\begin{eqnarray} z _i^{-P}(q^E,t^E) \equiv \max \, \lbrace u_i (q ^P +q^E, T^P(q^P)+t^E): q^P \ge 0 \rbrace . \end{eqnarray}$$(A1) Because ui is strictly quasiconcave and TP is convex, the maximum in (A1) is attained at a unique |$\widehat{q} _i^P(q^E,t^E)$|⁠, and |$(\widehat{q}_i^P(q_i^E,T^E(q_i^E)),q_i^E)$| is a solution to (3) if and only if $$\begin{eqnarray} q_i^E \in \arg \max \lbrace z_i^{-P}(q^E,T^E(q^E)):q^E \ge 0\rbrace . \end{eqnarray}$$(A2) According to Attar et al. (2019, Lemma 1), the convexity of the tariff TP and the strict single-crossing condition for the functions ui imply the following single-crossing condition for the functions |$z_i^{-P}$|⁠: $$\begin{eqnarray} \mbox{For all} \,\underline{q}^E \lt \overline{q}\, \! ^E, \underline{t}^E, \, {\rm and}\, \overline{t}\, \! ^E, z _1^{-P}(\underline{q}^E,\underline{t}^E) \lt z _1^{-P}(\overline{q}\, \!^E,\overline{t}\, \! ^E) \, {\rm implies}\, z _2^{-P}(\underline{q}^E ,\underline{t}^E) \lt z _2^{-P}(\overline{q}\, \!^E,\overline{t}\, \! ^E). \end{eqnarray}$$ To conclude, suppose that |$q_2^E \lt q_1^E$| at some solution |$((q_i^P,q_i^E))_{i=1,2}$| to (3). By (A2), $$\begin{eqnarray} z_2^{-P}(q_2^E, T^E(q_2^E)) \ge z_2^{-P}(q_1^E, T^E(q_1^E)). \end{eqnarray}$$ Because |$q_2^E \lt q_1^E$|⁠, the above single-crossing condition then implies $$\begin{eqnarray} z_1^{-P}(q_2^E, T^E(q_2^E)) \ge z_1^{-P}(q_1^E, T^E(q_1^E)). \end{eqnarray}$$ Thus |$(\widehat{q}_1^P(q_2^E,T^E(q_2^E)),q_2^E)$| is also a solution to (3) for type 1. The result follows. Notes This paper supersedes the first part of ‘Multiple Contracting in Insurance Markets’ (TSE Working Paper no. 14-532) by the same authors. We thank the editor, Gilat Levy, and three anonymous referees for very thoughtful and detailed comments. Financial support from the ANR (Programme d’Investissement d’Avenir ANR-17-EURE-0010) and the Chaire SCOR-TSE is gratefully acknowledged. Footnotes 1 This in particular the case when the equilibrium allocation involves some amount of pooling, as in Akerlof (1970), Miyazaki (1977), Wilson (1977), Spence (1978) and Attar et al. (2011). 2 We refer to the surveys of Thomson and Mossialos (2009) and Thomson et al. (2013) for institutional details and cross-country evidence. 3 Technically, this is because such a tariff may cause the consumers’ indirect utility functions, as defined in the proof of Lemma 3, to fail to satisfy a single-crossing condition. Notice in any case that the existence of a budget-balanced allocation robust to side trading is always guaranteed. References Akerlof G.A. ( 1970 ). ‘ The market for “lemons”: quality uncertainty and the market mechanism ’, Quarterly Journal of Economics , vol. 84 ( 3 ), pp. 488 – 500 . OpenURL Placeholder Text WorldCat Allen F. ( 1985 ). ‘ Repeated principal–agent relationships with lending and borrowing ’, Economics Letters , vol. 17 ( 1–2 ), pp. 27 – 31 . OpenURL Placeholder Text WorldCat Attar A. , Mariotti T. and Salanié F. ( 2011 ). ‘ Nonexclusive competition in the market for lemons ’, Econometrica , vol. 79 ( 6 ), pp. 1869 – 918 . 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( 1977 ). ‘ A model of insurance markets with incomplete information ’, Journal of Economic Theory , vol. 16 ( 2 ), pp. 167 – 207 . OpenURL Placeholder Text WorldCat © 2020 Royal Economic Society. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)

Bhattacharya,, Puja;Nielsen,, Kirby;Sengupta,, Arjun

doi: 10.1093/ej/ueaa042pmid: N/A

Abstract Using an experiment, we demonstrate that a communication regime in which a worker communicates about his intended effort is less effective in: (i) soliciting truthful information; and (ii) motivating effort than one in which he communicates about his past effort. Our experiment uses a real-effort task, which additionally allows us to demonstrate the effects of communication on effort over time. We show that the timing of communication affects the dynamic pattern of work. In both treatments, individuals are most co-operative closest to the time of communication. Our results reveal that the timing of communication is a critical feature that merits attention in the design of mechanisms for information transmission in strategic settings. Across a wide range of settings, agents take actions that are not observable by their strategic counterparts. In these situations, the interacting parties often communicate to overcome the informational asymmetry that results from hidden action. Over the last decade, a large literature has analysed these environments, focusing on the effect of pre-play communication on static choices. These papers have established that statements of intent or non-binding promises can be informative and increase co-operation in social dilemmas (Charness and Dufwenberg, 2006; Miettinen and Suetens, 2008; Vanberg, 2008; Van den Assem et al., 2012; Ederer and Stremitzer, 2016; Di Bartolomeo et al., 2017). Two theories have been proposed to explain such behaviour: belief-dependent utility, in which individuals incur costs for failing to meet the raised expectations created in the promisee (Charness and Dufwenberg, 2006; Ederer and Stremitzer, 2016), and preference for consistency between one’s action and his message (Vanberg, 2008). However, many interesting and economically relevant interactions do not fall into the realm of environments that the literature addresses. Communication does not always occur pre-play, nor does it necessarily surround static choices. Communication is inherently dynamic and can happen before or after an individual makes a decision. For instance, contractors make informal commitments to use high-quality materials before commencing a project, while sellers advertise their investment in quality only after production.1 In contrast to the breadth of evidence that we have accumulated about the incentive effects of ex ante communication, we know little about whether these positive effects hold to the same extent when individuals anticipate the opportunity to communicate ex post.2 Additionally, communication often surrounds decisions that unfold piecewise over time. For example, companies commit to reduce emissions over the course of a year or to set public targets to improve energy efficiency by a future date. The effect of communication in these environments may differ from that of communicating about immediate decisions. To capture these two previously under-studied aspects of communication, we design a two-person hidden action game that can be interpreted as a manager–worker interaction. Workers make non-binding statements about their effort either before or after working on a real-effort task for the manager. We study the degree of truthful reporting, workers’ effort exerted and managers’ behaviour across these two communication frameworks. Our experiment builds on the previous literature in a few key ways. First, we analyse and compare the efficacy of exante and ex post communication in transmitting information and encouraging co-operation in strategic environments. We will refer to this as the effect across time. There are a number of reasons why this difference in timing might affect behaviour, and a priori it is not clear which environment better supports co-operation and truth telling. Individuals may treat a broken promise about the future differently from a lie about a past action, and their behaviour would reflect differences in the moral costs of promise breaking versus lying. Furthermore, if workers view ex ante messages as public ‘goals’ for performance, this could lead to higher effort after ex ante communication, while uncertainty surrounding future performance could lead to lower effort after ex ante communication. Our experiment attempts to answer which communication regime leads to higher co-operation and less misinformation. Secondly, within each treatment, we explore how co-operation evolves in relation to the distance in time from when communication occurs. We will refer to this as the effect over time. In our experiment, the worker exerts effort on a project and the manager chooses whether to invest in the project. Effort is costly for the worker but increases the manager’s expected payoff from investing. The worker does not get paid directly for working on the project, but receives a fixed payment if the manager invests. The worker’s effort on the project is unobservable to the manager, and the manager has to rely on the worker’s communication about his effort level in determining whether to invest. Our treatments vary when this communication opportunity is presented to workers: either before or after the worker exerts effort. In the Message Before treatment, the worker’s message takes the form of a statement of intent or ‘promise’, where the worker communicates about the effort that he plans to exert on the project. In the Message After treatment, he sends a message or ‘report’ only after he finishes working. We design our game such that a self-interested worker with no costs of deception will have no incentive to work on the project. However, since he receives a positive payoff when the manager invests, he will want to convince the manager that sufficiently high effort has been (or will be) exerted to make the manager’s investment profitable. Our game captures many of the relevant features of strategic environments with misaligned incentives. It is in these environments where we expect deception to be most prevalent and also where communication can have the greatest impact in facilitating co-operation. In order to observe how effort evolves over time, we implement the worker’s effort decision through a real-effort task. The worker is given four minutes to work on converting letters to numbers. We track his effort over the entire span of the Work Stage. This allows us to explore how co-operation changes as the worker gets further from the time when he sent his message in the Message Before treatment or gets closer to the time of sending the message in the Message After treatment. Comparing messages with the actual effort exerted, we find messages sent in the Message Before treatment inflate effort by 81% while those sent in the Message After treatment inflate by only 41%. Not only do more workers deceive in the Message Before treatment, but the magnitude of the deception is also greater. The observed difference in informational content is driven by workers both communicating higher effort and exerting less effort in the Message Before treatment compared with the Message After treatment. On average, managers anticipate that messages will be inflated and as a result expect a lower level of effort than what is stated in the messages. Additionally, we find that managers partially anticipate the impact of the timing of communication on deception. Looking at the dynamic allocation of effort, we find that the highest effort is exerted closest to the time of communication in both treatments. In the Message Before treatment, the highest percentage of workers work at the beginning of the Work Stage, while in the Message After treatment, the highest percentage of workers are working at the end. To our knowledge, this is the first study that explores the effects of communication over time, and our results suggest that co-operation may be highest when messages are at the top of mind. As further evidence and an exercise in robustness, we explore the effect of timing of communication in a binary matrix game designed to be strategically similar to the manager–worker environment. As in the real-effort task, the sender can signal his action to the receiver through a message. Treatments vary when the sender can send the message, either before or after he takes his action. Behaviour in the matrix game largely confirms our main results. We find a higher frequency of deceptive signals when the sender can signal before compared with after. Results from the matrix games and additional analysis allow us to eliminate a number of potential explanations of our results, including inaccuracy in predicting future performance, manager expectations and moral wiggle room. We find that a number of factors influence behaviour, but the data suggest that intrinsic differences in costs of deception between these two environments is a key driver of the treatment differences. Our results reveal new insights regarding intrinsic preferences for honesty. In particular, we show that timing of communication is a critical factor in determining deception and co-operation, and therefore can be an important variable in the hands of the contract designer. There are many situations where timing of communication is a variable of interest. Capital budgeting decisions are often based on unverifiable information which is solicited at one of two points in time (Arya et al., 2000): Divisions of a firm receive funding by self-reporting either on the anticipated expenses of projects (Church et al., 2012) or on realised expenses after production (Fellingham and Young, 1990). Our results suggest that firms could choose a late information system to facilitate more truthful reporting and more efficient spending. In a simple organisational design problem, managers could schedule weekly meetings at the end of the week, where employees talk about the week’s progress versus goal-setting meetings held at the start of the week. Additionally, corporate social responsibility statements are used by interest groups and society at large to form an idea of a company’s contribution to society, however the reporting is largely voluntary and unregulated in most countries. Companies often have been found to misreport existing standards as well as overstate future environmental goals to build brand image (Cohen, 2011; Ward, 2014). Our results indicate that the form of reporting—as a statement of goals or report on achievements—could have implications for the accuracy of these statements. 1. Related Literature Our article contributes most directly to the literature on strategic communication. Theoretical and experimental work in strategic communication has followed two largely separate strands: communication regarding an exogenous state of the world as in the sender–receiver games (⁠|$\grave{a}$| la Crawford and Sobel, 1982) and pre-play communication regarding future decisions. In sender–receiver games, an individual has private information about an external state of the world and may convey the information through a message. An uninformed strategic counterpart then may take an action after observing this message. Experiments in this paradigm focus explicitly on the degree of honest reporting by the informed agent and how credible the uninformed agent considers the message to be (Gneezy, 2005; Cai and Wang, 2006; Sánchez-Pagés and Vorsatz, 2007). Their findings are consistent with individuals showing an aversion to misreporting, as most subjects sacrifice substantial payoff gains and do not misreport maximally. Similar results are observed in related papers where individuals report on an outcome of chance, e.g., rolling a die or tossing a coin (Fischbacher and Föllmi-Heusi, 2013; Abeler et al., 2014), and in papers in which individuals self-report on past performance in simple tasks or contribution games (Brosig et al., 2005; Mazar et al., 2008; Shu et al., 2012).3 These experiments convincingly establish the existence of costs of misrepresentation as individuals are unwilling to make false statements, even at the expense of large monetary gains. The second strand of literature investigates the effect of pre-play communication in social dilemmas (Charness and Dufwenberg, 2006; Vanberg, 2008; Miettinen and Suetens, 2008; Van den Assem et al., 2012) and co-ordination games (Cooper et al., 1992; Charness, 2000). In these games, players make non-binding commitments about their future actions. In contrast to the sender–receiver literature, subjects in these experiments make two decisions: (i) what message to send; and (ii) what action to take. These papers confirm the conclusion drawn above, that individuals are averse to misrepresentation and do not take the opportunity to misreport maximally. As a result, pre-play statements of intent are informative. This literature additionally demonstrates that statements of intent increase co-operation. Communication increases expectations in the receiver, and senders change their actions in conjunction with these raised expectations. As a result, overall co-operation rates increase compared with a baseline without communication. Our article bridges the gap between these two strands of literature and extends analysis into new domains. We analyse truth telling and co-operation, directly comparing strategic environments with ex ante statements of intent with those with ex post reporting. To date, there has been limited research on how ex post reports can be used to influence decisions and increase co-operation, which has been the main focus of the pre-play communication literature. Additionally, we extend both literatures into a richer decision domain. Rather than focusing on static decisions, we analyse a dynamic real-effort environment that allows us to look at co-operation rates over time. Ours is not the first article to directly compare ex ante and ex post communication. A small literature has studied the role of timing of communication in stag hunt games. In an early influential paper, Farrell (1988) conjectures that ex ante, but not ex post, communication will allow agents to co-ordinate on the efficient equilibrium in the stag hunt game. Given the structure of the stag hunt game, the sender always prefers the receiver hunt the stag. Therefore, after taking either action, the sender would always signal for the receiver to hunt the stag and his message is entirely uninformative. However, if the sender can communicate before taking an action, he might choose to hunt the stag, too, if he believes that his message will be influential over the receiver’s choice. Hence, ex ante communication can facilitate co-ordination. Charness (2000) provides experimental support for Farrell’s conjecture. Recently, two interesting papers have provided different approaches to formalise Farrell’s conjecture. Zultan (2013) uses a dual self model, in which the ‘acting self’ (who takes an action) and the ‘signalling self’ (who communicates) are treated as separate entities. Schlag and Vida (2015) provide a more general framework to analyse cheap talk surrounding play of games with multiple equilibria. While this literature highlights the importance of timing of communication in strategic interactions, it concentrates on games with multiple equilibria and focuses on the role of timing in equilibrium selection. In our environment, there is a single equilibrium and therefore timing of communication should be irrelevant theoretically. The paper most closely related to our work is that of Serra-Garcia et al. (2013). In a clever experiment, they show that individuals are much more willing to lie about a state of nature than about their action, even when these statements lead to the same outcome for a strategic counterpart. The authors suggest that the difference can be attributed to communication about actions having an inherent ‘promise’ element, which messages about pre-determined states of nature do not. To test this, in a secondary treatment they allow subjects to communicate about their own past actions and compare this with communication about current actions.4 They find support for the claim that statements about current actions in particular increase co-operation. Our work attempts to build on their findings by exploring the impact of timing in a unified framework expressly aimed at answering the question of whether ex ante versus ex post communication affects behaviour differently. Furthermore, our use of a real-effort task completed over time allows us to explore a richer set of results. In particular, we study the impact of communication over the duration of the real-effort task and how this interacts with the timing of communication. We also analyse several other games as robustness checks, varying payoffs and the degree of alignment in payoff incentives. 2. Experimental Design We conduct a between-subject analysis of two separate treatments. In the Message Before treatment (hereafter MB), an individual sends a message about an action that he will take in the future. In the Message After (MA) treatment, an individual sends a message about his action only after he has taken it. We begin by outlining the structure and payoffs of the game, which we will call the Manager–Worker Game. 2.1. The Manager–Worker Game The game that we design is a two-player hidden action game. For simplicity of exposition, we will call the players manager and worker.5 The manager has to decide whether to invest (I=1) in a project, which we will call the Joint Project. The return on her investment depends upon the outcome of the Joint Project, θ, which could be either a success (θ = S) or a failure (θ = F). The manager’s payoffs are denoted by πM in Eq (1). The manager receives 130 points if the Joint Project is successful and she invests. If the project fails and she invests, she receives 10 points. If she does not invest, she receives an outside option, which pays her 70 points.6 The payoffs ensure that the manager will find it profitable to invest only when the project is successful. $$\begin{eqnarray} \pi ^M= \left\lbrace \begin{array}{@{}l@{\quad }l@{}}130 \text{ points } & \text{if } \, \, \theta =S \, \, \text{and} \, \, I=1 \\ 10 \text{ points } & \text{if } \, \, \theta =F \, \, \text{and} \, \, I=1 \\ 70 \text{ points } & \text{if } \, \, I=0 \end{array}\right. \end{eqnarray}$$(1) The outcome of the Joint Project, in turn, depends on the worker’s real effort on the Joint Project. The amount worked on the Joint Project determines the probability of success. Denoting the worker’s effort on the Joint Project by wJ, the outcome function, p, is $$\begin{eqnarray} p=Pr(\theta =S) = \frac{w_{J}}{w_{J}+23}. \end{eqnarray}$$(2) This function is monotonic, concave and bounded above at 1.7 Hence, the more the worker works, the higher the chance that the project will be successful, but he can never guarantee its success with certainty. The worker completes work on the Joint Project prior to the manager making her investment decision. However, at the time of investment, the manager does not observe the outcome of the Joint Project or the amount of work done. The worker can send a non-binding message, m ∈ [0, ∞), informing the manager of his level of work on the Joint Project. Since our primary focus is on deceptive behaviour, the worker’s payoffs were set up such that a self-interested worker will find it beneficial to overstate his work in the message. To make it costly for the worker to work on the Joint Project, the worker has an outside option, called the Personal Project, that he could work on instead. Working on the Personal Project pays the worker directly. If the worker completes wP tasks for the Personal Project, he earns |$\frac{w_{P}}{w_{P}+23}\times 100$| points.8 In addition to his earnings from the Personal Project, he receives a fixed payment of 120 points if the manager invests in the Joint Project. If the manager does not invest, he receives only his earnings from the Personal Project. The worker is given four minutes to divide his time between working on the two projects. The worker’s payoff is denoted by πW in (3). $$\begin{eqnarray} \pi ^W = \frac{w_{P}}{w_{P}+23}100 +120I \end{eqnarray}$$(3) Note from (3) that the worker’s earnings do not depend directly on how much he has worked for the Joint Project or on its outcome. This ensures that, for a self-interested worker with no other-regarding preferences and no cost of deception, any strategy in which the worker devotes positive time to the Joint Project is strictly dominated; he will devote all his time to the Personal Project. Anticipating this, the manager should never invest, regardless of the message sent by the worker. Hence, the theoretical prediction for self-interested players with no cost of deception is that the worker does not work on the Joint Project and the manager does not invest. The above equilibrium outcome is inefficient and is Pareto dominated by outcomes in which a risk-neutral manager invests and the worker works sufficiently on the Joint Project to ensure at least 50% chance of the project being successful. If individuals are other-regarding or incur costs from deceiving, there could exist equilibria with positive levels of work done for the Joint Project and positive levels of investment.9 However, the theoretical predictions would be the same for MB as for MA.10 We implement the worker’s decision to work on the two projects with a real-effort task that lasts four minutes. The task chosen was the Encoding Task, which we describe below. 2.2. Encoding Task The real-effort task consisted of converting letters into numbers (Erkal et al., 2011; Charness et al., 2014). The workers’ screen displayed a table with two rows. The first row contained all the letters in the alphabet and the second row provided a number (from 1 to 26, in random order) to go along with each letter. During the task, participants were given a letter and had to enter the corresponding number from the table. Once a participant successfully converted a letter, the table would reset, matching each letter with a new number and presenting the participant with another letter to encode, and so on. We use the number of letters encoded for each project as a measure of work done for that project. To limit a potential source of variation across subjects, all individuals faced the same order of letters to be encoded. The work stage lasted four minutes, during which workers encoded letters for the two projects. The workers began the work stage by choosing which project to start working on.11 Thereafter, workers could decide in real time which project they wanted work to go towards. A button on the screen allowed workers to switch between working for the two projects at any time. The dynamic nature of this set-up allows us to measure work over time and patterns of work allocation between the two projects. To help workers keep track of their performance, there were counters on the screen that displayed the current number of letters that they had encoded for each project. A screenshot of the work stage is shown in Online Appendix Figure A1. 2.3. Treatments We consider treatments that differ according to when the communication opportunity is presented to workers. In the MB treatment, the worker sends a message prior to the work stage. In the MA treatment, the worker sends a message after completing the work stage. We refer to this message sending opportunity as the message stage. Table 1 lists the message options available to workers in either treatment. Table 1. Message Options. . Message After (MA) . Message Before (MB) . (i) Hi, I have encoded |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should invest. Hi, I will encode |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should invest. (ii) Hi, I have encoded |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should not invest. Hi, I will encode |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should not invest. (iii) No message No message . Message After (MA) . Message Before (MB) . (i) Hi, I have encoded |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should invest. Hi, I will encode |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should invest. (ii) Hi, I have encoded |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should not invest. Hi, I will encode |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should not invest. (iii) No message No message Open in new tab Table 1. Message Options. . Message After (MA) . Message Before (MB) . (i) Hi, I have encoded |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should invest. Hi, I will encode |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should invest. (ii) Hi, I have encoded |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should not invest. Hi, I will encode |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should not invest. (iii) No message No message . Message After (MA) . Message Before (MB) . (i) Hi, I have encoded |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should invest. Hi, I will encode |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should invest. (ii) Hi, I have encoded |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should not invest. Hi, I will encode |$\rule {1cm}{0.15mm}$| letters for the Joint Project. You should not invest. (iii) No message No message Open in new tab If a worker chose message option (i) or (ii), he could fill in any non-negative number in the blank. It was stated in the instructions, as well as on subjects’ screens, that workers were free to choose any number and managers would only see the message, never the actual number of letters encoded for the Joint Project. The messages also contained a recommended action for the manager to eliminate any ambiguity about whether the worker intended for the manager to rely on his message. It is worth making a brief aside to discuss our form of communication. A robust finding in the literature is that free-form messages are more effective than fixed-form messages in increasing co-operation (Charness, 2000; Glaeser et al., 2000; Charness and Dufwenberg, 2010; Brandts et al., 2016).12 Message language is an important part of communication, and adopting a limited message space runs the risk of excluding key features that make communication more effective. However, the dynamic nature of our design and the relation of effort to success probability would have provided workers with many possible dimensions over which to communicate. When allowed to converse freely, they may communicate about the level of work, the corresponding probability or even time allocation. Given our research question, we wanted the worker to communicate about only the work done and hence needed to restrict the message space for clean comparisons.13 Previous research has shown free-form messages to be more informative than pre-specified messages in the domain of ex ante promises (Charness and Dufwenberg, 2010) as well as ex post reports (Lundquist et al., 2009; Khalmetski and Tirosh, 2012). Hence, we expect free-form communication to increase trust and co-operation in both treatments, but its effect on treatment differences is unclear. It remains an interesting open question to understand whether free-form communication would differ in these two environments. The manager made her investment decision after the work and message stages in both treatments. Note that even though the manager receives the message before the work stage in the MB treatment, she makes her investment decision only after the worker finishes working. Therefore, in both treatments the timing of when a manager invests is the same.14 The treatments are identical in all aspects other than the sequence in which the message and the work stages were presented. We also collected beliefs from the workers and managers about their counterparts’ actions. The managers were asked to guess the number of letters encoded by the worker for: (i) the Joint Project; and (ii) both projects in total. The workers were asked to state their second-order beliefs by guessing the managers’ answer to (i). The elicitation of beliefs was incentivised by the quadratic scoring rule.15 2.4. Ability Measure In most organic communication environments, it is difficult to disentangle intentional deception from unintentional broken promises due to forecast errors. Part of our motivation in using a lab experiment is to separate these two effects. Since future uncertainty is an important consideration in applying results outside the lab, we leave room for unintentional misrepresentation to enter our environment while taking care to separate this effect from intentional deception. In our experiment, unintentional misrepresentation could arise from forecast errors if workers are overconfident about their abilities. These forecast errors could affect behaviour differently across treatments. For example, an overconfident worker in the MB treatment might be unable to accomplish the work stated in his message and would appear dishonest even if he did not intend to be. Such considerations do not arise in the MA treatment since the worker sends a message only after he has worked. In our experiment, we will address this by both reducing and measuring forecast errors. First, to mitigate miscalibration, we introduced an additional part, which we call Part 1, before participants were introduced to the manager–worker game. In Part 1, every participant worked on the Encoding Task for four minutes. The first minute was an unincentivised practice round to familiarise subjects with the task and interface. In the next three minutes, participants again worked on the task, but this time were paid for the number of letters they encoded. The payment scheme used was identical to the participants’ payoff from the Personal Project to maintain parity in incentives. If a participant encoded w letters in three minutes, his payoff was given by |$\frac{w}{w+23}100$| points. At the end of the three minutes, participants saw a minute-by-minute breakdown of their performance, providing them with feedback on their ability. Their performance in this part also provides us with a baseline measure of their ability on the task. Additionally, after participants viewed their performance, we collected data on their projections of how many letters they would be able to encode if they had to perform the task again, this time for four minutes.16 Comparing this forecast with their performance in Part 2, we can investigate whether forecast errors contribute to any observed treatment differences we find. 2.5. Implementation and Feedback Figure 1 shows the timeline of the experiment. Participants were first read the instructions for Part 1. After the four minutes in Part 1 and the performance forecast elicitation, we handed out instructions for Part 2. Participants were assigned either the role of a worker or the role of a manager. They played the game only once, so our design captures a one-shot interaction. Since our primary interest is in understanding the behaviour of the workers, we randomised approximately three quarters of the participants in a session to be workers and the remaining participants to be managers.17 Consequently, a manager may have been matched with more than one worker; she made separate decisions for every worker and one of the decisions was chosen randomly for payment. Instructions were read aloud using slide illustrations as an aid, followed by a comprehension quiz to ensure understanding of the game (see Online Appendix C). Fig. 1. Open in new tabDownload slide Timeline of Decisions. Fig. 1. Open in new tabDownload slide Timeline of Decisions. After Part 2, subjects participated in a series of matrix games, which we call Part 3. Subjects did not receive any feedback about Part 2 before starting Part 3. These matrix games act as a robustness check for our main treatment, and we defer the description of this part to Subsection 4.2. At the end of the experiment, one part was chosen randomly and participants were paid their earnings for that part. All participants were informed about the outcomes of the Joint Projects and the workers were informed of the managers’ investment decisions. The managers only got to know whether their Joint Project was a success or not; they never got to know the number of letters the worker encoded for the Joint Project. 2.6. Procedures All experiments were computerised, using z-Tree (Fischbacher, 2007). 16 sessions (eight sessions per treatment) were conducted at the Ohio State Experimental Economics Lab, with a total of 284 participants recruited through ORSEE (Greiner, 2004). We had 111 participants as workers in the MB treatment and 100 participants as workers in the MA treatment. We had 37 and 36 participants in the role of manager in the MB and MA treatments respectively. Each session lasted about 90 minutes and the average payment to a subject was $15. 3. Results The vast majority of workers—102 workers (92%) in the MB treatment and 88 workers (88%) in the MA treatment—sent a message recommending investment. Our primary analysis and all tables and figures will focus on these 190 workers, unless noted otherwise.18 For comparisons of raw data across treatments, we report p-values from two-tailed Fisher-Pitman permutation tests for two independent samples for non-binary data and two-tailed Wilcoxon rank-sum tests for binary data. Recall that participants in both treatments completed three minutes of the Encoding Task before they were presented with instructions for Part 2. Though performance varies across participants, as expected there is no difference in the average number of letters encoded in Part 1 across the two treatments. Participants encoded 62.4 and 62.5 letters on average in the MB and MA treatment, respectively (p-value=0.87). Figure A2 in the Online Appendix illustrates the distribution of ability across treatments. The number of letters participants encoded in the three minutes serves as a measure of a subject’s ability in the effort task and will be included in all subsequent regressions along with a dummy for gender, a dummy for native language, year-of-study dummies, and a dummy indicating whether the participant is a graduate student. 3.1. Informativeness of Messages We first present results on the information content of the messages. For ease of exposition, we will refer to messages sent in the MB treatment as ‘promises’ and messages in the MA treatment as ‘reports’, with ‘message’ being an overarching term across both treatments. A message is fully informative if the stated number of letters in the message is equal to the actual number of letters encoded by the worker for the Joint Project (m − wJ = 0). If m − wJ ≠ 0, a worker is said to misinform the manager. If m − wJ > 0, the message is inflated, while if m − wJ < 0, the message is conservative. The dependent variable in our analysis is m − wJ, a measure of message inflation. Figure 2 shows the cumulative density of misinformation by treatment. First, the wedge in the distributions at zero indicates that fewer workers inflate their messages in the MA than in the MB treatment. The CDF of the MA treatment always lies above that of the MB treatment for positive values of misinformation, indicating greater misinformation in the latter. Aggregate statistics confirm these observations. The average amount of misinformation in MB is 32.1 letters compared with only 18.0 letters in MA (p-value=0.002; K-S p-value=0.002). Thus, on average, messages are 79% more inflated in the MB treatment. This is robust to considering other measures of message inflation. Fig. 2. Open in new tabDownload slide Distribution of Misinformation by Treatment. Fig. 2. Open in new tabDownload slide Distribution of Misinformation by Treatment. To formalise our findings, Table 2 Column (1) presents results from an OLS regression predicting the amount of message inflation after controlling for ability and demographic characteristics. Message Before is a dummy equal to 1 for the MB treatment and 0 for the MA treatment. Part 1 Performance is the number of letters the participant encoded in Part 1 of the experiment, which we use as a measure of the worker’s ability on the task. Column (1) confirms that the amount of misinformation is significantly higher in the MB treatment. Table 2. Message Inflation. . m − wJ . Dependent variable: . (1) . (2) . (3) . Message Before 14.61*** 17.18*** 10.67** (4.20) (4.11) (5.31) Part 1 performance 0.20 0.27 0.46 (0.24) (0.26) (0.32) Overestimate −0.37 −0.71 (0.37) (0.52) Overestimate × Message Before 1.27** 1.05 (0.54) (0.67) Constant 1.19 −4.99 −4.68 (16.73) (17.65) (21.61) Controls Yes Yes Yes No. of obs. 190 190 128 R2 0.12 0.16 0.14 . m − wJ . Dependent variable: . (1) . (2) . (3) . Message Before 14.61*** 17.18*** 10.67** (4.20) (4.11) (5.31) Part 1 performance 0.20 0.27 0.46 (0.24) (0.26) (0.32) Overestimate −0.37 −0.71 (0.37) (0.52) Overestimate × Message Before 1.27** 1.05 (0.54) (0.67) Constant 1.19 −4.99 −4.68 (16.73) (17.65) (21.61) Controls Yes Yes Yes No. of obs. 190 190 128 R2 0.12 0.16 0.14 Notes: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are robust standard errors. Controls include a dummy for gender, a dummy for native language, year-of-study dummies and a dummy for being a graduate student. Message Before is a treatment dummy variable (1=MB, 0=MA), Part 1 Performance is a subject’s performance in the Part 1 calibration, and Overestimate is the measure of forecast error. Column (3) conditions on workers who sent inflated messages. Open in new tab Table 2. Message Inflation. . m − wJ . Dependent variable: . (1) . (2) . (3) . Message Before 14.61*** 17.18*** 10.67** (4.20) (4.11) (5.31) Part 1 performance 0.20 0.27 0.46 (0.24) (0.26) (0.32) Overestimate −0.37 −0.71 (0.37) (0.52) Overestimate × Message Before 1.27** 1.05 (0.54) (0.67) Constant 1.19 −4.99 −4.68 (16.73) (17.65) (21.61) Controls Yes Yes Yes No. of obs. 190 190 128 R2 0.12 0.16 0.14 . m − wJ . Dependent variable: . (1) . (2) . (3) . Message Before 14.61*** 17.18*** 10.67** (4.20) (4.11) (5.31) Part 1 performance 0.20 0.27 0.46 (0.24) (0.26) (0.32) Overestimate −0.37 −0.71 (0.37) (0.52) Overestimate × Message Before 1.27** 1.05 (0.54) (0.67) Constant 1.19 −4.99 −4.68 (16.73) (17.65) (21.61) Controls Yes Yes Yes No. of obs. 190 190 128 R2 0.12 0.16 0.14 Notes: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are robust standard errors. Controls include a dummy for gender, a dummy for native language, year-of-study dummies and a dummy for being a graduate student. Message Before is a treatment dummy variable (1=MB, 0=MA), Part 1 Performance is a subject’s performance in the Part 1 calibration, and Overestimate is the measure of forecast error. Column (3) conditions on workers who sent inflated messages. Open in new tab Uncertain Future. There is an obvious reason why promises might overstate work more than reports. In the MB treatment, workers send a message before they work, and the higher misinformation in the MB treatment may reflect workers incorrectly forecasting the number of letters they will be able to encode.19 Overconfidence might prompt them to send ambitious messages and may lead to work unintentionally falling short of the promised amount. Workers in the MA treatment would be unaffected by miscalibration, as they send a message after working and therefore know their true performance when sending their message. Our design allows us to test for this explanation, and we will demonstrate that higher misinformation in the MB treatment cannot be attributed to uncertainty surrounding future ability. Recall that after the participants viewed their Part 1 performance results but prior to receiving instructions for Part 2, they were asked to forecast the number of letters they would encode if they performed again for four minutes. We use this forecast, |$\hat{w}_{total}$|⁠, as a measure of the worker’s ex ante beliefs of the total number of letters he can encode in Part 2. A promisor overestimates if |$\hat{w}_{total} - w_{total}\gt 0$|⁠, where wtotal is the actual number of letters encoded in four minutes for both projects. For these promisors who overestimated, we add the number of letters they fell short by to the work done on the Joint Project and recalculate misinformation. $$\begin{eqnarray} { {Misinformation}} ^{ {Adj}}= m - (w_{J} + (\hat{w}_{ {total}} - w_{ {total}})) \end{eqnarray}$$(4) This adjustment assumes the following: if an overconfident promisor hypothetically could accomplish what he anticipated when sending the message, we assume that he would have encoded all the letters by which he fell short for the Joint Project. In reality, we do not know what he would have done; he could have encoded all for the Personal Project or split them between the Joint and Personal Projects. We make the most conservative assumption that he would have encoded these additional letters all for the Joint Project, thereby giving promisors the best chance at being honest. After this adjustment, the average amount of misinformation in MB falls from 32.1 to 29.5 letters, but is still significantly higher than the 18.0 letters in MA (p-value=0.009).20 Hence, we find that forecast errors cannot account for the difference in information transmitted across the treatments.21 To test whether forecast errors affect misinformation more generally, we augment the regression in Table 2 with (⁠|$\hat{w}_{total} - w_{total}$|⁠), which we call Overestimate, and the interaction of Overestimate and Message Before. We include the interaction of Overestimate and Message Before on the basis of our hypothesis that initial forecast errors would have no effect on the amount of misinformation in the MA treatment as workers send a message after observing their actual performance. However, forecast errors may affect the amount of misinformation in the MB treatment as workers send a message ex ante. Column (2) reports results. Our hypothesis is supported by the observation that the combined magnitude of the coefficient on the interaction and Overestimate is positive and significant. Overestimation by 1 letter results in roughly 0.9 letters of inflation. More crucially, the coefficient on the treatment variable is unaffected after controlling for overestimation. Thus, the difference in misinformation across treatments is not being driven by forecast errors. We deliberately designed our experiment to allow for future uncertainty and unintentional misrepresentation to enter into our game since these forces are relevant in many communication environments. We see that future uncertainty does lead to higher misinformation in MB compared with MA, though the overall magnitude of this effect is small in our domain. Column (3) reports the same regression conditioning on workers who sent inflated messages, leaving out all conservative and fully informative messages. It shows that higher misinformation in the MB treatment is driven not only by a larger number of workers lying but by the fact that the lies are of greater magnitude than in the MA treatment. Overall, we conclude that misinformation is significantly higher in the MB treatment than in the MA treatment. Result 1. Individuals are more dishonest when they speak of their future actions than when they report on past actions. In the next two subsections, we break down misinformation into its two components—message and action—and show that both are responsible for the observed difference in behaviour. 3.2. Effort The total number of letters encoded by workers for both projects combined is identical across treatments (an average of 87.6 letters in the MB treatment and 86.8 letters in the MA treatment, p-value=0.66). This is expected since there is no difference in the ability to encode across treatments as measured by their Part 1 performance. If workers had allocated all their work to the Joint Project, this would translate to a 78.9% and 78.8% chance of the Joint Project being successful in the MB and MA treatment, respectively. However, most workers distribute their time working across both projects; hence, the mean number of letters encoded for the Joint Project and the corresponding probability of success are considerably lower.22 Allocation of Effort Over Time. Recall that a worker decides which project he wants to start working on and can switch between working on his two projects any number of times during the work stage. Figure 3 illustrates the fraction of workers working on the Joint Project at every point in time in the work stage. We find that the temporal distribution of work is different between the two treatments. When the work stage begins, around 50% of workers start by working on the Joint Project, and this does not differ across treatments. As time elapses, this fraction shows a significant downward trend in the MB treatment (p-value<0.001), while in the MA treatment, this fraction increases over time (p-value<0.001).23 This leads to 55% of workers in the MA treatment allocating more than half their time to working on the Joint Project, while only 40% do so in the MB (p-value=0.03).24 Fig. 3. Open in new tabDownload slide Temporal Distribution of Work on the Joint Project. Fig. 3. Open in new tabDownload slide Temporal Distribution of Work on the Joint Project. We find that, in both treatments, the highest fraction of workers work on the Joint Project closest to the time of sending the message. In the MB treatment, work on the Joint Project is highest in the first quarter of the work stage, while in the MA treatment work is highest in the last quarter of the work stage. This suggests that the moral cost of sending a false message may be at the ‘top of mind’ closest to the time of sending the message, and may motivate the worker to work on the Joint Project. The dynamic nature of our task also provides an interesting insight on worker ‘type’. Across both treatments, we find those workers who start with the Joint Project encode nearly three times as much for the Joint Project as those who start with the Personal Project (57 letters vs 20 letters, p-value<0.001). Hence, initial choice of project is a good indicator of future behaviour. In the Online Appendix, we present a number of secondary results on workers’ switching patterns. Work Across Time. A closer look at Figure 3 reveals that the work allocation decisions start diverging around the halfway mark of the work stage. There is no difference in the average number of letters encoded for the Joint Project across treatments in the first two minutes of the work stage (21.6 in MB vs. 20.7 in MA, p-value=0.757). However, in the second half of the work stage, workers in the MA treatment encoded significantly more letters for the Joint Project (14.8 in MB vs. 22.4 in MA, p-value=0.003). Over the entire work stage, this leads to higher work for the Joint Project in MA than in MB. Though subjects work directionally more on the Joint Project in the MA treatment on average (36.4 letters in MB and 43.2 letters in MA), the raw difference is not significant at conventional levels (p-value=0.125). After controlling for ability and demographics, work done on the Joint Project is significantly different across the treatments (p-value=0.055), as reported in the regression in Table 3 Column (2).25 Our results are robust to considering the following as dependent variables: the fraction of total work done on Joint Project, fraction of total time devoted to the Joint Project, and the probability of success of the Joint Project (Online Appendix Table A2). Overall we find that the act of sending a message after the Work Stage, instead of before, induces workers to be more co-operative on average. Table 3. Allocation of Effort. . Predicting number of letters encoded for . . Both Projects . Joint Project . . (1) . (2) . (3) . (4) . . . All obs. . <= Median . > Median . Message Before 0.60 −8.16* −10.60*** −5.37 (0.99) (4.22) (3.20) (3.86) Part 1 performance 1.19*** 0.40 −0.03 0.12 (0.05) (0.26) (0.17) (0.24) Constant 10.68*** 22.82 25.83** 56.45*** (3.75) (18.02) (12.55) (17.01) Controls Yes Yes Yes Yes No. of obs. 190 190 95 95 R2 0.72 0.09 0.20 0.14 . Predicting number of letters encoded for . . Both Projects . Joint Project . . (1) . (2) . (3) . (4) . . . All obs. . <= Median . > Median . Message Before 0.60 −8.16* −10.60*** −5.37 (0.99) (4.22) (3.20) (3.86) Part 1 performance 1.19*** 0.40 −0.03 0.12 (0.05) (0.26) (0.17) (0.24) Constant 10.68*** 22.82 25.83** 56.45*** (3.75) (18.02) (12.55) (17.01) Controls Yes Yes Yes Yes No. of obs. 190 190 95 95 R2 0.72 0.09 0.20 0.14 Notes: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are robust standard errors. Controls include a dummy for gender, a dummy if the participant’s native language is English, dummies for year in school and a dummy for graduate student. Message Before is a treatment dummy variable (1=MB, 0=MA) and Part 1 performance is a subject’s performance in the Part 1 calibration. The median subject in the MB and MA treatment encoded 37 and 43.5 letters respectively for the Joint Project. Open in new tab Table 3. Allocation of Effort. . Predicting number of letters encoded for . . Both Projects . Joint Project . . (1) . (2) . (3) . (4) . . . All obs. . <= Median . > Median . Message Before 0.60 −8.16* −10.60*** −5.37 (0.99) (4.22) (3.20) (3.86) Part 1 performance 1.19*** 0.40 −0.03 0.12 (0.05) (0.26) (0.17) (0.24) Constant 10.68*** 22.82 25.83** 56.45*** (3.75) (18.02) (12.55) (17.01) Controls Yes Yes Yes Yes No. of obs. 190 190 95 95 R2 0.72 0.09 0.20 0.14 . Predicting number of letters encoded for . . Both Projects . Joint Project . . (1) . (2) . (3) . (4) . . . All obs. . <= Median . > Median . Message Before 0.60 −8.16* −10.60*** −5.37 (0.99) (4.22) (3.20) (3.86) Part 1 performance 1.19*** 0.40 −0.03 0.12 (0.05) (0.26) (0.17) (0.24) Constant 10.68*** 22.82 25.83** 56.45*** (3.75) (18.02) (12.55) (17.01) Controls Yes Yes Yes Yes No. of obs. 190 190 95 95 R2 0.72 0.09 0.20 0.14 Notes: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are robust standard errors. Controls include a dummy for gender, a dummy if the participant’s native language is English, dummies for year in school and a dummy for graduate student. Message Before is a treatment dummy variable (1=MB, 0=MA) and Part 1 performance is a subject’s performance in the Part 1 calibration. The median subject in the MB and MA treatment encoded 37 and 43.5 letters respectively for the Joint Project. Open in new tab To gain more insight into how timing affects the distribution of work done on the Joint Project, we split the sample around the respective medians (37 letters in MB and 43.5 letters in MA) and estimate the treatment effect. Columns (3) and (4) provide the results. We find that the effect of timing is only significant among the lower quantiles.26 These regressions indicate that timing does not affect the entire distribution, but the primary effect of the treatment is concentrated on individuals in the lower quantiles of effort. Through additional tasks reported in Section B.B3 of the Online Appendix, we find that the lower quantiles represent individuals who are less altruistic in general, and hence have a larger margin to deceive. Therefore, our results suggest that the timing of communication primarily affects individuals who are less altruistic. These results make an important addition to the literature on pre-play communication, which to date has focused on static decision tasks.27 Our dynamic decision context tracks co-operation over a longer time horizon, and we find that patterns of work allocation differ conditional on timing. More importantly, we find that individuals change their overall behaviour as a response to the difference in timing. Result 2. Aggregate real-effort work on the Joint Project decays after communicating in Message Before but increases in Message After. Overall, we find higher work on average in Message After. 3.3. Messages Before turning our attention to the managers’ investment decisions, we analyse the information managers have at the time of investment by comparing messages sent in the MB and MA treatments. We show that messages are more inflated in MB—conditional on (perceived) ability, messages sent in the MB treatment state higher levels of work compared with messages in the MA treatment. Figure 4 shows the frequency of messages sent by workers in MB and MA. Lower messages are more common in the MA treatment while higher messages are more common in the MB treatment. The modal message interval is 70–80 letters for the MB treatment, while it is 50–60 for the MA treatment. On average, workers in the MB treatment promise to encode 68.5 letters for the Joint Project, while workers in the MA treatment report they had encoded 61.2 letters (p-value=0.01, K-S p-value=0.004).28 Fig. 4. Open in new tabDownload slide Distribution of Messages. Notes: Frequency of the number of letters indicated in messages sent in the MB (darker) and the MA (lighter) treatments. Bin width is 10 letters. Messages in which workers did not recommend investment are excluded. Fig. 4. Open in new tabDownload slide Distribution of Messages. Notes: Frequency of the number of letters indicated in messages sent in the MB (darker) and the MA (lighter) treatments. Bin width is 10 letters. Messages in which workers did not recommend investment are excluded. As previously discussed, messages could be exaggerated in the MB treatment due to workers being overconfident about their ability. It is therefore important to compare messages across treatments conditional on the information that the workers had about their performance in Part 2 at the time of sending the message. We consider two variables. First, we compare the fraction of the total work that workers state they will allocate (or have allocated) to the Joint Project. In the MA treatment, workers know how much they have worked, so a message m implies allocating |$\frac{m}{w_{total}}$| to the Joint Project. In the MB treatment, a message m implies allocating |$\frac{m}{\hat{w}_{total}}$|⁠, where |$\hat{w}_{total}$| is the worker’s forecast of the total number of letters he will be able to encode in four minutes. We find that workers promise 81% of their total work on average to the Joint Project, compared with reporting that they have devoted 70% of the total on average when they communicate after (p-value=0.005).29 Another clear indication that a worker intends to deceive the manager is if his message states a number which he believes is unachievable for him in the four minutes of work time. This occurs when m > wtotal in the MA treatment or |$m\gt \hat{w}_{total}$| in the MB treatment. Such unachievable messages comprise 18% of all messages in the MB treatment and only 7% in the MA treatment (p-value=0.03). These results indicate that workers knowingly inflate their messages more when sending a message before working than when sending one after. Result 3. Messages state higher levels of work on average in the Message Before treatment compared with in the Message After treatment. Thus, the higher misinformation in the MB treatment documented in Subsection 3.1 is a result of both lower work and higher messages. 3.4. The Manager Decision The next question that naturally arises is how managers respond to messages and whether this varies by treatment. We focus on managers who received a message recommending investment. Recall that a manager is matched with multiple workers (maximum three), so most managers make three investment decisions and can potentially receive three messages.30 We have a total of 73 subjects in the role of manager, out of which 71 subjects received at least one message recommending investment. Non-parametric tests are based on subject averages of the relevant variables. We first explore whether managers expect work on the Joint Project to be different across the treatments. Analysing managers’ beliefs, there is no significant difference in the number of letters they think the worker will encode for the Joint Project. Overall managers expect workers to encode on average 46.3 letters in the MB treatment and 51.1 letters in the MA treatment (p-value=0.35). Managers’ investment decisions reflect this as they are equally likely to invest across treatments. On average, managers invest 55.8% of the time in the MB treatment compared with 55.4% in the MA treatment (n1=37, n2=34, p-value=0.95).31 To understand how informative managers expect the messages received to be, we look at correlations between message received and the managers' expectation of the work on the Joint Project (EM(wJ)). On average, managers expect messages to be more informative in MA (ρ=0.57) than in MB (ρ=0.22) (p=0.004). Though workers’ messages are more informative in MA and the managers expect this directionally, we do not find this translating to managers in MA forming more accurate beliefs about realised work. The correlation between realised and expected work is 0.29 in MA and 0.25 in MB (p=0.78). If the managers correctly discounted the messages, then on average they would have discounted by 32.1 letters in MB and 17.9 letters in MA, the amount of actual message inflation. In our data, managers are too trusting, discounting messages less than they should. Managers in MB discount messages by 22.3 letters, thus taking into account 69% of the message inflation. In MA, managers discount by 11.4 letters, thus taking into account only 63% of the actual message inflation. Hence, we find that although managers correctly anticipate the higher misinformation in MB, they misjudge its magnitude. This has potentially meaningful consequences for the managers. Managers’ expected payoffs are the same across treatments ($6.96 vs $7.24, p-value=0.50). However, the empirical best response for risk-neutral managers would guarantee weakly higher payoffs for managers in MA than MB ($8.30 vs $8.60, p-value=0.09). Figure 5 shows the cumulative distribution functions of managers’ actual expected payoffs and their expected payoffs under the assumption that work is perfectly observable. We calculate this assuming the risk-neutral best response for managers given actual worker effort. That is, if the worker encoded more than 23 letters, we say that the manager will invest, but will not invest otherwise. There is a significant gap between the MB and MA best response distributions, but actual manager behaviour does not capture this. Hence we find that managers in MA are unable to reap the potential advantages of the more informative communication. Fig. 5. Open in new tabDownload slide CDF of Expected Payoff. Notes: The best response is computed assuming risk neutrality. Managers are assumed to invest only when wJ ≥ 23. Fig. 5. Open in new tabDownload slide CDF of Expected Payoff. Notes: The best response is computed assuming risk neutrality. Managers are assumed to invest only when wJ ≥ 23. Result 4. Managers anticipate higher misinformation in Message Before compared with Message After but underestimate the extent of the treatment difference. 4. Possible Explanations Overall, we find that the timing of communication affects behaviour. Workers are more honest and cooperative when communicating after taking actions compared to communicating before. We designed our experiment to be a first step in establishing the existence of a phenomenon, but our design does not allow for disentangling all possible explanations of the observed pattern. In this section, we explore possible explanations for our observed treatment differences. We provide some initial evidence for/against these explanations, but we believe focused analysis on the underlying mechanisms will be a fruitful avenue for future research. 4.1. Beliefs of the Manager’s Perception of the Message It is possible that, independent of the workers’ actual behaviour, workers expect managers to discount a given message more in the MB treatment than in the MA treatment.32 Workers could respond to such beliefs in two ways. One: workers can send a higher message in the MB treatment to compensate for this, leading to higher observed misinformation. Two: workers send the same message in both treatments, but work less in the MB treatment as they believe managers expect them to do so.33 To test whether the difference in misinformation is a response to what workers think managers expect, we first examine whether workers expect managers to discount a given message differently across the two treatments. Recall that we asked managers to estimate the number of letters the worker encoded for the Joint Project, (EM(wJ)). Then we asked the worker to guess the number the manager reported, (EW(EM(wJ))). We use the worker’s guess as a measure of his beliefs of the amount of work the manager expects him to do. We calculate a measure of how much the worker expects the manager will discount his message by calculating the difference between the message sent and the work the worker thinks the manager expects (Discount:= m − EW(EM(wJ))). We find that workers expect messages to be discounted by 17.7 letters on average in the MB treatment compared with 10.1 letters in the MA treatment (p-value= 0.03).34 If higher misinformation in MB were driven by workers’ beliefs of the managers’ expectations, this difference should account for the higher observed misinformation in the MB treatment. Table 4 augments our regressions predicting misinformation in Table 2 with the variable Discount. Discount significantly increases the amount of misinformation, although the magnitude of the effect is small. Additionally, the coefficient of MB is still significant implying that the difference in expectations is not sufficient to explain the difference in misinformation between the two treatments. Thus, it’s not the case that the difference in misinformation across treatments is due solely to workers’ differing expectations of the managers' beliefs. Table 4. Amount of Misinformation. Dependent variable: m − wJ . Message Before 11.24*** (3.77) Part 1 performance 0.18 (0.21) Overestimate −0.39 (0.30) Overestimate × Message Before 1.08** (0.45) Discount 0.65*** (0.06) Constant −4.31 (13.05) Controls Yes No. of obs. 190 R2 0.39 Dependent variable: m − wJ . Message Before 11.24*** (3.77) Part 1 performance 0.18 (0.21) Overestimate −0.39 (0.30) Overestimate × Message Before 1.08** (0.45) Discount 0.65*** (0.06) Constant −4.31 (13.05) Controls Yes No. of obs. 190 R2 0.39 Notes: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are robust standard errors. Controls include a gender dummy, a dummy for native language, and year-of-study dummies. Message Before is a treatment dummy variable (1=MB, 0=MA), Part 1 performance is a subject’s performance in the Part 1 calibration, Overestimate is a measure of forecast error, and Discount is how much by which the worker expects the manager will discount his message. Open in new tab Table 4. Amount of Misinformation. Dependent variable: m − wJ . Message Before 11.24*** (3.77) Part 1 performance 0.18 (0.21) Overestimate −0.39 (0.30) Overestimate × Message Before 1.08** (0.45) Discount 0.65*** (0.06) Constant −4.31 (13.05) Controls Yes No. of obs. 190 R2 0.39 Dependent variable: m − wJ . Message Before 11.24*** (3.77) Part 1 performance 0.18 (0.21) Overestimate −0.39 (0.30) Overestimate × Message Before 1.08** (0.45) Discount 0.65*** (0.06) Constant −4.31 (13.05) Controls Yes No. of obs. 190 R2 0.39 Notes: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are robust standard errors. Controls include a gender dummy, a dummy for native language, and year-of-study dummies. Message Before is a treatment dummy variable (1=MB, 0=MA), Part 1 performance is a subject’s performance in the Part 1 calibration, Overestimate is a measure of forecast error, and Discount is how much by which the worker expects the manager will discount his message. Open in new tab 4.2. Moral Wiggle Room A second potential explanation of our treatment differences is that workers’ intentions are less apparent in the MB treatment and the workers may use this moral wiggle room or veil of deniability to be more dishonest. This is perfectly captured in one subject’s post-session questionnaire justification of why he would prefer to be the manager in MA rather than MB: ‘I think (workers) may use the failed promise as an excuse to encode more for themselves and just say they couldn’t do as much as they hoped.’ In our game, managers are unable to infer whether a failed Joint Project in the MB treatment was a result of intentional deception or was due to the worker overestimating his ability and not being able to encode as many letters as expected. This concern is not present in MA since workers communicate after seeing their realised effort. If workers have a preference for appearing truthful rather than actually being truthful, they may exploit this second-order uncertainty to deliberately inflate their message in the MB treatment. We use standard one-shot matrix games to address the impact of moral wiggle room and explore the robustness of our results to other decision contexts. The binary nature of the task eliminates concerns about managers’ inability to infer workers’ intentions, so moral wiggle room has no room to affect behaviour in these games. After the real-effort task, before receiving any feedback on Part 2, participants made decisions in five 2×2 matrix games. In each game, the sender first chooses an action, followed by the receiver. Even though the sender moves first, his choice is unobservable to the receiver. As in the real-effort task, the sender can signal his action to the receiver through a message. Treatments vary in when the sender could send the message, either before or after he took his action. In the message, the sender could signal his intended action or chosen action depending upon the treatment, as well as recommend an action to the receiver. Our primary interest is in the games depicted in Table 5. Note, the games in Table 5 have the same strategic considerations as the real-effort manager–worker game, with a reduction in the number of choices available for the worker (in this case the sender). The sender has a dominant strategy to choose D, identical to the worker having a dominant strategy to work on his Personal Project in the real-effort task. The receiver faces a co-ordination game, in which she wants to choose C if the sender chooses C (invest if worker works on Joint Project), and otherwise will choose D (not invest). Assuming self-interested players with no costs of deception, the Nash equilibrium outcome for the game with communication is both players choose D. However, if individuals are other-regarding and/or suffer costs of deceiving, we would expect outcomes to be more co-operative as seen in the real-effort task. We look to see whether subjects misinform more in the MB treatment than in the MA treatment, in line with results from our real-effort task. Table 5. Matrix Games in the Choice Task. Receiver D C (a) Manager–Worker (High) Sender D 70, 70 130, 30 C 30, 80 90, 90 Receiver D C (b) Manager–Worker (Low) Sender D 70, 70 110, 30 C 30, 80 90, 90 Receiver D C (a) Manager–Worker (High) Sender D 70, 70 130, 30 C 30, 80 90, 90 Receiver D C (b) Manager–Worker (Low) Sender D 70, 70 110, 30 C 30, 80 90, 90 Open in new tab Table 5. Matrix Games in the Choice Task. Receiver D C (a) Manager–Worker (High) Sender D 70, 70 130, 30 C 30, 80 90, 90 Receiver D C (b) Manager–Worker (Low) Sender D 70, 70 110, 30 C 30, 80 90, 90 Receiver D C (a) Manager–Worker (High) Sender D 70, 70 130, 30 C 30, 80 90, 90 Receiver D C (b) Manager–Worker (Low) Sender D 70, 70 110, 30 C 30, 80 90, 90 Open in new tab In addition, we present subjects with two versions of this game to test directly how behaviour responds to changing the benefit from misinformation. The games in Table 5 differ only in that the temptation payoff for the sender is reduced from 130 (high stakes) to 110 (low stakes). This weakens the incentives to misinform and, if individuals have a positive cost of deceiving, we should see less frequent deception in the low-stakes games compared with the high-stakes games. At the beginning of the Choice Task, participants were randomised into roles of sender and receiver and played in fixed roles for all five rounds. In each round, they were presented with a different payoff matrix. In addition to the two games in Table 5, we include three other games for robustness. Discussion of these games can be found in Online Appendix Section B.B4. The order of the games was randomised across sessions. If this part were chosen for payment, participants were paid for their decisions in one randomly selected round. Results. We begin by reporting the fraction of senders who misinform.35 The first row of Table 6 indicates the fraction of senders who misinform in each game across treatments. In the high-stakes game, we find strong confirmation of our previous results—senders deceive significantly more in the MB than the MA treatment. However, the data fail to support these hypotheses when considering the low-stakes games. Table 6. Signal and Actions. . High stakes . Low stakes . . Message . Message . . Message . Message . . . Before . After . p-value . Before . After . p-value . Percent misinforming 63.5 38.2 0.003 45.9 48.5 0.76 Percent signalling C 91.9 75.0 0.007 82.4 80.9 0.81 Percent choosing C 29.7 44.1 0.08 36.5 32.4 0.61 . High stakes . Low stakes . . Message . Message . . Message . Message . . . Before . After . p-value . Before . After . p-value . Percent misinforming 63.5 38.2 0.003 45.9 48.5 0.76 Percent signalling C 91.9 75.0 0.007 82.4 80.9 0.81 Percent choosing C 29.7 44.1 0.08 36.5 32.4 0.61 Open in new tab Table 6. Signal and Actions. . High stakes . Low stakes . . Message . Message . . Message . Message . . . Before . After . p-value . Before . After . p-value . Percent misinforming 63.5 38.2 0.003 45.9 48.5 0.76 Percent signalling C 91.9 75.0 0.007 82.4 80.9 0.81 Percent choosing C 29.7 44.1 0.08 36.5 32.4 0.61 . High stakes . Low stakes . . Message . Message . . Message . Message . . . Before . After . p-value . Before . After . p-value . Percent misinforming 63.5 38.2 0.003 45.9 48.5 0.76 Percent signalling C 91.9 75.0 0.007 82.4 80.9 0.81 Percent choosing C 29.7 44.1 0.08 36.5 32.4 0.61 Open in new tab These results are formalised in Table 7, which reports results from probit regressions predicting whether or not a sender misinformed. In addition to the treatment dummy (Message Before) and demographic controls, we include: (i) Round, a variable signifying the period in which the game was presented; and (ii) Worker, a dummy equal to one if the the sender had been a worker in the real-effort task. The positive coefficient on Message Before in Column (1) confirms our conjecture that individuals are more reluctant to lie about a past action compared with a future action in the high-stakes game. Being in the MB treatment increases the probability of misinforming by 24 percentage points. Since treatments no longer differ in how transparent the sender’s intentions are, this difference cannot be driven by moral wiggle room. Table 7. Probit Predicting Whether Sender Misinforms in the Choice Task. Dependent variable: probability sender misinforms . . Manager–worker . . High . Low . . (1) . (2) . Message Before 0.24*** 0.04 (0.07) (0.08) Round 0.02 0.05** (0.03) (0.03) Worker −0.01 0.06 (0.10) (0.10) Controls Yes Yes No. of obs. 142 142 Dependent variable: probability sender misinforms . . Manager–worker . . High . Low . . (1) . (2) . Message Before 0.24*** 0.04 (0.07) (0.08) Round 0.02 0.05** (0.03) (0.03) Worker −0.01 0.06 (0.10) (0.10) Controls Yes Yes No. of obs. 142 142 Notes: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are robust standard errors. Controls include a dummy for gender, a dummy if the participant’s native language is English, dummies for year in school, and a dummy for being a graduate student. Message Before is a treatment dummy variable (1=MB, 0=MA), Worker is a dummy variable for role in Part 2 (1=worker, 0=manager), and Round is the order of the matrix game. Marginal effects reported. Open in new tab Table 7. Probit Predicting Whether Sender Misinforms in the Choice Task. Dependent variable: probability sender misinforms . . Manager–worker . . High . Low . . (1) . (2) . Message Before 0.24*** 0.04 (0.07) (0.08) Round 0.02 0.05** (0.03) (0.03) Worker −0.01 0.06 (0.10) (0.10) Controls Yes Yes No. of obs. 142 142 Dependent variable: probability sender misinforms . . Manager–worker . . High . Low . . (1) . (2) . Message Before 0.24*** 0.04 (0.07) (0.08) Round 0.02 0.05** (0.03) (0.03) Worker −0.01 0.06 (0.10) (0.10) Controls Yes Yes No. of obs. 142 142 Notes: *p < 0.10, **p < 0.05, ***p < 0.01. Numbers in parentheses are robust standard errors. Controls include a dummy for gender, a dummy if the participant’s native language is English, dummies for year in school, and a dummy for being a graduate student. Message Before is a treatment dummy variable (1=MB, 0=MA), Worker is a dummy variable for role in Part 2 (1=worker, 0=manager), and Round is the order of the matrix game. Marginal effects reported. Open in new tab In the low-stakes games, while we observe a positive coefficient on Message Before, this is not statistically significant. There are several possible explanations for this. It is possible that the timing is relevant only for a subset of participants—those who have substantial costs of misinforming. Since the benefit from misinforming shrinks in the low-stakes game (the difference between the temptation payoff and co-operation payoff is only $2), one would expect only senders with very low costs of deception to misinform. Alternatively, note that the sender’s decision and signal are binary variables. Unlike the real-effort task, where we captured the size of the misinformation, the choice task only allows us to capture whether or not the sender misinformed. This could possibly make it harder to identify a small treatment effect. Analogous to the real-effort task, we can decompose the misinformation in the Choice Task into its two components: signal and action. Due to the binary nature of our decision variables, we compare the frequency of co-operative signals and actions across treatments. Table 6 displays the overall fraction of senders who signal the co-operative action C and the fraction of senders who choose C. Recall that, in the real-effort task, messages sent before the action was taken promised a higher level of co-operation. Row 2 of Table 6 indicates that same pattern. A vast majority of senders choose to signal C in both treatments. The percentage of C signals is always higher in the MB treatment, and significantly more so in the high-stakes game. Not only do workers send higher messages in MB; they also co-operate less often. Row 3 shows that individuals are significantly more likely to choose C in MA than in MB in the high-stakes game. Overall, we find that individuals misinform more in MB than MA when the potential gains from misinformation are high, even when we remove potential moral wiggle room. This suggests that moral wiggle room is not the only mechanism driving our main result. 4.3. Differential Cost of Deception We asked subjects directly whether and why they think that timing of communication would impact behaviour. In a post-session questionnaire all subjects (managers and workers) were presented with the following question before seeing the results: Imagine you are (the manager) and you can now determine when you want (the worker) to send you the message. Choose which scenario you would pick. Scenario 1: (The worker) sends a message before he begins working. Scenario 2: (The worker) sends a message after he finishes working. In both scenarios, you do not learn how many letters (the worker) encoded or whether or not the project was successful. You only see his message before deciding to invest. Table 8 presents their responses. A large percentage of subjects stated a strict preference for the worker sending a message only after he has worked. We also asked subjects to give reasons supporting their choice of response. Though the reasons varied, they could be categorised into three broad justifications: accuracy, differential cost of deception, and moral wiggle room. Table 8. Preferred Treatment. Responses . MB . MA . p-value . Prefer MB 10.8 19.9 0.03 Prefer MA 51.4 45.6 0.33 Indifferent 37.8 34.6 0.57 Responses . MB . MA . p-value . Prefer MB 10.8 19.9 0.03 Prefer MA 51.4 45.6 0.33 Indifferent 37.8 34.6 0.57 Notes: Percentage of subjects in each treatment who stated preferring MB or MA or being indifferent to the two treatments. Open in new tab Table 8. Preferred Treatment. Responses . MB . MA . p-value . Prefer MB 10.8 19.9 0.03 Prefer MA 51.4 45.6 0.33 Indifferent 37.8 34.6 0.57 Responses . MB . MA . p-value . Prefer MB 10.8 19.9 0.03 Prefer MA 51.4 45.6 0.33 Indifferent 37.8 34.6 0.57 Notes: Percentage of subjects in each treatment who stated preferring MB or MA or being indifferent to the two treatments. Open in new tab The most commonly cited argument (≈ 60%) for preferring Scenario 2 was that the worker could have a better estimate of his performance when sending a message after working. Some subjects qualified this argument by stating this preference was based on the assumption that workers would be honest. However, given our analysis, we already know that this uncertain ability is not the reason driving the difference in behaviour. Some representative responses are given below. ‘At least there’s a better chance of the number being more accurate than a projection before Player A starts.’ ‘Would prefer to know what was actually done, assuming they are being honest.’ The remaining justification, and the explanation that we find most compelling, is that the moral cost of deception in MA is higher than that in MB. A number of participants’ responses hinted at it being psychologically more difficult to deceive later (≈ 27%), with a few illustrative responses below. ‘I think it’s harder to lie about something you *just* did.’ ‘It would be harder to lie, knowing what the results were.’ ‘...After they’ve already completed it, there is no uncertainty, and lying about the number would weigh more heavily on their conscience.’ These responses point towards the idea that a realised level of work is morally difficult to misrepresent outright. It may be that subjects find it harder to attribute their dishonesty to external factors when the work has been realised.36 This differs from moral wiggle room, where promise breaking results from individuals hiding behind a ‘veil of deniability’. While moral wiggle room is likely to play a role in certain environments, results from the matrix games and the responses above together point to the idea that individuals may have differential costs of deception depending on timing, absent moral wiggle room. 5. Discussion Over the past decade, an extensive literature has documented that non-binding statements of intent or promises can be informative and can increase co-operation in social dilemmas. But not all instances of communication are forward looking. We design a two-player hidden action game to compare ex ante and ex post communication. We find that a communication regime in which individuals report on past decisions results in more truthful communication and in higher overall effort than one in which individuals communicate about their intended future effort. Our results show that timing of communication is a critical variable that merits attention in the design of mechanisms. In addition, our results raise questions about the appropriateness of conflating promise breaking and lying about a past action. Over the years, legal thinkers and philosophers have discussed whether misrepresenting intent is the same as misrepresenting a fact (Cavico, 1997; Ayres and Klass, 2008). We provide empirical investigation into this question and show that they are, in fact, different. We hypothesise that the observed difference in our data has two behavioural foundations. First, the moral cost of lying about a past action is higher than the cost of breaking a promise. Qualitative responses from subjects, as well as our own introspection, suggest that lies about past actions weigh more heavily on our consciences than do broken promises. Previous papers have shown that higher mutability of an outcome is associated with more misreporting (Batson et al., 1997, Shalvi et al., 2011, Shalvi et al., 2012, Shalvi et al., 2015). We don’t directly manipulate mutability, which was the focus of their papers, but ‘moral wiggle room’ under ex ante communication could be thought to play a similar role. The future is inherently more mutable than the past, which could contribute to higher misinformation in statements about future actions. We think it would be interesting for future research to look into disentangling the pure timing aspect from other related notions of mutability and uncertainty. Secondly, our results on the patterns of work over time suggest that communication may trigger moral responses that operate, at least partially, through salience which is asymmetric for past and future actions. Such temporal asymmetry has previously been demonstrated in Caruso et al. (2008) in a non-strategic decision context. Caruso et al. (2008) find that individuals value future events more than past events. Whether this ‘temporal value asymmetry’ is similarly driving results in our environment leaves an interesting question for future research. In addition, we know relatively little about the impact of communication in environments with long time horizons. Our article takes a first step in addressing this, but our understanding of communication would benefit greatly from more focused study in this area. Finally, our results bring to light the need for more concentrated research on the salience effect of norms and moral decision making. Shu et al. (2012) find that signing tax forms on top versus at the bottom increases the frequency of truthful reporting. They suggest that signing on top primes individuals to have morality at the top of mind, so they are more likely to follow the honest social norm. In their environment, however, individuals are deciding how truthfully to report on an exogenous outcome.37 We show that when a person is able to jointly optimise message and action, the patterns of lying may be reversed. Our environment differs from theirs in many other regards. In particular, subjects were primed with a moral stance to report truthfully in their experiment. In contrast, we made no mention of morality and subjects were free to choose their own honesty levels. Most daily interactions are free from moral priming, so if this aspect of the environment is contributing to the differences in our results, the direction of misreporting in our article is what we should expect to observe more frequently. Experiments looking into the aspects of these environments that contribute to these differences in behaviour would be very interesting. This strikes us as particularly important for policy makers and institutional designers who may wish to use this information to nudge behaviour toward truth telling and co-operation. Additional Supporting Information may be found in the online version of this article: Online Appendix Replication Package Notes The data and codes for this paper are available on the Journal website. They were checked for their ability to reproduce the results presented in the paper. We would like to thank Hal Arkes, Katie Baldiga Coffman, Lucas Coffman, Paul J. Healy, John Kagel, Jim Peck, Huanxing Yang, Rick Young, the Editor, two anonymous referees and the seminar participants at Econometric Society European Winter Meeting, Economic Science Association North American Meeting and the Ohio State Accounting Department Brownbag for their helpful comments and suggestions. Research support was provided by the Decision Science Collaborative, Ohio State University. Footnotes 1 Interactions in these environments could occur repeatedly. To isolate the aspect of timing on preferences for truth telling, this article considers a one-shot environment. 2 In a notable paper, Brandts et al. (2016) introduce a rich communication framework in which buyers and sellers can communicate over the planning as well as execution period to establish informal contracts. 3 In these papers, subjects were not aware of the reporting opportunity when completing the task or making contribution decisions. As a result, their message became akin to reporting on an exogenous state as the outcome had already been determined. 4 In their treatment in which subjects communicate about current actions, Serra-Garcia et al. (2013) present action and message decisions to subjects on the same screen, so decisions were essentially simultaneous rather than sequential, and it is unclear which question subjects answer first. 5 During the experiment we use neutral language and refer to the players as ‘Player A’ and ‘Player B’. 6 All experimental points were converted into dollar payments at the end of the session, at a rate of 10 points = 1 USD. 7 The specific functional form was chosen so that an average worker could guarantee roughly 80% chance of success if he works for all four minutes. We calibrated this from an incentivised pilot session. 8 We use the same functional form for the Personal Project payoff and the Joint Project success function because we wanted to remove anchoring effects that may make subjects lean towards working on one project over the other. 9 There could be many motivations for a person to be unwilling to deceive, including belief-dependent guilt aversion (Charness and Dufwenberg, 2006; Battigalli et al., 2013), fixed cost of being inconsistent (Vanberg, 2008) or aversion to lying (Gneezy, 2005). 10 Theoretical predictions taking into account other-regarding preferences and preferences for honesty would depend on many variables, such as preference parameters, distribution of types in the population, fraction of naive managers, etc. But unless one or more of these variables is assumed to differ across treatments, the predictions for MB and MA would be equivalent. Given that we do see empirical differences between MA and MB, it would be interesting for future research to isolate and measure these parameters independently and compare across timing of communication. 11 To avoid framing effects, the order of these buttons was randomised on their screens. 12 Our message space is slightly richer than a yes–no check box used in these papers. When sending a message, subjects choose any number to state in their messages, making the range of promises and reports large. Since the subjects are free to choose any number, there is no clear ‘expected’ message as there is in a bare promise. Bare promises run the risk that sending a promise is simply expected by everyone (in fact, Glaeser et al. (2000) find that bare promises anchor responses on the rule), but there is no one message in our design that carries this expectation. So while we use pre-specified messages, subjects did have many available message options. But our message space certainly lacks the personal elements present in free-form communication. 13 Previous research has shown that the object of communication affects the cost of lying. Misreporting is lower when individuals communicate about their effort versus private information (Serra-Garcia et al., 2013) and the monetary value of effort (Desai and Kouchaki, 2015). 14 While this may seem a bit unnatural in the MB treatment, research on epistemic versus aleatory uncertainty suggests that individuals treat unknowable uncertainty differently from uncertainty that is due to one’s lack of knowledge but theoretically discoverable (Rothbart and Snyder, 1970). To avoid such confounds affecting the manager’s investment decision, we keep the timing of investment the same across treatments. 15 Belief elicitation was done only after actions were taken. In the instructions, subjects were told that there would be a bonus stage where they could earn additional points, but were not told any details about the questions they would be asked. 16 The elicitation was not incentivised to avoid moral hazard problems. In general, the literature offers support for the idea that beliefs should be paid for using incentive-compatible mechanisms (Schotter and Trevino, 2014). In eliciting the forecast, we faced a trade-off—incentivising the accuracy of the forecast may have led to a distortion of the effort in Part 2 of the experiment. As a precaution, we specifically looked out for real-effort tasks where monetary incentives may matter less. We chose the encoding task as Clark and Friesen (2009) elicit forecasts of future performance in the encoding task using small incentives and no incentives and find no difference in participants’ forecast accuracy in the encoding task. All other beliefs in our experiment were properly incentivised. 17 Specifically, we randomised subjects into groups of four, with one subject as the manager and the other three as the worker. In four sessions, we did not have an even multiple of four subjects and had a remainder of two additional subjects. In this case, one of those subjects was a worker and one was a manager. So in these four instances, a manager was matched to only one worker. All other managers were matched with exactly three workers. 18 We analyse only these workers to begin with, since our main focus is on deception, which is only applicable when workers do send a message. There are no significant differences in the frequency of message categories selected across treatments. 19 It’s possible that miscalibration can work in the opposite direction as well, and we do find a positive fraction of workers with conservative messages in the MB treatment. We discuss this in Section B.B1 of the Online Appendix, but it is important to note that since misinformation is higher in the MB treatment, such conservative messages only bring down the average message inflation in the MB treatment. 20 Online Appendix Figure A3 illustrates this in the distribution of misinformation after this calibration. 21 In fact, as Online Appendix Table A1 shows, the workers’ predicted (⁠|$\hat{w}_{total}$|⁠) and actual performance (wtotal) in Part 2 are very close on average, deviating by only ≈ two letters. We find nearly 50% of the workers have an individual forecast error of less than equal to five letters and 70% predict performance within an interval of 10% of their actual performance. Hence, our training helped calibrate the subjects about their ability on average. 22 69.0% of workers work on both projects, 18.4% work only on the Personal Project and 12.6% work on only the Joint Project. 23 In the first half of the work stage, the fraction of workers working on the Joint Project falls in both treatments (p-value<0.001). However, while in the second half this fraction continues to show a downward trend in MB (p-value=0.001) it increases in the MA treatment (p-value<0.001). The increase in the number of workers working on the Joint Project in the second half is so strong that over the entire work stage of four minutes we observe an upward trend in the MA treatment. All p-values are calculated from regressions with fraction of workers who work on the Joint Project as the dependent variable and time elapsed in the work stage as an independent variable. 24 It is possible that the decline in the fraction of promisors working on the Joint Project over time results from demotivated promisors who realise they cannot achieve the promised amount. We do not find evidence of this. Figure A4 in the Online Appendix shows a similar trend when conditioning only on promisors who were able to encode the promised amount. 25 Each of our controls tightens the standard errors. We see that the treatment effect is very strong for graduate students, so including the graduate dummy significantly reduces the standard errors. If we run the same regression dropping the graduate students, the coefficient on the treatment dummy is -6.78 and the p-value=0.12. 26 This is clearly shown in the CDF reported in Figure B2 of the Online Appendix. 27 Typically, subjects make a single binary choice after sending a message. In contrast, the subjects in our setting make a choice at every point in time over an interval of four minutes. 28 Online Appendix Table A3 confirms these results by regressing a worker’s message on the treatment dummy, proxy for ability, forecasted performance and our standard set of controls. 29 In reality, workers devote 42% and 49% of their total work to the Joint Project in the MB and MA treatments, respectively (p-value=0.15). 30 To make each decision independent, the managers are paid for one randomly selected decision and the worker’s level of work corresponding to that decision. 31 Though managers saw up to three messages, we do not find any effect of decision order or message rank on investment decisions. See Online Appendix Table A4 for details. 32 A possible reason could be if managers think that workers’ messages are unintentionally inflated in the MB treatment due to overconfidence. 33 This is in line with expectations-based guilt-aversion hypotheses, which propose that individuals suffer a psychological cost proportional to the amount by which they think they fail to meet others’ expectations of them (Charness and Dufwenberg, 2006; Ederer and Stremitzer, 2016; Di Bartolomeo et al., 2017). In our experiment, this would imply that a worker’s effort on the Joint Project will depend on how much effort he thinks that the manager expects him to put forth (the worker’s second-order belief: EW(EM(wJ))). A worker will encode a higher number of letters for the Joint Project when he thinks the manager expects him to do so compared with when he thinks that the manager does not expect him to do so. 34 This is confirmed by running an OLS regression predicting workers’ beliefs from the treatment dummy, the message sent and our standard set of controls. Table A5 shows that higher messages increase the number of letters the worker believes the manager expects him to encode for the Joint Project. Furthermore, controlling for the message, workers in the MB treatment have significantly lower second-order beliefs. 35 Although the sender can misinform the receiver in two possible ways—by signalling C while choosing D or by signalling D while choosing C—the latter strategy is hard to rationalise and extremely rare, constituting less than 1% of our observations. Our main analysis includes these observations, although all results are robust to excluding them. 36 We also asked participants who they would punish more: a person who broke his promise or a liar. 71% of participants stated that they wanted to punish a liar more than someone who broke his promise. 37 In their paper, subjects were not aware of the reporting opportunity when completing the task about which they later reported. As a result, their message became akin to reporting on an exogenous state as the outcome had already been determined. References Abeler J. , Becker A., Falk A. ( 2014 ). ‘ Representative evidence on lying costs ’, Journal of Public Economics , vol. 113 , pp. 96 – 104 . OpenURL Placeholder Text WorldCat Arya A. , Fellingham J., Glover J., Sivaramakrishnan K. ( 2000 ). ‘ Capital budgeting, the hold-up problem, and information system design ’, Management Science , vol. 46 ( 2 ), pp. 205 – 16 . OpenURL Placeholder Text WorldCat Ayres I. , Klass G. ( 2008 ). 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Bloom, David, E;Kuhn,, Michael;Prettner,, Klaus

doi: 10.1093/ej/ueaa061pmid: N/A

Abstract We analyse the economic consequences for poor countries of investing in female health within a unified growth model featuring health-related gender differences in productivity. Better female health accelerates the demographic transition and thereby the take-off towards sustained economic growth. By contrast, male health improvements delay the transition and take-off because they tend to raise fertility. However, households tend to prefer male health improvements over female health improvements because they imply a larger static utility gain. This highlights the existence of a dynamic trade-off between the short-run interests of households and long-run development goals. Although the interplay between gender (in)equality and economic development has received considerable attention in the literature, a key aspect of gender inequality relates to health, and this aspect has not yet been thoroughly examined.1 Generally, five channels appear to matter in this context: Healthy women are more able to participate productively in the labour market with direct consequences for effective labour supply and hence the level and growth of economic output (Albanesi and Olivetti, 2016). Better health increases the return on educational investment: this occurs both through lower morbidity, allowing for greater labour market participation at the intensive margin, and lower mortality, affecting labour market participation at the extensive margin (Jayachandran and Lleras-Muney, 2009; Albanesi and Olivetti, 2014). Better health of mothers affects the health of children directly through in utero effects and mothers’ ability to breastfeed and nourish their children in other ways (Field et al., 2009; Bhalotra and Rawlings, 2011). Female health thereby improves development prospects over the long run through direct intergenerational transmission of human capital (cf. Case and Ardington, 2006; Bloom et al., 2014a). In families with healthier mothers, child labour tends to occur less and the educational attainment of children tends to be higher (Mendolia et al., 2019). Better female health may lower fertility and thus youth dependency, with a knock-on effect on female labour participation and educational investments (Bloom et al., 2009; 2017). Lower fertility may arise as a direct consequence of improved reproductive health through availability of contraceptives (Bailey, 2006). But increases in the female opportunity cost of child rearing, following improvements in labour market prospects for healthier women, and health-driven increases in the return on education also trigger lower fertility indirectly. The consequence is a swing in the quality–quantity trade-off towards the quality of children (e.g., Galor and Weil, 2000; Soares and Falcão, 2008; Diebolt and Perrin, 2013a,b). Clearly, channels (iii)–(v) are specific to women. Moreover, as long as the opportunity cost of women’s time predominantly drives the quality–quantity trade-off, the effects of health improvements through channels (i) and (ii) are not gender neutral either. In this article, we contribute to the debate on the drivers and mechanisms of economic development by highlighting how the economic–demographic transition hinges on gender-specific health. To this end, we develop a micro-founded dynamic general equilibrium model that examines some of the mechanisms by which improvements in female health can stimulate economic development. Overlapping generations of families choose consumption, number of children, and educational investments in their children. Education in turn translates into the stock of human capital of the next generation. We integrate this decision making at the household level into a two-sector economy in which effective labour is either combined with a fixed factor in the production of goods or employed within an education sector. We solve for the dynamic general equilibrium and study the macroeconomic repercussions of individual choices and thereby the conditions under which the economy switches from a low-growth regime, corresponding to a poverty trap with high fertility and no educational investments, into a modern sustained growth regime with declining fertility and increasing educational investments. We examine how household choices vary with the level of female health and what the implications are for macroeconomic outcomes. Specifically, we seek to understand whether better female health contributes to higher rates of economic growth and an earlier transition from stagnation to sustained growth. As healthier women have better access to the labour market (and higher earnings), raising children incurs a higher opportunity cost even within the high-fertility regime. The resulting reduction in fertility tends to enhance economic growth from technology adoption, although the impact may be insubstantial until the take-off. More importantly, better female health facilitates the economic transition by lowering the earnings threshold at which educational investments in children become profitable. These investments then trigger both the educational and demographic transition that underlie economic development. While this suggests a decidedly positive role for female health in economic development, an offsetting tendency exists. This is because greater participation of healthy women in the labour market raises aggregate labour supply, which in turn depresses earnings in the low-growth regime and, thereby, the incentive for households to undertake investments in education. We show that despite this offsetting effect, female health unambiguously accelerates the economic transition. We contrast these findings with the impact of improvements in male health alone and with equiproportional improvements in the health of both genders. As long as men spend much less of their time on child rearing than do women—as in low-income countries—male health improvements tend to increase fertility through an income effect. This, in turn, slows down economic growth and the progress towards economic transition. For equiproportional health improvements for both genders, we find that economic growth during the low-growth regime remains unaffected, while it rises in the sustained growth regime. Strikingly, this finding mirrors the empirical results of Cervellati and Sunde (2011), according to which health improvements foster growth of per capita income after the demographic transition but not prior to it. Furthermore, we find that equiproportional health investments promote the transition from low growth to sustained growth, although not to the same extent as female health investments alone do.2 A recent empirical study provides some corroborating evidence. Klasing and Milionis (2020) show that vaccine-driven reductions in infectious disease mortality tend to be associated with larger GDP increases than reductions in infectious disease mortality that are unrelated to vaccination. In light of extensive evidence from medical research that, due to a gender-specific immune response, vaccines tend to yield greater gains in female as opposed to male survival, the authors interpret their findings as evidence for female health improvements being more conducive to economic growth. Several studies building on randomised controlled trials in Guatemala and India strongly indicate a negative impact of female health on fertility (Hoddinott et al., 2013; Nandi et al., 2020). We also identify a negative correlation between indicators of female health and the total fertility rate in macroeconomic data covering a wide range of countries (see Online Appendix A). Although attempts to identify a causal impact of female health on fertility remain ongoing, our analysis suggests a case for the promotion of female health. Potential policies might include the reduction of iodine deficiency, which, during pregnancy, has a negative effect on the cognitive abilities especially of girls (cf. Field et al., 2009); vaccination against human papilloma virus to prevent cervical cancer, which is the second-deadliest cancer among women in low-income countries (cf. Luca et al., 2018); and the establishment of equal access for women and girls to general healthcare facilities and programs of food supplementation (cf. Hoddinott et al., 2013; Nandi et al., 2020). Although such policies may be based on female disadvantage regarding access to healthcare to begin with,3 our analysis suggests an additional rationale on development grounds: targeting female health tends to lead economies out of poverty traps or at least to accelerate progress towards an economic take-off. Furthermore, female health tends to foster long-run growth prospects as well. Put the other way round, our analysis shows that the ongoing discrimination against women in terms of their health in developing countries constitutes a considerable obstacle to economic development. However, targeting female rather than male health comes at a lower instantaneous utility gain to the household. This highlights a conflict between the short-term interests of utility-maximising households and long-run development goals (cf. Duflo, 2012). To the extent that an underlying intergenerational externality (by which contemporary households are insufficiently rewarded for investments in women’s health) stands in the way of households actively pursuing improvements in women’s health, this only serves to strengthen the case for policy intervention. Our particular focus on gender-specific health, rather than education or human capital more generally, arises from the chronology of an economic-demographic take-off. As complementary components of human capital and productivity, health and education take on a similar role in shaping the quality–quantity trade-off after the onset of the economic–demographic transition, but they differ in a crucial way before. If the economic–demographic take-off is understood to be the point at which households engage in sizeable investments in education at the expense of fertility, only health matters for labour supply and fertility before the take-off, and thus, only health influences the timing of the take-off (cf. Cervellati and Sunde, 2015a,b; Andersen et al., 2016). While in the models by Cervellati and Sunde (2005), Soares (2005) and Soares and Falcão (2008), children's longevity needs to surpass a certain threshold to generate a sufficient return on educational investment, our focus lies on the mother’s morbidity as a determinant of the opportunity cost of children. Thus, our model differs: (i) in its focus on morbidity rather than mortality, reflecting empirical evidence in Andersen et al. (2016) about eye disease caused by ultraviolet radiation being a prime deterrent to an economic–demographic take-off; and (ii) in highlighting the role of gender-specific health impacts, especially in the run-up to the take-off.4 By emphasising the role of female health in economic development, our model bears some resemblance to the theoretical analyses in Jayachandran and Lleras-Muney (2009), Albanesi and Olivetti (2014; 2016), de la Croix and Vander Donckt (2010) and Agénor et al. (2010). Of these, only Agénor et al. (2010) consider a complex household model within a general equilibrium framework. Their work highlights the role of public infrastructure in accessing healthcare, thus giving the analysis a different focus. Furthermore, they concentrate on balanced growth paths, whereas we are particularly interested in the transition process. The other works do not explicitly analyse the general equilibrium repercussions that non-trivially govern the net impact of changes in female and male health both on the timing and on the strength of the economic–demographic take-off. Finally, we differ from Jayachandran and Lleras-Muney (2009), Albanesi and Olivetti (2014) and de la Croix and Vander Donckt (2010) by focusing on morbidity rather than mortality, and from Albanesi and Olivetti (2016) by considering general female health rather than maternal health. The remainder of the article is organised as follows. Section 1 introduces the model, solves for optimal choices at the household level and sets out the market equilibrium. Section 2 is devoted to the dynamics of the model and develops our main result regarding the impact of female and male health on the economic transition, while Section 3 considers policy implications. Section 4 characterises the impact of gender-specific health on the development process numerically, and Section 5 provides some discussion and conclusions. We have relegated to an Online Appendix a set of modelling extensions demonstrating the robustness of our results and some of the proofs. 1. The Model Consider a low-income economy in which time |$t \in [0, 1,{\ldots})$| evolves discretely and refers to generations. The adult population consists of Nt|$/$|2 couples formed out of a pool of Nt individuals. We assume that males and females pair randomly after coming of age. Each couple jointly decides on consumption, the number of children and the educational investments in each child. The last two decisions determine the population growth rate and the individual human capital level, which jointly determine the aggregate human capital stock of the economy in the next generation t + 1. The aggregate human capital stock can be employed in two sectors: goods production and education. Educational investments determine employment in the education sector, while aggregate consumption determines employment in final goods production. Low-income countries are assumed to have no research sector for the development of new technologies but rather adopt technologies developed in rich countries (cf. Jones, 2002; Keller, 2002; Ha and Howitt, 2007). This process determines income growth as the long-run driver of the economic–demographic transition. In the following subsection, we derive the household allocation, including an earnings threshold that needs to be crossed before households invest in education and reduce their fertility. 1.1. Household Choices We assume that the following utility function captures a male–female couple’s preferences: $$\begin{eqnarray} u=\log \left( c_{t}\right) +\gamma \log \left( n_{t}\right) +\delta \log \left( \bar{e}+e_{t}\right) , \end{eqnarray}$$(1) where ct denotes joint adult consumption, nt refers to the number of children, et denotes investment in the education of each child, and |$\bar{e}\ge 0$| represents the education that children obtain informally at no cost even in the absence of deliberate parental educational investments. The parameters γ and δ measure the utility weight of the number of children and their education, respectively. Following Strulik et al. (2013) we adopt a shortcut formulation in which investments in education enter the utility function directly. The notion that individuals experience a ‘warm glow’ from providing their children with a certain level of education justifies this shortcut (cf. Andreoni, 1989; Glomm and Ravikumar, 1992; Casarico and Sommacal, 2012; Strulik et al., 2013). The inclusion of informally acquired education, |$\bar{e}$|⁠, captures a context dependence of the warm glow. As we will see shortly, a higher level of |$\bar{e}$| tends to reduce the parents’ inclination to invest in education, reflecting a lower perceived need for additional investments. In Remark 1 at the end of this subsection, we provide a more detailed discussion of this modelling feature and demonstrate the robustness of our results in respect to a more general formulation. For robustness, we also consider in Online Appendices B.2 and B.3 collective preferences and preferences for children's human capital, respectively. The budget constraint of the couple is given by $$\begin{eqnarray} \xi _{m}\widehat{w}_{t}+\xi _{f}\widehat{w}_{t}(1-\psi n_{t})=c_{t}+e_{t}n_{t}, \end{eqnarray}$$(2) where |$\widehat{w}_{t}=w_{t}h_{t}$| refers to the wage rate per unit of time, depending on the human capital of adults, ht, and the wage rate per unit of human capital, |${w}_{t}$|⁠.5 The parameter ξj, in which j = {m, f}, measures the extent to which gender-specific health allows an individual to work productively, while the parameter ψ ∈ (0, 1) refers to the fraction of time required for giving birth to and caring for one child. Altogether, household income on the left-hand side of the equation comprises the husband’s and the wife’s earnings, both increasing in the (common) level of human capital, in gender-specific health as a determinant of an individual’s productive capacity, and in the fraction of time available net of childcare commitments. Time-use patterns show that the contribution of mothers to childcare dwarfs the contribution of fathers, particularly in low-income countries (cf. Berniell and Sánchez-Páramo, 2011; Duflo, 2012).6 Thus, we assume that female earnings decrease by the (full) amount of time ψnt required for bearing and rearing nt children. This means that quality-independent child costs are represented by forgone female earnings. By contrast, quality-dependent child costs are represented by total educational expenditure etnt on the right-hand side of (2).7 In the following, ξm and ξf represent the proportion of time that men and women, respectively, spend in good health.8 Based on World Health Organization data on years lived with disability (YLDs) (WHO, 2016), we obtain ξm = 0.88337 and ξf = 0.86920 for Sub-Saharan Africa, implying that men spend more than 88% of their time in good health, while women only spend a little less than 87% of their time in good health (see Section 4 for details of the calculation). Assuming that individuals can provide (market) labour only when in good health, it follows that male labour supply is given by ξm; women, however, have to divide their healthy time between labour and child rearing, implying an effective labour supply of ξf(1 − ψnt). This formulation aligns well with empirical evidence on the impact of health on male and female labour supply: Pelkowski and Berger (2004) show that while a permanent condition of poor health lowers female wages by more than male wages, it lowers female hours worked by less than male hours worked. This fully agrees with our model, in which a unit decrease in ξm lowers male employment by one, whereas a unit decrease in ξf lowers female employment by 1 − ψnt. Cai et al. (2014) show that the same holds for the impact of a health shock on hours worked. Direct evidence is provided by Pagan (2013), who studies time-use patterns for the non-disabled as opposed to the disabled (including those with chronic illnesses) in Spain. He shows that an increase in the number of children up to age 12 leads to a significant reduction in market work for non-disabled women, but neither for disabled women nor for men. This implies that the opportunity cost of having children is larger for healthy rather than unhealthy women (or men for that matter). Several recent studies from Sub-Saharan Africa show that the same applies to low-income countries. Thirumurthy et al. (2008) report for West Kenya that health improvements due to HIV treatment lead to a greater increase of hours worked for men rather than women. Levinsohn et al. (2011) consider evidence from South Africa and show that HIV-positive status affects the probability of being unemployed more for men than for women. Bor et al. (2012) follow a cohort of HIV patients in rural South Africa over a time period of eight years before and four years after the initiation of treatments. Although they find a similar pattern of negative employment effects for women and men, setting in three years before and ebbing out four years after the treatment, both the decline and the recovery are significantly more pronounced for men. Finally, Nwosu and Woolard (2017) show for South Africa that the impact of self-assessed health on labour-force participation is stronger for men than for women. For fertility to be non-negative and not to exceed the amount that would induce women to spend more time on childcare than their available time budget allows, we assume that γ ∈ (δ, ξf|$/$|ξm) holds. Solving the couple’s utility maximisation problem then yields optimal consumption, $$\begin{eqnarray} c_{t}=\frac{(\xi _{m}+\xi _{f})\widehat{w}_{t}}{1+\gamma }, \end{eqnarray}$$(3) while optimal fertility and optimal human capital investments are given by $$\begin{eqnarray} n_{t}& = \left\lbrace \begin{array}{@{}l@{\quad }l@{}}\displaystyle\frac{\gamma (\xi _{m}+\xi _{f})}{(1+\gamma )\xi _{f}\psi } & \qquad \mbox{for }\widehat{w}_{t}\le \displaystyle\frac{\gamma \bar{e}}{\delta \xi _{f}\psi }, \\ \displaystyle\frac{(\gamma -\delta )(\xi _{m}+\xi _{f})\widehat{w}_{t}}{(1+\gamma )(\xi _{f}\psi \widehat{w}_{t}-\bar{e})} & \qquad \mbox{otherwise, } \end{array}\right. \end{eqnarray}$$(4) $$\begin{eqnarray} e_{t}& = \left\lbrace \begin{array}{@{}l@{\qquad }l@{}}0 & \qquad \qquad \mbox{for }\widehat{w}_{t}\le \displaystyle\frac{\gamma \bar{e}}{ \delta \xi _{f}\psi }, \\ \displaystyle\frac{\delta \xi _{f}\psi \widehat{w}_{t}-\gamma \bar{e}}{\gamma -\delta } & \qquad \qquad \mbox{otherwise. } \end{array}\right. \end{eqnarray}$$(5) At low levels of wages, |$\widehat{w}_{t}\le \gamma \bar{e}/(\delta \xi _{f}\psi )$|⁠, the couple divides household income between consumption ct and fertility nt alone, while educational investments et are zero. The reason is that parents prefer a corner solution in which children learn only incidentally because income is so low that the marginal utility from consumption and fertility outweighs the marginal utility from any investment into formal education. However, once wages surpass the threshold |$\widehat{w}_{t}=\gamma \bar{e}/(\delta \xi _{f}\psi )$|⁠, investing in their children’s education becomes optimal for parents, and et turns positive (cf. Strulik et al., 2013). Notably, the threshold depends on female health alone. By raising the opportunity cost of childcare, improved female health tends to skew the quality–quantity trade-off towards educational investments rather than the number of children. For increasing income and human capital, the model replicates a transition from high to low fertility—that is, fertility converges from above to $$\begin{eqnarray} \lim _{\widehat{w}_{t}\rightarrow \infty }n_{t}=\frac{(\gamma -\delta )(\xi _{m}+\xi _{f})}{(1+\gamma )\xi _{f}\psi }\lt \frac{\gamma (\xi _{m}+\xi _{f})}{ (1+\gamma )\xi _{f}\psi}, \end{eqnarray}$$(6) where the right-hand side represents fertility in the low-growth regime. Furthermore, inspecting (5) shows that once the income threshold for positive educational investments is surpassed, these investments rise with income, paving the way for mass education (cf. Galor, 2005; 2011; Strulik et al., 2013). With regard to the impact of gender-specific health on the household allocation, we can now state the following:9 Proposition 1. Given the level of earnings, |$\widehat{w}_{t}$|, consumption increases (symmetrically) with male (ξm) and female (ξf) health, fertility increases (decreases) with male (female) health in both the low-growth and modern growth regime and in the long-run limit, educational investments in the modern growth regime increase with female health and are unaffected by male health, and the earnings threshold for the onset of the economic–demographic transition decreases with female health and is unaffected by male health. Proof. Immediate from differentiation of (4), (5) and (6) with respect to ξf and ξm. Improvements in male health yield an income effect that unambiguously leads to an expansion of both consumption and the number of children. By contrast, female health improvements yield both an income and a substitution effect. The income effect leads again to an unambiguous expansion of consumption, but this is no longer true with regard to the number of children. Here, the substitution effect, driven by the greater opportunity cost of children, leads to a reduction in the number of children. While this is true even in the low-growth regime, in the modern growth regime the reduction in fertility comes with greater educational investments.10 Finally, and importantly, by raising the opportunity cost of childcare for any level of earnings, female health improvements lower the earnings threshold for the onset of the economic–demographic take-off. The central mechanism in our model—namely that greater female health leads to a decline in fertility—is fully consistent with recent empirical evidence on the role of malnutrition and stunting during childhood on (early) adult fertility. Employing data from a randomised food-supplementation trial in Guatemala, Hoddinott et al. (2013) show that childhood stunting led to lower schooling (and thus lower productivity), which translated into higher fertility. Using data from a similar trial in India, Nandi et al. (2020) show that food supplementation during early childhood led to a later age at menarche, typically associated with better adult health and delayed pregnancy. In Online Appendix A we present macroeconomic evidence of a negative correlation between female health and total fertility for the countries under consideration. Thus, while our results are consistent with this evidence, we admit that so far this only indicates a negative link between female health and fertility, with strong causal evidence for different countries still missing. Turning to education, our findings are consistent with evidence provided by Bratti and Mendola (2014) and Mendolia et al. (2019) that a negative health shock to the mother reduces the educational enrolment of children, whereas a negative health shock to the father does not. Finally, our results are consistent with evidence that rising male income leads to higher fertility, while rising female income leads to lower fertility (cf. Butz and Ward, 1979; Schultz, 1985; Heckman and Walker, 1990; Bloom et al., 2009). For the remainder of this section, we discuss several generalisations and extensions of the model to establish the robustness of our results. Remark 1. Our specification, |$\delta \log \left( \overline{e}+e_{t}\right)$|⁠, of a warm glow benefit from educational investments in (1) can be interpreted as a special case of the more general form $$\begin{eqnarray} \delta \log \left( \widehat{e}\left( \overline{e},w_{t}\right) w_{t}+e_{t}\right), \end{eqnarray}$$(7)where|$\widehat{e}\left( \overline{e},w_{t}\right) w_{t}$|assigns a monetary value to the level of informal education, |$\overline{e}$|⁠, which, as we have seen, acts as a threshold for parents’ own investments. Specifically, we assume that the function|$\widehat{e}\left( \overline{e},w_{t}\right)$|⁠, as measured in units of education, satisfies|$\partial \widehat{e}/\partial \overline{e}\ge 0$|and|$\partial \widehat{e} /\partial w_{t}\le 0$|⁠. Intuitively, parents perceive a higher threshold and assign a lower value to spending on formal education, the greater the level of informally acquired human capital (as investments into additional education seem less necessary) and the lower the current (and observable) value of human capital, as measured by wt.11Conversely, parents are more inclined to invest (at all) if they observe a low level of informally acquired human capital and/or if the value of human capital is high.12 Based on the specification in (7), we obtain the first-order condition for optimal educational expenditure: $$\begin{eqnarray} e_{t}=\max \left\lbrace 0,\frac{\left[ \delta \psi \xi _{f}h_{t}-\gamma \widehat{e }\left( \overline{e},w_{t}\right) \right] w_{t}}{\gamma -\delta }\right\rbrace . \end{eqnarray}$$(8)We then have $$\begin{eqnarray} e_{t}\gt 0\Leftrightarrow h_{t}\gt \frac{\gamma \widehat{e}\left( \overline{e} ,w_{t}\right) }{\delta \psi \xi _{f}}. \end{eqnarray}$$(9)While this condition does not directly depend on earnings, it does so indirectly as a higher level of earnings (per unit of human capital) lowers the threshold. For a more specific solution, assume that $$\begin{eqnarray} \widehat{e}\left( \overline{e},w_{t}\right) =\overline{e}^{\varepsilon _{1}}w_{t}^{-\varepsilon _{2}},\quad \varepsilon _{1},\varepsilon _{2}\in \left[ 0,1\right] . \end{eqnarray}$$Substituting this into (9) and rearranging, we obtain $$\begin{eqnarray} e_{t}\gt 0\Leftrightarrow \widehat{w}_{t}\gt \left( \frac{\gamma \overline{e} ^{\varepsilon _{1}}}{\delta \psi \xi _{f}h_{t}^{1-\varepsilon _{2}}}\right) ^{1/\varepsilon _{2}}, \end{eqnarray}$$implying that parents invest in education if and only if earnings (per unit of labour), |$\widehat{w}_{t},$|are sufficiently high. Here, the earnings threshold increases with the level of informally acquired human capital and declines with the current level of human capital. Note that the expression is equivalent to our formulation for ε1 = ε2 = 1. Similarly, we find that for ε1 = ε2 = 1 we have|$\widehat{e}\left( \overline{e},w_{t}\right) =\overline{e}/w_{t}$|⁠, and inserting this into (7) we obtain $$\begin{eqnarray} \delta \log \left( \widehat{e}\left( \overline{e},w_{t}\right) w_{t}+e_{t}\right) =\delta \log \left( \overline{e}+e_{t}\right) , \end{eqnarray}$$i.e., the specification we are using as a special case. Thus, it can be checked from the expressions in (8) and (9) that all the key mechanisms within our model are robust to the more general specification in (7). To further gauge the robustness of our modelling, we consider two alternative specifications of preferences and two alternative assumptions about child caring. Referring the reader to the Online Appendix for further details, we briefly summarise our findings as follows. In Online Appendix B.2, we consider collective household preferences and find the impacts of female and male health, as described in Proposition 1, to be magnified if women exhibit a relative preference for the quality rather than the quantity of children, and bargaining power depends on the distribution of health across the spouses. In Online Appendix B.3, we consider a specification in which parents have preferences about the expected income of their children (akin to, e.g., Galor and Weil, 2000; Galor, 2005; 2011), which is assumed to increase with the expected wage rate and with the children's human capital and expected health. The latter is possibly directly correlated with maternal health through in utero effects (as in, e.g., Field et al., 2009; Bhalotra and Rawlings, 2011). For this specification, we also assume that child health enters the production function of human capital. Although this opens up additional and realistic influences of maternal health, our key results remain broadly unaffected. Changes arise from the fact that expected child health now lowers fertility and raises education in the post-transition regime, and lowers the transition threshold in terms of earnings. To the extent that parental health is correlated with child health, this implies that the impacts of female health described in Proposition 1 are magnified, whereas the impacts of male health are dampened. We believe that the correlation is much stronger between mother’s health and child health as it not only embraces a genetic correlation, but also direct in utero effects. In Online Appendix B.4 we assume that female health not only frees time for the provision of additional labour but also lowers the time cost of child rearing such that |$\psi =\widehat{\psi }(\xi _{f})$| with |$\widehat{\psi } ^{\prime }\lt 0$|⁠. This model variant yields two insights: (i) Our results are robust such that both the transition threshold and fertility decrease in female health if the child cost responds sufficiently inelastically to female health improvements. While we did not find direct evidence on the health dependency of the cost of childcare, the empirical evidence by Pagan (2013) for the opportunity cost of childcare being larger for healthy women implies that the health gradient of the childcare cost must be sufficiently weak. (ii) For the case that female health is sufficiently low, such that ξf ≤ γξm, a corner solution arises for which women do not supply labour and fertility is given by |$n_{t}=\widehat{\psi }\left( \xi _{f}\right)^{-1}$|⁠. It follows that, in this regime, fertility increases when improvements in female health alleviate medical or social restrictions to child bearing and/or family formation (e.g., Baudin et al., 2020). Note that the possibility of such a regime is consistent with our empirical findings in Online Appendix A. Finally, in Online Appendix B.5 we consider male contributions to childcare. The results in Proposition 1 are robust as long as men contribute less time to childcare than women do, a plausible assumption for most low-income countries. The only difference is that improvements in male health now tend to lower the transition threshold but only in proportion to their contribution to childcare. 1.2. Population Development and Labour Force Participation Because each couple gives birth to nt children in period t, the replacement rate of fertility is given by nt = 2 and the adult population evolves according to $$\begin{eqnarray} N_{t+1}=\frac{n_{t}}{2}N_{t}. \end{eqnarray}$$(10) As far as labour market participation is concerned, we abstract from leisure and assume that individuals inelastically supply their available time net of child rearing. While interpreting ξm and ξf as health-dependent participation or as health-dependent productivity (cf. Online Appendix B.7) makes no difference to the household analysis nor to the key macroeconomic relationships summarised below in the system of (25)–(32), the subsequent intermediate analysis of employment in terms of workers (Lt) is based on the interpretation of ξm and ξf as health-dependent labour participation. Note that for this case human capital ht is homogeneous so that the wage rate, |$\widehat{w}_{t}$|⁠, is gender neutral, while labour supply $$\begin{eqnarray} L_{t}=\frac{N_{t}}{2}\left[ \xi _{m}+\xi _{f}\left( 1-\psi n_{t}\right) \right] \end{eqnarray}$$(11) depends on health in addition to the time that women devote to childcare. 1.3. Education Sector Once the income threshold for positive educational investments is surpassed, aggregate spending on formal education is given by education expenditures per couple (etnt) multiplied by the number of couples (Nt|$/$|2), thus amounting to $$\begin{eqnarray} e_{t}n_{t}\frac{N_{t}}{2}=\frac{\delta \xi _{f}\psi \widehat{w}_{t}-\gamma \bar{e}}{\xi _{f}\psi \widehat{w}_{t}-\bar{e}}\cdot \frac{(\xi _{m}+\xi _{f}) \widehat{w}_{t}}{1+\gamma }\cdot \frac{N_{t}}{2}. \end{eqnarray}$$(12) Aggregate education spending is then used to employ Lt,E teachers whose aggregate wage bill is given by |$\widehat{w}_{t}L_{t,E}$|⁠. Thus, we can derive the equilibrium number of teachers as $$\begin{eqnarray} L_{t,E}=\frac{e_{t}n_{t}}{\widehat{w}_{t}}\cdot \frac{N_{t}}{2}=\frac{\delta \xi _{f}\psi \widehat{w}_{t}-\gamma \bar{e}}{\xi _{f}\psi \widehat{w}_{t}- \bar{e}}\cdot \frac{\xi _{m}+\xi _{f}}{1+\gamma }\cdot \frac{N_{t}}{2}. \end{eqnarray}$$(13) These teachers produce the human capital level of the next generation with a teaching productivity per unit of human capital of η. Because the human capital level of teachers is ht and educational resources devoted to each child are given by Lt,E|$/$|Nt+1 with Nt+1 = ntNt|$/$|2, the following production function describes formal education per child: $$\begin{eqnarray} h_{t+1} - \bar{e} = \frac{\eta h_t L_{t,E}}{n_{t}N_{t}/2}, \end{eqnarray}$$(14) where |$h_{t+1} - \bar{e}$| is the human capital added through formal education. Consequently, the law of motion for individual human capital is given by $$\begin{eqnarray} h_{t+1}= \left\lbrace \begin{array}{@{}l@{\quad }l@{}}\bar{e} & \qquad \mbox{for }\widehat{w}_{t}\le \displaystyle\frac{\gamma \bar{e}}{\delta \xi _{f}\psi }, \\ \displaystyle\frac{\eta h_{t}L_{t,E}}{n_{t}N_{t}/2}+\bar{e}=\displaystyle\frac{\eta e_{t}}{w_{t}}+\bar{ e}=\displaystyle\frac{\eta (\delta \xi _{f}\psi \widehat{w}_{t}-\gamma \bar{e})}{\left( \gamma -\delta \right) w_{t}}+\bar{e} & \qquad \mbox{otherwise.} \end{array}\right. \end{eqnarray}$$(15) In the infinite limit, the growth factor of human capital converges to $$\begin{eqnarray} \lim _{h_{t}\rightarrow \infty }\frac{h_{t+1}}{h_{t}}=\frac{\eta \delta \xi _{f}\psi }{\gamma -\delta } \end{eqnarray}$$(16) for rising levels of human capital. The following result is immediate. Proposition 2. The long-run growth factor of human capital increases with female health but is unrelated to male health. The intuitive explanation is that the income and substitution effects with respect to fertility cancel out for increasing male income, while the substitution effect dominates for increasing female income. Consequently, improvements in male health leave the quantity–quality trade-off unchanged, while improvements in female health raise investments in education at the expense of fertility. If men spend some time on childcare but less than women do, their health also bears positively on the growth factor of human capital, however, to a lesser extent than women’s health. For a scenario in which education takes place within the household, the allocation of labour to the production sector, educational outcomes, and the macroeconomic dynamics are equivalent to those in our model (for a formal proof, see Prettner and Strulik, 2017b). 1.4. Production Sector We follow Galor and Weil (2000) and assume that the production technology is given by $$\begin{eqnarray} Y_{t}=H_{t,Y}^{\alpha }\left( A_{t}X\right) ^{1-\alpha }, \end{eqnarray}$$(17) where Ht,Y = htLt,Y refers to aggregate human capital employed in production, with Lt,Y being the number of workers, where At ≥ 1 denotes the stock of technologies that a country has at its disposal, where X denotes natural resources of fixed supply, and where α denotes the elasticity of output with respect to human capital. This production function implies, ceteris paribus, that an increase in human capital employed in goods production and an increase in the technological sophistication of a country both raise output.13 Following Galor and Weil (2000) and assuming that no property rights are defined on the fixed resource X (such that its return is zero), the wage per unit of human capital is given as the average product of human capital, that is, $$\begin{eqnarray} w_{t}=\frac{Y_{t}}{H_{t,Y}}=\left( \frac{A_{t}X}{h_{t}L_{t,Y}}\right) ^{1-\alpha }. \end{eqnarray}$$(18) The wage rate per unit of time is then given by $$\begin{eqnarray} \widehat{w}_{t}=h_{t}w_{t}=h_{t}^{\alpha }\left( \frac{A_{t}X}{L_{t,Y}} \right) ^{1-\alpha }, \end{eqnarray}$$(19) which declines with labour supply and increases with individual human capital. 1.5. Market Clearing Following Walras’s Law, we can determine the volume of human capital employed in production by recognising that production of final goods has to equal aggregate consumption—that is, goods markets are cleared. Hence, production per capita yt = Yt|$/$|Nt has to equal consumption per capita such that $$\begin{eqnarray} y_{t}=\frac{c_{t}}{2}=\frac{(\xi _{m}+\xi _{f})\widehat{w}_{t}}{2(1+\gamma )} . \end{eqnarray}$$(20) Employing this in the relationship wt = Yt|$/$|Ht,Y = ytNt|$/$|Ht,Y, we obtain the following expressions for human capital and labour employment in final goods production:14 $$\begin{eqnarray} H_{t,Y}=\frac{(\xi _{m}+\xi _{f})h_{t}}{2(1+\gamma )}N_{t}\qquad \Rightarrow \qquad L_{t,Y}=\frac{\xi _{m}+\xi _{f}}{2(1+\gamma )}N_{t}. \end{eqnarray}$$(21) Using (18) and (19), we can recalculate wages per unit of human capital and per unit of time as $$\begin{eqnarray} w_{t} & =\left[ \displaystyle\frac{2(1+\gamma )A_{t}X}{h_{t}\left( \xi _{m}+\xi _{f}\right) N_{t}}\right] ^{1-\alpha } \end{eqnarray}$$(22) $$\begin{eqnarray} \Leftrightarrow \widehat{w}_{t} & =h_{t}^{\alpha }\left[ \displaystyle\frac{2(1+\gamma )A_{t}X}{\left( \xi _{m}+\xi _{f}\right) N_{t}}\right] ^{1-\alpha }. \end{eqnarray}$$(23) 1.6. International Technology Diffusion In specifying the diffusion of technologies from countries that are advancing the world technological frontier we follow Benhabib and Spiegel (2005), p. 941, and assume that $$\begin{eqnarray} A_{t+1}=\max \left\lbrace \frac{h_{t}}{\bar{h}_{t}}\left( \frac{\bar{A}_{t}}{ A_{t}}-1\right) A_{t}+A_{t},\bar{A}_{t}\right\rbrace , \end{eqnarray}$$(24) where |$\bar{A}_{t}$| and |$\bar{h}_{t}$| refer to the technological frontier and the human capital level in the most advanced countries, respectively. The larger the technological gap between rich and poor countries, the faster is the process of technology diffusion (cf. Howitt, 2000; Acemoglu et al., 2006). The notion that the return to the adoption of new technologies increases with the additional output that can be produced justifies this assumption. Furthermore, the gap between the average human capital of the low-income country and that of the technology leaders, |$h_{t}/\bar{h}_{t}$|⁠, acts as a technology adoption barrier (cf. Nelson and Phelps, 1966; Parente and Prescott, 1994).15 2. Dynamic Behaviour of the Economy in General Equilibrium Combining our building blocks, we obtain the following dynamic system that describes our model economy in the low-growth regime: $$\begin{eqnarray} A_{t+1}& =\displaystyle\frac{h_{t}}{\bar{h}_{t}}\left( \displaystyle\frac{\bar{A}_{t}}{A_{t}}-1\right) A_{t}+A_{t}, \end{eqnarray}$$(25) $$\begin{eqnarray} h_{t+1}& =\bar{e}, \end{eqnarray}$$(26) $$\begin{eqnarray} N_{t+1}& =\displaystyle\frac{\gamma (\xi _{m}+\xi _{f})}{2 (1+\gamma )\xi _{f}\psi}N_{t}, \end{eqnarray}$$(27) $$\begin{eqnarray} w_{t+1}& =\left[ \displaystyle\frac{2(1+\gamma )A_{t+1}X}{(\xi _{m}+\xi _{f})h_{t+1}N_{t+1}}\right] ^{1-\alpha }, \end{eqnarray}$$(28) while the modern-growth regime is characterised by $$\begin{eqnarray} A_{t+1}& =\displaystyle\frac{h_{t}}{\bar{h}_{t}}\left( \displaystyle\frac{\bar{A}_{t}}{A_{t}}-1\right) A_{t}+A_{t}, \end{eqnarray}$$(29) $$\begin{eqnarray} h_{t+1}& =\displaystyle\frac{\eta \delta \xi _{f}\psi \widehat{w}_{t}-\gamma \bar{e}}{ \left( \gamma -\delta \right) w_{t}}+\bar{e}, \end{eqnarray}$$(30) $$\begin{eqnarray} N_{t+1}& =\displaystyle\frac{(\gamma -\delta )(\xi _{m}+\xi _{f})\widehat{w}_{t}}{ 2(1+\gamma )(\xi _{f}\psi \widehat{w}_{t}-\bar{e})}N_{t}, \end{eqnarray}$$(31) $$\begin{eqnarray} w_{t+1}& =\left[ \displaystyle\frac{2(1+\gamma )A_{t+1}X}{(\xi _{m}+\xi _{f})h_{t+1}N_{t+1}}\right] ^{1-\alpha }. \end{eqnarray}$$(32) Recall that a transition from the low-growth to the modern-growth regime requires earnings to exceed a threshold. In the absence of human capital investments, the necessary earnings growth is generated only by the growth in the stock of technologies adopted from rich countries, which needs to be large enough to offset population growth. Consider now the development of the economy from some time t0 onward, assuming that at t0 the economy is in the low-growth regime. We then have $$\begin{eqnarray} h_{t_{0}}=\bar{e};\quad n_{t_{0}}=\displaystyle\frac{\gamma (\xi _{m}+\xi _{f})}{(1+\gamma )\xi _{f}\psi};\quad e_{t_{0}}=0;\quad w_{t_{0}}=\left[ \displaystyle\frac{ 2(1+\gamma )A_{t_{0}}X}{(\xi _{m}+\xi _{f})\bar{e}N_{t_{0}}}\right] ^{1-\alpha }\lt \displaystyle\frac{\gamma }{\delta \xi _{f}\psi }, \end{eqnarray}$$ where the inequality implies |$\widehat{w}_{t_{0}}\lt \gamma \bar{e}/(\delta \xi _{f}\psi )$| such that fertility is high and no education investments are undertaken. A condition for sustained economic development is the ongoing growth of wages due to international knowledge diffusion. Using (23), we can calculate the growth rate of wages as $$\begin{eqnarray} g_{t}:=\displaystyle\frac{\widehat{w}_{t+1}}{\widehat{w}_{t}}-1=\left( \displaystyle\frac{h_{t+1}}{ h_{t}}\right) ^{\alpha }\left( \displaystyle\frac{A_{t+1}/A_{t}}{n_{t}/2}\right) ^{1-\alpha }-1, \end{eqnarray}$$(33) where |$A_{t+1}/A_{t}=\max \left\lbrace \left(h_{t}/\overline{h}_{t}\right)\left( \overline{A} _{t}/A_{t}-1\right) +1,1\right\rbrace .$| It is sufficient for sustained wage growth (gt > 0) that ht+1|$/$|ht ≥ 1, i.e., human capital is nondecreasing, and that At+1|$/$|At ≥ nt|$/$|2, i.e., technological progress does not fall short of population growth, implying that the wage rate is non-decreasing. We can then derive the following sufficient conditions for a transition from low growth to modern growth and for sustained economic growth in the very long run. Proposition 3. The following holds for the occurrence of a transition and for its sustainability, respectively: A transition from low growth to modern growth arises if $$\begin{eqnarray} \displaystyle\frac{A_{t+1}}{A_{t}}\gt \displaystyle\frac{\gamma (\xi _{m}+\xi _{f})}{2 (1+\gamma )\xi _{f}\psi}, \end{eqnarray}$$(34)with |$A_{t+1}/A_{t}=\max \left\lbrace \left(\overline{e}/\overline{h}_{t}\right)\left( \overline{A}_{t}/A_{t}-1\right) +1,1\right\rbrace$| up until the point of transition. Sustained economic development in the very long run arises if $$\begin{eqnarray} \ln \left( \displaystyle\frac{\eta \delta \xi _{f}\psi }{\gamma -\delta }\right) \ge \displaystyle\frac{1-\alpha }{\alpha }\ln \left[ \displaystyle\frac{(\gamma -\delta )(\xi _{m}+\xi _{f})}{2(1+\gamma )\xi _{f}\psi }\right] . \end{eqnarray}$$(35) Proof. See Online Appendix C. Within the low-growth regime the wage rate can only increase through a rising ‘baseline’ wage per unit of human capital. This requires that technological progress, |$A_{t+1}/A_{t}$|⁠, outweighs population growth, nt|$/$|2, under high fertility. Given that, realistically, nt|$/$|2 > 1 in these economies, this requires that technological growth is positive and sufficiently strong as by condition (34). Assuming that technological growth abates in the very long run, wages continue to increase unambiguously if human capital continues to outgrow the population by a sufficient amount. Thus, considering the long-run limits of human capital growth given in (16) and fertility given in (6), we find condition (35) sufficient for sustained long-run growth.16 We can now identify the role of female health in sustained growth and in a transition to a modern growth regime. To this end, assume that the transition takes place at τ ≥ t0 + 1 and that technology growth |$A_{t+1}/A_{t}\simeq \widehat{A}$| is roughly constant over the interval [t0, τ]. Defining |$\widehat{w}_{\tau }=\gamma \bar{e} /(\delta \xi _{f}\psi )$| as the wage level at which the transition occurs and combining this with the initial wage level, $$\begin{eqnarray} \widehat{w}_{t_{0}}=\bar{e}^{\alpha }\left[ \displaystyle\frac{2(1+\gamma )A_{t_{0}}X}{ (\xi _{m}+\xi _{f})N_{t_{0}}}\right] ^{1-\alpha }, \end{eqnarray}$$(36) and with the growth rate in the low-growth regime, $$\begin{eqnarray} g=\left[ \displaystyle\frac{2\widehat{A}(1+\gamma )\xi _{f}\psi }{\gamma (\xi _{m}+\xi _{f})}\right] ^{1-\alpha }-1, \end{eqnarray}$$(37) we can use the relationship |$\widehat{w}_{\tau }=\left( 1+g\right) ^{\tau -t_{0}}\widehat{w}_{t_{0}}$| to solve for the time to transition as a function of ξf and ξm, $$\begin{eqnarray} \Delta =\tau -t_{0}=\displaystyle\frac{\ln \widehat{w}_{\tau }-\ln \widehat{w}_{t_{0}}}{ \ln \left( 1+g\right) }. \end{eqnarray}$$ We then obtain $$\begin{eqnarray} \displaystyle\frac{\partial \Delta }{\partial \xi _{f}} &=&\displaystyle\frac{1}{\xi _{f}\ln \left( 1+g\right) }\left[ -1+\left( 1-\alpha \right) \displaystyle\frac{\xi _{f}}{\xi _{m}+\xi _{f}}-\left( 1-\alpha \right) \Delta \displaystyle\frac{\xi _{m}}{\xi _{m}+\xi _{f}} \right] \lt 0, \end{eqnarray}$$(38) $$\begin{eqnarray} \displaystyle\frac{\partial \Delta }{\partial \xi _{m}} &=&\displaystyle\frac{\left( 1-\alpha \right) \left( 1+\Delta \right) }{\left( \xi _{m}+\xi _{f}\right) \ln \left( 1+g\right) }\gt 0, \end{eqnarray}$$(39) which allows us to state our main result. Proposition 4. Better female (male) health—that is, a higher ξf (ξm) leads to faster (slower) wage growth in the low-growth regime and in the long-run limit, and reduces (increases) the time to the transition to modern growth. Proof. Part (i) follows immediately when inserting the low-growth and limiting values of nt [cf. (4) and (6)] and the limiting value of ht+1|$/$|ht [cf. (16)] into (33) and taking the appropriate derivatives with respect to ξf and ξm. Part (ii) follows immediately from (38) and (39). Economies with better female health tend to experience faster wage growth during the low-growth regime and in the long-run limit. This is because they tend to exhibit less downward pressure on the wage rate for an expanding population throughout and, in addition, greater accumulation of human capital in the modern growth regime. While greater wage growth in the low-growth regime suggests that economic transition is taking place earlier, this is not a foregone conclusion. The reason is that while wages grow faster within economies with healthy women [the last term in (38)] and while these economies enter the transition at a lower wage level [the first term in brackets in (38)], they are also starting at a lower wage level [the second term in (38)]. This is because greater female labour participation (or productivity) initially tends to depress wages. As it turns out, the economy with a healthier (and more productive) female labour force experiences economic take-off at an earlier time. We note from (38) that the impact of female health on the speed to transition decreases with the growth rate on the path to transition and increases with the time to transition. Finally, we note that the reduction in the transition threshold is a crucial factor. This is because when the time to transition is short, the impact of lower fertility on the growth rate is insufficient to offset the initial reduction in the wage rate. All of this contrasts with the impact of male health, which, by raising fertility, tends to slow the pace of economic development. This is consistent with the empirical evidence provided by Schultz (1985) and Heckman and Walker (1990), showing that fertility increases with male income. Indeed, male health impedes economic transition by lowering both the initial level of wages and its growth rate. 3. Policy Implications From a development policy perspective, our main result in Proposition 4 implies that efforts towards health improvements should be targeted at women. Indeed, the model suggests that redistributing opportunities for health improvements from men to women may be beneficial in the long run. The following result shows, however, that such a policy would create a conflict with the interests of the unitary household in the short run. This argument abstracts from the justification of the redistribution of healthcare opportunities to women based on an unequal distribution biased against women to begin with (cf. the literature referenced in the introduction). Proposition 5. Consider a redistribution of public healthcare resources from men to women such that dξf = −dξm > |$0$|⁠. Such a policy unambiguously raises economic growth rates throughout and speeds up the economic transition, but for any given wage,|$\widehat{w}_{t}$|⁠,it unambiguously lowers household utility, both in the low-growth and in the modern growth regime. Proof. See Online Appendix C. Thus, while enhancing economic growth and hastening economic transition, a redistribution of health also lowers household utility. This is true even when such a policy fosters educational investments in the modern growth regime or induces a transition. Indeed, this follows from a revealed preference argument: noting from the budget constraint in (2) that redistribution unambiguously lowers family income, it must be true that the household with better male health could always mimic the allocation chosen by a household with better female health and thereby do at least as well. Any deviation in the allocation (i.e., the choice of more children) must then be associated with even greater utility. We realise that this result depends on the assumption of unitary household decision making and may well change in the presence of collective decision making. This notwithstanding, it highlights the scope for a conflict between the short-term interests of utility-maximising households, which may favour male health improvements, and the long-term interests of development policies that favour female health improvements. This tension may give rise to a development trap, wherein households primarily care for the health of the ‘male breadwinner’, not accounting for the harmful effect on economic prosperity in the long run. Note that this is tantamount to the presence of an intergenerational externality in a setting in which the household decides on gender-specific health investments, as studied in Online Appendix B.1. When deciding on female (male) health investments, households do not internalise the gains (losses) to future cohorts from faster (slower) development. The very presence of this externality then speaks to a need for external policy intervention in favour of female health investments. In many instances, health policies are not targeted at particular individuals within the household. One may wonder then what the implications are for the pace of economic development if women and men benefit equally from a particular health policy. Proposition 6. Consider an increase in the health of both genders by a common factor λ > |$1$|⁠. Such a policy leaves the growth rate unaffected in the low-growth regime and raises the growth rate in the long-run limit, and reduces the time to transition. Proof. See Online Appendix C. Given the opposing effects of male and female health on growth and development it is unclear a priori whether health improvements that affect both genders alike promote development. Indeed, to some extent this depends on the economic regime itself. While a proportional increase in the health of both males and females promotes growth by lowering fertility and raising education in the modern growth regime, this is not true in the low-growth regime. In the absence of educational investments, proportional health improvements do not reduce fertility and thereby leave the growth rate unaffected. This result echoes the finding of Cervellati and Sunde (2011) that the impact of health on economic growth depends on whether the demographic transition has occurred or not. According to their analysis, health improvements, as measured by increases in life expectancy, tend to reduce fertility after the demographic transition to the extent that population growth slows down and per capita income growth increases. Before the transition, however, health improvements raise life expectancy but do not reduce fertility. The resulting increase in population size compromises per capita income growth. Our findings reveal a similar dependency of the relationship between health and economic growth on whether or not an economy has entered the economic transition but now for the case where health changes affect morbidity rather than mortality. Our analysis also shows that health improvements for both men and women do facilitate a take-off towards sustained economic development, albeit more slowly.17 4. Numerical analysis We illustrate the analytical results with a numerical example based on a parametrisation for Sub-Saharan Africa (year 2012), as given in Table 1. Specifically, we consider two exercises: first, we examine the impact of gender-specific health on the time to transition, seeking to assess the size of the effect; secondly, we solve the dynamic system as given by (25)–(32) numerically, seeking to assess the impact of gender-specific health on the overall development process. Table 1. Parameter Values for Simulation. Parameter . Value . Parameter . Value . δ 0.08715 α |$2/3$| γ 0.14322 gh (foreign) 0.00% per year ψ 0.04945 gA (foreign) 3.67% per year ξf 0.86920 ξm 0.88337 |$\bar{e}$| 1.000 η 14.9700 Period length t 35 years Parameter . Value . Parameter . Value . δ 0.08715 α |$2/3$| γ 0.14322 gh (foreign) 0.00% per year ψ 0.04945 gA (foreign) 3.67% per year ξf 0.86920 ξm 0.88337 |$\bar{e}$| 1.000 η 14.9700 Period length t 35 years Open in new tab Table 1. Parameter Values for Simulation. Parameter . Value . Parameter . Value . δ 0.08715 α |$2/3$| γ 0.14322 gh (foreign) 0.00% per year ψ 0.04945 gA (foreign) 3.67% per year ξf 0.86920 ξm 0.88337 |$\bar{e}$| 1.000 η 14.9700 Period length t 35 years Parameter . Value . Parameter . Value . δ 0.08715 α |$2/3$| γ 0.14322 gh (foreign) 0.00% per year ψ 0.04945 gA (foreign) 3.67% per year ξf 0.86920 ξm 0.88337 |$\bar{e}$| 1.000 η 14.9700 Period length t 35 years Open in new tab To proxy the impact of health on labour participation, we use data from WHO (2016) on the YLD for Sub-Saharan Africa. Assuming that the lifespan in which women face a trade-off between participating in the labour force and child rearing stretches from age 15 to age 50,18 we employ the age-gender specific values YLDf,15−29 = 0.10545, YLDf,30−49 = 0.149821, YLDm,15−29 = 0.093425, and YLDm,30−49 = 0.134035 to calculate $$\begin{eqnarray} \xi _{j}= \displaystyle\frac{15\times \left( 1-\textit{YLD}_{j,15-29}\right) +20\times \left( 1-\textit{YLD}_{j,30-49}\right) }{35} \end{eqnarray}$$ for j = f, m. We then obtain ξf = 0.8692 and ξm = 0.88337 as the gender-specific shares of the 35-year lifespan between ages 15 and 50 that individuals spend in good health. The parameters δ, γ, and ψ, capturing preferences for education, the number of children, and the time cost of children, respectively, have been chosen to match the total fertility rate [(4)] and female labour force participation, ξf(1 − ψnt), for Sub-Saharan Africa in the year 2012, as well as an asymptotic fertility rate [(6)] at the replacement level of 2 (reflecting a balanced gender ratio at birth and the absence of mortality). Using the calibrated values, we then set the parameter η so as to induce the long-run stationarity of human capital according to (16). Finally, we set α = 2|$/$|3 in line with Hansen and Prescott (2002) and we normalise |$\overline{e}=1$|⁠. Consistent with the data on which we base our numerical example, we assume a period length of 35 years. Regarding the levels and growth rates of foreign human capital and technology, we assume values that guarantee a take-off towards the modern growth regime in the late twentieth century. We use these values for the baseline scenario and then assess (in Scenario 1) the impact of a 5% increase in healthy time enjoyed by women. Similarly, we consider a 5% increase in healthy time enjoyed by men in Scenario 2, and a 5% increase in healthy time enjoyed by both genders in Scenario 3. Note that a 5% increase in healthy time enjoyed by women amounts to a reduction of the (average) time per year spent in disability by a third, from 48 to 32 days.19 Table 2 presents for the baseline case and for the three scenarios the pre-transition outcomes in terms of fertility, female labour force participation, economic growth, and the time to transition. According to World Bank (2016) data for Sub-Saharan Africa in 2012, fertility is around 5.1 children per household, and female labour force participation amounts to 0.64964.20 Annual growth (averaged over the time span 1961–2012) is on the order of 0.789% and amounts to an almost stagnating economy.21 We assign a stock of land X such that the baseline economy reaches transition after 75 years, corresponding to the third model period. Table 2. Impact of Health on Pre-Transition Outcomes and Time to Take-Off. . Baseline . Scenario 1 . Scenario 2 . Scenario 3 . Health parameters ξf 0.86920 0.91266 0.86920 0.91266 ξm 0.88337 0.88337 0.92754 0.92754 Pre-transition outcomes Fertility n 5.1081 4.9855 5.2369 5.1081 Participation ξf(1 − ψn) 0.64964 0.68766 0.64411 0.68212 Yearly growth rate g 0.00789 0.00812 0.00765 0.00789 Time to transition (years) 75 67.834 78.421 70.861 Years gained on baseline − 7.166 −3.421 4.139 . Baseline . Scenario 1 . Scenario 2 . Scenario 3 . Health parameters ξf 0.86920 0.91266 0.86920 0.91266 ξm 0.88337 0.88337 0.92754 0.92754 Pre-transition outcomes Fertility n 5.1081 4.9855 5.2369 5.1081 Participation ξf(1 − ψn) 0.64964 0.68766 0.64411 0.68212 Yearly growth rate g 0.00789 0.00812 0.00765 0.00789 Time to transition (years) 75 67.834 78.421 70.861 Years gained on baseline − 7.166 −3.421 4.139 Open in new tab Table 2. Impact of Health on Pre-Transition Outcomes and Time to Take-Off. . Baseline . Scenario 1 . Scenario 2 . Scenario 3 . Health parameters ξf 0.86920 0.91266 0.86920 0.91266 ξm 0.88337 0.88337 0.92754 0.92754 Pre-transition outcomes Fertility n 5.1081 4.9855 5.2369 5.1081 Participation ξf(1 − ψn) 0.64964 0.68766 0.64411 0.68212 Yearly growth rate g 0.00789 0.00812 0.00765 0.00789 Time to transition (years) 75 67.834 78.421 70.861 Years gained on baseline − 7.166 −3.421 4.139 . Baseline . Scenario 1 . Scenario 2 . Scenario 3 . Health parameters ξf 0.86920 0.91266 0.86920 0.91266 ξm 0.88337 0.88337 0.92754 0.92754 Pre-transition outcomes Fertility n 5.1081 4.9855 5.2369 5.1081 Participation ξf(1 − ψn) 0.64964 0.68766 0.64411 0.68212 Yearly growth rate g 0.00789 0.00812 0.00765 0.00789 Time to transition (years) 75 67.834 78.421 70.861 Years gained on baseline − 7.166 −3.421 4.139 Open in new tab The 5% improvement in healthy time enjoyed by women (Scenario 1) leads to a reduction in fertility of 2.4% and to an increase in female labour participation of about 5.9%. As a consequence, the time to transition is reduced by seven years and two months, which is enough to trigger a transition after two rather than three periods as in the baseline. By contrast, a 5% increase in healthy time enjoyed by men (Scenario 2) raises the time to transition by three years and five months. Given our assumption of a period length of 35 years, this does not have a bearing on the simulated transition process (see below). Finally, a 5% improvement in the healthy time enjoyed by both genders reduces the time to transition by four years and two months, which again is not enough to induce an earlier transition in the numerical example. A period length of 35 years leads to rather extreme impacts of changes in health on the transition process as it is modelled. Relatively small differences in the latent time to transition (as, for example, the three years' difference when comparing Scenarios 1 and 3) may either trigger no effect (as for Scenario 3) or a change in the timing of transition by 35 years (as for Scenario 1). In that regard, changes in the latent time to transition are a more realistic measure of the likely impact of health on the transition process. Moreover, a long period length is associated with a second problem: whether or not a health improvement advances or delays economic transition (by a generation) is very sensitive to the level of the initial wage |$\widehat{w}_{t_{0}}$| and therefore depends crucially on the assumptions about the initial state of the economy. In light of these concerns we can arrive at a more robust statement about the role of health for economic take-off by considering the following stochastic setting. Suppose the initial conditions of the economy |$\left\lbrace A_{t_{0}},N_{t_{0}},X\right\rbrace$| are randomly drawn from a set of values G so that they generate an initial wage |$\widehat{w}_{t_{0}}^{b}\in \left[ \underline{w}^{b},\overline{w}^{b}\right]$| for which transition arises after three periods (and three periods only) in the baseline scenario (b).22 Clearly, the range of initial wages |$\left[ \underline{w}^{1},\overline{w}^{1}\right]$| for which transition arises after three periods in Scenario 1 satisfies |$\underline{w}^{1}\lt \underline{w}^{b}$| and |$\overline{w}^{1}\lt \overline{w}^{b}$| (i.e., the range is shifted “downward”). Intuitively this is due to the fact that better female health reduces the threshold wage for economic take-off. Furthermore, for any given |$\left\lbrace A_{t_{0}},N_{t_{0}},X\right\rbrace \in G$|⁠, the initial wage in Scenario 1 will satisfy |$\widehat{w}_{t_{0}}^{1}\in \left[ \left( \widehat{w}_{t_{0}}^{1}/\widehat{w}_{t_{0}}^{b}\right) \underline{w}^{b},\left( \widehat{w}_{t_{0}}^{1}/\widehat{w} _{t_{0}}^{b}\right) \overline{w}^{b}\right]$| with |$\widehat{w}_{t_{0}}^{1}/ \widehat{w}_{t_{0}}^{b}\lt 1.$| This is because of the greater effective labour supply associated with better female health in Scenario 1. Nevertheless, an interval |$\left[ \overline{w}^{1},\left( \widehat{w}_{t_{0}}^{1}/ \widehat{w}_{t_{0}}^{b}\right) \overline{w}^{b}\right]$| exists such that a draw |$\widehat{w}_{t_{0}}^{1}\in \left[ \overline{w}^{1},\left( \widehat{w} _{t_{0}}^{1}/\widehat{w}_{t_{0}}^{b}\right) \overline{w}^{b}\right]$| will induce a transition after three periods in the baseline case but a transition after two periods in Scenario 1. The probability of such a draw, |$\pi _{b1}=\left[ \left( \widehat{w}_{t_{0}}^{1}/\widehat{w} _{t_{0}}^{b}\right) \overline{w}^{b}-\overline{w}^{1}\right] \left[ \left( \widehat{w}_{t_{0}}^{1}/\widehat{w}_{t_{0}}^{b}\right) \left( \overline{w} ^{b}-\underline{w}^{b}\right) \right] ^{-1},$| can now be read as the probability that the improvement in female health in Scenario 1 advances the economic transition by one period (i.e., by 35 years). Assuming that the initial wages are uniformly distributed and applying the data from our numerical example, we obtain πb1 = 0.188, which is of sizeable magnitude.23 In our second exercise, we graph the development paths for human capital, population, and income, embracing both pre- and post-transition periods. Figure 1 shows the impact of female health improvements. The solid line refers to the baseline case, whereas the dashed line refers to Scenario 1, i.e., an economy that experienced at the initial time (1900) a 5% increase in female healthy time. Fig. 1. Open in new tabDownload slide Illustration of the Differential Take-Off in Scenario 1. Notes: The baseline simulation is reflected by the solid line. The dashed line refers to a simulation with similar parameter values except that female health increases by 5% compared with the baseline simulation. Fig. 1. Open in new tabDownload slide Illustration of the Differential Take-Off in Scenario 1. Notes: The baseline simulation is reflected by the solid line. The dashed line refers to a simulation with similar parameter values except that female health increases by 5% compared with the baseline simulation. Both economies start with the same population size, the same state of technology and the same land endowment. They follow the same path until around the year 1970, when they are still in a low-growth regime without the accumulation of human capital [see Panel (b)] and very sluggish earnings growth [see Panel (f)]. The sole reason that wages grow at all is that the technological frontier in the rest of the world grows at a constant rate such that the distance to the frontier increases, leading to more intense technology adoption (cf. Howitt, 2000; Acemoglu et al., 2006). At the point of take-off (for the baseline scenario this is the year 2005 and for Scenario 1 this is the year 1970), per capita income surpasses the value at which it becomes optimal for individuals to invest in the education of their offspring. From then on parents choose to have fewer children but to educate them better. Consequently, a fertility transition sets in and the rate of population growth declines [see Panel (d)]. The resulting increase in human capital helps to close the gap between the human capital level of the country under consideration and the rest of the world. This in turn leads to faster technology adoption and an increase of per capita income growth [see Panels (e) and (f)]. In comparison with the baseline scenario we see that the benefits from female health improvements materialise only over time, but then in an accelerating way. This is due to diverging growth rates of human capital and income in the modern growth regime, implying that an initial advantage is magnified. Interestingly, little perceivable difference exists between the two economies in the ‘immediate’ aftermath of the early transition (i.e., over the years 1970–2005). Thus, female health improvements appear to create only a small initial advantage in terms of slightly higher growth rates at a slightly earlier point in time, but this effect is vastly magnified over the subsequent 70 years. In Online Appendix B.8 we provide equivalent sets of simulations for Scenarios 2 and 3. The outcomes are fully in line with our earlier findings, one aspect being that for both scenarios the difference in post-transition growth rates is rather limited, implying that these economies do not follow dramatically divergent development paths. We should mention that the path of development is not invariant to the sequencing of events. If female health is improved earlier (later) than male health, the economy ends up on a higher (lower) income trajectory. This suggests that targeted health interventions for women are more effective for economic development the earlier they occur, conferring substantial cumulative benefits that would not be realised if intervention were delayed. 5. Discussion and Conclusions We have studied the impact of productivity- and earnings-enhancing female versus male health improvements within a dynamic general equilibrium model of economic development with endogenous education and fertility. We solved the model and studied the conditions under which the economy switches from a low-growth regime with high fertility and no educational investments to a modern-growth regime with declining fertility and increasing educational investments. By raising female labour participation/productivity and thus the opportunity cost of children, improved female health has a direct negative impact on fertility. While this moderately enhances earnings growth during the low-growth phase, which is otherwise driven by technology adoption, it also has important level effects: on the one hand, it lowers the earnings threshold that must be met to initiate educational and demographic transitions; on the other hand, it lowers the wage level by increasing aggregate labour supply. As it turns out, however, starting from the same initial condition, an economy with better female health will always take off at an earlier date. In contrast, by raising income at the household level, male health improvements tend to increase fertility and thereby slow growth, the progress towards demographic and economic transition, and the resulting economic take-off. This is the case as long as men do not spend a substantial amount of their time on child rearing. Given that female health improvements do, indeed, reduce fertility, as is suggested by individual-level evidence in Hoddinott et al. (2013) and Nandi et al. (2020) and by macroeconomic correlations (see Online Appendix A), a case exists for health improvements to be targeted to women. Potential policies are the reduction of iodine deficiency (cf. Field et al., 2009) and the vaccination against human papilloma virus to prevent cervical cancer (cf. Luca et al., 2018), which tend to benefit females in particular; and the establishment of equal access for women and girls to general healthcare facilities and programmes of food supplementation (cf. Hoddinott et al., 2013; Nandi et al., 2020). The case appears less clear, however, for investments in maternal healthcare, as advocated by e.g., WHO (2009), a form of healthcare we have not modelled. Albanesi and Olivetti (2014; 2016) and Bhalotra et al. (2018) show that while improvements in maternal mortality and morbidity tend to raise fertility and female labour supply in the short run, a subsequent increase in female education tends to lower fertility in the long run (Jayachandran and Lleras-Muney, 2009; Albanesi and Olivetti, 2014). Although targeted investments in women may also be justified on intra-household equity grounds, male health improvements are more effective in promoting household utility in the short run. This is because in societies in which males supply a greater share of their time to the labour market, household income increases more if men rather than women benefit from a health-related increase in their earnings. The resulting conflict between the short-term interests of the household and long-term development goals may give rise to a development trap, wherein households primarily care for the health of the ‘male breadwinner’, although this has harmful side effects in the long run. Overcoming the associated intergenerational externality would then justify policy interventions in favour of female health. When health improvements benefit both genders alike, growth is only promoted when an economic–demographic transition has already taken place. Only then will the increase in educational investments associated with better female health lead to an increase in the cost of children that overcompensates for the positive income effect on fertility. Nevertheless, economic take-off is still sped up as long as health improvements are not disproportionately enjoyed by men. We show in the Online Appendix that our main result, female health being more conducive to economic development than male health, is remarkably robust to a large set of extensions: (i) endogenous gender-specific health investments; (ii) collective household preferences and intra-household bargaining; (iii) preferences over the expected income of children—including spillovers from parental to child health—instead of a warm glow motive of investing in education; (iv) childcare productivity depending on parental health; (v) male childcare; (vi) physical capital and foreign direct investment (FDI); (vii) health-dependent productivity; and (viii) imperfect substitutability between men and women in goods production. Referring the reader to the Online Appendix for detail, we restrain ourselves here to summarising what these generalisations imply for the role of female rather than male health in development. While we find a strong and robust case for female health in speeding up the economic transition, some extensions suggest that our baseline model may exaggerate a case against male health. This holds if spillovers from father’s to child’s health tend to raise the return to educational investments [extension (iii)]; if men provide significant amounts of childcare [extension (v)], implying that the opportunity cost of childcare increases in male health, too; and if in a setting of poor substitutability between male and female labour and a relatively high labour share, health-related increases in male labour supply lead to an increase in female wages [extension (viii)]. However, our results also reveal female health to be the more forceful agent even if male health facilitates the transition. Conversely, we find that our results tend to be reinforced if the spouses’ bargaining power depends on the distribution of health within the household [extension (ii)] and when households engage in gender-specific investments into their health [extension (i)]. Especially the latter may act as a powerful multiplier: with the return on investment in women’s health increasing in their labour participation rate, any reduction in fertility will boost the incentive to invest in female health. With the underlying health improvements leading to a reduction in fertility, in turn, potential exists for a virtuous cycle towards take-off. Conversely, however, to the extent that households choose to invest primarily in male health, as this yields the greater short-run returns, and to the extent this leads to the maintenance of high fertility, this stifles female health investments and may, consequently, stall the process of development. Male-biased investment strategies are well documented (cf. Pitt et al., 1990; Dercon and Krishnan, 2000; Qian, 2008; Barcellos et al., 2014; Saikia et al., 2016). While our analysis lends some rationale to such strategies, it also identifies their potential to generate a development trap. Two limitations of our model relate to its focus on a representative household and on the morbidity rather than the mortality aspect of health. Heterogeneity at the household level clearly matters beyond gender (see, e.g., the analysis of the childlessness of particularly poor women in otherwise high-fertility countries and the analysis of differential fertility on human capital accumulation in de la Croix and Doepke, 2003; Vogl, 2016; Baudin et al., 2020), and an understanding of how it is shaped through matching during the process of household formation is important from a micro-policy perspective. However, our focus on the macroeconomic consequences of gender-specific health improvements justifies the representative agent approach that is common in the macroeconomic literature on economic development. In addition, as we have argued earlier, while clearly relevant for the cross-section of households, assortative matching on health per se would not bear on the dynamics of family choices that are at the core of our analysis. That reductions in mortality can initiate an economic take-off by rendering investments in education profitable is well established (e.g., Cervellati and Sunde, 2005; Soares, 2005, among many others). While this channel has its own weight, it should also be expected that the decline in morbidity we are considering would ultimately translate into greater longevity.24 We would argue, however, that consideration of this channel would only strengthen our results: assume an increase in longevity only for girls, as would occur with an exclusive improvement in female morbidity. As Jayachandran and Lleras-Muney (2009) and Albanesi and Olivetti (2014) show, reductions in (maternal) mortality serve as an additional lever for economic development by fostering investments in female education, which again translate into higher labour participation and lower fertility. Clearly, this complements and magnifies the morbidity channel we are considering.25 Now, consider an increase in longevity for both genders that would trigger educational investments into boys and girls alike.26 One feature of note is that, through the mortality channel, male health improvements would contribute to speeding up the economic transition. However, to the extent that this is offset through the delaying impact of male morbidity improvements, male health continues to be the weaker catalyst in promoting an economic transition as compared with female health. Soares and Falcão (2008) show that greater human capital investments into children lead to a further reduction in fertility and an increase in female labour force participation amounting to a reinforcement of our mechanism after the onset of transition. In summary, we do not see why incorporating longevity effects should do anything but strengthen our findings. We would like to remind the reader, however, that by altering labour supply and fertility in a gender-specific way before the onset of transition, the gender distribution of morbidity has a distinct and nontrivial impact on the timing of the transition process. Altogether, we believe that our theoretical framework could provide guidance on household-level empirical analyses with respect to the relations between female health and development and between female health and household income. This offers a promising avenue for further research. Additional Supporting Information may be found in the online version of this article: Online Appendix Replication Package Notes The data and codes for this paper are available on the Journal website. They were checked for their ability to reproduce the results presented in the paper. We thank the Editor Morten Ravn, two anonymous referees, Hendrik Jürges, Alyssa Lubet, Elizabeth Mitgang, Alexia Prskawetz, Christa Simon, Harald Uhlig, Katharina Werner, Joshua Wilde and Maria Winkler-Dworak for valuable comments and suggestions. We are grateful to the Norwegian Agency for Development Co-operation for funding this study under grant number QZA-0408-QZA-12/0628. This article was also made possible by the National Institute on Aging, National Institutes of Health, under award number P30AG024409. Footnotes 1 On the effect of gender inequality on economic development, see, for example, Galor and Weil (1996), Knowles et al. (2002), Lagerlöf (2003; 2005), Abu-Ghaida and Klasen (2004), Iyigun and Walsh (2007), Soares and Falcão (2008), Doepke and Tertilt (2009; 2019), Kimura and Yasui (2010), Schober and Winter-Ebmer (2011), Rees and Riezman (2012), Diebolt and Perrin (2013a,b), Hiller (2014) and Prettner and Strulik (2017a). For the potential effects of female health in the context of economic development, see Stenberg et al. (2014). Onarheim et al. (2016) present an extensive systematic review of the economic and non-economic literature on female health and its role for development. 2 For the effects of overall population health on economic development, see, for example, Bloom et al. (2019a). 3 See, e.g., Deaton (2008), Molini et al. (2010) and Barcellos et al. (2014) for evidence that the distribution of height and body mass index is biased against women; Bhalotra (2010) and Baird et al. (2011) for disproportionate mortality of girls in the presence of economic crisis; Qian (2008) for the dependency of excess mortality on the household income distribution; and Bloom et al. (2001), Self and Grabowski (2012), and Saikia et al. (2016) for evidence on difficulties for women to access healthcare. 4 The focus on female morbidity and its role in female labour supply is further motivated by several salient empirical observations: first, health is a crucial element of human capital and as such represents a central determinant of individual productivity (cf. Shastry and Weil, 2003; Bloom et al., 2004; 2019b; Schultz, 2005; Weil, 2007; Bleakley, 2007; 2010; Prettner et al., 2013; Kotschy, 2019). Secondly, while women have a longer lifespan than men, they experience higher productivity losses due to poorer health during their working lives (cf. Pitt et al., 1990; Dercon and Krishnan, 2000; Molini et al., 2010; Vos et al., 2012, for evidence regarding nutrition, body mass index, and time lost due to disability). In addition, widespread evidence indicates that in many developing countries women continue to be subjected to discrimination in respect to health and healthcare opportunities (e.g., Deaton, 2008; Qian, 2008; Bhalotra, 2010; Barcellos et al., 2014; Saikia et al., 2016). Thirdly, healthier women tend to have lower fertility (Hoddinott et al., 2013; Nandi et al., 2020), which can have strong implications for economic development (Galor and Weil, 2000; Galor, 2005; 2011). 5 In Online Appendix B.8 we consider gender-specific wages by means of a general constant elasticity of substitution (CES) production function with female and male labour inputs being imperfect substitutes. We show that all our results generalise under a mild assumption about the production elasticity of the labour composite. 6 Trivers and Willard (1973) provide an argument grounded in evolutionary biology for why men spend much less of their time on child rearing: while fertility of women is capped from above, this is not necessarily the case for men because of polygyny. Pregnancy and breastfeeding in low-income pre-demographic transition regions can take up to four years such that a woman can have about seven children throughout her fecund lifespan. Thus, women are more likely to be at the corner solution of the quality–quantity choice and, for this reason, tend to invest more time in caring. 7 In Online Appendices B.4 and B.5 we consider settings in which the cost of childcare depends on female health and in which men provide some childcare, respectively. At the end of this subsection, we briefly discuss the robustness of our results with respect to these alternative specifications. 8 See Online Appendix B.7 for an alternative interpretation of ξm and ξf as measures of health-dependent productivity. 9 Note that we operate under the assumption that the costs of health interventions are borne by foreign governments or development agencies and that no cost differentials exist between male and female health interventions. See Online Appendix B.1 for an extension in which the household undertakes health investments. 10 All subsequent derivations hold irrespective of whether fertility is above or below the replacement rate. 11 Note that we could rewrite (7) to |$\delta \log w_{t}+\delta \log \left( \widehat{e}\left( \overline{e},w_{t}\right) + e_{t}/w_{t}\right)$| and obtain the warm glow benefit from real units of education, where δlog wt is a constant from the perspective of period t maximisation. 12 Note that this renders the warm glow formulation intuitive in many ways for a setting in which individuals are unable rationally to anticipate the value of human capital for their children. This is plausible, as they are unlikely to know which wages their children will be facing, nor how their educational expenditures translate into the accumulation of human capital. Hence, they rest their decisions merely on what they observe, namely the level of informally acquired human capital and its current value, as can be gleaned from current wages. 13 In Online Appendix B.8 we consider a general CES production function with female and male labour inputs being imperfect substitutes. We show that, for female and male labour being gross substitutes, all of our results in regard to female health generalise, while our findings with regard to male health generalise if and only if the elasticity α is sufficiently low. 14 In labour market equilibrium, we have |$L_{t,Y}=L_{t}-L_{t,E}=(N_{t}/2)\left[ \xi _{m}+\xi _{f}\left( 1-\psi n_{t}\right) - e_{t}n_{t}/\widehat{w}_{t}\right]$|⁠. Substituting the optimal values of et and nt, this simplifies to the right-hand side expression in (21). 15 If education levels converge between low-income and high-income countries, technological levels also converge. In this case, the low-income country approaches the technology leader in the very long run. 16 A fall back to the low-growth regime cannot be entirely ruled out for a precipitous exogenous fall in the rate of technological progress immediately after the transition to the sustained growth regime. A closer investigation of this rather unrealistic case is available from the authors upon request. 17 A large body of evidence hints at a strong interspousal correlation in health status (cf. Meyler et al., 2007), a considerable part of which can be traced back to assortative matching (cf. Chiappori et al., 2012; Banks et al., 2014; Guner et al., 2018). According to part (i) of Proposition 6, perfect assortative matching on health would then imply the absence of a gradient in fertility across households before a transition and the presence of a downward sloped gradient in fertility when moving from less healthy to healthier households. The absence of a health gradient before the transition would be broken by either of two effects: first, inert health is typically not fully observable at the point of marriage, implying that matching remains imperfect, as is evidenced, e.g., in Guner et al. (2018). In such a case our model would predict a decline in fertility when moving from households in which the husband’s health exceeds the wife’s health to those in which the opposite is true. Secondly, greater variation exists in female health than in male health, which would imply a downward sloped gradient in fertility when moving from households with poor health to those with good health even in the presence of perfect matching. The opposite would be true if male health were more variable. While the consideration of matching thus suggests testable implications between health and fertility at the household level, it leaves unaffected our key insights on the implications of (differential) health improvements for the process of economic transitions. This is because in the (ongoing) presence of assortative matching, shifts in the level of female and/or male health would leave the distribution of matches unaffected. 18 This reflects the notion that women give birth approximately during the age interval 15–35 years and that children require care up to age 15. 19 If women spend 48 days per year in disability on average, their healthy time per year amounts to 365 − 48 = 317 days. A 5% increase of the time spent in good health is therefore tantamount to an increase by 16 days to 333 days. 20 Note that the plausible fertility rates are capped from above by the maximum possible fertility rate of women. 21 We assume for this experiment constant technology adoption of about 5.8% per year. In our subsequent numerical experiment, technology adoption is specified according to the flexible form of (24), giving rise to an average on the same order. 22 More specifically, |$\underline{\textit{w}}^{b}:=\gamma \overline{e}/ \left[\delta \psi \xi _{f}^{b} \left( 1+g^{b}\right) ^{3} \right]$| and |$\overline{w} ^{b}:= \gamma \overline{e}/\left[\delta \psi \xi _{f}^{b} \left( 1+g^{b}\right) ^{2} \right]$| with gb as defined by (37). Thus, the lower (upper) bound corresponds to the baseline threshold wage discounted by the growth over three (two) periods. If |$\widehat{w} _{t_{0}}^{b}\,{\lt}\, \underline{\textit{w}}^{b}$|⁠, the transition would occur after four periods; if |$\widehat{w}_{t_{0}}^{b}\gt \overline{w}^{b}$|⁠, the transition would occur after two periods. 23 Similarly, we obtain πb3 = 0.116 as the probability that an equiproportional increase of health for both genders advances economic take-off by one generation, and (in an analogous way) we obtain πb2 = 0.114 as the probability that an improvement in male health delays take-off by one generation. 24 We are grateful to a reviewer for pointing this out. 25 One subtle difference relates to the sequence of events: in the case of mortality decline, investments in female education increase before female labour participation increases, whereas reductions in morbidity trigger greater female participation before they trigger greater educational investments. 26 Note that this scenario is structurally similar to the model extension in Online Appendix B.3, in which parents care about their children's human capital. 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Dippel,, Christian;Greif,, Avner;Trefler,, Daniel

doi: 10.1093/ej/ueaa030pmid: N/A

Abstract In economies with a large informal sector firms can increase profits by reducing workers’ outside options in that informal sector. We formalise this idea in a simple model of an agricultural economy with plantation owners who lobby the government to enact coercive policies—e.g., the eviction and incarceration of squatting smallhold farmers—that reduce the value to working outside the formal sector. Using unique data for 14 British West Indies ‘sugar islands’ from 1838 (the year of slave emancipation) until 1913, we examine the impact of plantation owners’ power on wages and coercion-related incarceration. To gain identification, we utilise exogenous variation in the strength of the plantation system in the different islands over time. Where planter power declined we see that incarceration rates dropped, and agricultural wages rose, accompanied by a decline in formal agricultural employment. The fact that the wage level in the capitalist sector depends upon earnings in the subsistence sector is sometimes of immense political importance, since its effect is that capitalists have a direct interest in holding down the productivity of the subsistence workers. Thus the owners of plantations […] if they are influential in the government, will not be found using their influence to expand the facilities for agricultural extension. They will not support proposals for land settlement, and are often instead to be found engaged in turning the peasants off their lands. —Lewis (1954) Many economists and historians would agree with Acemoglu and Wolitzky’s (2011) assessment that ‘the majority of labour transactions throughout much of history and a significant fraction of such transactions in many developing countries today are coercive’. Indeed, labour coercion is at the heart of much of the literature on long-run development and institutional change (Domar, 1970; Engerman, 1999; Acemoglu et al., 2001; 2002; Engerman and Sokoloff, 2002; Greif, 2005; Nunn, 2008; Dell, 2010; Naidu, 2010; Nunn and Wantchekon, 2011; Naidu and Yuchtman, 2013; Bobonis and Morrow, 2014; Ashraf et al., 2020; Lowes and Montero, 2018). Despite this, rigorous empirical evidence on labour coercion is scarce and mostly focused on relating present-day outcomes to historical labour coercion.1 Focusing on the workings of labour coercion rather than its long-run consequences, we exploit a historical setting involving 14 British West Indies sugar colonies from 1838—the year slaves were emancipated in the British Empire—to 1913. We are thus studying 14 free labour markets at their inception. Before 1838, the 14 colonies we study were exceedingly similar. Economically, all were slave societies and all were completely specialised in sugar cane production. Institutionally, all had the same political and legal systems inherited from Britain and were dominated by a small group of white planters. After emancipation, ‘the main fact of life in the free West Indies was that black labourers were unwilling to remain submissive and disciplined cane workers’ (Green, 1976, p. 170). We study how planters over the ensuing 76 years used their influence over the state to enact coercive policies that kept wages low and secured a steady supply of labour. In keeping with Lewis’s quote, our focus is on ‘legal coercion’, i.e., the use of the state’s legislative and judicial institutions to manipulate workers’ outside options. This focus is particularly pertinent where workers’ wages in the formal sector are determined by outside options generated in the informal sector. Our paper has two empirical objectives: one, we want to test to what extent legal coercion was used to lower wages. Two, we study the importance of the planters’ economic and political influence over the government in shaping legal coercion. To guide our empirics, we employ a simple model where workers earn a wage w that is equal to their outside option in the informal sector. Coercion C reduces this outside option, e.g., by evicting smallholders from their plots. Coercive policies C are set by the government to benefit the planters as in Grossman and Helpman’s ‘Protection for Sale’ framework (1994), and the government chooses a higher C when planters’ influence is greater.2 Planter influence depends on the number of plantations on the island (N), which in turn depends on the extent to which Caribbean plantations offer higher returns to British investors than returns obtainable elsewhere. In our model a shrinking plantation sector leads to lower levels of coercive activity which raises wages: N → C → w. Exogenous factors act as an instrument for N. The data are collected from the British Colonial Office’s Blue Books: wages wit are reported as the annual average of the agricultural spot market wage. Cit is measured by incarceration rates per capita. Nit is measured as the share of sugar in total exports or as the share of all plantation crops in total exports. Our empirical focus is on within-colony over-time panel variation. Our hypothesis is that where the plantation system went into decline, Cit decreased and wit increased relative to other islands. A generalised difference-in-differences strategy robustly bears this out across a range of different specifications. We instrument for Nit using exogenous variation in the returns to investing in Caribbean plantations relative to investing elsewhere. Across islands, returns in the Caribbean were lower where smallholders could easily escape work on plantations. Some colonies had large hinterlands while others had next to none.3Over time, returns to investing outside of the Caribbean improved rapidly over the nineteenth century. As the Empire expanded, opportunities to export British manufactures grew much faster than opportunities in Caribbean agriculture, and English investors turned their attentions away from the Caribbean. Combining these exogenous elements, our instrument Oit is the product of the cross-section of islands’ hinterlands and the time-series of English exports to non-Caribbean destinations. In the data, a higher Oit led to a decline in Nit and Cit and a rise in wages. When we instrument for Nit we get two-stage least-squares (TSLS) estimates that are highly statistically significant and economically large: a 50% decline in the plantation system—roughly the average over the 76 years we study—would have increased wages by about 50% and reduced incarceration rates by close to their mean of 1 in 100 people. These results hold up under an extensive set of robustness checks. We also provide evidence on the mechanisms linking N, C and w. A causal mediation analysis shows that three-quarters of the negative effect of the plantation system on wages operated via measured coercion, prima facie evidence for our hypothesis. To lend support to our assumption that coercion was ‘legal coercion’ exercised by the government in response to pressure from the plantation system, we study the effects of an exogenous shock which changed the composition of the plantation-owning elite, while keeping the size of the plantation sector constant. This shock strengthened the plantation system’s lobbying power with each island’s government apparatus, but severed the localised ties between the previous plantation owners and the parochial constabulary and judges. We find that this shock increased coercive legislation, which was set centrally, but decreased incarceration, which depended on these parochial ties. This evidence suggests that legal coercion adjusted when the planters’ form of influence changed. We conclude this introduction with a literature review. The importance of using the legislative, judicial and policing powers of the state to reduce the outside options of workers and to benefit a small elite is emphasised by Lewis (1954) and also in Acemoglu and Robinson’s (2012) study of apartheid. In the focus on the manipulation of workers’ outside options, we relate to Alston and Ferrie’s account of Southern paternalism (1993). The closest empirical study to ours is Bobonis and Morrow (2014) who show that coffee price shocks in Puerto Rico in the mid-1800s led elites to reduce human capital investments so as to depress plantation workers’ outside options. We also connect to a large literature on labour coercion. This literature is more focused on the coercion of workers on the job (Chwe, 1990; Basu, 1999; Bloch and Rao, 2002; Naidu and Yuchtman, 2013); however, in a principal–agent framework, there is a complementarity between coercing workers on the job, and reducing their outside options as non-workers (Acemoglu and Wolitzky, 2011).4 In our setting, the latter form of coercion was clearly dominant. In an interesting counterpoint to our findings, Dell and Olken (2020) show that the location of Dutch colonial sugar plantations on the island of Java had positive long-run effects on local infrastructure and economic development. This line of research suggests that there are potentially positive and non-institutional long-run consequences of colonial extraction. Lastly, our focus on the political consequences of geographic variation in the ability to evade the plantation system connects us to a broader literature on the institutional consequences of geography; see, e.g., Acemoglu et al. (2002); Engerman and Sokoloff (2002).5 1. History British West Indies plantations were a source of vast profits for British planters and investors. These profits were dealt a severe blow by the emancipation of slaves in 1838. Emancipation initially led to sharply rising wages as freed slaves rejected plantation life in favour of squatting on abandoned estates or small plots in the hinterland. This ‘flight off the estates’ did not last long. Within a few years of emancipation, the white planter elite had developed a system of legal coercion over labour that lowered wages and slowed the demise of the plantation system. We now describe the workings of this system.6 1.1. Legal Coercion Cit Legal coercion in our setting took three main forms. First, coercion restricted access to land. The full force of the law was brought to bear on peasants who attempted to squat on abandoned estates or Crown land. Squatting was so rampant that it seriously undermined the ability of planters to keep peasants on plantations. In Jamaica there were 10,000 squatters by 1844 and this number probably climbed to 40,000 by the mid-1860s (Eisner, 1961, pp. 215–6). The Colonial Blue Books list the titles of all colonial statutes and a quick perusal shows that every colony repeatedly enacted and strengthened trespass and vagrancy laws in order to prevent squatting. The salience of the squatting-incarceration issue is illustrated by Jamaica’s Morant Bay Rebellion, which left 600 dead and many more imprisoned (Underhill, 1895; Craton, 1988).7 Other examples abound: in Dominica, the ‘Queen’s Three Chains’ unrest of 1856 was driven by a dispute over whether several black families had implicit title to or were squatting on the land they were farming. It was resolved by the rapid dispatch of troops from nearby Antigua (Honychurch, 1984, pp. 136–8). The ‘Toll Bar Riot’ and the ‘Florence Hall Riot’ in Jamaica were triggered respectively by objections over limiting smallholders’ access to water sources, and over the sentencing of squatters for trespassing on an abandoned estate. See Cundall (1906, pp. 5–12).8 A feature of land conflicts in the post-emancipation Caribbean was that they resulted from planters’ attempts to reduce peasant smallholders’ outside options. Planters were not grabbing the land for themselves. In fact, there was plenty of fallow plantation land during the period we study. For example, in mid-century Jamaica, less than one-quarter of all land was under cultivation and, even on the active plantations, less than half of the plantation land was in use. That is, disputes were not over land that could be or ever was used for plantation crops. See Satchell (1990, ch. 4 and especially, pp. 63–4). Land conflict in our case was thus different from historical episodes in other parts of the world where planters cultivated land stolen from peasants. See for example Sánchez et al. (2010) on Colombia’s land conflicts 1850–1925 and Acemoglu and Robinson (2012, ch. 9) on Guatemalans' coffee land grabs during the same period. Second, coercion was manifest in asymmetric terms of employment contracts. If a worker started employment without a formal contract the laws of many colonies stated that he or she had implicitly entered into a one-month contract. Failure to work during that month was a ‘breach of contract’ that resulted in fines or imprisonment (House of Commons Parliamentary Papers, 1839b, pp. 205–6). If in addition to wages a worker also received a cottage and a plot for growing crops, he or she was obligated to work on the plantation for a full year. The law allowed the planter to evict a peasant for absenteeism (‘breach of contract’) and threats of eviction were very effective in forcing peasants back to work.9 Laws additionally allowed planters to burn or confiscate cottages and crops of evicted peasants.10 The resulting destruction led to retribution by peasants who could then be sentenced to lengthy imprisonment for ‘malicious injury to property’. Third, coercion was manifest in a tax system that penalised smallholders. This was most apparent in the biased taxation of imports. Planters imported flour and rice to feed plantation workers and these imports competed directly with smallhold crops, making smallholding less attractive. High tariffs on foodstuffs were therefore ‘opposed by the estate interests since they tended to deplete labour reserves by driving workers from plantations to the hinterland, where they grew ground provisions’ (Rogers, 1970, p. 96). Green (1976, p. 186) similarly states that there was much political conflict ‘over import duties on food, [which] enticed freedmen to abandon estate labour in favour of the production and sale of provisions’. Property taxation was also biased against smallholders. A smallholder with 5 acres could pay higher taxes than a planter with 500 acres. Not only did such abusive smallhold taxes reduce the returns to smallholding, they also led to punitive loss of title. For example, Satchell (1990, ch. 4 and table 4.3) documents that 18,000 acres of Jamaican smallholds were repossessed after 1869 for failure to pay taxes. Many other discriminatory taxes have been documented, including export taxes that were higher on smallhold crops than on sugar, e.g., Underhill (1895, p. xvii). Dookhan (1975, p. 156) emphasises the importance of such regressive taxes, arguing in particular that the 1853 ‘Chateau Belair’ Riots in the Virgin Islands were caused by a new tax on cattle. In his words, ‘as cattle rearing was primarily the occupation of the rural negro population, this tax fell principally on them’. Legal coercion was a fact of life in the British West Indies. Its role was simple: reduce the returns to smallholding so as to encourage peasants to work on the plantations for low wages. Restated in more theoretical language, legal coercion did not affect plantation workers directly; rather, it affected them indirectly by reducing their outside options. 1.2. The Government Apparatus The three pillars of the law—lawmakers, judges and police—were all controlled by planters. To gauge their coercive effects, it is useful to apply Acemoglu and Robinson’s (2008) distinction between officially sanctioned de jure power and unofficially sanctioned de facto power. Planters’ de jure power was exercised primarily through their influence on discriminatory laws passed by legislators in the islands’ legislative assemblies.11 Planters’ de facto power was exercised primarily through the selective application of these laws in different locations: rural magistrates did much of their work on plantations, had little legal training and were frequently former plantation overseers (McLewin, 1987, pp. 85–7). Local police were also beholden to planters. The first post-abolition laws constituting the police force (‘Police Acts’) stated that rural police were to be appointed by planters. The Leewards governor complained that this was unconstitutional, but found it difficult to pressure planter-dominated legislatures into changing the laws (House of Commons Parliamentary Papers, 1839b, p. 49). 1.3. Planters’ Relative Political Power Nit We are interested in the impact of the planter elite’s political power Nit on coercion Cit. The previous section described Cit. We now describe Nit. Planters’ political power was based on their economic power relative to the peasantry. Economic power in the Caribbean hinged on exports. Marshall (1968, pp. 253–4) concludes from his survey of the British West Indies that the period from roughly 1850 to 1900 was one of ‘continuing expansion of the number of peasants and, more important, a marked shift by the peasants to export crop production’. This growing peasant participation in exports was clearly accompanied by the declining acreage of plantations, and the rising number of freeholders and squatters (Riviere, 1972, pp. 15–7). Eisner (1961, p. 235) argues that the ‘increasing prosperity of the peasantry is thus seen to be mainly due to their growing share in export crops’.12 Our measure of the relative economic power of the plantation system is thus the share of plantation crops in total exports.13 Sugar is consistently identified with a plantation mode of production and has often been argued to be detrimental to economic and social development, e.g., Sokoloff and Engerman (2000) and Easterly (2007).14 In the British West Indies, sugar was also by far and away the dominant plantation crop, completely eclipsing all other crops such as cotton or coffee. We therefore use the share of sugar in total exports as one measure of the strength of the planter elite relative to the peasantry. Figure 1 displays the lowess-smoothed share of sugar in total exports by colony. It is best to focus on the two dominant features. First, in 1838 every colony was highly specialised in sugar. Second, by 1913 there were substantial cross-colony differences in sugar export shares. Colonies roughly divided into three groups. Five colonies remained heavily involved in sugar for the entire period (Antigua, Barbados, Guyana, St Kitts and Nevis). Four colonies saw sugar decline to less than half of total exports (St Lucia, Trinidad, Tobago, and Jamaica). Five colonies exited sugar entirely by the end of period (Virgin Islands, Grenada, Dominca, St Vincent and Montserrat). In Figure 1 and the econometric analysis below we use lowess-smoothed export shares because we are interested in capturing long-run changes in the strength of the plantation system rather than short-run agricultural fluctuations.15 Fig. 1. Open in new tabDownload slide The Differential Decline of the Plantation Economy. Notes: This figure reports the share of sugar in total exports Nevis is not reported because it stayed above 0.99 in each panel. Also, Nevis merged with larger St Kitts in 1883 and Tobago merged with larger Trinidad in 1899. Fig. 1. Open in new tabDownload slide The Differential Decline of the Plantation Economy. Notes: This figure reports the share of sugar in total exports Nevis is not reported because it stayed above 0.99 in each panel. Also, Nevis merged with larger St Kitts in 1883 and Tobago merged with larger Trinidad in 1899. The data displayed in Figure 1 were intimately linked to the planter’s power and influence over government, in particular their success in securing plantation labour at low wages.16 Dookhan (1977, p. 11) argues that across the Caribbean, labourer ‘drift from the estates’ was lowest in Antigua, St Kitts and Barbados, i.e., in precisely the three islands where the plantation system survived the longest. Green (1976, p. 258) similarly argues that the success of Barbados’s plantations was ‘not due to new technology but rather due to a large and disciplined labour pool’. Over time, some planters shifted to other plantation crops, which were similar to sugar in that they also incentivised labour coercion. To handle this shift in coercive crops, we construct the share of all plantation-produced goods in total exports as a second measure of elite power. Using a 76-year panel of exports by colony and crop, we used historical accounts to code up the share of each crop’s production accounted for by wage-paying plantations, Plgit ∈ [0, 1], and used this to calculate the share of plantation-crop exports in total exports. The detailed coding is described in Online Appendix A.17 1.4. Exogenous Drivers of the Strength of the Plantation System The preceding discussion of Caribbean history suggests regressions of wages and coercion on the power of the planters. There is naturally a concern that the varying power of the planters displayed in Figure 1 was endogenous to factors that may also have affected wages and coercion directly. It is therefore desirable to identify drivers of Nit that were exogenous in the sense of impacting wages and coercion only through Nit. Our first candidate for such a driver was a source of cross-sectional variation across colonies that became very salient to peasants after emancipation. In a colony like Barbados, all of the land was sugar-suitable and in 1838 only 4% of land was not under cultivation (1838 Barbados Blue Book). By contrast, a colony like Jamaica had sugar-suitable coastal plains but a higher-elevation interior (which was fertile but not sugar-suitable). During slavery, this difference between Barbados and Jamaica did not matter because sugar-suitable land was similarly suitable everywhere and the hinterland was largely inaccessible to slaves and not used by many others. After emancipation, differences in the availability of a fertile but sugar-unsuitable hinterland led to stark differences in the ease with which peasants could evade the plantation system and resist coercion (Engerman, 1984; Richardson, 1997; Patterson, 2013, respectively pp. 137, 134–5, 157–8).18 To measure this differential ability to evade the planters we carefully calculated the share of each colony’s land that is unsuitable for sugar cane, Oi.19 The relationship between Oi and the historical outside options that peasants actually had is visually displayed in Figure 2 for Jamaica, the only colony with historical maps on evolving land-use patterns. In the left panel, the black areas are lands that we have coded as highly suitable for sugar cane. In the right panel, the shaded areas (both black and grey) were plantations in 1790. The two are spatially correlated and, averaging across Jamaica, the share of land under plantation in 1790 was very close to the share of highly sugar-suitable land.20 This map and all the post-emancipation history make clear that Oi is a good proxy for the amount of hinterlands available to freed slaves after 1838. We note that Oi is an extremely good predictor of the long-run survival of the plantation system. This point is made visually in Online Appendix Figure B.6: the higher is Oi, the smaller is the 1913 sugar export share. Fig. 2. Open in new tabDownload slide Sugar-Suitable Land in Jamaica (left), and Plantations in 1790 and 1890. Notes: The left panel shows the spatial distribution of land that is sugar-suitable (black), only moderately sugar-suitable (dark grey), not sugar-suitable (light grey) and totally sugar-unsuitable (white). See Online Appendix B for details. The right panel shows the extent of sugar plantations in 1790 (black plus grey areas) and 1890 (black areas). There is a good match between our estimate of sugar-suitable land in the left panel, and the historical sugar plantation land in Jamaica. The left panel is based on authors’ calculations. The right panel is a digitised version of Higman’s (2001) remarkable Figure 2.9. Fig. 2. Open in new tabDownload slide Sugar-Suitable Land in Jamaica (left), and Plantations in 1790 and 1890. Notes: The left panel shows the spatial distribution of land that is sugar-suitable (black), only moderately sugar-suitable (dark grey), not sugar-suitable (light grey) and totally sugar-unsuitable (white). See Online Appendix B for details. The right panel shows the extent of sugar plantations in 1790 (black plus grey areas) and 1890 (black areas). There is a good match between our estimate of sugar-suitable land in the left panel, and the historical sugar plantation land in Jamaica. The left panel is based on authors’ calculations. The right panel is a digitised version of Higman’s (2001) remarkable Figure 2.9. In the eighteenth century, British investors made their fortunes in Caribbean sugar. During the nineteenth century, however, investment opportunities shifted to other regions. Panel (a) of Figure 3 displays the per capita GDPs of Britain’s largest export destinations at the start of our sample. Data are from an update of the Madisson data (Bolt et al., 2018). The only British West Indies colony with the Madisson data is Jamaica. See the solid line at the bottom of the panel. The figure shows that while Jamaica languished, the majority of Britain’s largest export destinations rapidly grew richer. Fig. 3. Open in new tabDownload slide British Markets and British Exports by Destination. Notes: Panel (a) is per capita GDP (1990 international dollars) from Madisson, 1850–1913. (Earlier data are not consistently available.) The countries included were the top destinations for British exports in 1846 (the earliest date available for exports by country) and accounted for 71% of all British exports. The legend reports 1846 export shares, e.g., Germany received 13% of all British exports in 1846. Panel (b) is British exports to the Caribbean and British exports excluding the Caribbean. These exports are in constant 1913 pounds sterling (£). All exports exclude re-exports. Fig. 3. Open in new tabDownload slide British Markets and British Exports by Destination. Notes: Panel (a) is per capita GDP (1990 international dollars) from Madisson, 1850–1913. (Earlier data are not consistently available.) The countries included were the top destinations for British exports in 1846 (the earliest date available for exports by country) and accounted for 71% of all British exports. The legend reports 1846 export shares, e.g., Germany received 13% of all British exports in 1846. Panel (b) is British exports to the Caribbean and British exports excluding the Caribbean. These exports are in constant 1913 pounds sterling (£). All exports exclude re-exports. Exogenous events elsewhere around the globe were overtaking Jamaica and drawing away the attention of British investors: the repeal of the Corn Laws in 1846 gave a tremendous impetus to free trade around the world, and started what eventually came to be called the ‘first globalisation’, which, buttressed by a precipitous decline in ocean freight rates, lasted until 1914 (North, 1958; O’Rourke and Williamson, 2001; 2002).21 In this period, the Caribbean was left behind partly because the repeal of the Corn Laws included provisions for a phasing-out of preferential tariffs on West Indies sugar over the period 1846–54 (Curtin, 1954). This globalisation-driven boon and shifting-away of British attention from the Caribbean towards the rest of the world can be seen in export volumes. Panel (b) plots British exports to the Caribbean and to all non-Caribbean destinations. Data are in constant 1913 pounds sterling (£) and purged of re-exports (e.g., Jamaican sugar that is shipped first to London and then to France). The underlying data are from Mitchell (1988) and detailed in Appendix B.5. British exports to non-Caribbean destinations display periods of rapid growth followed by shorter periods of stagnation (e.g., the 1890s) and infrequent bursts of decline. However, the overall picture is one of rapid growth, with real exports growing at an annually compounded rate of 3.4%. In comparison, British exports to the Caribbean experienced practically no growth. Judged by exports, then, British investors had largely turned their focus away from the Caribbean in response to exogenously improving opportunities elsewhere. We have focused on two exogenous drivers of the strength of the plantation system that will be useful for our identification strategy. Across colonies, coercion on plantations was more difficult where the hinterland was large. Over time, the plantation system declined in part because British investors shifted their attention away from Caribbean sugar and towards opportunities in regions that were experiencing rapid growth. 1.5. Other Major Drivers of the Plantation System’s Strength 1.5.1. Crop price movements One challenge for identification is that pressures on the coercive plantation system came in part from variation in smallhold crop prices. In fact, there was a secular decline in plantation crop prices relative to smallholder crop prices in the Caribbean during this time.22 Higher smallhold crop prices would have raised smallhold exports in revenue terms and therefore reduced Nit, while they would have also increased smallhold profits, and by extension wages, even if planters’ actual power over governance had been unaffected. We therefore carefully control for changes in the export prices of smallhold crops.23 We also note the importance of inspecting the responses of Cit to Nit in addition to the wage responses. We are also concerned with the fact that crop choices were endogenous, irrespective of the fact that world crop prices were plausibly exogenous to Caribbean production.24 Smallholders’ profits rose more if they substituted towards crops whose prices increased. The impact of the crop price changes on smallholder profits in turn was biggest in places where the crops with the best geographic suitability and the steepest price increases coincided. We therefore embed a model of crop choice into our theory, and include into our empirics an exogenous crop-suitability-driven export-price basket, estimated as in Costinot et al. (2016).25 1.5.2. Labour supply shocks Crop prices were not the only factor shaping plantation labour supply during this period. Fortunately, Caribbean history is quite clear on what the other big labour supply shocks were during this period: the immigration of indentured East Indian immigrants (Laurence, 1971; Riviere, 1972) and the construction of the Panama Canal (Maurer and Yu, 2013, ch. 4). 1.5.3. Hurricanes Finally, we note that the Virgin Islands are an outlier in Online Appendix Figure B.6: the plantation system had collapsed by 1913 despite low values of Oi. Nowhere else in the Caribbean did planter power diminish as rapidly as in the Virgin Islands. As it turns out, the Virgin Islands plantation system collapsed because of two major hurricanes in 1848 and 1852, which destroyed the colony’s sugar infrastructure and left planters too indebted to rebuild. Hurricanes do two types of damage: they destroy crops and they destroy structures such as sugar mills. Since sugar cane must be processed within hours of harvesting and since cane is difficult to transport, there was always a sugar mill either on the plantation or nearby, e.g., Higman (2001, figure 2.5). Sugar mills were unique in Caribbean agriculture in that they were expensive and long-lived assets. They were also prone to hurricane damage. In the post-emancipation Caribbean, an increasing share of planters could only cover their variable costs but not their fixed costs. In other words, it made sense for a marginal planter to operate an existing mill, but not to rebuild a destroyed mill (Lobdell 1996, pp. 322, 326; Marshall 1996, p. 73). As a result, hurricane landfalls that destroyed mills had long-lasting effects. To control for hurricane damage, we geo-referenced the paths of every major hurricane that hit the Caribbean between 1838 and 1913, and assigned each Caribbean hurricane landfall an island-specific damage index HDIit. Data sources, the list of all hurricanes and their measured impact appear in Online Appendix D. 2. A Simple Model of Coercive Labour Market Institutions To fix ideas and provide additional motivation for the empirics, we now turn to a simple theory of coercive labour markets. 2.1. Technology and Crop Choice There is an exogenous measure L of workers (former slaves) and an endogenous measure N of planters (members of the planter elite). There is a continuum of heterogeneous plots indexed by ω, each of which can be planted in one of g = 1,…, G crops. We follow Costinot et al. (2016) in modelling crop choice by assuming that plot ω planted in crop g has a baseline yield of zg(ω) where zg(ω) is a random variable with a Fréchet distribution: |$Pr\lbrace z_g(\omega )\lt z \rbrace = e^{ -T_g z^{-\theta }}$|⁠. On a plantation, plot ω combined with one worker produces output |$\tau ^p_g z_g(\omega )$| where |$\tau ^p_g \ge 0$| describes the efficiency of plantation agriculture, e.g., |$\tau ^p_g$| is large for sugar and small for livestock. On a smallhold, plot ω combined with one worker produces output |$\tau ^s_g z_g(\omega )$| where |$\tau ^s_g \ge 0$| describes the efficiency of smallhold agriculture. The crop-specific |$\tau ^p_g$| and |$\tau ^s_g$| explain why some crops are better suited than others for plantation agriculture. We consider a small open economy so that crop prices |$\mathbf {p} = (p_1,\ldots ,p_G)$| are exogenous. Crops are chosen to solve |$\max _g p_g \tau ^j_g z_g(\omega )$| where j = p if it is a plantation plot and j = s if it is a smallhold plot. The optimal choice varies across plots, but on average the expected revenue per plot will be $$\begin{eqnarray} r(\mathbf {p},\tau ^j) = \mathbf {E} \max _g p_g \tau ^j_g z_g(\omega ) = \left( \Sigma _k T_k ( \tau ^j_k p_k )^{\theta } \right)^{\frac{1}{\theta }} \Gamma \, , \, \, j=p,s \end{eqnarray}$$(1) where |$\mathbf {\tau }^j = (\tau ^j_1,\ldots ,\tau ^j_G)$| and |$\Gamma=\Gamma(1/\theta-1)$| is the gamma function. See Appendix A for the proof or Costinot et al. (2016, p. 215). |$r(\mathbf {p},\tau ^j)$| captures how crop choices respond to prices. Each smallholder is randomly allocated one plot and each planter is randomly allocated l(N) ≥ 1 plots. Since each plot uses one worker, the maximum number of planters is N = L and when N = L each planter receives one plot, i.e., l(L) = 1. We also assume that the more planters there are, the more land they receive collectively (⁠|$\frac{\partial \ln l(N) N}{\partial \ln N}\gt 0$|⁠), but not individually (⁠|$\frac{\partial \ln l(N)}{\partial \ln N}\lt 0$|⁠). The latter creates a ‘congestion cost’ which ensures that not all agriculture is plantation agriculture. 2.2. The Worker’s Occupational Choice and Coercion Each smallholder must choose between plantation work and smallholding. Utility from working on the plantation is w.26 Utility from smallholding is |$r(\mathbf {p},\tau ^s)-C$| where C is the negative impact of planters’ legal coercion on the returns to smallholding. C is endogenous. It follows that in any equilibrium with both plantation and smallhold agriculture, $$\begin{eqnarray} w = r(\mathbf {p},\tau ^s) - C. \end{eqnarray}$$(2)|$r(\mathbf {p},\tau ^s)$| captures how wages respond to prices when crop choices are endogenous. The costs of coercion (e.g., building jails) are given by Cγ where γ > 1. These costs are funded by a head tax on planters of |$C^{\gamma }/N$|. Consider planter profits. When there are N planters, each receives l(N) plots, earns per plot revenues of |$r(\mathbf {p},\tau ^p)$|⁠, pays per plot wages of |$r(\mathbf {p},\tau ^s) - C$| and is left with profits of $$\begin{eqnarray} \pi (C,N) \, \, = l(N) \left[ r(\mathbf {p},\tau ^p) - r(\mathbf {p},\tau ^s) + C \right] - C^{\gamma }/N. \end{eqnarray}$$(3) We use Grossman and Helpman’s (1994) ‘Protection for Sale’ framework to determine the level of coercion C. C ≥ 0 is chosen to maximise a weighted sum of the profits of the N planters and the L workers: $$\begin{eqnarray} W(C) = \alpha N \pi + Lw. \end{eqnarray}$$(4) α is the weight given to planters’ profits. Our key assumption is that α > 1 so that planters have greater sway over the choice of coercion. Substituting equations (2)–(3) into (4) and maximising with respect to C subject to C ≥ 0 yields the following characterisation of optimal coercion. Let |$\bar{N}$| be the value of N for which αl(N)N − L = 0. Under our assumptions, |$\bar{N}$| is unique and |$0\lt \bar{N}\lt L$|⁠. The optimal level of coercion is $$\begin{eqnarray} C^*(N) = \left( \frac{\alpha l(N) N-L}{\alpha \gamma }\right) ^{\frac{1}{\gamma -1}} \, \, \, \, \, \, \, \text{for} \, \, N \ge \bar{N} \end{eqnarray}$$(5) and C*(N) = 0 for |$N\lt \bar{N}$|⁠. Since the land controlled by planters is increasing in the number of planters [l(N)N is increasing in N], equation (5) implies one of our key results, namely, |$C^*_N \gt 0$| when N is sufficiently large. The insight is simple: the stronger is the planter elite, the greater is its political influence (as measured by αN) and hence the higher is the level of coercion. Equation (5) further implies a threshold effect: when the number of planters drops below |$\bar{N}$|⁠, there is no coercion. See Appendix A for proofs.27,28 2.3. Worker Resistance and Planters’ Entry Decision As discussed in the history section, workers often resisted white rule, which resulted in deaths, property damage and incarceration. Since worker motivations for resistance do not enter into the empirics, we model resistance simply as a probability χ that resistance is successful. χ(O) is increasing in the share of non-sugar-suitable land O because it is costly for the police and military to operate in these more remote and often highland areas.29 Without loss of generality we assume χ(O) = O. If resistance is successful, neither planters nor workers are able to plant their crops and returns to each are normalised to 0. If resistance is unsuccessful, then workers and planters generate the earnings, profits and coercion levels that appear in equations (2)–(5). We next turn to the free entry condition for planters. Each potential planter must choose between (1) staying in England where he can invest, export to non-Caribbean countries and earn |$\overline{W}$| versus (2) moving to the colony where he can invest in sugar, export back to England and earn planter profits. Conditional on no resistance, planter profits are given by equation (3), namely, π(N) ≡ π(C*(N), N). Thus, in the colony the planter earns expected profits (1 − O)π(N). If |$(1-O)\pi (N) \lt \overline{W}$| for all N then no planter moves to the colony and there is only smallholding. If |$(1-O)\pi (N) \gt \overline{W}$| for all N then L planters move, each has one plot and one worker, and there are no smallholders. We focus on the intermediate case where planters and smallholders coexist. In that case there is an N* such that |$(1-O) \pi (N^*) = \overline{W}$| or $$\begin{eqnarray} \pi (N^*) = \frac{\overline{W}}{1-O} \, . \end{eqnarray}$$(6) This equation pins down the equilibrium number of planters N*. In Appendix A we provide sufficient conditions on the underlying parameters of the model for such an N* to exist and to be stable in the usual sense that πN(N*) < 0. In any stable equilibrium, N* is decreasing in O and |$\overline{W}$|⁠. Further, N* depends on the interaction of O with |$\overline{W}$|⁠. We exploit this interaction in the empirical work.30 2.4. General Equilibrium and Comparative Statics An equilibrium in our small open economy is a crop choice for each plot ω and mode j = p, s that solves |$\max _g p_g \tau ^j_g z_g(\omega )$|⁠, a wage w that leaves each smallholder indifferent between plantation work and smallholding (equation (2)), a level of coercion C*(N*) that maximises planter-biased societal welfare (equation (5)), and a mass of planters N* that leaves each planter indifferent between staying in England and moving to the colony (equation (6)). Our main comparative statics results are as follows. First, the wage is increasing in an index of prices |$r(\mathbf {p},\tau ^s)$| and decreasing in coercion C. See equation (2). Second, coercion is increasing in the number of planters. See equation (5). Third, in the absence of coercion, wages are given by |$w=r(\mathbf {p},\tau ^s)$| (equation (2)) so that we have a benchmark for competitive wages that deals explicitly with the crop substitution problem identified in Subsection 1.5.1. Fourth, planter strength N* is decreasing in |$\overline{W}/(1-O)$| and |$\overline{W}/(1-O)$| has no direct impact on anything but N*.31 3. The Evidence Our main hypothesis is that the powerful Caribbean planter elite held enough sway over government to institute forms of legal coercion such as the incarceration of squatters, which were aimed at reducing wages. We begin by testing this hypothesis in OLS regressions of coercion (Cit) and wages (wit) on the relative economic power of the planters (Nit): $$\begin{eqnarray} & w_{{\textit it}} =\beta ^{w}_{N} \cdot N_{{\textit it}} +\gamma ^{w}_{X} \cdot X_{{\textit it}} + \lambda ^{w}_i + \lambda ^{w}_t + \epsilon _{{\textit it}}^{w}; \end{eqnarray}$$(7) $$\begin{eqnarray} & C_{{\textit it}} = \beta ^{C}_{N} \cdot N_{{\textit it}} + \gamma ^{C}_{X} \cdot X_{{\textit it}} + \lambda ^{C}_i + \lambda ^{C}_t + \epsilon _{{\textit it}}^{C}, \end{eqnarray}$$(8) where λi are colony fixed effects, λt are year fixed effects or year trends, and Xit are controls. Data: Our wage data come from the Blue Books, which report wages for ‘praedial’ or agricultural workers. This was the wage paid to plantation workers. These wages were the largest component of the cost of the most important economic activity in the colonies (sugar). It is thus not surprising that wages were a constant subject of discussion in contemporary sources. The Blue Book wage data are identical to the sporadic data from reliable sources discussing wages for sugar cultivation (e.g., West India Royal Commission, 1897, p. 107). Further, the Blue Books themselves are sometimes the source of data quoted by contemporaries (e.g., Sewell, 1861). In short, the Blue Books reliably reported the well-known and very public data on wages for plantation work. Appendix B.1 discusses wages at greater length.32,33 Our coercion data are incarceration rates per capita from the Blue Books. The Books report the daily average number of prisoners, averaged over the year, for 1838 to 1913. These data contain incarcerations for all reasons, but as discussed below and in Appendix B.3 our best estimate is that two-thirds of incarcerations at the start of our period were associated with legal coercion.34 New incarcerations per capita (expressed as a percent) had a sample mean of 1.1%, indicating that 1.1% of the population entered jail each year. Incarceration rates are admittedly a fairly narrow measure of what was in reality a bundle of policies of legal coercion. The reason we focus on incarceration rates is that it is the only empirical counterpart to legal coercion that we could consistently code for the entirety of our wage sample. In the later years we are able to validate this measure using data on court sentencing that targeted smallholders. See Appendix B.3. In equations (7)–(8), Xit are controls for observable factors that may have directly affected wages. Smallholder returns, and therefore plantations wages, were a function of exogenous price shocks and islands’ crop-specific soil productivity; see the wage equation (2). To construct |$r_{i}(\mathbf {p}_{t},\tau ^s)$|⁠, we used the Blue Books to construct a 76-year panel of exports by colony and crop—generating a database containing exports by colony and year for 17 products accounting for 98% of exports—and combined it with fine-grained information on islands’ agro-climactic conditions to develop suitability indexes for the most important crops. We then estimated a Fréchet-based structural model of crop choice, as in Costinot et al. (2016), to recover estimates of the |$r_i(\mathbf {p_t},\tau ^s)$|⁠. |$r_i(\mathbf {p_t},\tau ^s)$| is an index of smallholder revenue based on exogenous crop suitability and it captures endogenous crop-switching in response to changes in the relative price of crops. It is an exogenous, model-based prediction. See Appendix B.2 for details. Also included in Xit are the major labour supply shocks discussed in Subsection 1.5.2. For this, we calculated the island-specific cumulative stock of East Indian immigrant arrivals over time. It turns out that this flow of migrants was heavily right-skewed. It only really affected Guyana, Trinidad and to a lesser extent Jamaica. For the Panama Canal shock, there are no destination-specific estimates of islands out-migration so we measure the shock with a time dummy for the years of Canal construction (1881–9 under the French and 1908–13 under the Americans) divided by distance from island centroids to Panama. See Appendix B.6 for details. We control for colony size using the log of population and the log of total export revenues. We control for each colony’s time-varying British support using the number of times the colony was discussed in the British Parliament.35 OLS results: Table 1 reports OLS estimates of equations (7) and (8), i.e., the effects of Nit on wit and Cit. Nit is measured as sugar’s share of exports. Columns 1–4 show results with wit as the outcome. As a baseline, column 1 includes only a linear and quadratic time trend, and the Fréchet-based index of smallholder export prices |$r_i(\mathbf {p}_t,\tau ^s)$|⁠. Consistent with the wage equation (2) in the model, we see that smallholder export prices positively impact wages. In column 2 we add the controls for Indian immigration and the construction of the Panama Canal, i.e., the two most important labour supply shocks in the Caribbean during this period. As expected, Indian immigration reduced wages in the islands.36 Proximity to the Panama Canal during the period of its construction had a positive but insignificant effect on wages. Column 3 additionally controls for factors that are likely endogenous: as expected, population growth lowered wages and higher economic activity raised wages. However, their inclusion does not affect the relationship between wages and Nit. The negative coefficient on the Hansard indicates that declines in parliamentary discussions of a colony correlate with declines in the colony’s wage. This is useful because it rules out a potential source of reverse causality: as a colony’s wage rose, sugar became unprofitable, Britain lost interest in the colony and stopped subsidising its white planter elite, and so Nit fell. That is, the Hansard result is not compatible with wit causing Nit through a British subsidy channel. Table 1. OLS Effect of the Plantation System (Nit) on Wages (wit) and Coercion (Cit). . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . Nit: Sugar exports as −0.3667 −0.3633 −0.3613 −0.3831 −0.3873 0.4459 0.4577 0.4918 0.4183 0.4535 share of total exports [0.0067] [0.0078] [0.0117] [0.0080] [0.0119] [0.0319] [0.0259] [0.0273] [0.0322] [0.0305] Fréchet smallholder export 0.3256 0.3263 0.2578 0.1608 0.2149 0.2657 price indexit [0.0027] [0.0032] [0.0273] [0.2844] [0.1556] [0.1442] log (net immigration)it −0.0266 −0.0244 −0.0224 −0.0181 −0.0013 −0.0099 0.0065 −0.0009 [0.0023] [0.0017] [0.0110] [0.0171] [0.9326] [0.6682] [0.7073] [0.9736] log(1|$/$|[dist to Panama])i × 0.0040 0.0036 0.0265 0.0338 −0.0185 −0.0184 0.3637 0.3756 D(1881–9)|(1908–13)t [0.3442] [0.4232] [0.6997] [0.5961] [0.0782] [0.0867] [0.0571] [0.0493] log(population)it −0.1197 −0.1281 0.1940 0.1193 [0.2866] [0.1810] [0.3896] [0.6527] log(value total exports)it 0.0716 0.0501 −0.0202 0.0235 [0.0629] [0.2569] [0.8468] [0.8140] log Hansard-mentionsit 0.0019 0.0076 [0.7091] [0.6692] Time controls t + t2 t + t2 t + t2 t-fe t-fe t + t2 t + t2 t + t2 t-fe t-fe Observations 908 908 908 908 908 798 798 798 798 798 R2 0.711 0.724 0.728 0.768 0.770 0.511 0.516 0.518 0.572 0.573 . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . Nit: Sugar exports as −0.3667 −0.3633 −0.3613 −0.3831 −0.3873 0.4459 0.4577 0.4918 0.4183 0.4535 share of total exports [0.0067] [0.0078] [0.0117] [0.0080] [0.0119] [0.0319] [0.0259] [0.0273] [0.0322] [0.0305] Fréchet smallholder export 0.3256 0.3263 0.2578 0.1608 0.2149 0.2657 price indexit [0.0027] [0.0032] [0.0273] [0.2844] [0.1556] [0.1442] log (net immigration)it −0.0266 −0.0244 −0.0224 −0.0181 −0.0013 −0.0099 0.0065 −0.0009 [0.0023] [0.0017] [0.0110] [0.0171] [0.9326] [0.6682] [0.7073] [0.9736] log(1|$/$|[dist to Panama])i × 0.0040 0.0036 0.0265 0.0338 −0.0185 −0.0184 0.3637 0.3756 D(1881–9)|(1908–13)t [0.3442] [0.4232] [0.6997] [0.5961] [0.0782] [0.0867] [0.0571] [0.0493] log(population)it −0.1197 −0.1281 0.1940 0.1193 [0.2866] [0.1810] [0.3896] [0.6527] log(value total exports)it 0.0716 0.0501 −0.0202 0.0235 [0.0629] [0.2569] [0.8468] [0.8140] log Hansard-mentionsit 0.0019 0.0076 [0.7091] [0.6692] Time controls t + t2 t + t2 t + t2 t-fe t-fe t + t2 t + t2 t + t2 t-fe t-fe Observations 908 908 908 908 908 798 798 798 798 798 R2 0.711 0.724 0.728 0.768 0.770 0.511 0.516 0.518 0.572 0.573 Notes: Column 1 includes a quadratic time trend and the Fréchet-based index of smallholder export prices |$r_i(\mathbf {p}_t,\tau ^s)$|⁠. Column 2 adds the most important labour supply shocks in the Caribbean during this period. Column 3 additionally controls for the log of population (a proxy for size), the log of total exports (a proxy for economic size), and parliamentary Hansard mentions (a proxy for British interest in the colony). Column 4 replaces the quadratic time trend with year fixed effects, and drops the export price index. Column 5 adds the same controls as column 3. In columns 6–10, we repeat the same specifications for incarceration as the outcome. Standard errors are clustered by colony and the corresponding p-values are in square brackets. Open in new tab Table 1. OLS Effect of the Plantation System (Nit) on Wages (wit) and Coercion (Cit). . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . Nit: Sugar exports as −0.3667 −0.3633 −0.3613 −0.3831 −0.3873 0.4459 0.4577 0.4918 0.4183 0.4535 share of total exports [0.0067] [0.0078] [0.0117] [0.0080] [0.0119] [0.0319] [0.0259] [0.0273] [0.0322] [0.0305] Fréchet smallholder export 0.3256 0.3263 0.2578 0.1608 0.2149 0.2657 price indexit [0.0027] [0.0032] [0.0273] [0.2844] [0.1556] [0.1442] log (net immigration)it −0.0266 −0.0244 −0.0224 −0.0181 −0.0013 −0.0099 0.0065 −0.0009 [0.0023] [0.0017] [0.0110] [0.0171] [0.9326] [0.6682] [0.7073] [0.9736] log(1|$/$|[dist to Panama])i × 0.0040 0.0036 0.0265 0.0338 −0.0185 −0.0184 0.3637 0.3756 D(1881–9)|(1908–13)t [0.3442] [0.4232] [0.6997] [0.5961] [0.0782] [0.0867] [0.0571] [0.0493] log(population)it −0.1197 −0.1281 0.1940 0.1193 [0.2866] [0.1810] [0.3896] [0.6527] log(value total exports)it 0.0716 0.0501 −0.0202 0.0235 [0.0629] [0.2569] [0.8468] [0.8140] log Hansard-mentionsit 0.0019 0.0076 [0.7091] [0.6692] Time controls t + t2 t + t2 t + t2 t-fe t-fe t + t2 t + t2 t + t2 t-fe t-fe Observations 908 908 908 908 908 798 798 798 798 798 R2 0.711 0.724 0.728 0.768 0.770 0.511 0.516 0.518 0.572 0.573 . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . Nit: Sugar exports as −0.3667 −0.3633 −0.3613 −0.3831 −0.3873 0.4459 0.4577 0.4918 0.4183 0.4535 share of total exports [0.0067] [0.0078] [0.0117] [0.0080] [0.0119] [0.0319] [0.0259] [0.0273] [0.0322] [0.0305] Fréchet smallholder export 0.3256 0.3263 0.2578 0.1608 0.2149 0.2657 price indexit [0.0027] [0.0032] [0.0273] [0.2844] [0.1556] [0.1442] log (net immigration)it −0.0266 −0.0244 −0.0224 −0.0181 −0.0013 −0.0099 0.0065 −0.0009 [0.0023] [0.0017] [0.0110] [0.0171] [0.9326] [0.6682] [0.7073] [0.9736] log(1|$/$|[dist to Panama])i × 0.0040 0.0036 0.0265 0.0338 −0.0185 −0.0184 0.3637 0.3756 D(1881–9)|(1908–13)t [0.3442] [0.4232] [0.6997] [0.5961] [0.0782] [0.0867] [0.0571] [0.0493] log(population)it −0.1197 −0.1281 0.1940 0.1193 [0.2866] [0.1810] [0.3896] [0.6527] log(value total exports)it 0.0716 0.0501 −0.0202 0.0235 [0.0629] [0.2569] [0.8468] [0.8140] log Hansard-mentionsit 0.0019 0.0076 [0.7091] [0.6692] Time controls t + t2 t + t2 t + t2 t-fe t-fe t + t2 t + t2 t + t2 t-fe t-fe Observations 908 908 908 908 908 798 798 798 798 798 R2 0.711 0.724 0.728 0.768 0.770 0.511 0.516 0.518 0.572 0.573 Notes: Column 1 includes a quadratic time trend and the Fréchet-based index of smallholder export prices |$r_i(\mathbf {p}_t,\tau ^s)$|⁠. Column 2 adds the most important labour supply shocks in the Caribbean during this period. Column 3 additionally controls for the log of population (a proxy for size), the log of total exports (a proxy for economic size), and parliamentary Hansard mentions (a proxy for British interest in the colony). Column 4 replaces the quadratic time trend with year fixed effects, and drops the export price index. Column 5 adds the same controls as column 3. In columns 6–10, we repeat the same specifications for incarceration as the outcome. Standard errors are clustered by colony and the corresponding p-values are in square brackets. Open in new tab In column 4 we use year fixed effects instead of the quadratic time trend. With year fixed effects the export price index is never close to significant. We therefore do not include it in any regressions with year fixed effects. This is done for expositional clarity and its exclusion has no bearing whatsoever on any of the other coefficients. Column 5 again adds the endogenous controls. Summarising columns 1–5, the partial correlation between changes Nit and wages is highly significant, very stable and appears economically large. The estimate |$\hat{\beta }^{w}_{N}$| in column 4 says that in a colony like Grenada where sugar’s share in exports had been reduced to zero by the end of the period, wages had increased by about 38% more over the 76 years than in a colony like Barbados where sugar’s share in exports remained close to 1 at the end of the period. The reader may worry about inference: we always cluster standard errors at the colony level, as this is intuitively appealing for our panel setting. However, with only 14 clusters we are naturally concerned about the asymptotic theory underlying standard clustering approaches (Moulton, 1986). For our core causal coefficients, we therefore also bootstrapped standard errors using the wild bootstrap, e.g., Cameron and Miller (2008); Davidson and MacKinnon (2010). These were published in earlier working paper versions of the paper, and never pushed the statistical significance of any of our coefficients of interest below 10%. In columns 6–10, we repeat these specifications for Cit as the outcome. The resulting estimates suggest that a complete collapse of the plantation system (from 1 to 0) is associated with a decrease in incarceration rates of about one person per two-hundred in a year, roughly one half the mean incarceration rate in the data.37 Consistent with the model, the labour supply (wage) controls have no direct effect on coercion. Only the Panama Canal control is significant, but switches signs across specifications. Our model, our intuition and our regression results all tell us that labour supply shocks do not effect incarceration. In the remainder of the paper, we estimate all results with two core specifications. The first corresponds to columns 2 and 7. The second corresponds to columns 4 and 9. That is, we include either a quadratic time trend or year fixed effects, but omit the potentially endogenous controls for population, total exports and the Hansard. (Including these endogenous controls alters none of the results.) In Table 2 we report the corresponding coefficients on Nit where Nit is now measured as plantation crops’ export share. The results are similarly robust and stable in magnitude. Across the board, the coefficients in Panel B are about one-third larger than in Panel A, but the economic effect is almost the same because sugar’s share in exports dropped less than the share of all plantation crops combined. The estimate |$\hat{\beta }^{w}_{N}$| in column 4 says that in a colony like Grenada where plantation crops’ share in exports had been reduced to about one-quarter by the end of the period, wages had increased by about 38% (0.55 × 0.75) more over the 76 years than in a colony like Barbados where the plantation system continued to completely dominate. Table 2. OLS Effect of Sugar Plantations on Wages (wit) and Coercion (Cit). . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . Nit: plantation exports as −0.5076 −0.5131 −0.5084 −0.5504 −0.5456 0.6923 0.6971 0.6963 0.6451 0.6502 share of total exports [0.0030] [0.0026] [0.0033] [0.0028] [0.0040] [0.0140] [0.0148] [0.0148] [0.0185] [0.0182] Time controls t + t2 t + t2 t + t2 t-fe t-fe t + t2 t + t2 t + t2 t-fe t-fe Observations 908 908 908 908 908 798 798 798 798 798 R2 0.717 0.730 0.734 0.776 0.778 0.518 0.522 0.523 0.578 0.578 . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . Nit: plantation exports as −0.5076 −0.5131 −0.5084 −0.5504 −0.5456 0.6923 0.6971 0.6963 0.6451 0.6502 share of total exports [0.0030] [0.0026] [0.0033] [0.0028] [0.0040] [0.0140] [0.0148] [0.0148] [0.0185] [0.0182] Time controls t + t2 t + t2 t + t2 t-fe t-fe t + t2 t + t2 t + t2 t-fe t-fe Observations 908 908 908 908 908 798 798 798 798 798 R2 0.717 0.730 0.734 0.776 0.778 0.518 0.522 0.523 0.578 0.578 Notes: This table replicates Table 1 with Nit instead measured as plantation crops’ export share. Open in new tab Table 2. OLS Effect of Sugar Plantations on Wages (wit) and Coercion (Cit). . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . Nit: plantation exports as −0.5076 −0.5131 −0.5084 −0.5504 −0.5456 0.6923 0.6971 0.6963 0.6451 0.6502 share of total exports [0.0030] [0.0026] [0.0033] [0.0028] [0.0040] [0.0140] [0.0148] [0.0148] [0.0185] [0.0182] Time controls t + t2 t + t2 t + t2 t-fe t-fe t + t2 t + t2 t + t2 t-fe t-fe Observations 908 908 908 908 908 798 798 798 798 798 R2 0.717 0.730 0.734 0.776 0.778 0.518 0.522 0.523 0.578 0.578 . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . Nit: plantation exports as −0.5076 −0.5131 −0.5084 −0.5504 −0.5456 0.6923 0.6971 0.6963 0.6451 0.6502 share of total exports [0.0030] [0.0026] [0.0033] [0.0028] [0.0040] [0.0140] [0.0148] [0.0148] [0.0185] [0.0182] Time controls t + t2 t + t2 t + t2 t-fe t-fe t + t2 t + t2 t + t2 t-fe t-fe Observations 908 908 908 908 908 798 798 798 798 798 R2 0.717 0.730 0.734 0.776 0.778 0.518 0.522 0.523 0.578 0.578 Notes: This table replicates Table 1 with Nit instead measured as plantation crops’ export share. Open in new tab Endogeneity of Nit aside, the reader may have a number of concerns with Tables 1 and 2. One potential concern pertains to the claim (and in the model, our assumption) that agricultural wages are only paid in the plantation sector. We validate this claim in Appendix B.1 where we provide prima facie evidence that wage employment was the domain of the plantation system, and that the only common alternative for plantation workers was independent smallhold farming, as opposed to wage labour outside of agriculture. Another potential concern pertains to the accuracy of the reported wage data. Wages sometimes included an in-kind component that usually involved a cottage and a small plot. For two-thirds of our sample the Blue Books indicate whether the wage includes in-kind payments. Only 9% of these observations include in-kind payments. Nevertheless, Online Appendix Table F.4 shows that our results are robust to an adjustment for in-kind payments. Also, wages are almost always reported as daily, but for 5% of our observations data are reported as weekly or monthly. When this happens, the Blue Books explicitly indicate that the data are for five-day weeks or 20-day months and so are easily converted to daily wages. Nevertheless, Online Appendix Table F.4 shows that our results are robust to adjustments for alternative conversions of weekly and monthly wages into daily wages. Another potential concern pertains to using incarceration rates as our measure of legal coercion. Mitigating this concern is the fact that the historical literature is quite clear that incarceration was indeed often the result of legal coercion aimed at smallholders. In Appendix B.3 we document this by very detailed category of offence for the Leewards for the start of our period. For the end of our period (1871–1913) we have court sentences but only by broad categories of offences, and only one of these—offences against property—maps into the legal coercion discussed in Subsection 1.1. In Appendix B.3 we show that this category’s share of total court sentences correlated positively with both Nit and Cit. Identification: The OLS estimates reported thus far should be interpreted with caution because Nit is likely to be endogenous in both the wage and coercion equations. In the wage equation, for example, productivity growth in plantation agriculture would have increased both Nit and wit. Unobserved differential productivity growth would thus bias the OLS results against finding a negative effect of Nit on wit. In the coercion equation, for another example, if, unobserved to the econometrician, peasants in some but not all colonies were actively resisting the plantation system this could have evoked a planter response (increased Cit) while also undermining the plantation system (decreased Nit).38 This would bias the OLS results against finding a positive effect of Nit on Cit. Equation (6) offers a path towards an instrument for Nit. A British investor chooses between investing in the Caribbean, which returns (1 − Oi)π(Nit), or investing elsewhere, which returns |$\overline{W}_t$|⁠. Across colonies, those colonies exogenously endowed with more hinterland Oi are less likely to receive the investment. Over time, improvements in non-Caribbean investment opportunities |$\overline{W}_t$| make it less likely that any colony receives the investment. Thus, the larger is |$O_i \cdot \overline{W}_t$| the smaller is Nit.39 We already have a hinterland measure Oi. We also argued in Subsection 1.4 that British exports to non-Caribbean countries is a good measure of non-Caribbean opportunities |$\overline{W}_t$|⁠.40 We expect that a higher |$O_i \cdot \overline{W}_t$| leads to a lower Nit, i.e., |$O_i \cdot \overline{W}_t$| has a negative sign in the first stage. The Virgin Islands’ experience—where the plantation system collapsed because of two major hurricanes despite low values of Oi—suggests the need for a second, hurricane-based instrument HDIit for Nit. (See Subsection 1.5.3.) It is important to be clear about what role HDIit plays: hurricanes are not central to our paper but we need them to fit the variation in Nit for the Virgin Islands. Without the Virgin Islands, hurricanes are no longer needed to fit Nit, but we prefer to retain them in order to reflect the full universe of British Caribbean sugar colonies, and because they were a particularly striking example of the mechanisms we highlight. First Stage and Reduced Form Estimation: In moving on to our TSLS estimation, we propose the following first stage equation $$\begin{eqnarray} \text{First Stage: }& N_{{\textit it}} = \beta ^{N}_{O} \cdot O_{{\textit it}} + \beta ^{N}_{H} \cdot \textit {HDI}_{{\textit it}} + \gamma ^{N}_{X} \cdot X_{{\textit it}} + \lambda ^{N}_i + \lambda ^{N}_t + \epsilon _{{\textit it}}^{N}, \end{eqnarray}$$(9) as well as the associated reduced form relations $$\begin{eqnarray} \text{Reduced Form (Wages): }& w_{{\textit it}} = \beta ^{w}_{O} \cdot O_{{\textit it}} + \beta ^{w}_{H} \cdot \textit {HDI}_{{\textit it}} + \gamma ^{w}_{X} \cdot X_{{\textit it}} + \lambda ^{w}_i + \lambda ^{w}_t + \epsilon _{{\textit it}}^{w}; \end{eqnarray}$$(10) $$\begin{eqnarray} \text{Reduced Form (Coercion): }& C_{{\textit it}} = \beta ^{C}_{O} \cdot O_{{\textit it}} + \beta ^{C}_{H} \cdot \textit {HDI}_{{\textit it}} + \gamma ^{C}_{X} \cdot X_{{\textit it}} + \lambda ^{C}_i + \lambda ^{C}_t + \epsilon _{{\textit it}}^{C}, \end{eqnarray}$$(11) where i indexes colonies and t indexes years, the λs are fixed effects, and Xit are the same control variables as in the OLS. Columns 1–4 of Table 3 report estimates of the First Stage equation (9) for our two favoured specifications and for the two different measures of planter power. In columns 1–4, |$\hat{\beta }^{N}_{O}$|⁠, the coefficient on |$O_i \cdot \overline{W}_{t}$| indicates that in islands with large hinterlands the plantation system declined faster in response to improving non-Caribbean opportunities for British interests. The hurricane damage index HDIit has a powerful negative impact on the plantation system. In columns 5–8, we report estimates of the two reduced-form equations (10) and (11). The estimate |$\hat{\beta }^{w}_{O}$| in column 3 says that compared to Barbados, wages in Grenada (where half the land was hinterlands) rose substantially more in response to an increase in |$\overline{W}_{t}$|⁠. At the same time, columns 7–8 show a significant effect on incarceration rates working in the opposite direction. Table 3. First Stage and Reduced Form. . Nit: Sugar’s export share . Nit: Plantations’ export share . wit: log wage . Cit: Incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Oi × English exports −0.4819 −0.5238 −0.2365 −0.2611 0.2351 0.2724 −0.4577 −0.4121 to all non-Caribbeant [0.0000] [0.0001] [0.0012] [0.0030] [0.0153] [0.0075] [0.0056] [0.0287] HDIit −0.0680 −0.0751 −0.0625 −0.0646 0.0483 0.0565 −0.0857 −0.0775 [0.0000] [0.0000] [0.0000] [0.0000] [0.0001] [0.0001] [0.0000] [0.0094] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 1,018 1,018 1,018 1,018 908 908 798 798 R2 0.853 0.867 0.843 0.851 0.721 0.772 0.526 0.580 . Nit: Sugar’s export share . Nit: Plantations’ export share . wit: log wage . Cit: Incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Oi × English exports −0.4819 −0.5238 −0.2365 −0.2611 0.2351 0.2724 −0.4577 −0.4121 to all non-Caribbeant [0.0000] [0.0001] [0.0012] [0.0030] [0.0153] [0.0075] [0.0056] [0.0287] HDIit −0.0680 −0.0751 −0.0625 −0.0646 0.0483 0.0565 −0.0857 −0.0775 [0.0000] [0.0000] [0.0000] [0.0000] [0.0001] [0.0001] [0.0000] [0.0094] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 1,018 1,018 1,018 1,018 908 908 798 798 R2 0.853 0.867 0.843 0.851 0.721 0.772 0.526 0.580 Notes: Columns 1–4 present estimates of equation (9), the First Stage relation between the instruments and the two measures of Nit. Columns 5–8 present estimates of equations (10) and (11), the Reduced Form relations between the instruments and the two main outcomes wit and Cit. For each outcome, we present the results for our two preferred specifications which include a quadratic time trend (odd-numbered columns) or year fixed effects (even-numbered columns). These correspond to columns 2 and 4 of Table 1. For brevity, we do not report coefficients on any of the controls that appear in Table 1. All specifications include colony fixed effects. Standard errors are clustered by colony, p-values are in square brackets. Open in new tab Table 3. First Stage and Reduced Form. . Nit: Sugar’s export share . Nit: Plantations’ export share . wit: log wage . Cit: Incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Oi × English exports −0.4819 −0.5238 −0.2365 −0.2611 0.2351 0.2724 −0.4577 −0.4121 to all non-Caribbeant [0.0000] [0.0001] [0.0012] [0.0030] [0.0153] [0.0075] [0.0056] [0.0287] HDIit −0.0680 −0.0751 −0.0625 −0.0646 0.0483 0.0565 −0.0857 −0.0775 [0.0000] [0.0000] [0.0000] [0.0000] [0.0001] [0.0001] [0.0000] [0.0094] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 1,018 1,018 1,018 1,018 908 908 798 798 R2 0.853 0.867 0.843 0.851 0.721 0.772 0.526 0.580 . Nit: Sugar’s export share . Nit: Plantations’ export share . wit: log wage . Cit: Incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Oi × English exports −0.4819 −0.5238 −0.2365 −0.2611 0.2351 0.2724 −0.4577 −0.4121 to all non-Caribbeant [0.0000] [0.0001] [0.0012] [0.0030] [0.0153] [0.0075] [0.0056] [0.0287] HDIit −0.0680 −0.0751 −0.0625 −0.0646 0.0483 0.0565 −0.0857 −0.0775 [0.0000] [0.0000] [0.0000] [0.0000] [0.0001] [0.0001] [0.0000] [0.0094] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 1,018 1,018 1,018 1,018 908 908 798 798 R2 0.853 0.867 0.843 0.851 0.721 0.772 0.526 0.580 Notes: Columns 1–4 present estimates of equation (9), the First Stage relation between the instruments and the two measures of Nit. Columns 5–8 present estimates of equations (10) and (11), the Reduced Form relations between the instruments and the two main outcomes wit and Cit. For each outcome, we present the results for our two preferred specifications which include a quadratic time trend (odd-numbered columns) or year fixed effects (even-numbered columns). These correspond to columns 2 and 4 of Table 1. For brevity, we do not report coefficients on any of the controls that appear in Table 1. All specifications include colony fixed effects. Standard errors are clustered by colony, p-values are in square brackets. Open in new tab Clearly, the time-varying component of |$O_{{\textit it}} = O_i \cdot \overline{W}_t$| is a strongly trending variable; see Panel (b) of Figure 3. Therefore, a potential concern with the results reported in Table 3 is whether the time path of the effect of Oi on the plantation system and on wages actually matches the evolution of |$\overline{W}_{t}$|⁠. The most flexible way to ask this question is to re-estimate equations (9) and (10), replacing Oit with an interaction between Oi and year fixed effects (while continuing to include year fixed effects on their own as in columns 2, 4, 6 and 8 of Table 3). Figure 4 plots the coefficients estimates on this interaction that result from doing so, with 1838 omitted because it gets absorbed by the colony fixed effects as the first year. The solid thick line shows a clearly discernible negative effect of Oi on Nit, and this effect sets in around the mid-1860s. The solid thin line shows a positive effect of Oi on wages kicking in around the same time.41 We view these time paths as consistent with the time path of |$\overline{W}_t$|⁠, and thus with our instrument: it is natural that the interaction effect on Nit in Figure 4 could not drop below −1 since Nit is bounded below at zero; and it is therefore equally natural that the positive effect of Oi on wit flattens off. Fig. 4. Open in new tabDownload slide The Year-Specific Effect of Oi on Nit and on wit. Notes: This figure reports the point estimates and 95th-percentile confidence bands on Oit in two estimations of regression equations (9) and (10), when Oit is replaced by a flexible interaction of Oi with year fixed effects (while also including year fixed effects on their own). The solid thick line reports on the estimated effect on Nit in (9), the solid thin line reports on the effect on wit in (10); dashed lines are confidence bands. Fig. 4. Open in new tabDownload slide The Year-Specific Effect of Oi on Nit and on wit. Notes: This figure reports the point estimates and 95th-percentile confidence bands on Oit in two estimations of regression equations (9) and (10), when Oit is replaced by a flexible interaction of Oi with year fixed effects (while also including year fixed effects on their own). The solid thick line reports on the estimated effect on Nit in (9), the solid thin line reports on the effect on wit in (10); dashed lines are confidence bands. TSLS Estimation: We now turn to the causal effect of the declining strength of the plantation system on coercion and wages, estimating equations (7) and (8) with TSLS, and using equation (9) as the first stage for both. Table 4 reports the results for our two preferred specifications. Columns 1–4 report estimates of equations (7) and columns 5–8 report estimates of equation (8). Columns 1–2 and 5–6 report results when Nit is measured as sugar’s share of exports. Columns 3–4 and 7–8 report results when Nit is measured as plantation crops’ share of exports. The estimates |$\hat{\beta }^{w}_{N}$| and |$\hat{\beta }^{C}_{N}$| are very robust in magnitude within pairs of columns (1–2, 3–4, etc.), indicating results do not hinge on the particular specification of the time controls. The F-statistics on the First Stage instruments are comfortably above critical threshold levels. The TSLS magnitudes |$\hat{\beta }^{w}_{N}$| in columns 1–2 and 3–4 are about 60% larger than the OLS estimates reported in columns 2 and 4 of Tables 1 and 2. The TSLS magnitudes |$\hat{\beta }^{C}_{N}$| in columns 5–6 and 7–8 are around twice the OLS estimates reported in columns 6 and 8 of Tables 1 and 2. In combination, this suggests that the OLS estimates are downward biased, consistent with the discussion at the start of the identification section. Table 4. TSLS Effect of the Plantation System (Nit) on Wages (wit) and Coercion (Cit). . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Nit (share of exports) −0.5789 −0.5811 −0.9091 −0.9641 1.0675 0.9018 1.6282 1.4638 [0.0006] [0.0084] [0.0000] [0.0018] [0.0001] [0.0057] [0.0000] [0.0003] Fréchet smallholder export 0.3380 0.3161 0.1636 0.2050 price indexit [0.0001] [0.0004] [0.2146] [0.1395] log (net immigration)it −0.0260 −0.0219 −0.0283 −0.0241 0.0011 0.0083 0.0062 0.0125 [0.0081] [0.0561] [0.0001] [0.0226] [0.9686] [0.7729] [0.7961] [0.6369] log(1|$/$|[dist to Panama])i × 0.0046 0.0533 0.0038 0.0596 −0.0201 0.2946 −0.0181 0.3246 D(1881–9)|(1908–13)t [0.2249] [0.3038] [0.3040] [0.2997] [0.0513] [0.1394] [0.0755] [0.1383] Nit measured based on Sugar Plantations Sugar Plantations Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 908 908 908 908 798 798 798 798 F-statistic (instruments) 22.9 21.5 24.8 22.3 20.2 21.6 19.2 21.1 . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Nit (share of exports) −0.5789 −0.5811 −0.9091 −0.9641 1.0675 0.9018 1.6282 1.4638 [0.0006] [0.0084] [0.0000] [0.0018] [0.0001] [0.0057] [0.0000] [0.0003] Fréchet smallholder export 0.3380 0.3161 0.1636 0.2050 price indexit [0.0001] [0.0004] [0.2146] [0.1395] log (net immigration)it −0.0260 −0.0219 −0.0283 −0.0241 0.0011 0.0083 0.0062 0.0125 [0.0081] [0.0561] [0.0001] [0.0226] [0.9686] [0.7729] [0.7961] [0.6369] log(1|$/$|[dist to Panama])i × 0.0046 0.0533 0.0038 0.0596 −0.0201 0.2946 −0.0181 0.3246 D(1881–9)|(1908–13)t [0.2249] [0.3038] [0.3040] [0.2997] [0.0513] [0.1394] [0.0755] [0.1383] Nit measured based on Sugar Plantations Sugar Plantations Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 908 908 908 908 798 798 798 798 F-statistic (instruments) 22.9 21.5 24.8 22.3 20.2 21.6 19.2 21.1 Notes: This table reports the TSLS specifications corresponding to the specification in Tables 1 and 2. Columns 1–4 report the estimates of the wage equation (7). Columns 5–8 report the estimates of coercion equation (8). In columns 1–2 and 5–6, Nit is measured as sugar’s share of exports and plantation crops’ share of exports, respectively. For each outcome, we present the results for our two preferred specifications which include a quadratic trend or year fixed effects. This corresponds to columns 3–4 of Table 1. For expositional clarity, we do not report coefficients on any of the controls. All specifications include colony fixed effects. Standard errors are clustered by colony. Open in new tab Table 4. TSLS Effect of the Plantation System (Nit) on Wages (wit) and Coercion (Cit). . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Nit (share of exports) −0.5789 −0.5811 −0.9091 −0.9641 1.0675 0.9018 1.6282 1.4638 [0.0006] [0.0084] [0.0000] [0.0018] [0.0001] [0.0057] [0.0000] [0.0003] Fréchet smallholder export 0.3380 0.3161 0.1636 0.2050 price indexit [0.0001] [0.0004] [0.2146] [0.1395] log (net immigration)it −0.0260 −0.0219 −0.0283 −0.0241 0.0011 0.0083 0.0062 0.0125 [0.0081] [0.0561] [0.0001] [0.0226] [0.9686] [0.7729] [0.7961] [0.6369] log(1|$/$|[dist to Panama])i × 0.0046 0.0533 0.0038 0.0596 −0.0201 0.2946 −0.0181 0.3246 D(1881–9)|(1908–13)t [0.2249] [0.3038] [0.3040] [0.2997] [0.0513] [0.1394] [0.0755] [0.1383] Nit measured based on Sugar Plantations Sugar Plantations Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 908 908 908 908 798 798 798 798 F-statistic (instruments) 22.9 21.5 24.8 22.3 20.2 21.6 19.2 21.1 . wit: log wage . Cit: incarceration (per cap.) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . Nit (share of exports) −0.5789 −0.5811 −0.9091 −0.9641 1.0675 0.9018 1.6282 1.4638 [0.0006] [0.0084] [0.0000] [0.0018] [0.0001] [0.0057] [0.0000] [0.0003] Fréchet smallholder export 0.3380 0.3161 0.1636 0.2050 price indexit [0.0001] [0.0004] [0.2146] [0.1395] log (net immigration)it −0.0260 −0.0219 −0.0283 −0.0241 0.0011 0.0083 0.0062 0.0125 [0.0081] [0.0561] [0.0001] [0.0226] [0.9686] [0.7729] [0.7961] [0.6369] log(1|$/$|[dist to Panama])i × 0.0046 0.0533 0.0038 0.0596 −0.0201 0.2946 −0.0181 0.3246 D(1881–9)|(1908–13)t [0.2249] [0.3038] [0.3040] [0.2997] [0.0513] [0.1394] [0.0755] [0.1383] Nit measured based on Sugar Plantations Sugar Plantations Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 908 908 908 908 798 798 798 798 F-statistic (instruments) 22.9 21.5 24.8 22.3 20.2 21.6 19.2 21.1 Notes: This table reports the TSLS specifications corresponding to the specification in Tables 1 and 2. Columns 1–4 report the estimates of the wage equation (7). Columns 5–8 report the estimates of coercion equation (8). In columns 1–2 and 5–6, Nit is measured as sugar’s share of exports and plantation crops’ share of exports, respectively. For each outcome, we present the results for our two preferred specifications which include a quadratic trend or year fixed effects. This corresponds to columns 3–4 of Table 1. For expositional clarity, we do not report coefficients on any of the controls. All specifications include colony fixed effects. Standard errors are clustered by colony. Open in new tab While we argue that the agro-climactic and international factors that underlie our instrument |$O_i\,\cdot \,\overline{W}_t$| have no direct impact on Caribbean wages or coercion, |$O_i \cdot \overline{W}_t$| may nevertheless fail to satisfy the exclusion restriction because it is correlated with omitted variables that influence wages or coercion. In this section we present a range of specifications which address this concern. Given the presence of both colony and year fixed effects, the precise concern is that |$O_i \cdot \overline{W}_t$| is correlated with differential trends across colonies. For concreteness consider the following example, chosen because it is particularly damaging to our exclusion restriction. (1) Suppose that in some colonies labour supply trended up, leading to a fall in wages and a resulting expansion of sugar (wit↓ → Nit↑) while in other colonies labour supply trended down, leading to a rise in wages and a resulting contraction of sugar (wit↑ → Nit↓). (2) Suppose that we have not controlled for these differential trends in labour supply. (3) Suppose that our instrument is correlated with these differential trends. Under (1)–(3), our exclusion restriction is violated and a TSLS regression of wit on Nit would be more negative than the true coefficient. Thus, differential labour supply trends can potentially explain away our results. In Online Appendix G.1–G.5, we show that controlling for a variety of different trends leaves the point estimates and significance levels of our results qualitatively unchanged. 4. Extensions In this section, we focus on showing that the negative effect of planter power on wages was in fact explained by the positive effect of planter power on coercion; and that coercion in our setting was of the type described in Subsections 1.1–1.2. The history, theory and econometrics presented thus far all point towards the following causal relations: |$O_{{\textit it}} \downarrow \, \, \rightarrow \, \, N_{{\textit it}} \downarrow \, \, \rightarrow \, \, C_{{\textit it}} \downarrow \, \, \rightarrow \, \, w_{{\textit it}} \uparrow .$| However, we have not shown that there is a causal impact of Cit on wit; we have only shown that Nit impacts Cit and wit. To remedy this, we estimate a model that regresses wit on Cit, and instruments Cit with Oit; reported in Online Appendix H (Extension I). The model establishes a causal impact of coercion on wages (⁠|$C_{{\textit it}} \, \rightarrow \, w_{{\textit it}}$|⁠). This, however, still does not quantify the relative importance of the politics–coercion mechanism we postulate (⁠|$N_{{\textit it}} \, \rightarrow \, C_{{\textit it}} \, \rightarrow \, w_{{\textit it}}$|⁠) because our estimates of the impact of plantation power on wages (⁠|$N_{{\textit it}} \, \rightarrow \, w_{{\textit it}}$|⁠) reported in Section 3 may be capturing our postulated mechanism along with other political mechanisms through which Nit impacts wit. It is therefore of interest to estimate how much of the impact of Nit on wit operates via coercion as opposed to other political mechanisms. A decomposition like this is done through a ‘mediation analysis’, which asks to what extent the ‘total effect’ of a treatment variable (e.g. Nit) on a ‘final outcome’ (e.g. wit) is explained by an intermediate outcome or mechanism (e.g., Cit) that is also an outcome of Nit. See for example Imai et al. (2010; 2011); Heckman et al. (2013); Heckman and Pinto (2015). We use the methodology developed in Pinto et al. (2019) for performing mediation analysis in an IV setting like ours, estimate that upwards of 75% of the estimated effect of Nit on wit operates through coercion Cit; reported in Online Appendix H (Extension II).42 One aspect of legal coercion that is emphasised in the historical discussion in Subsection 1.2 is the distinction between officially sanctioned de jure power and unofficially sanctioned de facto power. We now supplement this historical discussion with econometric evidence by investigating the consequences of the Caribbean Incumbered Estates Act (IEA) of 1854, an exogenous shock to planters’ de facto relative to their de jure power in the exercise of coercion. The IEA originated in the Irish Potato Famine (1845–9), which left Irish estate owners without operating capital and deeply in debt. In response, the Irish Incumbered Estates Act of 1849 strengthened creditor rights by allowing forced foreclosures (estate sales), which allowed capital to return to the Irish estates. The success of this legislative innovation, the result of a famine that was exogenous to the British West Indies, led the British Parliament to enact a Caribbean IEA in 1854.43 The most important consequence of the Caribbean IEA was a change in the composition and identity of the planter elite, because buyers of encumbered estates were often London-based merchant houses rather than local Caribbean planters (Hall, 2011, p. 97). This meant that planters with deep local roots at the parish level were being replaced by London-based merchant houses that set up offices in colonial capitals, which changed the way legal coercion operated. The de facto power of the traditional planters elite over local parish police and magistrates made incarceration an easy method of intimidation and coercion. By contrast, the new merchant-house planters that were based in the islands’ metropoles had more direct access to influence the colonial administration and the islands’ legislatures (de jure power). We therefore conjecture that the IEA led coercion to become more legislated, i.e., de jurebased. To test this we need a measure of legislated coercion. Planter elites enacted many coercive laws, such as discriminatory taxes on smallholds and licensing requirements for the transportation and sale of smallhold crops. Most of the coercive laws are very difficult to code up as a regressor.44 A less complex coercive law is the tariff on imports of foodstuffs. As noted in Subsection 1.1, food imports competed with smallhold crops so low foodstuff tariffs made smallholding less attractive. Low foodstuff tariffs were de jure coercive. We also need to code up the IEA as a regressor. Using the full records of IEA court proceedings during the period it was in effect (1858–89), we identified all 398 cases of court-ordered sales of plantations.45 Our reading of the IEA court cases is that the petitions for forced sale were often initiated by family members, sometimes distant family members, who had randomly fallen on hard times. To be safe, we also instrument court-ordered sales with court petitions. There were 523 IEA petitions in total, of which 398 led to court-ordered sales. Figure 5 shows the cumulative sales and petitions by colony over time.46 Fig. 5. Open in new tabDownload slide Incumbered Estate Act Petitions and Sales. Notes: This figure shows colony-specific time series of the cumulative number of IEA petitions and sales. In total, there were 523 IEA petitions (by claimants) to force sales and 398 plantations were actually sold through the IEA between 1858 and 1889. The IEA was passed in London but needed to be incorporated on each island to apply there. St Lucia, Guyana, Trinidad and Barbados are not in the figure because they never incorporated the IEA, and thus no IEA sales took place in those colonies (Hall, 2011, p. 97). Fig. 5. Open in new tabDownload slide Incumbered Estate Act Petitions and Sales. Notes: This figure shows colony-specific time series of the cumulative number of IEA petitions and sales. In total, there were 523 IEA petitions (by claimants) to force sales and 398 plantations were actually sold through the IEA between 1858 and 1889. The IEA was passed in London but needed to be incorporated on each island to apply there. St Lucia, Guyana, Trinidad and Barbados are not in the figure because they never incorporated the IEA, and thus no IEA sales took place in those colonies (Hall, 2011, p. 97). To summarise, we will regress wages, incarceration rates and foodstuff tariffs on IEA sales and instrument IEA sales with IEA petitions. We will also include Nit as before. Panel B of Table 5 reports first stages. There is a very clean statistical separation between the instruments for IEA sales and Nit. That is, IEA petitions have a strong impact on IEA sales, but no effect on Nit (see columns 1–4). Likewise, Oit and HDIit have a strong effect on Nit, but no effect on IEA sales (see columns 5–6). Table 5. The Effect of the IEA. Panel A. TSLS estimation of effects of Nitand IEA salesiton three outcomes . . wit: log wage . Cit: incarceration (per cap.) . Import duties flour (£) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . Nit: sugar exports −0.7151 −0.5683 1.2239 0.9346 −1.0126 −0.6124 share of total exports [0.0004] [0.0181] [0.0001] [0.0031] [0.3102] [0.5148] IEA salesit −0.0388 −0.0589 −0.0662 −0.0547 −0.3593 −0.4226 [0.0495] [0.0258] [0.2909] [0.4050] [0.0026] [0.0298] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 908 908 798 798 942 942 p-value: Test[2 coefficients equal] 0.001 0.031 0.000 0.002 0.515 0.835 F-statistic (instruments) 18.878 15.111 17.581 17.279 21.146 17.397 Panel B. First stage for two endogenous regressors: Nitand IEA salesit Nit: plantations’ export share Nit: sugar’s export share IEA salesit Outcome (1) (2) (3) (4) (5) (6) Oi × English exports −0.2399 −0.2359 −0.4452 −0.4925 0.0517 0.1095 to all non-Caribbeant [0.0075] [0.0025] [0.0001] [0.0001] [0.5780] [0.3414] HDIit −0.0665 −0.0665 −0.0677 −0.0718 0.0076 0.0140 [0.0000] [0.0000] [0.0000] [0.0000] [0.3717] [0.2126] Incumbered Estate Act −0.0227 −0.0214 −0.0133 −0.0177 1.0367 1.0522 petitionsit [0.1734] [0.2438] [0.5498] [0.4786] [0.0000] [0.0000] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 1,018 1,018 1,018 1,018 1,018 1,018 R2 0.882 0.884 0.891 0.897 0.991 0.990 Panel A. TSLS estimation of effects of Nitand IEA salesiton three outcomes . . wit: log wage . Cit: incarceration (per cap.) . Import duties flour (£) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . Nit: sugar exports −0.7151 −0.5683 1.2239 0.9346 −1.0126 −0.6124 share of total exports [0.0004] [0.0181] [0.0001] [0.0031] [0.3102] [0.5148] IEA salesit −0.0388 −0.0589 −0.0662 −0.0547 −0.3593 −0.4226 [0.0495] [0.0258] [0.2909] [0.4050] [0.0026] [0.0298] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 908 908 798 798 942 942 p-value: Test[2 coefficients equal] 0.001 0.031 0.000 0.002 0.515 0.835 F-statistic (instruments) 18.878 15.111 17.581 17.279 21.146 17.397 Panel B. First stage for two endogenous regressors: Nitand IEA salesit Nit: plantations’ export share Nit: sugar’s export share IEA salesit Outcome (1) (2) (3) (4) (5) (6) Oi × English exports −0.2399 −0.2359 −0.4452 −0.4925 0.0517 0.1095 to all non-Caribbeant [0.0075] [0.0025] [0.0001] [0.0001] [0.5780] [0.3414] HDIit −0.0665 −0.0665 −0.0677 −0.0718 0.0076 0.0140 [0.0000] [0.0000] [0.0000] [0.0000] [0.3717] [0.2126] Incumbered Estate Act −0.0227 −0.0214 −0.0133 −0.0177 1.0367 1.0522 petitionsit [0.1734] [0.2438] [0.5498] [0.4786] [0.0000] [0.0000] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 1,018 1,018 1,018 1,018 1,018 1,018 R2 0.882 0.884 0.891 0.897 0.991 0.990 Notes: (a) Panel A presents the TSLS estimation of the effect on three outcomes. Online Appendix Table H.10 reports additional robustness checks on Panel A. Panel B presents the first stage results for two endogenous regressors, i.e., Nit and IEA salesit. Because there are three different numbers of observations in Panel A, we report the first stage in Panel B for all available data. In Online Appendix Table H.11, we also report the first stage for each of the three sets of observations in Panel A. This does not materially affect any coefficients. (b) For each outcome, we present the results for our two preferred specifications, i.e., the second and third specifications shown in all results in Section 3. (c) Standard errors are clustered by colony, p-values in square brackets. Open in new tab Table 5. The Effect of the IEA. Panel A. TSLS estimation of effects of Nitand IEA salesiton three outcomes . . wit: log wage . Cit: incarceration (per cap.) . Import duties flour (£) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . Nit: sugar exports −0.7151 −0.5683 1.2239 0.9346 −1.0126 −0.6124 share of total exports [0.0004] [0.0181] [0.0001] [0.0031] [0.3102] [0.5148] IEA salesit −0.0388 −0.0589 −0.0662 −0.0547 −0.3593 −0.4226 [0.0495] [0.0258] [0.2909] [0.4050] [0.0026] [0.0298] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 908 908 798 798 942 942 p-value: Test[2 coefficients equal] 0.001 0.031 0.000 0.002 0.515 0.835 F-statistic (instruments) 18.878 15.111 17.581 17.279 21.146 17.397 Panel B. First stage for two endogenous regressors: Nitand IEA salesit Nit: plantations’ export share Nit: sugar’s export share IEA salesit Outcome (1) (2) (3) (4) (5) (6) Oi × English exports −0.2399 −0.2359 −0.4452 −0.4925 0.0517 0.1095 to all non-Caribbeant [0.0075] [0.0025] [0.0001] [0.0001] [0.5780] [0.3414] HDIit −0.0665 −0.0665 −0.0677 −0.0718 0.0076 0.0140 [0.0000] [0.0000] [0.0000] [0.0000] [0.3717] [0.2126] Incumbered Estate Act −0.0227 −0.0214 −0.0133 −0.0177 1.0367 1.0522 petitionsit [0.1734] [0.2438] [0.5498] [0.4786] [0.0000] [0.0000] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 1,018 1,018 1,018 1,018 1,018 1,018 R2 0.882 0.884 0.891 0.897 0.991 0.990 Panel A. TSLS estimation of effects of Nitand IEA salesiton three outcomes . . wit: log wage . Cit: incarceration (per cap.) . Import duties flour (£) . Outcome . (1) . (2) . (3) . (4) . (5) . (6) . Nit: sugar exports −0.7151 −0.5683 1.2239 0.9346 −1.0126 −0.6124 share of total exports [0.0004] [0.0181] [0.0001] [0.0031] [0.3102] [0.5148] IEA salesit −0.0388 −0.0589 −0.0662 −0.0547 −0.3593 −0.4226 [0.0495] [0.0258] [0.2909] [0.4050] [0.0026] [0.0298] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 908 908 798 798 942 942 p-value: Test[2 coefficients equal] 0.001 0.031 0.000 0.002 0.515 0.835 F-statistic (instruments) 18.878 15.111 17.581 17.279 21.146 17.397 Panel B. First stage for two endogenous regressors: Nitand IEA salesit Nit: plantations’ export share Nit: sugar’s export share IEA salesit Outcome (1) (2) (3) (4) (5) (6) Oi × English exports −0.2399 −0.2359 −0.4452 −0.4925 0.0517 0.1095 to all non-Caribbeant [0.0075] [0.0025] [0.0001] [0.0001] [0.5780] [0.3414] HDIit −0.0665 −0.0665 −0.0677 −0.0718 0.0076 0.0140 [0.0000] [0.0000] [0.0000] [0.0000] [0.3717] [0.2126] Incumbered Estate Act −0.0227 −0.0214 −0.0133 −0.0177 1.0367 1.0522 petitionsit [0.1734] [0.2438] [0.5498] [0.4786] [0.0000] [0.0000] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 1,018 1,018 1,018 1,018 1,018 1,018 R2 0.882 0.884 0.891 0.897 0.991 0.990 Notes: (a) Panel A presents the TSLS estimation of the effect on three outcomes. Online Appendix Table H.10 reports additional robustness checks on Panel A. Panel B presents the first stage results for two endogenous regressors, i.e., Nit and IEA salesit. Because there are three different numbers of observations in Panel A, we report the first stage in Panel B for all available data. In Online Appendix Table H.11, we also report the first stage for each of the three sets of observations in Panel A. This does not materially affect any coefficients. (b) For each outcome, we present the results for our two preferred specifications, i.e., the second and third specifications shown in all results in Section 3. (c) Standard errors are clustered by colony, p-values in square brackets. Open in new tab Panel A of Table 5 reports the TSLS estimates of the effects of Nit and IEA sales on wages, incarceration rates and foodstuff tariffs. To compare magnitudes, we have scaled IEA sales by their mean.47 The coefficients on IEA sales are thus the average effect of the IEA. The effects of Nit on wages and incarceration rates (columns 1–4) are almost identical to our baseline Table 4 results. The average total impact of the IEA on wages was to lower them by approximately 5.89 percent (in column 2). In contrast, Nit declined on average by 0.5 and so lowered wages by approximately 28.4 percent (=0.5 × 0.568). This suggests that the collapse of the plantation system (Nit) was the much more fundamental shock to labour markets than the introduction of the IEA, which is fully consistent with the historical literature. This eyeball observation is also borne out in a statistical test of the equality of the two coefficients of interest (on Nit and on IEA sales), which we report at the bottom of Panel A. When it comes to incarceration, the effect of IEA sales was not only much smaller than that of Nit but was in fact statistically not distinguishable from zero (in columns 3–4). This stands in contrast to the effects on foodstuff tariffs, where columns 5–6 show that as the plantation system weakened (Nit fell), foodstuff tariffs rose to the benefit of smallholders, but that this effect is statistically insignificant. In contrast, and as hypothesised, columns 5–6 also show the higher de jure access of the new merchant-planters brought in by the IEA to the islands’ lawmakers led to a much more precisely estimated reduction in foodstuff tariffs.48 In summary, the IEA sales provide evidence on the use of de facto versus de jure coercion. IEA sales did not increase de facto coercion as measured by incarceration rates (the results in columns 3–4 are insignificant), did increase de jure coercion as measured by lower foodstuff tariffs. The shape of legal coercion in the British West Indies varied with changes in the political power of the planter elite. 5. Conclusion In this paper, we provide the first rigorous empirical evidence on the importance of legal coercion in informal developing-country labour markets. Following Lewis’s famous assessment quoted at the beginning of this paper, we hypothesise that legal coercion aimed at depressing workers’ outside options in the informal sector is an important factor in determining wages, and that the formal sector’s influence over government is a key driver of the use of legal coercion. We focus on a uniquely relevant empirical setting, studying 14 Caribbean plantation islands at the inception of free labour markets, i.e., starting right after the emancipation of slaves. We measure the formal sector’s influence over government Nit by the plantation sector’s share of overall production. To gain identification, we instrument for Nit with a interaction between the planters’ time-varying reservation wages outside the Caribbean plantation system and variation across islands in the peasants’ ability to evade the plantation system. Controlling for possibly confounding crop price variation, labour demand and labour supply shocks, we find strong support for both hypotheses in the data: the plantation system had powerful effects on wages and legal coercion (see Tables 1 and 4). A complete collapse of the plantation system raised agricultural wages by 100% and lowered coercion by two times its mean level in the data. At the sub-island parish level we can also show that it lowered mortality rates. Pushing further towards identifying the causal mechanism linking these patterns, we find that upwards of three-quarters of the plantation system’s effect on wages is explained by the plantation system’s effect on coercion (see Online Appendix Table H.9). We also provide suggestive evidence that planters shaped legal coercion both through legislation passed in the islands as well as through personal connections to the police and judicial apparatus in the countryside. In summary, Lewis was right. Appendix A. Mathematical Proofs Proof of Equation (1): Drop j superscripts, i and t subscripts, and |$\mathbf {p}_t$| arguments. Define |$\widehat{T}_g \equiv T_{g} (\tau _g p_g)^{\theta }$|⁠. Let |$r_g(\omega ) = \widehat{T}_g z_g(\omega )^{\theta }$| be revenue per plot generated by crop g. Then rg(ω) has cumulative distribution |$e^{-\widehat{T}_g r_g^{-\theta }}$|⁠, density |$\theta \widehat{T}_g e^{-\widehat{T}_g r^{-\theta }}$| and mean |$\widehat{T}_g^{1/\theta } \Gamma (1-1/\theta )$|⁠. As is well known from Eaton and Kortum (2002), |$Pr \lbrace r_k(\omega ) \lt r \, \forall k \ne g \rbrace = e^{-(\widehat{T}-\widehat{T}_g) r^{-\theta }}$| where |$\widehat{T} = \Sigma _{k=1}^{G} \widehat{T}_k$| and |$Pr\lbrace \text{choose } g \rbrace = \widehat{T}_g / \widehat{T}$|⁠. Hence, the joint probability of g being the optimal crop choice and rg(ω) = r is $$\begin{eqnarray} Pr \lbrace \, \lbrace \text{choose } g \rbrace \text{ and } \lbrace r_g(\omega )=r\rbrace \, \rbrace = Pr \lbrace r_k(\omega ) \lt r \, \forall k \ne g \rbrace Pr \lbrace r_g(\omega ) = r \rbrace = (\theta \widehat{T} e^{-\widehat{T}r^{-\theta }} ) ( \widehat{T}_g / \widehat{T} ) \, . \end{eqnarray}$$ The first term in parentheses is a Fréchet density with scale parameter |$\widehat{T}$| and hence with mean |$\widehat{T}^{1/\theta } \Gamma$|⁠. Hence the expected revenues generated by crop g are $$\begin{eqnarray} r_g(\widehat{T}_g) \equiv \mathbf {E}[r_g(\omega ) ] =&& \widehat{T}^{1/\theta } \Gamma ( \widehat{T}_g / \widehat{T} ) = \widehat{T}_g \widehat{T}^{\frac{1}{\theta }-1} \Gamma \, . \end{eqnarray}$$(A1) Further, the expected revenues generated by all crops are $$\begin{eqnarray} r(\widehat{T}_g) \equiv \Sigma _g r_g(\widehat{T}_g) = \widehat{T}^{\frac{1}{\theta }} \Gamma, \end{eqnarray}$$(A2) where |$\widehat{T} \equiv \Sigma _{g=1} \widehat{T}_g$|⁠. Substituting |$\widehat{T}_g \equiv T_{g} (\tau _g p_g)^{\theta }$| into this mean yields equation (1).☐ Characterisation of C*(N): Substituting equations (2)–(3) into (4) yields |$W(C) = (\alpha l(N) N - L) C - \alpha C^{\gamma } + \alpha l(N) N [r(\mathbf {p},\tau ^p) - r(\mathbf {p},\tau ^s) ] +L r(\mathbf {p},\tau ^s)$|⁠, which is concave in C for γ > 1. Hence C* is unique. ∂W|$/$|∂C = 0 implies (C*)γ−1 = [αl(N)N − L]|$/$|[αγ]. From the definition of |$\bar{N}$| before equation (5), |$\alpha l(N)N-L\gt 0 \Leftrightarrow N\gt \bar{N}$|⁠. Hence the constrained (C ≥ 0) optimal solution is C* = 0 for |$N\lt \bar{N}$| and equation (5) for |$N \ge \bar{N}$|⁠. Existence, Interior Solutions and Stability of N*: The equilibrium number of planters N* is given by equation (6). We first derive a sufficient condition which ensures an interior solution N* ∈ (0, L). Start by defining |$\Delta r \equiv r(\mathbf {p},\tau ^p) - r(\mathbf {p},\tau ^s)$|⁠. A sufficient condition for an interior N* is |$\pi (0) \gt \overline{W}/(1-O) \gt \pi (L)$|⁠. From equation (5), C*(0) = 0 so that from equation (3), π(0) = l(0)Δr. Also, it is tedious but straightforward to show that π(L) < ΔrL1/(γ − 1). Hence a sufficient condition on parameters is |$l(0)\Delta r \gt \overline{W}/(1-O) \gt \Delta r L^{1/(\gamma -1)}$|⁠. To see stability, consider a plot of π(N) and |$\overline{W}/(1-O)$| against N. As we move from N = 0 to N = L, π(N) must cut the horizontal |$\overline{W}/(1-O)$| line from above, which is the requirement for stability. Finally, at such an intersection N = N* and πN(N*) < 0. Appendix B. Data We made use of two types of original data sources. The first is a new data set of geographic and agro-climatic conditions in the Caribbean. To calculate predetermined outside options as well as Fréchet-based structural model of crop choice, we need detailed spatial data on soil suitability for different crops. Standard sources for crop-suitability data are too coarse for our colonies.49 We therefore gathered agro-climatic data on the Caribbean at an unusually fine spatial level and then developed agro-climatic suitability indexes for the eight most important crops in our data. The second source of novel data is archival. Starting in the mid-1830s, Britain began collecting statistics on colonial conditions. Each colony filled out an annual Blue Book and sent it to London where it is now stored in the British National Archives. We photographed thousands of the relevant Blue Book pages. We also made use of the Statistical Tables Relating to the Colonial and Other Possessions of the United Kingdom, annual Censuses, and various other House of Commons parliamentary papers. We manually entered the relevant data into spreadsheets and built a panel data set on exports and export prices by crop, race demographics, wages, incarceration rates, coercive taxes and military expenditures. The panel consists of 14 colonies from 1838 to 1913. B.1. Wage and Employment Data Praedial wages:The Blue Books report wages for trade, domestic labour and praedial labour (praedial means agricultural). We treat the praedial wage as the wage paid for plantation work. While the Blue Books do not explicitly state this, it is implicit from the context, namely, that there was no other agricultural activity that paid wages. Aside from plantation work, the only significant amount of agricultural work was on smallholds and we now provide evidence that smallholds did not hire workers. Eisner (1961) shows that the majority of Jamaican smallholds were under 2 hectares, which even today is considered a very small farm50 and hence requires the peasant to search for off-smallhold work, i.e., it was rare for smallholders to hire workers and hence to pay wages. Anecdotal evidence supports the claim the smallholders were subsistence farmers who did not make wage offers. Paget (1964) provides many contemporary quotes from the 1838–40 period. For example: ‘It appears to me that the land which they purchase is … too little in extent to be looked to as a permanent source of subsistence and that they must calculate either on obtaining additional means of comfort by going out to labour, or on taking more land on lease’ (Paget, 1964, p. 48). For a later period, the West Indies Royal Commission of 1897 makes the stronger point that, except for plantation work, there were no other wage opportunities in agriculture: ‘If work cannot be found for the labouring population on estates, they must either emigrate or support themselves by cultivating small plots of land on their own account’ (West India Royal Commission, 1897, p. 17). This discussion establishes that praedial wages were plantation wages and those paid them were either full-time employees or part-timers with subsistence smallholds. Employment and non-agricultural outside options: Were there other, non-agricultural options for peasants? These appear to have been very limited or non-existent, as suggested by the Royal Commission quote above. More systematic evidence to this effect can be gleaned from the Blue Books. The Blue Books list three types of employment: agricultural, manufacturing and commercial. The Books report that there was virtually no manufacturing employment and commercial employment was typically tiny. The population share of those employed in commerce never exceeded 7%, while that in agriculture was as high as 90% in some colony years.51 Table B1 shows in columns 1–2 that a complete collapse of the plantation system (ΔNit = −1) was associated with a 33-percentage-point decline in the population share in agricultural employment. This exactly equals the average agricultural employment share. By way of a counterfactual argument, if wage labour on smallholds had been an option for plantation workers, we might have expected this correlation to be close to zero given as plantation agriculture was replaced by smallhold agriculture. Columns 3–6 of Table B1 also show no significant correlation between Nit and employment in commerce or manufacturing. By way of a counterfactual argument, if wage work in the towns had been an option for plantation workers, we might have expected this correlation to be significantly negative. Table B1. Partial Correlation between Nit and Agricultural Employment. . (1) . (2) . (3) . (4) . (5) . (6) . Outcome: . Number employed in agriculture/population . Number employed in commerce/population . Number employed in manufacturing/population . Panel A: Planter power Nit: plantation exports as 0.3319 0.0007 −0.5276 share of total exports [0.0003] [0.9716] [0.4356] Nit: sugar exports as 0.2392 −0.0030 −0.1515 share of total exports [0.0002] [0.8117] [0.7084] Observations 125 125 102 102 16 16 R2 0.381 0.374 0.291 0.293 0.823 0.762 Panel B: Outside options Oi × English exports −0.0955 −0.1363 −0.0004 0.0003 0.0124 0.0124 to all non-Caribbeant [0.0058] [0.0326] [0.9526] [0.9671] [0.7840] [0.7840] HDIit 0.1103 −0.0020 [0.2516] [0.8966] Observations 125 125 102 102 16 16 R2 0.311 0.323 0.291 0.291 0.745 0.745 . (1) . (2) . (3) . (4) . (5) . (6) . Outcome: . Number employed in agriculture/population . Number employed in commerce/population . Number employed in manufacturing/population . Panel A: Planter power Nit: plantation exports as 0.3319 0.0007 −0.5276 share of total exports [0.0003] [0.9716] [0.4356] Nit: sugar exports as 0.2392 −0.0030 −0.1515 share of total exports [0.0002] [0.8117] [0.7084] Observations 125 125 102 102 16 16 R2 0.381 0.374 0.291 0.293 0.823 0.762 Panel B: Outside options Oi × English exports −0.0955 −0.1363 −0.0004 0.0003 0.0124 0.0124 to all non-Caribbeant [0.0058] [0.0326] [0.9526] [0.9671] [0.7840] [0.7840] HDIit 0.1103 −0.0020 [0.2516] [0.8966] Observations 125 125 102 102 16 16 R2 0.311 0.323 0.291 0.291 0.745 0.745 Notes: This table presents results of OLS regressions where the outcome is the total number of people employed in agriculture (columns 1–2), commerce (3–4) and manufacturing (5–6) divided by the total population and the regressor is our Nit. With so few observations, we otherwise only include colony fixed effects. Open in new tab Table B1. Partial Correlation between Nit and Agricultural Employment. . (1) . (2) . (3) . (4) . (5) . (6) . Outcome: . Number employed in agriculture/population . Number employed in commerce/population . Number employed in manufacturing/population . Panel A: Planter power Nit: plantation exports as 0.3319 0.0007 −0.5276 share of total exports [0.0003] [0.9716] [0.4356] Nit: sugar exports as 0.2392 −0.0030 −0.1515 share of total exports [0.0002] [0.8117] [0.7084] Observations 125 125 102 102 16 16 R2 0.381 0.374 0.291 0.293 0.823 0.762 Panel B: Outside options Oi × English exports −0.0955 −0.1363 −0.0004 0.0003 0.0124 0.0124 to all non-Caribbeant [0.0058] [0.0326] [0.9526] [0.9671] [0.7840] [0.7840] HDIit 0.1103 −0.0020 [0.2516] [0.8966] Observations 125 125 102 102 16 16 R2 0.311 0.323 0.291 0.291 0.745 0.745 . (1) . (2) . (3) . (4) . (5) . (6) . Outcome: . Number employed in agriculture/population . Number employed in commerce/population . Number employed in manufacturing/population . Panel A: Planter power Nit: plantation exports as 0.3319 0.0007 −0.5276 share of total exports [0.0003] [0.9716] [0.4356] Nit: sugar exports as 0.2392 −0.0030 −0.1515 share of total exports [0.0002] [0.8117] [0.7084] Observations 125 125 102 102 16 16 R2 0.381 0.374 0.291 0.293 0.823 0.762 Panel B: Outside options Oi × English exports −0.0955 −0.1363 −0.0004 0.0003 0.0124 0.0124 to all non-Caribbeant [0.0058] [0.0326] [0.9526] [0.9671] [0.7840] [0.7840] HDIit 0.1103 −0.0020 [0.2516] [0.8966] Observations 125 125 102 102 16 16 R2 0.311 0.323 0.291 0.291 0.745 0.745 Notes: This table presents results of OLS regressions where the outcome is the total number of people employed in agriculture (columns 1–2), commerce (3–4) and manufacturing (5–6) divided by the total population and the regressor is our Nit. With so few observations, we otherwise only include colony fixed effects. Open in new tab Thus, the Blue Books do not provide any evidence of non-agricultural outside options for plantation workers. B.2. Export Price Index $r_{i}(\mathbf {p}_{t},\tau ^s)$ We used the Blue Books to construct a 76-year panel of exports by colony and crop, generating a database containing exports by colony and year for 17 products accounting for 98% of exports.52 We then built prices as export unit values (export revenues divided by export quantities) for the 17 products. See Online Appendix C for a description of the price data. We validated our series against the sporadic contemporary sources available. For example, for sugar our export unit values are virtually identical to data in Deerr (1950), the seminal work on the subject, and to sugar prices in Blattman et al. (2007). We now describe how we estimate |$r_i(\mathbf {p}_\mathit{t},\tau ^s)$| in equation (1). First, except for sugar, no other crop was exclusively a plantation crop, e.g., coffee was typically grown both on plantations and smallholds. We therefore had to determine for each island whether a crop was fully or partly grown by plantations; see discussion in Online Appendix A. Second, we use the same information on agro-climactic conditions that we utilised for section Appendix B.4 and develop the agro-climatic suitability indexes for the seven most important plantation crops beyond sugar.53 Let Agi be a vector of crop suitability characteristics on island i pertaining to crop g. We estimate the parameters of |$r_i(\mathbf {p}_\mathit{t},\tau ^s)$| using an almost standard gravity equation method common to Fréchet-based models. That is, we relate crop-level exports to the |$T_{{\textit gi}} ( \tau ^j_g)^{\theta } (p_{{\textit gt}})^{\theta }$| terms in equation (1). In the standard gravity approach a plot’s productivity is drawn from a single distribution, but here it is drawn from two distributions, depending on whether the plot is a plantation (⁠|$\tau ^p_g$|⁠) or a smallhold (⁠|$\tau ^s_g$|⁠). To keep the estimation within a standard framework we assume that a plot’s productivity is drawn from a single distribution with a parameter τg which is the geometric average of |$\tau ^p_g$| and |$\tau ^s_g$|⁠. Specifically, $$\begin{eqnarray} \tau _g(Pl_\textit {git}) \equiv (\tau ^p_g)^{Pl_\textit {git}}(\tau ^s_g)^{1-Pl_\textit {git}} \end{eqnarray}$$(B1) where Plgit is the share of crop g in colony i in year t produced on plantations.54 We also assume that ln Tgi = αgAgi where αg is a parameter vector. Gravity estimation very roughly boils down to regressing log exports on Agi, Plgit, a crop dummy, and ln pgt.55 Substituting |$\widehat{T}_g \equiv T_{g} (\tau _g p_g)^{\theta }$| into equation (A1) of Appendix A and adding subscripts, the average earnings per plot from crop g are $$\begin{eqnarray} r_{{\textit gi}}(\mathbf {p}_t,\tau ) = \left[ T_{{\textit gi}} ( \tau _g p_{{\textit gt}} )^{\theta } \right] \left[ \Sigma _k T_{{\textit ki}} ( \tau _k p_{{\textit kt}} )^{\theta } \right]^{\frac{1}{\theta }-1} \Gamma \, . \end{eqnarray}$$(B2) To estimate the parameters of this equation, recall that we assumed ln Tgi = αgAgi and |$\tau _g = \tau _g(Pl_{{\textit git}}) \equiv (\tau ^p_g)^{Pl_{{\textit git}}}(\tau ^s_g)^{1-Pl_{{\textit git}}}$| where Plgit is the share of exports produced on plantations. Then differentiating equation (B2) between crop g and any other crop g′ yields $$\begin{eqnarray} &&\ln r_{{\textit gi}}(\mathbf {p}_t,\tau ) - \ln r_{g^{\prime }i}(\mathbf {p}_t,\tau ) \\ &&= \ln \left[ T_{{\textit gi}} ( \tau _g(Pl_{{\textit git}}) p_{{\textit gt}} )^{\theta } \right] - \ln \left[ T_{g^{\prime }i} ( \tau _{g^{\prime }}(Pl_{g^{\prime }{\textit it}}) p_{g^{\prime }t} )^{\theta } \right] \\ &&= \alpha _g A_{{\textit gi}} - \alpha _{g^{\prime }} A_{g^{\prime }i} +\theta \ln (\tau ^p_g/\tau ^s_g)Pl_{{\textit git}} - \theta \ln (\tau ^p_{g^{\prime }}/\tau ^s_{g^{\prime }})Pl_{g^{\prime }{\textit it}} +\theta \ln (\tau ^s_g/\tau ^s_{g^{\prime }}) +\theta \ln p_{gt}/p_{g^{\prime }t} \, . \end{eqnarray}$$ We assume that exports per plot are a noisy measure of output per plot: ln xgit|$/$|ni = ln rgi + εgit where ni is the number of plots. Then we obtain the estimating equation $$\begin{eqnarray} \ln (x_\textit {git}/x_{g^{\prime }\textit {it}}) = && \beta _g A_{{\textit gi}} + \beta _s A_{g^{\prime }i} + \beta ^{\prime }_g Pl_\textit {git} + \beta ^{\prime }_{g^{\prime }} Pl_{g^{\prime }{\textit it}} + \beta ^{\prime \prime }_g D_g + \beta ^{\prime \prime \prime } \ln p_{{\textit gt}}/p_{g^{\prime }t} \\ && + \nu _\textit {git} \, \, \forall \, i,t \, \text{and} \, g \ne g^{\prime } \end{eqnarray}$$(B3) where βs are regression coefficients, g′ is fixed (it will be sugar), Dg is a crop dummy and |$\nu _{{\textit git}} \equiv \varepsilon _{{\textit git}}-\varepsilon _{g^{\prime }{\textit it}}$|⁠. It is easy to verify that the estimates of equation (B3) identify all the parameters of (B2) except |$\tau ^s_{g^{\prime }}$|⁠, e.g., β‴ = θ. Thus, |$r_{gi}(\mathbf {p}_t,\tau )$| and |$r_i(\mathbf {p}_t,\tau ) = \Sigma _g r_{gi}(\mathbf {p}_t,\tau )$| (see equation (A2)) are known up to the multiplicative constant |$\tau ^s_{g^{\prime }}$|⁠. Recall that if Plgit = 0 for all g then τ = τs, i.e., if there is no plantation production, then τ takes on its smallhold value τs. Hence, setting Plgit = 0 for all g, |$r_i(\mathbf {p}_t,\tau ^s)$| is also known up to the multiplicative constant |$\tau ^s_{g^{\prime }}$|⁠. In regressions we use |$\ln r_i(\mathbf {p}_t,\tau ^s)$| so that the additive constant |$\ln \tau ^s_{g^{\prime }}$| is subsumed into intercepts. Equation (B3) is our gravity equation, where g′ is sugar. Data on the share of exports produced on plantations (Plgit) are described in Online Appendix A. Data on agro-climactic conditions (Agi) are described Online Appendix B. The bin-level agro-climactic variables are averaged up to the colony level to create the Agi. Data on export prices (pgt) are described in Online Appendix C. Online Appendix Table C.3 displays the estimates of the key parameters. There are 7,126 = 1,018 × 7 observations where 1,018 is the number of colony-year pairs and 7 is the number of (non-sugar) crops. We estimate θ to be 2.30 (t =3.93). This is in line with Costinot et al. (2016) who estimate it to be 2.46. The remaining estimates reported in Online Appendix Table C.3 are the coefficients on Plgit. Except for livestock they are all positive as expected. There are several things to note. The negative livestock coefficient is largely driven by a comparison of Virgin Island smallholds with Tobago plantation and it is thus not surprising to find that the Virgin Islands did better. Cotton is always a smallhold crop, which means that its coefficient (⁠|$\beta ^{\prime }_g = \theta \ln (\tau ^p_g/\tau ^s_g)$|⁠) and hence |$\tau ^p_g$| are not identified; however, we do not need to know |$\tau ^p_g$| in order to recover |$r_i(\mathbf {p}_t,\tau ^s)$|⁠.56 Likewise, the sugar coefficient is not identified because sugar is always a plantation crop. This does not matter because sugar does not enter into the Fréchet smallholder price index. In summary, the gravity equation (B3) identifies the parameters |$\lbrace \alpha _g,\tau ^p_g, \tau ^s_g\rbrace _{g=1}^G$| and θ needed to recover estimates of the |$r_i(\mathbf {p_t},\tau ^s)$|⁠. B.3. Coercion Data In this appendix we address two questions. First, what share of incarcerations or court convictions were associated with legal coercion? Second, what is the relationship between incarcerations and court convictions, given that the latter involved both fines and incarcerations? Incarceration and conviction data were rarely reported in sufficient detail to isolate crimes associated with legal coercion. Fortunately, in the earliest post-abolition years, London was concerned about the abuse of legal coercion by planters and so requested detailed reports on each colony’s Acts, incarcerations, convictions and evictions of peasants from plantations. Colonial assemblies did not want to comply and often did not: sometimes there are no tables and sometimes the tables are very imperfect. Where they are available, they are reported in complicated ways. For example, in some colonies there is a table for each magistrate separately along with details of each case and its outcome (fine, incarceration, eviction). This is a useful source for our fine-grained historical discussion of legal coercion, but not for statistical analysis. Fortunately, in 1838, four of the Leewards (Antigua, St Kitts, Nevis, the Virgin Islands) actually filled in London’s standardised and very detailed tables of convictions by detailed crime. These tables appear amid hundreds of pages of detailed exegesis on colonial laws, and as a result the detailed crimes can be fully understood and categorised as coercive or not. The tables were combined into a single table that appears as our Table B2. The first column lists the detailed crimes. The first group (‘Coercive’) are the crimes that were described in Subsection 1.1 and are clearly related to legal coercion. Note that breach of contract, vagrancy and trespass were all lumped in the Vagrancy Acts of a number of colonies,57 which illustrates that one cannot classify crimes as coercive or non-coercive without detailed knowledge of the laws of each colony. Turning to the other coercive crimes in Table B2, licensing was used to limit the opportunities for non-plantation activities such as huckstering (selling goods), jobbing (handyman), boating (transporting goods) and deporting (moving peasants to another island, which was illegal in the Leewards).58 Malicious injury to property could stem from the eviction of a peasant from the plantation, the subsequent fight over the peasant’s access to his/her crops, and retribution on both sides for perceived injustices.59 Table B2. Convictions (Fines and Incarceration) by Type of Crime. . Jan.–Sept. 1838 . July–Sept. 1838 . . Number . % . Number . % . Coercive 991 41 425 45 Breach of contract 479 20 227 24 Vagrancies 192 8 91 10 Trespass 137 6 54 6 Hucksters without licence 2 0 0 0 Jobbing without licence 44 2 5 1 Plying unlicensed boat 4 0 0 0 Deportation without licence 4 0 2 0 Malicious injury to property 129 5 46 5 Partially coercive 886 37 348 37 Police Act 257 11 91 10 Riotous, disorderly conduct 77 3 26 3 Assault and battery 552 23 231 25 Non-coercive 516 22 166 18 Larceny 75 3% 22 2 Miscellaneous 441 18% 144 15 Total 2,393 100% 939 100 . Jan.–Sept. 1838 . July–Sept. 1838 . . Number . % . Number . % . Coercive 991 41 425 45 Breach of contract 479 20 227 24 Vagrancies 192 8 91 10 Trespass 137 6 54 6 Hucksters without licence 2 0 0 0 Jobbing without licence 44 2 5 1 Plying unlicensed boat 4 0 0 0 Deportation without licence 4 0 2 0 Malicious injury to property 129 5 46 5 Partially coercive 886 37 348 37 Police Act 257 11 91 10 Riotous, disorderly conduct 77 3 26 3 Assault and battery 552 23 231 25 Non-coercive 516 22 166 18 Larceny 75 3% 22 2 Miscellaneous 441 18% 144 15 Total 2,393 100% 939 100 Notes: Data compiled by authors from House of Commons Parliamentary Papers (1839b), pp. 78–9 (Antigua), 225–6 (St Kitts), 286–7 (Nevis) and 332–4 (Virgin Islands). Hucksters are sellers of small wares. Jobbers are handymen. The Police Act varies from colony to colony. It always covers day-to-day non-coercive offences (e.g., startling a horse) and, in some colonies, offences relating to coercion. Riotous and disorderly conduct ranges from public drunkenness to organised peasant protests. Assault and battery includes assaulting an employer. ‘Miscellaneous’ is the authors’ own category and collects crimes that are not related to coercion of smallholders, e.g., petty theft, mutiny and abusive language. The results are very similar for January–September and July–September. See footnote 60 for a discussion of the differences between these two periods. Open in new tab Table B2. Convictions (Fines and Incarceration) by Type of Crime. . Jan.–Sept. 1838 . July–Sept. 1838 . . Number . % . Number . % . Coercive 991 41 425 45 Breach of contract 479 20 227 24 Vagrancies 192 8 91 10 Trespass 137 6 54 6 Hucksters without licence 2 0 0 0 Jobbing without licence 44 2 5 1 Plying unlicensed boat 4 0 0 0 Deportation without licence 4 0 2 0 Malicious injury to property 129 5 46 5 Partially coercive 886 37 348 37 Police Act 257 11 91 10 Riotous, disorderly conduct 77 3 26 3 Assault and battery 552 23 231 25 Non-coercive 516 22 166 18 Larceny 75 3% 22 2 Miscellaneous 441 18% 144 15 Total 2,393 100% 939 100 . Jan.–Sept. 1838 . July–Sept. 1838 . . Number . % . Number . % . Coercive 991 41 425 45 Breach of contract 479 20 227 24 Vagrancies 192 8 91 10 Trespass 137 6 54 6 Hucksters without licence 2 0 0 0 Jobbing without licence 44 2 5 1 Plying unlicensed boat 4 0 0 0 Deportation without licence 4 0 2 0 Malicious injury to property 129 5 46 5 Partially coercive 886 37 348 37 Police Act 257 11 91 10 Riotous, disorderly conduct 77 3 26 3 Assault and battery 552 23 231 25 Non-coercive 516 22 166 18 Larceny 75 3% 22 2 Miscellaneous 441 18% 144 15 Total 2,393 100% 939 100 Notes: Data compiled by authors from House of Commons Parliamentary Papers (1839b), pp. 78–9 (Antigua), 225–6 (St Kitts), 286–7 (Nevis) and 332–4 (Virgin Islands). Hucksters are sellers of small wares. Jobbers are handymen. The Police Act varies from colony to colony. It always covers day-to-day non-coercive offences (e.g., startling a horse) and, in some colonies, offences relating to coercion. Riotous and disorderly conduct ranges from public drunkenness to organised peasant protests. Assault and battery includes assaulting an employer. ‘Miscellaneous’ is the authors’ own category and collects crimes that are not related to coercion of smallholders, e.g., petty theft, mutiny and abusive language. The results are very similar for January–September and July–September. See footnote 60 for a discussion of the differences between these two periods. Open in new tab This discussion of Table B2 explains why it is so difficult to identify legal coercion from the crime statistics. It also makes clear that we can do so for 1838 because we have the supporting Acts and legal discussion of them. Assuming that half of the ‘partially coercive’ crimes were coercive, 60% of convictions involved legal coercion (⁠|$60 = 41 + 37/2$|⁠). Legal coercion was thus an important source of convictions.60 We next turn to the question of what percentage of these court convictions involved incarceration. Recall that convictions led to either fines or incarceration. From inspection of convictions tables from 1838, a year in which such tables were collected and published in a major House of Commons report, several patterns emerge. First, the vast majority of higher court convictions involved incarceration, e.g., House of Commons Parliamentary Papers (1839b, p. 72). Second, lower court cases involved either mediation (no conviction, one party agrees to indemnify the other), or conviction with fine, or conviction with imprisonment (for more significant crimes such as long or repeat absenteeism and neglect leading to death of livestock).61 The only comprehensive account of lower court cases for 1838 is a single table for Barbados (1 August–15 October). In that table, 68% of the convictions involved imprisonment (House of Commons Parliamentary Papers, 1839a, pp. 104–5). Summarising what we could glean from these reports, the majority of court convictions were for offences that involved legal coercion, and the majority of court convictions resulted in incarceration, albeit usually only for two weeks or one month, often at hard labour. For the end of our period (1871–1913) we have an annual panel of court convictions (with no information on what share resulted in incarceration). It would thus be of interest to use these convictions as an alternative measure to legal coercion. To this end, we must identify which convictions are associated with legal coercion. Unfortunately, the conviction data are only available by four broad categories: (i) offences against property; (ii) offences against the person; (iii) praedial larceny (the theft of livestock and crops); (iv) other. The best we can do is equate offences against property with legal coercion. There are pros and cons to this. The Blue Books state that offences against property include both offences against rights of property and injuries to the subjects of property, which means that offences against property include trespass.62 The Blue Books further state that ‘by praedial larceny is meant the offence—prevalent in the sugar-growing and Cooley-importing colonies—of robbing provision grounds and homesteads’. By 1871, it probably had only a small component of legal coercion, i.e., of evicted peasants recovering their crops.63 Offences against the person is a category that, as with assault and battery, likely had only a small component of legal coercion, i.e., of peasant retribution against plantation overseers for loss of cottage and crops. ‘Other’ could subsume any number of offences listed in Table B2 and, since it makes up about 55% of the convictions in our data, it is too much of a catch-all category to be called legal coercion. In summary, we conclude that offences against property are the only category that can be linked to the legal coercion discussed in Subsection 1.1, but this must be done with caution. Note that crimes against property only make up about 15% of the convictions in our data. Table B3 shows that this category’s share of all convictions correlates strongly with Nit. Specifically, columns 1–4 of the table report a regression of the share of court convictions for offences against property on our two measures of Nit. The full specification corresponds to our two baseline specifications in Table 1. There is also a somewhat weaker positive correlation with Cit in columns 5–6. We view these patterns as validation of incarceration as our measure of coercion. Table B3. OLS Regressions of Court Convictions on Nit and Cit. . (1) . (2) . (3) . (4) . (5) . (6) . Outcome . Share of court convictions for offences against property . Nit: sugar exports as 0.2471 0.2204 share of total exports [0.0372] [0.0898] Nit: plantation exports as 0.3298 0.3190 share of total exports [0.0206] [0.0512] Incarceration (per cap.) 0.0309 0.0325 [0.2650] [0.2100] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 502 502 502 502 408 408 R2 0.141 0.227 0.140 0.226 0.136 0.226 . (1) . (2) . (3) . (4) . (5) . (6) . Outcome . Share of court convictions for offences against property . Nit: sugar exports as 0.2471 0.2204 share of total exports [0.0372] [0.0898] Nit: plantation exports as 0.3298 0.3190 share of total exports [0.0206] [0.0512] Incarceration (per cap.) 0.0309 0.0325 [0.2650] [0.2100] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 502 502 502 502 408 408 R2 0.141 0.227 0.140 0.226 0.136 0.226 Notes: (a) From 1871 to 1913 we observe data on local court sentences by categories of offences. There are four categories: offences against property, offences against the person, ‘praedial larceny’ (the theft of livestock and crops) and ‘other’. Only one of these—offences against property—corresponds closely to the legal coercion discussed in Subsection 1.1. In this table we run our set of three core specifications on three relationships: in columns 1–4, we regress the share of all court sentences that were levied for offences against property, for our two core specifications. In columns 5–6, we regress it on our incarcerations measure. (b) Standard errors are clustered by colony, p-values in square brackets. Open in new tab Table B3. OLS Regressions of Court Convictions on Nit and Cit. . (1) . (2) . (3) . (4) . (5) . (6) . Outcome . Share of court convictions for offences against property . Nit: sugar exports as 0.2471 0.2204 share of total exports [0.0372] [0.0898] Nit: plantation exports as 0.3298 0.3190 share of total exports [0.0206] [0.0512] Incarceration (per cap.) 0.0309 0.0325 [0.2650] [0.2100] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 502 502 502 502 408 408 R2 0.141 0.227 0.140 0.226 0.136 0.226 . (1) . (2) . (3) . (4) . (5) . (6) . Outcome . Share of court convictions for offences against property . Nit: sugar exports as 0.2471 0.2204 share of total exports [0.0372] [0.0898] Nit: plantation exports as 0.3298 0.3190 share of total exports [0.0206] [0.0512] Incarceration (per cap.) 0.0309 0.0325 [0.2650] [0.2100] Time controls t + t2 t-fe t + t2 t-fe t + t2 t-fe Observations 502 502 502 502 408 408 R2 0.141 0.227 0.140 0.226 0.136 0.226 Notes: (a) From 1871 to 1913 we observe data on local court sentences by categories of offences. There are four categories: offences against property, offences against the person, ‘praedial larceny’ (the theft of livestock and crops) and ‘other’. Only one of these—offences against property—corresponds closely to the legal coercion discussed in Subsection 1.1. In this table we run our set of three core specifications on three relationships: in columns 1–4, we regress the share of all court sentences that were levied for offences against property, for our two core specifications. In columns 5–6, we regress it on our incarcerations measure. (b) Standard errors are clustered by colony, p-values in square brackets. Open in new tab B.4. Measuring Oi To measure Oi we carefully calculated the share of each colony’s land that is not suitable for sugar cane. This was a major undertaking, but only insofar as the Caribbean islands small size forced us to collect geographic data at an unusually fine level of disaggregation. See Online Appendix B for details. B.5. Measuring $\overline{W}_{t}$ Real British exports to non-Caribbean destinations (⁠|$\overline{W}_{t}$|⁠) is constructed from data in Mitchell (1988). Real British exports to all destinations are from Table IX.19. These data exclude re-exports.64 Nominal British exports to the Caribbean are from Tables IX.5 (1838–47) and IX.16 (1846–1913). Over our period, 83% of British exports were manufactures, so we convert nominal exports to the Caribbean into real exports using the price index for British manufacturing exports. The price index is constructed from data in Tables IX.5 and IX.19. Our instrument |$\overline{W}_{t}$| is real British exports less real British exports to the Caribbean. Data are in millions of 1913 pounds sterling. B.6. Additional Labour Supply Shocks There was relatively little cross-island migration in the Caribbean in the nineteenth century. From 1838 to 1913 the most significant movement of people in the Caribbean was the arrival of indentured immigrants from India. We coded up the annualised data as a cumulative stock from Roberts and Byrne (1966). Between 1838 and 1913, cumulative net immigration was 230,000 for Guyana, 124,000 for Trinidad, 37,000 for Jamaica and small amounts for Grenada, St Lucia, Antigua and Dominica. The ratio of cumulative net immigration to 1913 population exceeded 0.15 for only two colonies, Trinidad where it was 0.37 and Guyana where it was 0.77. Restated, immigration was important in only two colonies but in those two it was indeed important. The other labour supply shock was much smaller. British West Indies workers left for Panama during the building of the canal by the French (1881–9) and Americans (1908–13) (Maurer and Yu, 2013, ch. 4). No destination-specific estimates exist of Caribbean emigration but the official numbers for overall emigration reported in the Colonial Blue Books were small throughout. We control for the Panama Canal shock with a time dummy for the years in question interacted with inverted distance as a measure of exposure to this shock. Additional Supporting Information may be found on the online version of the article: Online Appendix Replication Package Notes The data and codes for this paper are available on the Journal website. They were checked for their ability to replicate the results presented in the paper. We are especially indebted to Jim Robinson who, in the initial stages of the project when we were wallowing in case studies drawn from disparate times and places, encouraged us to focus on the British Empire and the under-exploited Colonial Blue Book data. We are also indebted to Elhanan Helpman for his encouragement in exploring the relationship between international trade and domestic institutions. We benefited from discussions with Daron Acemoglu, Lee Alston, Quamrul Ashraf, Magda Bisieda, Kyle Bagwell, Abhijit Banerjee, Stanley Engerman, James Fenske, Murat Iyigun, Sara Lowes, Karthik Muralidharan, Suresh Naidu, Luigi Pascali, Diego Puga, Manisha Shah, Shanker Satyanath, Alan Taylor, Duncan Thomas, Vitaly Titov, Francesco Trebbi and seminar participants at Boulder, CIFAR, ERWIT, Harvard (PIEP), LSE, Los Andes Namur, the NBER Development Economics Conference, PSE, Ryerson, Stanford, Toronto (Law Faculty), Toulouse, Western, the World Bank, UBC, UC Davis and UC San Diego. We thank Scott Orr, Nicolas Gendron-Carrier, Jacob Whiton and especially Jake Kantor for fantastic research assistance. A previous version of this paper was circulated under the title ‘The Rents from Trade and Coercive Institutions: Removing the Sugar Coating'. Footnotes 1 Two exceptions are Naidu and Yuchtman (2013) and Bobonis and Morrow (2014), summarised below. 2 One may think of planter influence as lobbying capacity but this is not explicitly modelled. Our own view is that legal coercion is in practice almost always the result of collective action by an elite that influences the state to regulate coercive labour laws to their benefit, e.g., to reduce rights at work, to harass workers in the informal sector or to limit worker mobility, with the ‘Black Codes’ in the post-bellum US South being a prominent example. In Section 1, we describe in detail the practical applications of legal coercion in our context. 3 During slavery, this difference did not matter: land that was unsuitable for sugar lay uncultivated even if it was very fertile. This basic explanation of the divergent post-emancipation fortunes of ex-slaves across the islands figures prominently in the literature on Caribbean history and indeed it was anticipated in the 1830s debates surrounding emancipation, see Merivale (1861, pp. 312–7), Engerman (1984, p. 137), Richardson (1997, pp. 134–5, 157–8) and Patterson (2013). 4 Lowering wages in the bad state in order to induce effort (i.e., relax workers’ incentive compatibility constraint) is easier if legal coercion simultaneously prevents the worker from walking away (i.e., relaxes the participation constraint). 5 Lastly, we naturally connect to a large literature on the Caribbean’s economic adjustment to emancipation (Eisner, 1961; Engerman, 1982; 1984). 6 See Merivale (1861, pp. 340–1), Engerman (1984, p. 134 and table 2) and Riviere (1972, p. 13). On the ‘flight’, see Hall (1978, p. 7), Engerman (1982, p. 199) and Green (1976, pp. 174–5, 198). 7 By 1865, a number of villages had been established illegally on Crown lands in the hills above Morant Bay. Tensions ran high as the government sought to limit further expansion of these villages. Things came to a head during a trespass case involving a villager who had been pasturing on an abandoned estate (Underhill, 1895, p. 59). A crowd gathered at the courthouse, violence broke out, and then quickly ignited all of Jamaica. 8 Planters also lobbied for a host of restrictions which limited worker access to affordable land with clear legal title. Large tracts of Crown land were kept off the market, made available only at artificially high prices, or sold only in large lot sizes, e.g., Craton (1997, pp. 390–3). For example, 83% of Trinidad’s landmass was owned by the Crown, yet was kept off the market for decades after emancipation (Sewell, 1861, pp. 103, 106, 133). Also, in many colonies peasants were prohibited from pooling their resources to buy plantations and bankrupt planters were pressured not to sell to smallholders (Eisner, 1961, p. 211, Craton, 1997, p. 390). 9 See House of Commons Parliamentary Papers (1839b, pp. 131, 134–6), Bolland (1981, p. 595), Dookhan (1975, p. 130) and Brizan (1984, p. 128). 10 These laws were repeatedly criticised by the governor of the Leewards in 1838 on the grounds that they were inequitable and unconstitutional, e.g., House of Commons Parliamentary Papers (1839b, pp. 61–2). 11 Carvalho and Dippel (2016) show that planters completely dominated colonial legislatures, especially in the early years of emancipation. 12 Eisner (1961, pp. 220, 221, 234) has fine-grained data on Jamaican smallholds and peasant exports. Our own calculations show that between 1850 and 1890 the share of Jamaican exports originating from freeholds and squatters rose spectacularly from 10.4% to 39.0%. 13 An acreage-based measure would be an appealing alternative, but the data are only sporadically available. 14 Sugar was unequivocally a plantation crop (Engerman, 1983). However, there is not complete consensus in the literature about the factors that made it so, and such a discussion is beyond the scope of this paper. However, we conjecture that three factors are important: (i) the sugar mill was a major capital asset that was beyond the financial reach of all but the richest members of Caribbean society (Lobdell, 1996, pp. 322, 326; Marshall, 1996, p. 73); (ii) sugar must be processed within hours of harvesting so that there was always a sugar mill either on the plantation or nearby (see Higman’s 2001, figure 2.5 map of Jamaican mills); (iii) labour demand during the sugar harvest was physically brutal (e.g., 90-hour work weeks) and conflicted with workers’ needs to harvest their own provision grounds (Higman, 1984, pp. 182–3). These factors favoured a system of production that vertically integrated harvesting with milling at a single location (the plantation) and which, in the racialised post-emancipation period, used coercion rather than overtime pay as an incentive device, i.e., these three factors favoured a plantation system. 15 The lowess smoothing faithfully reproduces the annual data. See Online Appendix Figure A.1. 16 While we do not focus on this, it is worth noting that the evolution of plantations displayed in Figure 1 also correlated tightly with the share of British whites in the Caribbean at the time. To European observers at the time, the exodus of whites was synonymous with the decline of the plantation system and the decline of the institutions that had until then characterised the British West Indies. See also Carvalho and Dippel (2016). 17 All available evidence strongly suggests that the share of other plantation crops is indeed strongly and negatively correlated with the number of smallholders and smallholder participation in exports. See, for example, Dookhan (1977, p. 136). 18 Engerman (1984, p. 137) quotes a Jamaican planter in the 1830s as arguing that emancipation ‘will be less mischievous to other colonies than ours. For in Barbados and Antigua and several other Islands the liberated slaves must work for wages or want the necessaries of life.’ 19 We defer data details to Section 3 and the Appendix sections cited therein. 20 The right panel of Figure 2 illustrates another point. The grey-shaded areas are plantations that shut down between 1790 and 1890. These were the lands that were most difficult to keep out of peasant hands and were thus a major focus of coercive interventions. 21 Falling ocean freight rates led to a shift from trade in only high unit-value products like sugar towards trade in many lower unit value products like heavy machinery exports to the USA and Europe. 22 This decline in plantation prices, particularly in sugar, was important. A previous version of this paper (Dippel et al., 2015) was about the impact of international trade (declining sugar prices) on wages, coercion and institutions. While we continue to carefully control for prices, they are no longer the focus of this paper. 23 We additionally control for other important changes in plantation labour supply in the Caribbean during this time, namely the immigration of East Indian labourers and work opportunities from the construction of the Panama Canal. See Appendix B.6. 24 World crop prices were exogenous to Caribbean production. Even for sugar, at their production peak in the early years of the data, the British West Indies produced only 18% of world sugar output and this number fell to 1% by the end of the sample. See Online Appendix Figure A.4. 25 See Appendix B.2. 26 By equating utility with income we are implicitly assuming that only the numeraire good is consumed and that all other goods are exported. 27 We note in passing that if α = 1 then |$\bar{N}=L$| so that C* = 0 for all N, which reflects the fact that coercion is an inefficient redistributive policy that would never be used if smallholders had equal say in choosing coercion. 28 This ‘Protection for Sale’ setup abstracts away from part of the collective action problem in that the level of coercion grows with the number of planters. However, planters do not solve the bigger collective action problem, namely, that of collectively restricting entry into planting and thereby preventing profits from being driven to zero. Historically, in the median colony whites represented only 1.6% of the population so that, in the highly racial colonial society, whites ‘stuck together’. Thus, empirically, there was no white collective action problem when it came to policies restricting black smallholders. 29 The classic example is the eighteenth-century Maroons operating in the mountainous interior of Jamaica. 30 From equation (6), |$\partial N^* / \partial \overline{W} = [(1-O)\pi _N(N^*)]^{-1} \lt 0$| because πN(N*) < 0. Likewise, |$\partial N^* / \partial O \lt 0$|⁠. While we do not need to sign |$\partial ^2 N^* / (\partial O \partial \overline{W})$|⁠, note that if π(N*) is linear in N in the neighbourhood of N* then an increase in O increases |$\partial N^* / \partial \overline{W} = [(1-O)\pi _N(N^*)]^{-1}$|⁠, i.e., a higher probability of revolt makes N* more sensitive to the returns from staying in England. 31 One could extend the model to include a market for plantation land. We have abstracted from this because land prices are not even remotely consistently available over time or across colonies. 32 We work with nominal wages. The Blue Books report that the major components of the cost of living were largely imported from Britain (clothing and many staples such as flour and rice) so that all 14 colonies shared a common cost of living. It follows that the cost of living deflator is absorbed in the year fixed effects used in our regressions. 33 Over 90% of the wage data are for a daily pay period and do not involve in-kind payments. Nevertheless, in Online Appendix Table F.4 we show that our results are not sensitive to adjustments for pay periods or in-kind payments. 34 Brizan (1984, p. 134) arrives at a similar number for Grenada, 1850–70. 35 Data are from the parliamentary Hansard and are available at https://hansard.parliament.uk/search. 36 The effect of immigration was statistically significant and economically large, but it only really affected two colonies. It depressed wages by 0.31 log points in Guyana (−0.028 × ln (230,000)) and by about 0.15 log points in Trinidad. 37 To put this number in context, in the USA in 2016, the stock of incarcerated was 0.7 persons per 100. 38 For instance, Caribbean historiography suggests that the unmeasured proliferation and influence of local missionaries was an important factor that encouraged civil disobedience and undermined the planters; see for example Dookhan (1977, p. 156), Lewis (1986, ch. 3), McLewin (1987, pp. 85–7) and Holt (1992, ch. 7). 39 In the model |$O_i \cdot \overline{W}_t$| appears in equation (6), though parameterised slightly differently. 40 We include both the British and non-British Caribbean in order to net out Cuba, which produced about one-third of world sugar cane in our period. 41 There was also a temporary spike in wages associated with a cholera epidemic that spread through the Caribbean in the early 1850s. 42 Results reported in Online Appendix Table H.9. 43 Before 1838, in the heyday of sugar, many plantations accumulated large encumbrances, that is, financial commitments to pay annual stipends to family members and to repay loans incurred for capital projects such as mills. After 1838, rising wages and falling sugar prices led many planters to ignore their encumbrances. They could do so with impunity because the law subordinated creditors to both the plantation owners and to the London-based merchant houses who profited from selling sugar. This and the subsequent discussion is based on Cust (1859, pp. 8–15). Cust was secretary to the West Indian Incumbered Estates Commission. See also Hall (2011, pp. 94–7). 44 These laws appear in the Blue Books. For example, most islands had regressive land and property taxes, but some taxes were levied in values, others were levied on acreage, and yet others had ad hoc qualifications such as tax adjustments for windmills, which were aimed at relieving planters. 45 Hall (2011, p. 96) gives a slightly lower number of 382. He likely pulled this number from the 1884 Royal Commission Report on the IEA, which preceded the actual ending of the IEA by five years (Crossman and Baden-Powell, 1884). To the best of our knowledge we are the first to code up the IEA records since 1884. The sales and petitions were recorded in the Colonial Office Records Series CO 318-282-50 and CO-441-2-11, respectively. 46 The IEA was passed in London but needed to be incorporated on each island to apply there. St Lucia, Guyana, Trinidad and Barbados never incorporated the IEA, and thus no IEA sales took place in those colonies (Hall, 2011, p. 97). 47 In the full panel data, the average observation (over time and across all islands with any sales) had a cumulative number of IEA sales of 28. See Figure 5. 48 Seeing as the point estimates of the effect of Nit on foodstuff tariffs are imprecise but large, we do not have the statistical power to reject that the effects of Nit and IEA salesit on tariffs are equal. In Online Appendix Table H.10 we report additional specifications where we control for general changes in public finance (revenues and expenditures) in our data. 49 For example, each grid cell in the Geographically Based Economic Data (GBED) database (e.g., Michalopoulos, 2012) has a resolution of 0.5○C latitude by 0.5○C longitude, which, at the equator, is over 3,000 square kilometres. Likewise, the crop-suitability data compiled by the FAO GAEZ project (e.g., Costinot et al., 2016) is at the 5 arc-minute level, which, at the equator, is 86 square kilometres. The smallest island in our data, Nevis, is as big as one cell in the FAO GAEZ data. The ten smallest islands in our data together fit into a single cell in the GBED database. 50 For example, “‘Profile of the Small-Scale Farming in the Caribbean’, Workshop on Small-Scale Farming in the Caribbean”, Barbara Graham (2012, IMF, page 13). 51 These data were reported in the population table. However, employment data were much more sparse because they were only occasionally reported or updated. Furthermore, it was reported at the parish level but with year-to-year variation in which parishes were reported so that aggregation to the colony level was frequently not possible. 52 The products are sugar, livestock, arrowroot, cocoa, lime juice, cotton, bananas, oranges, pimento, coffee, charcoal, lumber, coconuts, ginger, other spices (cloves, mace and nutmeg), balata (a natural tar) and asphalt. 53 This entails identifying the agro-climactic factors relevant for each crop. For example, lime has seven factors including average temperature (23–30○C is very suitable) and soil pH (6.1–6.5 is very suitable). For each crop, the relevant factors are ranked in their importance and aggregated into discrete suitability bins that reflect meaningful cutoffs in overall suitability for given crops. The details of our crop suitability coding appear in Online Appendix B and Online Appendix Tables B.1 and B.2. 54 This is closely related to the more rigorous solution to this problem in Antràs and de Gortari (2017). 55 To see this note that |$\ln \tau ^j_g =Pl_{{\textit git}}\ln \tau ^p_g + (1-Pl_{{\textit git}})\ln \tau ^s_g = \ln (\tau ^p_g / \tau ^s_g) Pl_{{\textit git}} + \ln \tau ^s_g$|⁠. Hence, |$\ln [T_{{\textit gi}} ( \tau ^j_g)^{\theta } (p_{{\textit gt}})^{\theta }] = \alpha _g A_{{\textit gi}} + \theta \ln (\tau ^p_g /\tau ^s_g) Pl_{{\textit git}} + \theta \ln \tau ^s_g D_g + \theta \ln p_{{\textit gt}}$| where Dg is a crop dummy. This explains the regressors Agi, Plgit, Dg and ln pgt. 56 This is important for another reason: most other smallhold crops (e.g., garden vegetables, roots and tubers) were perishable, and therefore do not appear in any of our export price series. It is worth noting that suitability for smallhold crops other than cotton would not have varied much across islands since these are hardy crops that could grow anywhere in the fertile Caribbean climate. This is witnessed by the fact that they were, in fact, grown everywhere; on plantations as well as in the hinterlands. 57 For example, the Vagrancy Act for St Kitts states that ‘all persons shall be deemed vagrants who [are] dwelling in any of the houses upon any plantation without the sanction of the owner or director thereof, or shall be found trespassing on the land of any plantation by attempting to cultivate … [or] have left without sufficient cause any work unfinished, which they have contracted to perform’ (House of Commons Parliamentary Papers, 1839b, p. 19). 58 The restrictive provisions of these Acts were condemned by London-appointed governors, e.g., House of Commons Parliamentary Papers (1839b, p. 41). 59 Again, classification is not neat. For example, the Virgin Islands Vagrancy Act covers attempts to burn down plantations (House of Commons Parliamentary Papers 1839b, p. 310) so that malicious injury is sometimes recorded as vagrancy. 60 These data are for January to September 1838 and so span 1 August 1838, the end of slavery. This is not an important issue because half of the convictions occurred in Antigua (the most populous colony), which had abolished slavery outright in 1834. (The remaining colonies had abolished slavery, but were in the transition apprenticeship period.) Erring on the side of caution we also report the results for the last quarter available (July, August and September, 1838). For this period, the percentage of legal coercion rises slightly to 64%. 61 Note that imprisonment for failure to pay a fine occurred, but this is not the same as saying that a prisoner could buy his or her way out of jail. 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Harding, Torfinn; Stefanski, Radoslaw; Toews, Gerhard

doi: 10.1093/ej/ueaa016pmid: N/A

Abstract We estimate the effect of giant oil and gas discoveries on bilateral real exchange rates. A giant discovery with the value of 10% of a country’s GDP appreciates the real exchange rate by 1.5% within ten years following the discovery. The appreciation starts before production begins and the non-traded component of the real exchange rate drives the appreciation. Labour reallocates from the traded goods sector to the non-traded goods sector, leading to changes in labour productivity. These findings provide direct evidence on the channels central to the theories of the Dutch disease and the Balassa–Samuelson effect. The Dutch disease theory and the Balassa–Samuelson hypothesis predict that a key mechanism through which economies adjust to windfalls or productivity shocks in the traded sector is an appreciation of the real exchange rate (Balassa, 1964; Samuelson, 1964; Corden and Neary, 1982; Eastwood and Venables, 1982; Corden, 1984). Despite the near canonical status of these theories, poor data quality and endogenous measures of resource or productivity shocks have made it challenging to provide robust empirical evidence on the appreciation channel across countries. In this paper, we estimate the appreciation channel by combining bilateral real exchange rate data with information on giant oil and gas discoveries. By exploiting the uncertainty in the timing of resource discoveries, we overcome the endogeneity problem. By using bilateral data, we obtain a vast increase in the statistical variation available for inference.1 Our exercise provides direct evidence on the appreciation channel for a wide set of countries. This complements Berka et al. (2018) and Chinn and Johnston (1996), who study eurozone countries and 14 OECD countries, respectively. We find that a country with the median discovery in our sample, 10% of a country’s GDP, experiences an appreciation of the real exchange rate of approximately 1.5% over the first ten years following a discovery. By comparison, Rogoff (1996) finds that GDP per capita in a country would have to increase by 4% (relative to the USA) in order to match this degree of appreciation. Berka et al. (2018) find that productivity in the traded sector would have to increase by 9% to generate a similar increase in the real exchange rate.2 The effect we find is thus quantitatively large. Economies also adjust to windfalls or traded-sector productivity shocks through the reallocation of labour across sectors. We provide additional direct evidence on the labour-reallocation channel and the associated changes in sectoral labour productivity by focusing on a subsample of 23 OECD countries. Following a giant discovery with the value of 10% of GDP, the employment share in the traded goods sector drops by 0.5 percentage points. Labour productivity increases by 1.8% in the traded sector, and decreases by 0.3% in the non-traded sector. To match these effects, the ratio of natural resources exports to GDP would have to increase by approximately 14%–30%, using the estimates of Kuralbayeva and Stefanski (2013).3 Again, our estimates are economically large and in line with previous results. Our contribution is threefold. First, the use of bilateral real exchange rates and unanticipated large resource discoveries allows for better identification of real exchange rate appreciation that follows such discoveries, a mechanism which is central in Dutch disease theories. More generally, we provide evidence for the Balassa–Samuelson effect if we interpret a large discovery as a productivity shock to the tradable sector (Neary, 1988).4 Second, focusing on the timing of the discovery allows us to remain agnostic about when the effects on the real exchange rate, labour reallocation and sectoral productivity occur. Arezki et al. (2017) and van der Ploeg and Venables (2013) point out that resource discoveries may have effects before production starts as agents borrow in anticipation of higher, future resource income. Engel and West (2005) find that expectation of higher future GDP can lead to nominal exchange rate appreciation. Our estimates show that appreciation and sector reallocation starts soon after the discoveries are made and before production begins, but that there is nonetheless a gradual build-up to the full effect. We emphasise this anticipation effect by constructing and calibrating a standard, dynamic, small-open-economy model. The model reproduces both the magnitudes and the paths of the real exchange rate, labour reallocation and sectoral productivity over the first ten years following a discovery but, possibly due to a lack of modelled frictions, it predicts a somewhat more rapid initial response to discoveries than what we find in the data. Third, we show that the appreciation is nearly exclusively driven by the non-tradable component of the real exchange rate. This provides strong evidence in favour of the traditional theory of real exchange rates, where prices of tradable goods are anchored internationally while prices of non-tradable goods are allowed to adjust to local conditions.5 1. Real Exchange Rates The appreciation of the real exchange rate is at the core of Dutch disease theories and is often considered to be responsible for the deterioration of the tradable goods sector, i.e., manufacturing. In this section we identify and quantify the cumulative effect of giant discoveries on the real exchange rate and its tradable and non-tradable goods component. 1.1. Structure Consider an economy which consists of mining and utilities, manufacturing as well as a non-resource non-manufacturing sector defined as the sum of agriculture (A), construction (C) and services6 (S): $$\begin{eqnarray} \text{Total Economy}=\overbrace{\underbrace{A+C+S}_{\text{Non Res. Non-Mfg. (N)}}+\underbrace{M}_{\text{Mfg. (T)}}}^{\text{Non-Resource Economy}}+\underbrace{MU}_{\text{Mining and Utilities}}. \end{eqnarray}$$(1) Throughout this paper we focus on the non-resource economy only. We treat the manufacturing sector as the traded-goods sector (T) and the non-resource non-manufacturing sector as the non-traded good sector (N).7 1.2. Exchange Rates We construct sector-specific price indices using data on one digit ISIC v.3 current and constant sectoral value-added in national currency units from the UN (2014). The IMF’s national currency–US exchange rate is used to transform the indices into comparable units. The transformed indices are then used to construct bilateral real exchange rates |$\textit {RER}^{ij}_{t}$| between country i and j in period t. Following Engel (1999) as well as Betts and Kehoe (2006; 2008), we decompose these as: $$\begin{eqnarray} \underbrace{\frac{p_{i,t}}{p_{j,t}} \vphantom{\left(\frac{p_{i,t}^T}{p_{j,t}^T}\right)} }_{\textit {RER}^{ij}_{t}} \equiv \underbrace{\left(\frac{p_{i,t}^T}{p_{j,t}^T}\right)}_{\textit {RERT}^{ij}_{t}}\times \underbrace{\left(\frac{p_{i,t}/p_{i,t}^T}{p_{j,t}/p_{j,t}^T}\right) \vphantom{\left(\frac{p_{i,t}^T}{p_{T,t}^j}\right)} }_{\textit {RERN}^{ij}_{t}}. \end{eqnarray}$$(2) Here, pi,t and |$p^T_{i,t}$| refer to the aggregate and traded-sector price indices in country i and time t. The first term on the right-hand side is the bilateral real exchange rate of traded goods, |$\textit {RERT}^{ij}_{t}$|⁠. It measures any deviations from the law of one price or differences in the composition of baskets of traded goods across countries. The second term in the above is a ratio of internal relative prices, denoted by |$\textit {RERN}^{ij}_{t}$|⁠. As is emphasised by Betts and Kehoe (2008), we could write this as: $$\begin{eqnarray} \textit {RERN}^{ij}_{t}= \frac{p_{i,t}(p_{i,t}^T,p_{i,t}^N)/p_{i,t}^T}{p_{j,t}(p_{j,t}^T,p_{j,t}^N)/p_{j,t}^T}, \end{eqnarray}$$(3) where |$p_{i,t}^N$| is a price index for non-traded goods in country i, and we make explicit the dependence of pi, t on the indices of both traded and non-traded goods. The functional form of |$\textit {RERN}^{ij}_{t}$| however depends on how statistical offices in each country construct aggregate price indices.8 To circumvent the need to assume a functional form or to measure the prices of non-traded goods, we follow Betts and Kehoe (2008) and use the equational form in (2) to calculate |$\textit {RERN}^{ij}_{t}$|⁠. Thus, we can decompose the real exchange rate into the tradable and non-tradable components just from data on traded goods price indices and aggregate price indices. Our sample covers N = 172 countries over the period 1970–2013. Not double-counting country pairs, the number of unique observations per year is |$\frac{N^{2}-N}{2}=14,\!706$|⁠. Using all available information gives us 12,536 unique country pairs and a total of 383,934 observations. See Table A.1 in the Online Appendix for a snapshot of the data. 1.3. Giant Oil and Gas Discoveries Information on the timing of individual giant oil and gas discoveries, as provided by Horn (2011), is essential for our study for two reasons. First, we need the timing of discoveries since we are interested in understanding Dutch disease dynamics and what happens to outcome variables between a discovery and the start of production. Second, the difficulty in anticipating discoveries places the timing of these discoveries at the centre of our identification strategy. We follow Lei and Michaels (2014) and Arezki et al. (2017) in arguing that discoveries are plausibly exogenous due to the uncertainty surrounding exploration and future technology developments, once we control for country and year fixed effects and previous discoveries.9 Countries and exploration companies are unlikely to make such discoveries, as only about 2% of the exploration wells in a global data set starting in 1965 turned into giant discoveries (Toews and Vezina, 2017). Consequently, predicting the exact timing of a giant oil discovery is difficult, even for the operating companies. Figure 1(a) presents the relationship between the real price of oil and the total number of giant discoveries. Note that the number of discoveries is uncorrelated with the real price of oil, with a correlation coefficient below 0.02 and a p-value of 0.9, increasing the confidence in our identification strategy. Fig. 1. Open in new tabDownload slide Overview of Giant Oil and Gas Discoveries. Our main measure of treatment is the net present values of giant oil and gas discoveries relative to GDP in country i and period t, |$d^i_{t}$|⁠, which we received from Arezki et al. (2017). The raw data on discoveries contains information on the timing, the location and the estimated total ultimately recoverable amount of oil and gas (Horn, 2011). To calculate the net present value of each discovery at the date of discovery, Arezki et al. (2017) combine the data from Horn (2011) with a generic approximated oil production profile, the nominal oil price at the date of discovery and a country specific interests rate to discount future revenues. They normalise the resulting value on nominal GDP measured at the date of discovery.10 The calculated values are presented in Figure 1(b). Between 1970 and 2013, 302 giant discoveries were made in 56 countries. The average and median size of discoveries is 67% and 10% of GDP, respectively. We use |$\delta ^i_t=1+d^i_t$| as a simple monotonic transformation of the discovery measure d above and define a bilateral measure of discoveries: $$\begin{eqnarray} D^{ij}_t\equiv \log \left(\frac{\delta ^i_t}{\delta ^j_t}\right). \end{eqnarray}$$(4)D is robust to zeros in the denominator and symmetric in that a discovery in country i and country j have the same quantitative impact, but opposite signs: |$\frac{\partial D^{ij}_t}{\partial \log (\delta ^i_t)}=-\frac{\partial D^{ij}_t}{\partial \log (\delta ^j_t)}=1$|⁠. 1.4. Estimation Strategy We estimate the following specification: $$\begin{eqnarray} gX^{ij}_t= \sum _{k=-5}^{10} \beta _k D^{ij}_{t-k}+ \eta ^{ij}+\rho _t +\varepsilon ^{ij}_{t} . \end{eqnarray}$$(5) Our dependent variable is the growth in the bilateral real exchange rate which we define as the change in the natural log of the real exchange rate and its components: |$gX^{ij}_t\equiv \log (X^{ij}_{t})-\log (X^{ij}_{t-1})$|⁠, where X = RER, RERT, RERN. Country-pair and time fixed effects are represented by ηij and ρt respectively. The latter capture global shocks. Since our dependent variables are growth rates, country-pair fixed effects capture trends in relative prices between the two countries. Thus, we study the impact of giant discoveries on deviations from country-pair specific trends. The βk terms represent the year-to-year growth effect of discoveries k periods after the discovery. We are interested in the cumulative effect of a discovery on the real exchange rate k periods after a discovery in period t, which is the sum of the year-to-year growth effects for the years t to t + k. Thus, we estimate the cumulative effect of an oil discovery on the real exchange rate via summation, |$\Omega _k=\sum _{j=1}^k \beta _j$|⁠, and use these to construct 95% and 90% confidence bands. Symmetrically, we present the cumulative estimates by adding up the βk’s of the leads: |$\Omega _{-k}=\sum _{j=-1}^{-k} \beta _j$|⁠.11 The country-pair specific error, |$\varepsilon ^{ij}_t$|⁠, is allowed to arbitrarily correlate with errors of other bilateral pairs containing either country i or country j (two-way clustering). 1.5. Results The main results are displayed in the three charts of Figure 2. The solid lines show the cumulative impulse response Ωt∈[1, 10] to a giant discovery, while the dashed and the dotted lines indicate 90% and 95% confidence intervals. The first chart depicts the cumulative response of the real exchange rate to a giant discovery. In the second and third charts we decompose the effect on the real exchange rate into the effect on the tradable and the non-tradable component, respectively. First of all, note that in the periods before the discoveries, indicated by the vertical line, there is no apparent and statistically significant difference in price changes in the countries which are about to be treated relative to the control group. This is important since the implicit assumption allowing us to interpret our results as causal is that prices in the treated and control group follow a similar trend in the absence of a discovery. In case of the prices of tradable goods we do not observe any significant divergence in prices following a discovery. Thus, we conclude that consistent with standard economic theory, prices of tradable goods remain unaffected by country-specific shocks. On the other hand, the third chart shows that discoveries positively affect the non-tradable goods component of the real exchange rate. The results imply that ten years after a median-sized discovery (10% of GDP) the non-tradable goods component of the real exchange rate increases by 1.7%.12 Also note that the prices of non-tradable goods component start increasing immediately following the discovery and are already significantly higher in the treated group by the time production typically starts, four to six years following the discovery (Arezki et al., 2017). This is in line with the idea that forward-looking agents may borrow and spend in anticipation of a higher future resource income before production starts, i.e., Dutch disease dynamics. Fig. 2. Open in new tabDownload slide Cumulative Effect of Large Discoveries on the Real Exchange for All Countries. Notes: All results include country-pair fixed effects and year fixed effects. The left-hand side (LHS) variable is either the change in the logged real exchange rate between two countries, the change in the tradable or the change in the non-tradable component of the logged real exchange rate. The solid line is the sum of year-to-year growth effects for the years t to t + k. The cumulative effect is calculated by adding βk’s which are estimated in equation (5): |$\Omega _k=\sum _{j=1}^k \beta _j$|⁠. Symmetrically, we present the cumulative estimates by adding up the βk’s of the leads: |$\Omega _{-k}=\sum _{j=-1}^{-k} \beta _j$|⁠. The dashed and the dotted lines represent the 90% and the 95% confidence intervals. To calculate the confidence intervals we employ a two-way clustering which allows the errors to correlate arbitrarily with errors of other bilateral pairs containing one of the countries within the pair. Consistent with the discussion above we find that the real exchange rate starts appreciating following a discovery. And while the cumulative effect on the real exchange rate is measured imprecisely we find that the exchange rate appreciates by 1.6% within ten years following a median-sized discovery. The magnitude of the real exchange rate appreciation is nearly identical to the appreciation of the non-tradable goods component of the real exchange rate. By comparing the three charts, it is apparent that the appreciation of the real exchange rate is entirely driven by its non-tradable goods component. Note that the large confidence interval originates in the imprecise estimation of the effect on the prices of tradable goods. This is consistent with the well-documented results that most of the variance in the bilateral exchange rates is attributable to fluctuations in the real exchange rate of traded goods (Engel, 1999). 1.6. Robustness In Online Appendix A we present a battery of robustness tests for our main results. First, we reproduce Figure 2 by adjusting our measure to taxation. In particular, we use tax data from Wood MacKenzie to estimate country-specific taxes, using total government take as our measure for the amount of taxes collected, to adjust the measure provided to us by Arezki et al. (2017) in attempt to control for differences in the proportion of the value of discoveries that accrue to government. The results are slightly larger but do not differ significantly from our baseline result as shown in Figure A.1. Second, instead of using the GDP adjusted measure of discoveries we reproduce our main results using time dummies. This allows us to address potential endogeneity concerns and measurement issues with the discovery measure by focusing exclusively on the timing of discoveries. The results are presented in Figure A.2 for the full sample and for the OECD subsample defined in the next section. Third, to examine whether our results are spurious, we conduct a randomisation test by randomly reallocating discoveries across countries and time. The distribution of point estimates from re-estimating equation (5) with the artificial data is symmetric and centred at zero, indicating that our econometric model is unlikely to produce spurious results (see Figure A.3). Fourth, we show that the results are robust to changing the treatment and control group by varying the number of lags and by reducing the sample to countries which had at least one giant discovery since 1970 (see Figures A.4 and A.5). Fifth, in Figure A.6 we control for cumulated past discoveries to account for potential path-dependence in discoveries. Sixth, we drop the top and the bottom 1% of the dependent variable to account for outliers (see Figure A.7). Seventh, to ensure that our results are not sensitive to specific sector classifications, we use alternative definitions of tradable and non-tradable goods and present the results in Figures A.8 and A.9. In all the robustness tests presented in Figures A.1–A.9, the results remain unaffected. Eight, following Betts and Kehoe (2008), we use producer prices as alternative price measures. The results are presented in Figure A.10. The magnitudes remain in line with our baseline specification, but the error bands are wider in this smaller sample. Finally, we also estimate the effect of oil discoveries on unilateral real effective exchange rates confirming our results (see Figure A.11). 2. Labour Reallocation and Productivity Economies adjust to resource windfalls not only through price changes, but also through the reallocation of factors across sectors. In this section we identify and quantify the effect of giant discoveries on the reallocation of labour as well as the associated changes in labour productivity for a subsample of countries. 2.1. OECD Sample To explore the reallocation channel we focus on countries that were OECD members by 1973.13 We restrict our analysis to these countries since our identification strategy relies on time-series variation which requires comparable, high-quality data going back to the beginning of our sample. Countries in this sample had the capacity and an explicit agenda to collect comparable sector-level data as early as 1970 (den Butter, 2007). Finally, it is important to emphasise that approximately 25% of the 302 giant discoveries between 1970 and 2013 were made by nine countries in this sample leaving us with enough variation for identification. 2.2. Employment Data We obtain sectoral employment data for 1970 to 2013 from the ILOSTAT online database, which is based on population censuses, national labour force surveys as well as official estimates.14 We use these data to compute employment shares of the traded and non-traded sector in each country. Using all available information gives us data on 23 countries up to 43 years and a total of 878 observations. 2.3. Productivity Data We construct data on sectoral labour productivity for 1970 to 2013. We obtain one digit ISIC v.3 sectoral value-added data from the UN in constant (2005) US dollars. Following the procedure outlined in Kuralbayeva and Stefanski (2013), we convert this into constant (2005) international (or PPP) dollars using country-sector specific price-level data from the World Bank’s 2005 International Comparison Program (ICP). Finally, we calculate value added per worker in constant (2005) international dollars in the traded and non-traded sectors by combining this data with the employment data described above. Using all available information gives us 878 observations. See Table A.2 in the Online Appendix for descriptive statistics. 2.4. Estimation Strategy As before, our identification strategy relies on the timing of giant discoveries and we emphasise the exogeneity of the timing by providing five year-long pre-trends. However, whereas before our focus was on price difference across countries over time, here we focus on sector level differences within the same country and, thus, we estimate the following specification: $$\begin{eqnarray} gX^{i}_t= \sum _{k=-5}^{10} \beta _k \log (\delta )^{i}_{t-k}+ \eta ^{i}+\rho _t +T^{i}_{t}+\varepsilon ^{i}_{t}. \end{eqnarray}$$(6) Here our LHS variable, |$gX^{i}_t$|⁠, is a placeholder for the employment share changes in the tradable sector, labour productivity growth in the tradable sector or labour productivity growth in the non-tradable goods sector in country i.15 Our measure of discoveries is now the unilateral, monotonic transformation of the discovery measure d—discussed in the previous section. Country fixed effects and time fixed effects are captured by ηi and ρt respectively. In our preferred specification we also add a country specific linear trend, Ti, to capture the systematic evolution of sectoral employment and productivity associated with structural transformation (see for example Herrendorf et al., 2014 or Lagakos and Waugh, 2013).16 As before, the βk terms represent the semi-elasticities of discoveries k periods away from the discovery which we add up according to the following formula |$\Omega _k=\sum _{j=1}^k \beta _j$| for the lags and according to the following formula |$\Omega _{-k}=\sum _{j=-1}^{-k} \beta _j$| for the leads. The country-specific error is |$\varepsilon ^{i}_t$| and standard errors are clustered on the country level. 2.5. Results The results are presented in Figure 3. The first row emphasises that our previous findings with respect to the bilateral real exchange rates remain quantitatively and qualitatively unchanged in this particular subsample: a discovery with the value of 10% of a country’s GDP leads to a 1.5% appreciation of the real exchange rate.17 Furthermore, unlike in the full sample, the result on the real exchange rate is significant at the 5% level. Fig. 3. Open in new tabDownload slide Cumulative Effect of Large Discoveries on the Real Exchange, Labour Shares and Productivities in OECD Subsample. Notes: Results are based on the subsample of OECD countries defined in the text. The LHS variable in the first row is either the change in the logged real exchange rate between two countries, the change in the tradable or the change in the non-tradable component of the logged real exchange rate. All results include country-pair fixed effects and year fixed effects. The LHS variable in the second row is either the change in the traded sector labour share, changes in traded sector labour productivity or changes in the non-traded sector labour productivity. All results include country fixed effects, year fixed effects and a country-specific linear trend. (See Figure A.12 in the Online Appendix for the results without the trend.) The solid line is the sum of year-to-year growth effects for the years t to t + k. The cumulative effect is calculated by adding βk’s which are estimated in equation (6): |$\Omega _k=\sum _{j=0}^k \beta _j$|⁠. Symmetrically, we present the cumulative estimates by adding up the βk’s of the leads: |$\Omega _{-k}=\sum _{j=-1}^{-k} \beta _j$|⁠. The dashed and the dotted lines represent the 90% and the 95% confidence intervals. To calculate the confidence intervals we employ a two-way clustering in the first row. This allows the errors to correlate arbitrarily with errors of other bilateral pairs containing one of the countries within the pair. We cluster the standard errors on the country level in the second row. Next, we turn to the estimation of employment and productivity effects of giant oil and gas discoveries. At the core of Dutch disease theories is the idea that an increase in income leads to higher spending and a reallocation of labour from the traded to the non-traded sector. In the first chart of the second row we provide evidence for the presence of this mechanism by exploring the effect on the employment share in the traded sector (see equation (1) for the definition). Changes in employment shares before the discovery do not differ significantly between the treated group and the control group. But following the discovery, labour shares in the tradable goods sector decreases relative to the control group. In particular, a median discovery decreases the employment share in the traded sector by 0.45 percentage points. Since the average country employs 14% of its labour force in the traded sector, our results suggest that traded-sector employment drops by 4% in the first ten years following a median discovery. Also note that by the time production typically starts approximately five years following the discovery, more than 50% of the ten-year cumulative effect has already occurred. This, once again, indicates that Dutch disease dynamics begin to operate well before production starts. We also report the effect of discoveries on labour productivity in the respective sectors in the two bottom-right charts. We focus on labour productivity both because models of Dutch disease offer stark predictions with respect to this measure (see Kuralbayeva and Stefanski, 2013 or the model in Online Appendix B) but also because—lacking sufficiently high-quality wage data going back to 1970—under minimal assumptions these measures can be interpreted as constant-price sectoral wages.18 A median discovery increases labour productivity in the traded sector by 1.8% and decreases it in the non-traded sector by 0.3%. Finally, to address potential endogeneity and measurement concerns related to our measurement of discoveries, we reproduce the results by replacing our discovery measure with time dummies. Results are qualitatively similar and are presented in Figure A.13. 3. Theory To put our estimates in perspective we summarise the empirical results of the previous section in rows 1 and 2 of Table 1 and compare them to the theoretical predictions of a calibrated model in the bottom row. These theoretical results are based on a simple, small-open-economy model calibrated to the experience of Canada—arguably a small, open and resource-rich country. The model, presented in Online Appendix B, is designed to capture the main mechanisms of the original model by Corden and Neary (1982). The real exchange rate is entirely driven by changes in the prices of non-tradable goods, labour can move freely to equalise the marginal revenue products across sectors and capital is sector-specific. In contrast to the original model we allow for forward-looking behaviour and borrowing to capture Dutch disease dynamics which have been emphasised by van der Ploeg and Venables (2013). In that setting, a discovery may trigger an increase in spending long before production starts. Intuitively, agents expecting future windfalls borrow from abroad to smooth consumption and hence increase their spending on tradable and non-tradable goods. While higher demand for tradable goods can be satiated by imports from abroad, more workers must be employed in the non-tradable sector to meet the higher demand for locally produced non-tradable goods. In order for this to happen, prices of non-tradable goods rise, increasing the wages in the non-tradable sector and pulling workers out of the tradable sector into the non-tradable sector. The reallocation of workers in the presence of a fixed factor leads to lower labour productivity in the non-traded sector and higher labour productivity in the traded sector. Notice that the response to the discovery in our model is not instantaneous, since there is a debt-elastic interest rate that increases with borrowing. This prevents agents from perfectly smoothing expected future revenues. We find that our empirical estimates match the predictions of the model very well, except that the instantaneous adjustments at the time of discovery are more muted in the data than in the model. Table 1. Summary of Responses to Giant Resource Discovery (Equivalent to 10% of GDP) After Ten Years. Responses . RER . RERT . RERN . Mfg. emp. sh. . Mfg. prod. . Non-mfg. prod. . Data (full) 1.6% −0.1% 1.7% – – – Data (OECD) 1.5% 0.3% 1.2% −0.45pp 1.8% −0.3% Model 1.4% 0% 1.4% −0.70pp 1.4% −0.3% Responses . RER . RERT . RERN . Mfg. emp. sh. . Mfg. prod. . Non-mfg. prod. . Data (full) 1.6% −0.1% 1.7% – – – Data (OECD) 1.5% 0.3% 1.2% −0.45pp 1.8% −0.3% Model 1.4% 0% 1.4% −0.70pp 1.4% −0.3% Notes:The model estimates are well within the 90% confidence bounds of our estimates. Open in new tab Table 1. Summary of Responses to Giant Resource Discovery (Equivalent to 10% of GDP) After Ten Years. Responses . RER . RERT . RERN . Mfg. emp. sh. . Mfg. prod. . Non-mfg. prod. . Data (full) 1.6% −0.1% 1.7% – – – Data (OECD) 1.5% 0.3% 1.2% −0.45pp 1.8% −0.3% Model 1.4% 0% 1.4% −0.70pp 1.4% −0.3% Responses . RER . RERT . RERN . Mfg. emp. sh. . Mfg. prod. . Non-mfg. prod. . Data (full) 1.6% −0.1% 1.7% – – – Data (OECD) 1.5% 0.3% 1.2% −0.45pp 1.8% −0.3% Model 1.4% 0% 1.4% −0.70pp 1.4% −0.3% Notes:The model estimates are well within the 90% confidence bounds of our estimates. Open in new tab 4. Conclusion We provide robust evidence for an appreciation of the real exchange rate in response to a large oil or gas discovery. A discovery equivalent in value to 10% of a country’s GDP causes the real exchange rate to appreciate by 1.5% within ten years. Consistent with traditional theories of exchange rates, we find that the appreciation is almost exclusively driven by the non-traded component of the real exchange rate. We also provide evidence for the reallocation of labour from the traded to the non-traded sector. In particular, we find that following a median discovery, half a percentage point of the total labour force reallocates from the tradable to the non-tradable goods sector within ten years. Finally, we provide additional evidence on changes in sectoral labour productivity associated with this reallocation. Following a median discovery, labour productivity rises by 1.8% in the traded sector and decreases by 0.3% in the non-traded sector. Importantly, the empirical findings match very well with the predictions of a standard, small-open-economy model of exchange rates. This paper thus provides the first direct evidence of the key appreciation and reallocation channels central to both the Dutch disease and the Balassa–Samuelson literature, in the framework of a quasi-natural experiment. Additional Supporting Information may be found in the online version of this article: Online Appendix Replication Package Notes The data and codes for this paper are available on the Journal website. They were checked for their ability to replicate the results presented in the paper. We would like to thank Rabah Arezki for generously sharing the data on giant oil discoveries. We would also like to thank an anonymous referee, Junior Maih, Marta Troya Martinez, Peter Neary, Ferdinand Rauch, Morten O. Ravn, Rick van der Ploeg, Anthony Venables and Pierre-Louis Vézina as well as seminar and conference participants at NHH, OxCarre, the Oxford Trade seminar, the OxCarre/NHH/UiS workshop in Stavanger, CAMP’s workshop at BI Oslo, CSAE 2018, WCERE 2018, RES 2018, ICEE 2018 and NES 2018 for useful comments. Support from the BP funded Oxford Centre for the Analysis of Resource Rich Economies (Oxcarre) and the Equinor chair in Economics at NHH is gratefully acknowledged. Footnotes 1 The bilateral real exchange rate has been used by Betts and Kehoe (2006; 2008), Engel (1999) as well as Imbs et al. (2005). Much of the remaining literature focuses on real effective exchange rates—trade-weighted averages of bilateral real exchange rates (Chen and Rogoff, 2003; Caahin et al., 2004). 2 Rogoff (1996) estimates that a country’s price level relative to the USA increases 0.366% as the country’s GDP per capita increases 1% relative to the USA (0.366 × 0.04 ≈ 0.015). Berka et al. (2018) estimate that a 1% increase in the productivity of the traded goods sector leads to a 0.18% appreciation of the real exchange rate (0.18 × 0.09 ≈ 0.015). 3 Kuralbayeva and Stefanski (2013) estimate that as a country’s resource-export share rises by 1%, manufacturing employment share decreases by 0.0169 percentage points (0.0169 × 30 ≈ 0.5), traded-sector labour productivity rises by 0.097 percent (0.097 × 19 = 1.8) and non-traded-sector labour productivity falls by 0.02 percent (0.021 × 14 = 0.3). 4 Many other papers have explored this mechanism in the context of the Balassa–Samuelson literature and found that this hypothesis does best in explaining real exchange rates in the longer run (Chinn and Johnston, 1996; Tica and Družić, 2006; Lothian and Taylor, 2008; Chong et al., 2012). For a review of this literature, see Taylor and Taylor (2004). Focusing on the variation in natural resource wealth, a variety of papers have examined Dutch disease predictions empirically by exploring the effects on employment and wages of traded and non-traded sectors (Ismail, 2010; Kuralbayeva and Stefanski, 2013; Smith, 2019), non-resource trade (Harding and Venables, 2016) as well as movements in real exchange rates (Chen and Rogoff, 2003; Caahin et al., 2004; Bjørnland and Thorsrud, 2016). These studies, however, either use endogenous resource measures or do not fully exploit the available cross-country variation for identification and provide quantitatively and qualitatively diverging results. There is also a literature exploiting the within country spatial variation and the reallocation of labour within a country (Beine et al., 2014; Allcott and Keniston, 2017; Aragón et al., 2018). While these papers typically improve on the empirical identification and the data quality, their results have little to add to the discussion on real exchange rate movements and traded-sector employment on the country level. 5 Traditional theories of the real exchange rate go back to Cassel (1918) and Pigou (1923). More recently papers by Rebelo and Vegh (1995), Stockman and Tesar (1995) or de Cordoba and Kehoe (2000) examine how sectoral productivity, demand or trade shocks can cause changes to non-traded goods prices, which then drive fluctuations in real exchange rates. 6 Services are defined as the sum of transportation, storage, communication, wholesale, retail, restaurants, hotels and other services. 7 Altering the sectoral specification by moving agriculture to the traded sector or considering only services as the non-traded sector does not affect our results. 8 For example, if we were to assume that |$p_{i,t}(p_{i,t}^T,p_{i,t}^N)=(p_{i,t}^T)^{\gamma _i} (p_{i,t}^N)^{1-\gamma _i}$|⁠, then |$\textit {RERN}^{ij}_{t}$| is an explicit function of relative internal prices, |$\textit {RERN}^{ij}_{t}=\frac{(p_{i,t}^N/p_{i,t}^T)^{1-\gamma _i}}{(p_{j,t}^N/p_{j,t}^T)^{1-\gamma _j}}$|⁠. 9 In contrast, more common measures of endowments such as resource wealth or exports are seen as endogenous. Brunnschweiler and Bulte (2008) and van der Ploeg and Poelhekke (2010) discuss this endogeneity in the context of the resource curse. Cust and Harding (forthcoming) focus on the quality of institutions as a source of endogeneity. 10 See equation (11) in Arezki et al. (2017) for the exact formula of the measure we use. 11 Note that this allows us to test for diverging pre-trends between the treatment and the control group before the discovery. Diverging pre-trends would indicate that we should be careful with the causal interpretation of our results. However, as will be shown throughout the paper, the pre-trend development of all outcomes in countries which are about to have a discovery is statically indistinguishable from the pre-trend developments in the control group. 12 From chart 3 of Figure 2, |$\Omega _{10}=\sum _{j=1}^{10} \beta _j=0.18$|⁠. The impact of a median discovery is thus |$0.017\approx 0.18\times \log (\frac{1+0.1}{1})$|⁠. 13 The sample consists of the following OECD countries: Australia, Austria, Belgium, Canada, Denmark, France, Germany, Greece, Iceland, Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK and USA. 14 We combine the ISIC revisions 2, 3 and 4 of the employment data. 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This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. © The Author 2020. Published by Oxford University Press on behalf of Royal Economic Society.

Herresthal,, Claudia

doi: 10.1093/ej/ueaa036pmid: N/A

Abstract I study students’ inferences about school quality from performance-based rankings in a dynamic setting. Schools differ in location and unobserved quality; students differ in location and ability. Short-lived students observe a school ranking as a signal about schools’ relative qualities, but this signal also depends on the abilities of schools’ past intakes. Students apply to schools, trading off expected quality against proximity. Oversubscribed schools select applicants based on an admission rule. In steady-state equilibrium, I find that rankings are more informative if more able applicants are given priority in admissions or if students care less about distance to school. Every year, school rankings are released to help prospective students compare schools in terms of the quality of their teaching. However, schools are ranked based on their performance, which depends on not only their intrinsic qualities but the ability of their past student intakes.1 This article studies how students learn about schools’ qualities from rankings if they cannot observe which schools had the most able intakes in the past.2 In addition, I analyse how features of the admission and application process affect student intakes and, therefore, influence how informative rankings are about school quality. I use a dynamic setting to study the interaction between student intakes and rankings. In each cohort, students first observe a ranking of schools and then apply to one of two schools of unknown quality. A school admits all applicants unless it is oversubscribed, in which case it selects among applicants based on an exogenously given admission rule. The probability that a school ranks high depends both on its quality and on the ability of its student intake in the previous cohort. In particular, if intakes across schools were equally able, then the better school is more likely to rank highly. In addition, if a school had a more able intake, its chances of ranking highly increase, irrespective of its quality. Specifically, if the worse school’s intake was sufficiently more able, the ranking is a misleading indicator of quality: the worse school is more likely to rank highly than the better school. Students do not observe past intakes or past applications. I study how schools’ admission rules affect students’ learning about school quality over time. Recent changes to the School Admissions Code in England have restricted the share of students admitted based on ability,3 and it has been argued that assigning more equal intakes across schools would make it more likely that differences in school quality are reflected in rankings.4 This seems intuitive at first. Suppose that a school’s admission rule gives priority to higher-ability applicants when a school is oversubscribed. If students believe that the high-ranked school is more likely to be better, then the high-ranked school will be oversubscribed and admit a more able intake than the other school. Therefore, we could end up in a situation in which the worse school persistently ranks high because its lower quality is covered up by a steady intake of more able students. Despite this, I show that, over time, students are strictly more likely to infer correctly which school is of better quality if the admission rule gives priority to higher-ability applicants than if it assigns equally able intakes to each school. To gain some intuition for why this holds, let us consider the following example. Each cohort consists of two students: one of high ability and one of low ability. Each school has capacity for one student. If both students apply, the high-ability student is accepted and the low-ability student attends the other school. A priori, students believe that each school is equally likely to be better. In period 0, the high-ability student is equally likely to attend either school.5 Students in period 1 observe the ranking in period 0. Since the better school was equally likely to teach the high- or the low-ability student in period 0, students in period 1 infer that the high-ranked school is more likely to be better. Hence, both students apply to the high-ranked school and the high-ability student is accepted. Then students in period 2 observe the ranking in period 1. Although they do not observe where the high-ability student in period 1 applied or enrolled, they conjecture correctly that he was more likely to attend the better school than the high-ability student in period 0. Therefore, they infer that the better school is even more likely to rank highly in period 1 than in period 0. Consequently, students in period 2 are more likely to identify the better school correctly than students in period 1, even though both cohorts observe only the most recent ranking. If an oversubscribed school instead accepted the high- or the low-ability student with equal probability in each cohort, students in period 2 would be no better informed than students in period 1.6 Indeed, even in the event that the worse school ranks high initially, students are more likely to identify correctly which school is better over time if the admission rule prioritises high-ability applicants. It is true that, once the worse school ranks high, it is more likely to rank highly again if it admits a more able intake than the other school. However, the worse school will not hold on to the high rank forever. In addition, once the better school ranks high, it will also be more likely to rank highly again if it admits a more able intake than the other school. In this event, not only the more able intake but also the superior quality work in favour of the better school. This implies that the better school is more likely to maintain a high rank than the worse school. Hence, over time, the better school is more likely to rank highly, and the ranking is more likely to reflect schools’ relative quality accurately if the admission rule prioritises high-ability applicants. In addition, I study how students’ learning about school quality is affected by the extent to which students perceive schools to be horizontally differentiated, whether due to their location, specialisation or other factors. I introduce horizontal differentiation by assuming that students are distributed along a Hotelling line between the two schools and that each student incurs a transport cost proportional to the distance to the school that he attends. Therefore, a student may face a trade-off between attending a school that is closer and one that is of higher expected quality.7 I show that students are better informed about the relative quality of schools if the distribution of transport costs shifts down (in the sense of first-order stochastic dominance (FOSD)), i.e., if students perceive schools to be less horizontally differentiated. Recent school choice reforms can be represented by a decrease in transport costs, since they allow students to attend a non-local school instead of requiring them to move into the school’s catchment area. Therefore, my findings show that school choice reforms interact with performance-based rankings to make it easier for students to identify better schools. Finally, I study what role students’ inference about school quality plays in the context of quasi-market reforms implemented in both the United States and the UK. The idea behind these reforms is to mimic a market mechanism by linking a school’s funding to the demand for its places, thereby putting pressure on unpopular schools to make changes or shut down. Clearly, these reforms are more effective at improving school quality if worse schools are less popular but, crucially, this depends on how well students can identify which schools are worse. My framework is well suited to studying the dynamic interaction between students’ inference about school quality from rankings, which affects demand for places, and the supply-side response, which affects the qualities of schools. I find that introducing such a policy improves the average quality of schools, and improves access to good schools for students of any ability level. However, in the presence of such policies: (i) if the admission rule assigns a larger share of spaces at an oversubscribed school based on ability; or (ii) if transport costs are lower, the average quality of schools improves further, but the additional benefit may accrue only to high-ability students. This shows that the regulation of admission rules can affect the overall quality of schools, whereas most policy discussions assume that admission rules have purely redistributive effects. This article is structured as follows: Section 1 outlines the model. Sections 2 to 4 solve for equilibrium and conduct comparative statics and welfare analysis. Section 5 studies quasi-market reforms. Section 6 contains robustness checks and Section 7 concludes. Omitted proofs are in the Online Appendix. Related Literature My article relates to the observational learning literature, e.g., Bikhchandani et al. (1992), because it studies a setting in which the inference by agents in the present is influenced by the choices of agents in the past. Past agents’ choices are usually assumed to be observable and they convey information about past agents’ private signals. My article is the first to derive comparative statics when agents observe a limited window of realisations of a public signal, whose distribution depends on past agents’ choices. A limited window of observations is also studied by Lobel et al. (2007), but their focus is on conditions for convergence. Callander and Hörner (2009) propose a steady-state analysis, but agents infer information from the relative frequency with which actions were taken by predecessors. In addition, my article relates to Meyer (1991)’s work on biased contests, where a decision-maker (DM) sequentially designs contests to learn which of two (non-strategic) workers is of higher ability. The DM optimally assigns the bias in the last contest in favour of the worker whom he believes to be of higher ability. The reason is that, if this worker loses despite the bias being in his favour, this is strong evidence that he is of lower ability. In my article, learning about school quality improves if the school of higher expected quality admits a more able intake and, hence, enjoys a bias in its favour. However, the reason is different because students cannot condition their application choices on whether the better-performing school had a more able intake in the past. In addition, intakes are not assigned by a forward-looking DM, but determined by the application choices of short-sighted students who do not care about their effect on future rankings. A key contribution of my article is to derive a tractable model for the endogenous link between a school’s rank and its pool of applicants. Gavazza and Lizzeri (2007) study the impact of making information about school quality public, assuming that otherwise higher-ability students are more likely to be informed about which school is better than low-ability students. They find that the effect on student allocation depends on whether schools select students based on ability. I show that when students infer school quality from rankings, policymakers cannot choose the admission rule without also affecting how informed students are about the quality of schools. De Fraja and Landeras (2006) study effects on attainment when students choose between schools based on rankings, but their focus lies on the incentives for schools to exert effort while the average intake ability at each school is assumed to vary exogenously with schools’ relative performance. My article also relates to the literature on matching algorithms, which derives optimal algorithms assuming that students have complete information about schools, e.g., Abdulkadiroglu and Sönmez (2003). Yet if students are incompletely informed about schools’ qualities, the student allocation today may influence future students’ beliefs about schools’ qualities and, hence, the preferences submitted to the algorithm. In addition, this insight has not been taken into account by empirical estimation strategies identifying how sensitive consumers’ demand is to quality, e.g., by Black (1999); Bayer and McMillan (2010); Hastings and Weinstein (2008); Burgess et al. (2015); and Imberman and Lovenheim (2016) in the context of education; and by Gaynor et al. (2016) in the context of health care. My article’s predictions are also consistent with empirical evidence by Chandra et al. (2016), who study the allocation of patients to US hospitals and with findings by Hoxby (2009) who analyse the allocation of students to US colleges. This will be discussed further in Section 3 after the main results have been presented. 1. Model Time is discrete and the horizon is infinite t = 0, 1, …. A population of students is located on the interval [0, 1]. The population comprises a unit mass of high-ability and a unit mass of low-ability students. A student’s type is given by (λ, α), where λ ∈ [0, 1] is the student’s location and α ∈ {H, L} is his ability, where H is high and L is low. The distribution of location parameter λ is continuous, symmetric about |$\lambda =\frac{1}{2}$| and independent of ability. Each student lives for one period. There are two schools: school 0 and school 1. School i is located at position i ∈ {0, 1} on the unit interval. There are two equiprobable states of the world: ω0 and ω1, where state ωi means that school i is of better quality. The state is drawn at the start of period 0 and is unobserved.8 An action a ∈ {a0, a1} for a student is to apply to school 0 or 1. A local student for school i ∈ {0, 1} is a student whose nearest school is school i. Each school has a capacity of unit mass. Schools are non-strategic and admit students based on the following admission rule. Each school admits all applicants unless a school has received more than a unit mass of applicants and is oversubscribed. If oversubscribed, a school uses the following rule: first, it admits all local high-ability applicants and a share s ∈ [0, 1] out of the pool of non-local high-ability applicants.9 Then it fills its remaining capacity with local low-ability applicants. If it has admitted all local low-ability applicants and still has spare capacity, it will prioritise high-ability over low-ability applicants. Rejected applicants enrol at the other school.10 At the end of each period t, after all students have enrolled at a school, a signal about schools’ relative quality is realised. This signal is denoted by |$W_{t}\in \left\lbrace W_{t}^{0},W_{t}^{1}\right\rbrace$| and can be interpreted as a ranking of schools, where |$W_{t}^{i}$| means that school i ranks first, i.e., school i is the winning school. The signal distribution depends on the endogenous enrolment of students in period t and on school qualities, i.e., the state of the world.11 The probability that a given school wins increases with the share of high-ability students enrolled at this school and with its quality.12 Formally, the probability that the better school wins in period t is given by p(ηt) where p: [0, 1] → [0, 1] and ηt is the share of high-ability students enrolled at the better school in period t. p(ηt) is differentiable in ηt and satisfies the following two properties. First, a more able intake introduces an upward bias in performance for either type of school, that is for any ηt ∈ [0, 1], $$\begin{eqnarray} \frac{\partial }{\partial \eta _{t}}p\left(\eta _{t}\right)\ge 0. \end{eqnarray}$$(1) Secondly, if we assume that a share κt of high-ability students are enrolled at school i, then school i is more likely to win if it is the better school than if it is the worse school, that is for any κt ∈ [0, 1], $$\begin{eqnarray} p\left(\kappa _{t}\right)\gt 1-p\left(1-\kappa _{t}\right).^{12} \end{eqnarray}$$(2) In13 each period t > 0, students first observe the most recent signal Wt−1 and then apply to schools.14 Note that they do not observe any past actions or signals pre-dating Wt−1.15 A strategy for a student of type (λ, α) in period t > 0 is: |$\sigma _{\lambda ,\alpha ,t}:\left\lbrace W_{t-1}^{0},W_{t-1}^{1}\right\rbrace \rightarrow \Delta \left\lbrace a^{0},a^{1}\right\rbrace$|⁠. It selects the probabilities with which the student applies to school 0 and school 1 conditional on which is the most recent winning school. The profile of strategies in period t is denoted by |$\overline{\sigma }_{t}$|⁠. Applications are costless and a student’s payoff depends only on the school at which he enrols. Let |$u_{\lambda ,\alpha ,t}\left(\epsilon ^{i},\omega \right)\in \mathbb {R}$| be the payoff of a student of type (λ, α) in period t enrolled in school i (ϵi) in state ω, where i ∈ {0, 1}. The student derives benefit V > 0 if and only if he enrols at the better school. In addition, he incurs a cost equal to his distance from school i. Hence, $$\begin{eqnarray} u_{\lambda ,\alpha ,t}\left(\epsilon ,\omega \right) & =\left\lbrace \begin{array}{@{}l@{\quad }l@{}}V\cdot 1_{\omega =\omega ^{0}}-\lambda & \text{if } \epsilon =\epsilon ^{0}}\\ V\cdot 1_{\omega =\omega ^{1}}-\left(1-\lambda \right) & \text{if } \epsilon =\epsilon ^{1}} \end{array}\right., \end{eqnarray}$$(3) where |$1_{\omega =\omega ^{i}}=1$| if ω = ωi and 0 otherwise. Given Wt−1, his expected payoff from being enrolled at school i is given by $$\begin{eqnarray} E\left(u_{\lambda ,\alpha ,t}\left(\epsilon ^{i}\right)|W_{t-1}\right)=\sum _{k=0,1}u_{\lambda ,\alpha ,t}\left(\epsilon ^{i},\omega ^{k}\right)Pr\left(\omega ^{k}|W_{t-1}\right). \end{eqnarray}$$(4) The expected payoff from a given application choice depends on the expected payoff from being enrolled at each school and the probability of being admitted at each school. Given Wt−1, the probability of being admitted at a given school depends on the student’s type (λ, α), the profile of strategies of all other types in period t, |$\overline{\sigma }\setminus \left\lbrace \sigma _{\lambda ,\alpha ,t}\right\rbrace$|⁠, and on the admission rule characterised by s. Each student chooses his strategy such as to maximise his expected payoff. Since a student will optimally base his strategy on the difference between his expected payoffs from applying to one school rather than the other, I define transport cost c(λ) ∈ [0, 1] as the additional distance that a student in location λ needs to travel to reach his non-local compared with his local school, i.e., c(λ) = |(1 − λ) − λ| ∈ [0, 1], with distribution F(c). I am interested in the Perfect Bayesian Equilibrium (PBE) as t → ∞. For this reason, I use the concept of a steady-state equilibrium. In steady state, the strategy profile |$\left\lbrace \overline{\sigma }_{t}\right\rbrace _{t\ge 0}$| is time-invariant, i.e., |$\overline{\sigma }_{t}=\overline{\sigma }$| for any t > 0, and the distribution of rankings is stationary in any given state of the world. Beliefs of students in period t about the state of the world are denoted by |$\mu _{t}:\left\lbrace W_{t-1}^{0},W_{t-1}^{1}\right\rbrace \rightarrow \Delta \left\lbrace \omega ^{0},\omega ^{1}\right\rbrace$|⁠. A steady-state equilibrium is a steady state with a strategy profile |$\left\lbrace \overline{\sigma }_{t}\right\rbrace _{t\ge 0}$|⁠, where |$\overline{\sigma }_{t}=\overline{\sigma }$| for any t > 0, and a system of beliefs {μt}t≥0, where μt = μ for any t ≥ 0, such that (i) for any period t > 0 and type of student (λ, α), strategy σλ, α is optimal given the profile of strategies of all other students and given beliefs μ and (ii) the system of beliefs {μt}t≥0 is derived from the stationary distribution using Bayes’ rule. This implies that if the signal distribution happened to be equal to the stationary distribution in steady-state equilibrium in some period T, then there is no reason for students in periods T + 1, T + 2, ... to deviate from the steady-state equilibrium strategy profile. I focus on strategy profiles that are symmetric with respect to schools’ identities, i.e., |$\sigma _{\lambda ,\alpha ,t}\left(W_{t-1}^{i}\right)=\sigma _{1-\lambda ,\alpha ,t}\left(W_{t-1}^{j}\right)$| for any i, j ∈ {0, 1} and j ≠ i. 2. Steady-State Equilibrium This section will solve for a steady-state equilibrium. I will show that, in equilibrium, students believe that the most recent winning school is more likely to be the better one and students apply to the most recent winning school if, and only if: (i) it is their local school; or (ii) it is their non-local school and their transport costs fall below a cut-off level. Definition 1 (Mobility). Given that school i is the winner in period t −1, mobility in period t, mt ∈ [0, 1], is defined as the share of non-local students who apply to school i where i ∈ {0, 1}. There is a one-to-one map between the strategy profile of students in period t and the level of mobility mt (as illustrated in Figure 1). In an abuse of terminology, I will refer to the level of mobility mt as the strategy profile in period t. Fig. 1. Open in new tabDownload slide Set-up. Notes: Students are distributed along a line between school 0 and school 1. Those with high transport costs live closer to their respective local school. The figure depicts the situation in which school 0 is the most recent winner and therefore receives applications from all local students, and from the share of non-local students whose transport costs lie below the cut-off V · It. Mobility is defined as the share of non-local students who apply to the most recent winner. Fig. 1. Open in new tabDownload slide Set-up. Notes: Students are distributed along a line between school 0 and school 1. Those with high transport costs live closer to their respective local school. The figure depicts the situation in which school 0 is the most recent winner and therefore receives applications from all local students, and from the share of non-local students whose transport costs lie below the cut-off V · It. Mobility is defined as the share of non-local students who apply to the most recent winner. I will solve for steady-state equilibrium mobility m* in three steps. First, I will take as given posterior beliefs about the state of the world held by students in period t and derive the optimal strategy profile |$\overline{m}_{t}$| in terms of these beliefs. Secondly, I will take as given a time-invariant strategy profile, |$m_{t}=\widehat{m}$| for all t, and derive the stationary distribution of rankings in steady state. Given the stationary probability that the better school ranks high, I will derive (time-invariant) posterior beliefs about the state of the world in terms of |$\widehat{m}$| using Bayes’ rule. Finally, I will solve for fixed points, i.e., I will find a time-invariant strategy profile m* such that m* is optimal given posterior beliefs and posterior beliefs are derived from the stationary probability that the better school ranks high in steady state, i.e., |$m^{*}=\overline{m}_{t}=\widehat{m}$|⁠. A fixed point always exists since the optimal mobility level |$\overline{m}_{t}$| increases in the posterior belief that the most recent winner is the better school and this posterior belief increases in steady-state mobility level |$\widehat{m}$|⁠. However, the fixed point is not necessarily unique. At the end of the section, I will motivate my selection of the smallest fixed point by showing that this corresponds to the limit of the sequence of (non-steady-state) equilibrium strategy profiles {mt}t≥0 as t → ∞, assuming that no ranking is available to students in period t = 0. 2.1. Optimal Mobility First, I will derive students’ optimal mobility given beliefs. Suppose that students in period t believe that the most recent winner is more likely to be the better school and their beliefs are independent of whether the recent winner is school 0 or 1. It is helpful to introduce informativeness It as a shortcut for how these posterior beliefs enter students’ expected payoff in period t.16 Definition 2 (Informativeness). Informativeness in period t, It ∈ [0, 1], is defined as $$\begin{eqnarray} I_{t}\equiv & Pr\left(\omega ^{i}|W_{t-1}^{i}\right)-Pr\left(\omega ^{j}|W_{t-1}^{i}\right), \end{eqnarray}$$(5)for i, j ∈ {0, 1} and i ≠ j, where|$Pr\left(\omega ^{k}|W_{t-1}^{i}\right)$|denotes the posterior belief of students in period t that schoolk ∈ {0, 1} is the better school conditional on observing that school i won in period t − 1. Lemma 1 (Optimal Mobility given Informativeness). The optimal strategy profile of students in period t given informativeness It is given by $$\begin{eqnarray} \overline{m}_{t}=F\left(V\cdot I_{t}\right). \end{eqnarray}$$(6) Proof: There is no down side for a student to apply to the school at which his expected payoff conditional on enrolment is higher.17 By enrolling at a better school, a student gains benefit V. Hence, his expected benefit of enrolling at the winning school instead of the losing school is V · It ≥ 0. If the winning school is local, a student incurs no transport cost when attending the winning school. Therefore, any local student applies to this school. If the winning school is non-local, a student incurs transport costs c(λ) when attending the winning school. Hence, any non-local student applies to the winning school if, and only if, the expected benefit of enrolling at the winning school rather than the losing school outweighs these transport costs c(λ), which is the case for a share F(V · It) of non-local students.18 2.2. Steady-State Informativeness Next, I will derive informativeness in steady state with a time-invariant strategy profile |$\widehat{m}$|⁠. Given mobility |$\widehat{m}$| and an admission rule characterised by s, the share of high-ability students enrolling at the most recent winner is denoted by |$h\left(\widehat{m},s\right)$|⁠, where h: [0, 1] × [0, 1] → [0, 1] and $$\begin{eqnarray} h\left(\widehat{m},s\right)=\frac{1+s\cdot \widehat{m}}{2}. \end{eqnarray}$$(7) Lemma 2 (Steady-State Informativeness given Mobility). The unique steady-state level of informativeness given|$m_{t}=\widehat{m}$|for all|$t > 0$|is $$\begin{eqnarray} I\left(\widehat{m}\right)=\frac{p\left(h\left(\widehat{m},s\right)\right)-\left(1-p\left(1-h\left(\widehat{m},s\right)\right)\right)}{p\left(1-h\left(\widehat{m},s\right)\right)+1-p\left(h\left(\widehat{m},s\right)\right)}\gt 0, \end{eqnarray}$$(8)and satisfies $$\begin{eqnarray} \frac{\partial I\left(\widehat{m}\right)}{\partial \widehat{m}}\ge 0, \end{eqnarray}$$(9)where the inequality is strict if and only if|$s > 0$|and equation (1) holds with strict inequality. The distribution of ranking is stationary because, in a given state of the world, the sequence of ranking realisations {Wt}t>0 follows a time-homogeneous Markov process. This is because the distribution from which Wt is drawn depends on the share of high-ability students at each school in period t, which depends only on the most recent realisation Wt−1 and on mobility level |$\widehat{m}$|⁠. Given this stationary distribution, steady-state informativeness is derived using Bayes’ rule. Since each school is equally likely to be better a priori, the likelihood that the better school is the winner equals the likelihood that the winner is the better school, i.e., P(Wi|ωi) = Pr(ωi|Wi) for i ∈ {0, 1}. Informativeness weakly increases in the level of steady-state mobility |$\widehat{m}$|⁠. To understand why, consider the transition probabilities of the time-homogeneous Markov process for a given state of the world (illustrated in Figure 2). At |$\widehat{m}=0$|⁠, h(0, s) = 1/2 and, hence, the probability that the better school wins in period t is independent of the ranking in period t − 1. By equation (2), the better school wins more frequently than the worse school in steady state. By contrast, if |$\widehat{m}$| rises above 0, then |$h\left(\widehat{m},s\right)$| raises above 1/2 and the school that currently ranks high is more likely to rank high again, whether it is of better or worse quality. Given the better school’s performance advantage, this must raise the frequency with which the better school wins relative to the worse school in steady state. Consequently, the better school ranks high even more frequently than the worse school at a higher level of mobility, which raises informativeness.19 Fig. 2. Open in new tabDownload slide Markov Process of Ranking Realisations. Notes: The arrows show the possible transitions between ranking realisations and the likelihood with which they occur, given time-invariant mobility level |$\widehat{m}$|⁠. Fig. 2. Open in new tabDownload slide Markov Process of Ranking Realisations. Notes: The arrows show the possible transitions between ranking realisations and the likelihood with which they occur, given time-invariant mobility level |$\widehat{m}$|⁠. 2.3. Fixed Point I characterise a steady-state equilibrium by the fixed point of mobility m* such that mobility m* is optimal given that posterior beliefs and posterior beliefs are derived using Bayes’ rule from the ranking distribution in steady state at mobility m* (as illustrated in Figure 3): $$\begin{eqnarray} m^{*}=F\left(V\cdot I\left(m^{*}\right)\right). \end{eqnarray}$$(10) Fig. 3. Open in new tabDownload slide Equilibrium Mobility. Notes: The graph shows the optimal mobility level |$\overline{m}$|⁠, which characterises the optimal strategy profile of students in steady state, as a function of steady-state mobility level |$\widehat{m}$|⁠. The intersection with the 45-degree line shows the steady-state equilibrium level of mobility m*. This graph is drawn assuming F(c) = c, V = 1, s = 1/2, p(h) = (1 + h)/2. Fig. 3. Open in new tabDownload slide Equilibrium Mobility. Notes: The graph shows the optimal mobility level |$\overline{m}$|⁠, which characterises the optimal strategy profile of students in steady state, as a function of steady-state mobility level |$\widehat{m}$|⁠. The intersection with the 45-degree line shows the steady-state equilibrium level of mobility m*. This graph is drawn assuming F(c) = c, V = 1, s = 1/2, p(h) = (1 + h)/2. Proposition 1 (Equilibrium). A steady-state equilibrium level of mobility m* is characterised by $$\begin{eqnarray} m^{*}=F\left(V\cdot \frac{p\left(h\left(m^{*},s\right)\right)-\left(1-p\left(1-h\left(m^{*},s\right)\right)\right)}{p\left(1-h\left(m^{*},s\right)\right)+1-p\left(h\left(m^{*},s\right)\right)}\right), \end{eqnarray}$$(11)and the corresponding steady-state equilibrium level of informativeness I(m*) is given by $$\begin{eqnarray} I\!\!\left(m^{*}\right)=\frac{p\left(h\left(m^{*},s\right)\right)-\left(1-p\left(1-h\left(m^{*},s\right)\right)\right)}{p\left(1-h\left(m^{*},s\right)\right)+1-p\left(h\left(m^{*},s\right)\right)}. \end{eqnarray}$$(12)Such a steady-state equilibrium level of mobility (and informativeness) always exists. Proof: |$I\!\left(\widehat{m}\right)$| is increasing in |$\widehat{m}$| given Lemma 2. Then |$F\!\left(V\cdot I\!\left(\widehat{m}\right)\right)$| is monotone increasing in |$\widehat{m}\in \left[0,1\right]$| since V > 0 and F( · ) is increasing. By Tarski’s fixed point theorem, there exists an m* such that F(V · I(m*)) = m*. 2.4. Convergence to Steady-State Equilibrium In the remainder of the article, I will focus on the smallest steady-state equilibrium level of mobility and informativeness. This is a natural choice because the sequence of (non-steady-state) equilibrium mobility levels {mt}t≥0 converges to the the smallest steady-state equilibrium mobility level as t → ∞, given that no ranking is available to students in period 0. Proposition 2 (Convergence). There is an infinite sequence {It}t≥0that corresponds to the sequence of levels of informativeness in non-steady-state equilibrium. As t → ∞, {It}t≥0converges to the smallest steady-state equilibrium level of informativeness, denoted by I1*. As {It}t≥0converges so does the sequence of mobility levels {mt}t≥0. The sequence {mt}t≥0converges to the smallest steady-state equilibrium level of mobility, denoted by m1*, where m1* = F(V · I1*). In period 0, students do not observe a ranking of schools and, hence, believe that each school is equally likely to be better, i.e., I0 = 0. They respond optimally and m0 = F(V · I0). For any period t > 0, students’ optimal strategy profile depends only on the current level of informativeness It (Markov property). Hence, the level of informativeness in period t and students’ optimal strategy profile in period t determine the level of informativeness in period t + 1, as captured by the following recurrence equation: $$\begin{eqnarray} I_{t} & =& I_{t-1}\left(p\left(h\left(m_{t-1},s\right)\right)-p\left(1-h\left(m_{t-1},s\right)\right)\right) \\ && +p\left(h\left(m_{t-1},s\right)\right)-\left(1-p\left(1-h\left(m_{t-1},s\right)\right)\right). \end{eqnarray}$$(13) From the point of view of students in period t, only the winner in period t − 1 is observed. In equilibrium, students know that I0 = 0 and they can deduce the distribution from which the winner in period t − 1 is drawn. The sequence of levels of informativeness that arises in equilibrium is increasing and will converge as t → ∞. Starting from I0 = 0, such a sequence will converge to the smallest steady-state equilibrium level of informativeness. As steady-state equilibrium levels of informativeness and mobility are jointly ordered, this also implies that the sequence of mobility levels will converge to the smallest steady-state equilibrium level of mobility.20 3. Comparative Statics This section will analyse how both the informativeness of rankings and the share of high-ability students at the better school vary across different environments. The following analysis will focus on the steady-state equilibrium associated with the smallest level of mobility (m1*), henceforth equilibrium level of mobility (see Subsection 2.4). Theorem 1 (Comparative Statics). The equilibrium levels of mobility and informativeness as well as the share of high-ability students attending the better school rise with an increase in the shares of non-local high-ability applicants admitted by an oversubscribed school; or a negative shift in the sense of FOSD of the distribution F(c) of transport costs. These exogenous changes raise the share of high-ability students who enrol at the most recent winning school for any given posterior belief about school qualities. This raises optimal mobility at any given level of steady-state mobility and, hence, equilibrium mobility rises (as shown in Figure 4). Fig. 4. Open in new tabDownload slide Comparative Statics. Notes: Consider the equilibrium mobility |$m_{A}^{1*}$|⁠. A negative shift in the sense of FOSD of the distribution F( · ) shifts up optimal mobility at any level of steady-state mobility, as illustrated by the dashed line. Equilibrium mobility increases to |$m_{B}^{1*}$| . An increase in s shifts up optimal mobility at any positive level of steady-state mobility, as illustrated by the dotted line. Equilibrium mobility increases to |$m_{C}^{1*}$|⁠. The solid line is drawn for F being a uniform distribution on |$\left[0,\overline{c}\right]$|⁠, |$\overline{c}=1$|⁠, V = 2, θ = 1/2, p(h) = (1 + h)/2. The dashed line is drawn for |$V/\overline{c}=16/3$|⁠, and the dotted line for s = 7/10, all else equal. Fig. 4. Open in new tabDownload slide Comparative Statics. Notes: Consider the equilibrium mobility |$m_{A}^{1*}$|⁠. A negative shift in the sense of FOSD of the distribution F( · ) shifts up optimal mobility at any level of steady-state mobility, as illustrated by the dashed line. Equilibrium mobility increases to |$m_{B}^{1*}$| . An increase in s shifts up optimal mobility at any positive level of steady-state mobility, as illustrated by the dotted line. Equilibrium mobility increases to |$m_{C}^{1*}$|⁠. The solid line is drawn for F being a uniform distribution on |$\left[0,\overline{c}\right]$|⁠, |$\overline{c}=1$|⁠, V = 2, θ = 1/2, p(h) = (1 + h)/2. The dashed line is drawn for |$V/\overline{c}=16/3$|⁠, and the dotted line for s = 7/10, all else equal. My results show that an admission rule that assigns priority to high-ability students (s > 0) facilitates learning about school quality relative to an admission rule that assigns equally able intakes to each school (s = 0). This is contrary to what has been suggested in recent discussions on how intakes should be assigned to improve the informativeness of rankings. For example, Burgess and Allen (2010) argue that ‘where schools are very similar in their intakes, the excellence of teaching and learning will be critical to where the school is placed in a local league table of academic performance’, whereas if intakes are very imbalanced then differences in school qualities are less likely to affect the ranking, ‘because differences in pupil intakes will produce very large differences in raw outcomes’ (Burgess and Allen, 2010, p.10). The authors conclude that equal intakes have the advantage that differences in school qualities are more likely to be reflected in rankings. Their statements are consistent with my assumptions on how the ranking realisation depends on the ability of exogenously given intakes. However, in a dynamic setting in which intakes are endogenously determined, I come to the opposite conclusion, i.e., differences in school qualities are less likely to be reflected in rankings when intakes are equal. In addition, my results show that learning about school quality from rankings is facilitated if schools are perceived to be less horizontally differentiated. Recent school choice reforms reduced the cost of choosing a school that is further from home, because under these reforms students no longer had to move to the school’s attendance area to be admitted, but could apply from outside this area and then commute. Therefore, school choice reforms should improve the informativeness of rankings and thereby help to target accountability pressures towards lower-quality schools. A further prediction is that, in areas where students have a larger set of schools within a reasonable distance, these schools’ relative performance should be a stronger indicator about their quality than in areas where students have less choice. The result fits with the observation that a decrease in the costs of attending a university further from home has coincided with students’ choice of college becoming less sensitive to distance and with selectivity at top colleges rising (Hoxby, 2009). In addition, it fits with empirical evidence that for patients who require non-emergency care (lower transport cost) the correlation between hospital quality and market share is higher than for patients who require emergency treatment (Chandra et al., 2016). Finally, in areas in which schools are more homogeneous, e.g., in terms of the curriculum that they offer, rankings should be more informative about schools’ relative quality. This suggests that there exists a trade-off as schools diverge in their specialisations: students are more likely to find a school that caters to their desired specialisation, but they are less likely to learn which school is of better quality. Recent policy efforts have focused on providing more students with information about schools’ performance. In their empirical analysis, Chandra et al. (2016) find that, over a period in which it became easier for patients to access information about hospital performance, the correlation between a hospital’s market share, its performance and its quality grew over time.21 In my framework, the cost c could be interpreted as the cost to look up the most recent ranking but, unlike in the baseline model, these costs would then be incurred independent of where the student ends up applying. Students would trade off researching schools and potentially applying to a better-performing school against remaining uninformed and applying to their local school. Therefore, a reduction in costs would again trigger more students to apply to the better-performing school, and my results suggest that such policies would contribute to improving the informativeness of rankings.22 3.1. Discussion Both exogenous changes, a decrease in transport costs and a rise in the share of non-local high-ability applicants admitted by an oversubscribed school have the following feature in common: at any given level of informativeness, these changes increase the share of high-ability students admitted by the high-ranked school and, therefore, increase the chances that the same school will rank high again. In this sense, both contribute to making the ranking more persistent. One could also build persistence into rankings by basing the ranking on some longer window of schools’ recent performance, e.g., let p( · ) be the probability that the better school has higher performance and construct the ranking as follows: in period 0, the school with higher performance ranks high, and in each period t > 0, the low-ranked school in period t − 1 becomes the high-ranked school in period t if and only if it had higher performance in periods t − 1 and t − 2. Such built-in inertia would increase the chances that the high-ranked school will rank high again, and would raise the equilibrium levels of mobility and informativeness. To understand why this is the case, it is important to realise that this inertia increases the steady-state level of informativeness at any given level of mobility. In particular, as a result of this inertia, a school becomes less likely to change its rank from one period to the next, irrespective of its quality. Without any inertia, the better school is more likely to maintain a high rank over time than the worse school, due to its superior quality. Therefore, introducing inertia must make the better school even more likely to maintain a high rank relative to the worse school, which increases the steady-state level of informativeness at any given level of mobility.23 As a consequence, the equilibrium levels of mobility and informativeness increase.24 4. Welfare This section analyses how a utilitarian social planner would optimally assign students to schools if he were subject to the same informational constraints as students—that is, if he could condition this assignment of students only on the identity of the most recent winning school. This benchmark helps to understand the inefficiencies that arise from students’ decentralised decision making, as an individual student ignores how their application affects the allocation of other students in the current period as well as how it affects the informativeness of future rankings. If all students derive the same benefit V from attending the better school, the planner’s objective amounts to minimising expenditure on transport costs. Hence, he optimally assigns students to their respective local schools, independent of the ranking. Suppose instead that a high-ability student values attending the better school at VH = V and a low-ability student at VL = δ · V, where δ ∈ (0, ∞). From the planner’s point of view, school quality and intake ability are complements if δ ≤ 1 and substitutes if δ ≥ 1. Let h ∈ [0, 1] be the share of high-ability students assigned to the most recent winner and let μ(h) be the posterior belief in steady state that the most recent winner is the better school. Then the planner’s problem is as follows: $$\begin{eqnarray} \max _{h\in \left[0,1\right]}U\left(h,\delta \right)= && V\left\lbrace \mu \left(h\right)\left[h+\left(1-h\right)\delta \right]+\left[1-\mu \left(h\right)\right]\left[1-h+h\delta \right]\right\rbrace \\ && -\int _{0}^{F^{-1}\left(|2h-1|\right)}cdF\left(c\right),^{24} \end{eqnarray}$$(14) where25F−1 denotes the inverse of F and26 $$\begin{eqnarray} \mu \left(h\right)=\frac{p\left(1-h\right)}{1-p\left(h\right)+p\left(1-h\right)}.^{25} \end{eqnarray}$$(15) We want to compare the efficient allocation to the equilibrium allocation h(m1*, s). Further, we want to ask which policy tools could be used to increase equilibrium efficiency. Clearly, a policymaker could change the share s of non-local high-ability applicants admitted to an oversubscribed school. Alternatively, he could affect students’ costs of attending a non-local school, e.g., through subsidising transport or charging a fee for enrolment at a non-local school. Let τ ≥ −1 be the rate at which the policymaker either raises or lowers the actual cost c so that the student’s perceived cost is c′ = c(1 + τ). A student’s optimal application choice depends on their perceived cost c′, while the first-best allocation of students depends on their actual cost c. Proposition 3 (Planner’s Optimal Allocation). Let|$h^{*}\in \text{argmax }_{h\in \left[0,1\right]}U\left(h,\delta \right)$|⁠. There exists|$\overline{\delta }\left(s,\tau \right)\in \left[0,1\right]$|such that for all|$\delta \ge \overline{\delta }\left(s,\tau \right)$|⁠, h* ≤ h(m1*, s). Further, there exists|$\underline{\delta }\left(s,\tau \right)\in \left[0,\overline{\delta }\left(s,\tau \right)\right]$|such that for all|$\delta \lt \underline{\delta }\left(s,\tau \right)$|⁠, h* > h(m1*, s). Both|$\overline{\delta }\left(s,\tau \right)$|and|$\underline{\delta }\left(s,\tau \right)$|depend positively on s and negatively on τ. If intake ability and school quality are substitutes, i.e., if δ ∈ [1, ∞), the planner allocates the majority of high-ability students to the losing school, i.e., h* ≤ 1/2, whereas in the decentralised equilibrium the majority of high-ability students attend the winning school, i.e., h(m1*, s) ≥ 1/2.27 The reason is that the planner’s utility decreases in h for h ≥ 1/2. First, if the planner were to ignore the impact of assignment on beliefs, that is if he were to take μ as given, he would raise his expected benefit by reducing the number of high-ability students at the winning school. Secondly, for a given majority of high-ability students at the winning school, his expected benefit is higher the lower the belief that the winning school is the better school. Therefore, lowering h unambiguously raises his benefit. Further, the expenditure on transport cost rises with the share of high-ability students assigned to their non-local school. If intake ability and school quality are complements, i.e., δ ∈ (0, 1], the planner allocates the majority of high-ability students to the winning school. However, it is unclear whether the optimal share of high-ability students attending the winning school is smaller or larger than in the decentralised equilibrium. The reason is that the planner’s objective differs from an individual student’s objective in two ways. First, the planner considers that informativeness increases with the share of high-ability students assigned to the winning school and this concern in isolation leads the planner to assign h > h(m1*, s). Secondly, the planner takes into account externalities arising between students within the same period. In particular, an additional high-ability student travelling to their non-local winning school means that an additional low-ability student has to travel to their non-local losing school. Further, the planner trades off the expected benefit against the total rather than the individual expenditure on transport costs. The concern for externalities in isolation leads the planner to assign h < h(m1*, s). The higher δ, the greater is the weight the planner assigns to the increase in total costs incurred relative to the increase in benefit and, therefore, the fewer high-ability students are optimally assigned to their non-local school. In case |$\delta \ge \overline{\delta }\left(s,\tau \right)$|⁠, the equilibrium share of high-ability students at a non-local school is inefficiently large. To improve efficiency, a policy invention could be to raise the perceived transport costs (raise τ) or to reduce the share s of non-local high-ability applicants admitted to an oversubscribed school. In case |$\delta \lt \underline{\delta }\left(s,\tau \right)$|⁠, the equilibrium share of high-ability students at a non-local school is inefficiently small. Then efficiency can be improved by lowering the perceived transport costs (lower τ) or by reducing the share s of non-local high-ability applicants admitted to an oversubscribed school. The following example shows that there exist functional forms and parameter values for which any first-best allocation lies above the equilibrium allocation, i.e., |$\underline{\delta }\left(s,\tau \right)\gt 0$|⁠. Example 1 (Planner’s Optimal Allocation). Suppose F(c) = c, p(h) = (1 + h)/2, V = 1, s = [0, 1/2]. Then |$\overline{\delta }\left(s,\tau \right)=\underline{\delta }\left(s,\tau \right)\in \left(0,1\right)$|⁠. As discussed in Section 2, multiple equilibria may exist. These equilibria can be ranked in terms of efficiency. The way in which δ affects this ranking is closely related to how δ affects the planner’s optimal allocation. Remark 1 (Welfare across Equilibria). Let m1*and m2*be two equilibria with m1* < m2*. Then there exists δ′ ∈ [0, 1] such that for allδ ≥ δ′, U(h(m1*, s), δ) ≥ U(h(m2*, s), δ), and for δ < δ′, U(h(m1*, s), δ) < U(h(m2*, s), δ). If F(c) = c4, V = 1.51, s = 1/2 and p(h) = (1 + h)/2, then δ′ ∈ (0, 1). 5. Extension: Quasi-Market Reforms This extension will analyse how overall school quality and students’ access to good schools are affected by quasi-market reforms. These reforms intend to mimic market forces by linking a school’s funding to the demand for its places, thereby putting pressures on unpopular schools to improve or shut down. Clearly, these reforms are more effective at improving school quality if worse schools are less popular, but this crucially depends on how well students can identify which schools are worse. My framework is well suited to studying the dynamic interaction between a student’s inference about school quality from rankings, which affects demand for places, and the supply-side response, which affects the qualities of schools.28 In the baseline model, school qualities were assumed to be exogenously determined. Therefore, students’ application strategies affected the allocation of students to schools, but not the overall quality of schools. To incorporate the supply-side response triggered by quasi-market reforms, I assume that the undersubscribed school’s quality is, with some probability, replaced by a new draw from an exogenously given quality distribution. This represents the fact that the undersubscribed school is under pressure to make changes, e.g., to experiment with new methodologies, or to replace their leadership, or in the worst case to close down. Such changes do not necessarily lead to improvements and, therefore, directing pressure at bad schools is valuable in order to observe long-term improvements in school quality.29 This extended framework allows me to study a steady-state equilibrium in which the overall quality of schools is endogenous because it depends on students’ application strategies, and students’ application strategies are optimal given the distribution of school qualities. The baseline model is amended as follows. Each school’s quality is either good or bad and drawn independently at the start of period 0. In addition, a given school’s quality is redrawn with probability γ ∈ [0, 1] in period t before the ranking of schools Wt is realised if, and only, if this school was undersubscribed in period t. Any draw of school quality is equally likely to be good or bad.30 Neither the event of a quality draw nor its realisation is observed. A steady-state equilibrium is a steady state such that (i) the time-invariant mobility mt = m* is optimal given beliefs and (ii) beliefs are derived from the stationary joint distribution of the pair of school qualities and the school ranking using Bayes’ rule.31 Optimal mobility depends on informativeness, which, as before, is given by the difference between the posterior belief that the most recent winner is a strictly better school and the posterior belief that the most recent winner is a strictly worse school. All proofs can be found in the Online Appendix. To study the effect of introducing quasi-market reforms, I compare the case in which the supply side is independent of the demand side, i.e., γ = 0, with the case in which the supply side is affected by the demand side, i.e., γ > 0.32 Proposition 4 (Quasi-Market Reforms). If|$\gamma > 0$|rather than |$\gamma = 0$|⁠, then the level of mobility and informativeness remains unchanged; and the average fraction of good schools increases; and both the share of low-ability students and the share of high-ability students who attend a good school increases. Mobility and informativeness remain unaffected as supply-side responses are incorporated, for two reasons. First, informativeness in steady-state equilibrium is independent of γ for γ > 0, because the relative frequency with which a good rather than a bad school is replaced is unaffected by γ, and hence the relative frequency with which a good school ranks higher than a bad school is also unaffected.33 Secondly, the chances that schools are of different quality at any time is unaffected by whether γ = 0 or γ > 0 because a new quality draw is equally likely to be good or bad. If an undersubscribed school’s quality is redrawn, the overall quality of schools increases in equilibrium. To remain in steady state, the proportion of good schools closing down must equal the proportion of good schools opening up. However, the average length of time that a good school operates increases and, therefore, the overall quality improves. Given that mobility is unaffected, the allocation of students conditional on the most recent ranking is unaffected. Consequently, both ability groups benefit from linking school replacement to students’ application choices. It is interesting to repeat some of the comparative static exercises of Theorem 1 when supply-side responses are incorporated. Proposition 5 (Quasi-Market Reforms–Comparative Statics). If |$\gamma > 0$|⁠, then an increase in the share s of non-local high-ability applicants admitted by an oversubscribed school; or a negative shift in the sense of FOSD of the distribution F(c) of transport costs increases the equilibrium levels of mobility and informativeness; and increases the average fraction of good schools; and increases the share of high-ability students at a good school. Given|$\gamma > 0$|, (1) or (2) decreases the share of low-ability students at a good school if at all h ∈[1/2, 1], $$\begin{eqnarray} \left(2-2h\right)\frac{\partial }{\partial h}p\left(h\right)\le 1-p\left(h\right)+p\left(1-h\right). \end{eqnarray}$$(16) These exogenous changes have two effects. First, they raise the share of high-ability students at the relatively better school (sorting effect), as in the case of exogenous school qualities. Secondly, they raise the average fraction of good schools (quality effect). Both the quality and the sorting effect cause the share of high-ability students at good schools to increase. However, the effect on the share of low-ability students at good schools is ambiguous. It is negative if the impact of student ability on performance is sufficiently weak, as this causes the sorting effect to dominate. Therefore, a policymaker may face a trade-off between equity and efficiency. While lowering transport costs or increasing how selective the admission rule is raises school quality overall, these benefits may accrue only to high-ability students.34 6. Robustness Checks This section shows the extent to which my findings are robust to different assumptions about how rankings are generated, how persistent school qualities are and how the admission rule selects between applicants. 6.1. Rankings My article shows that equilibrium informativeness increases as transport costs are lowered or as the share of non-local high-ability applicants admitted by an oversubscribed school increases. The argument is based on the assumption that the worse school is never guaranteed to win even if it admitted all high-ability students, as implied by equation (2). Suppose that, instead, I allowed for the possibility that some critical level |$\overline{h}$| exists for the share of high-ability students such that, if any school i ∈ {0, 1} enrols h students, where |$h\gt \overline{h}$|⁠, then school i is guaranteed to win.35 Then, for some sufficiently high level of mobility, the stationary distribution of rankings in steady state would no longer be unique. It would assign either probability 1 to the worse school winning or probability 1 to the better school winning. This is because a self-perpetuating cycle arises in which the same school continues to rank high: once it has attracted sufficiently many high-ability students to rank high it will then be able to attract these high-ability students again and again, irrespective of its quality.36 Given these assumptions, it is no longer true that the level of informativeness necessarily increases in the share s of non-local high-ability applicants admitted by an oversubscribed school. However, the higher the share s of non-local high-ability applicants admitted, the more likely it is that the better school rather than the worse school will be the first to reach the critical level |$\overline{h}$|⁠. Therefore, from an ex ante perspective, informativeness is still at least as high if oversubscribed schools select on ability as if intakes are equal across schools. Furthermore, I assume students observe only the most recent ranking. The insights of this article still apply if students instead observed a longer window of rankings. If this were the case, students would have access to some of the information based on which students in previous periods applied to schools. However, crucially, they still would not have access to all the information available to students in all previous periods. This is the feature on which the proofs for equilibrium existence and comparative statics results are based. In Section B.2 of the Online Appendix, I analyse the situation when, in each period t, students observe the two most recent rankings. I solve for equilibrium and show that Theorem 1 still applies. 6.2. School Qualities In the baseline model, school qualities are assumed to be fixed but, in reality, they might change over time. The results of my model are qualitatively unaffected when school qualities change exogenously. In particular, suppose that schools’ relative quality, i.e., the state of the world, changes with some fixed probability g ∈ [0, 1/2) each period and that such changes are unobserved by students. Then the steady-state level of informativeness still increases with mobility and, hence, Theorem 1 still holds. The proof can be found in Section B.3 of the Online Appendix.37 6.3. Admission Rule Even in situations in which schools’ admission rules do not select among applicants based on their ability, the insights developed in this article can be useful. Informativeness increases over time if and only if, in any period t, the share of high-ability students enrolling at the school which ranked high in period t − 1 increases in their level of informativeness, It. In the model studied, this requires that the admission rule selects a strictly positive share of applicants based on their ability, i.e., s > 0. However, there are alternative sets of assumptions under which this condition is met even if the admission school selects among applicants at random. For example, suppose that high-ability students derive a larger benefit from attending a better school, i.e., VH > VL > 0, and that the distribution for transport costs is uniform.38 Then high-ability students are willing to incur higher transport costs than low-ability students to attend the most recent winning school at any given level of informativeness. Hence, the applicant pool of the most recent winning school contains more high-ability than low-ability students and the share of high-ability students is greater the higher the level of informativeness.39 Therefore, even if places at this school were allocated to applicants at random independent of their ability, the school would admit a larger share of high-ability students than the other school and the share of high-ability students admitted would increase with the level of informativeness. More detail can be found in Section B.4 in the Online Appendix. In addition, even if an oversubscribed school had to admit those students who live nearest to the school irrespective of their ability, some of the effects captured in the analysis may still be present. Students would consider the quality of schools when choosing where to live (Tiebout choice).40 If high-ability students are more likely to move into the proximity of the better-performing school, either because they value school quality more or because they are more likely to be able to afford housing there, then again a better-performing school may admit more high-ability students than the other school.41 7. Conclusion This article studies students’ inferences about school quality from rankings when students in each period observe which school performed better in the previous period, but they do not observe past allocations or applications. I develop a dynamic framework in which the pool of applicants at a school and its relative performance are endogenously linked and analyse comparative statics in a steady-state equilibrium. I find that a performance-based ranking is more informative about school quality if the admission rule leads oversubscribed school to prioritise more able applicants. I also find that such a ranking is more informative if students perceive schools to be less horizontally differentiated. My article is the first in the observational learning literature to derive comparative statics when agents observe a limited window of realisations of a public signal, whose distribution depends on past agents’ choices. Furthermore, my findings contribute to recent discussions on school choice and on the design of school admission rules. I view the framework developed as a building block for future research on analysing the link between information and match outcomes.42 In addition, the framework is also suitable to explore what could cause persistent differences between schools to arise, and a starting point to explore how schools build and maintain reputations over time when students have limited access to past performance information. Appendix A A.1. Lemma 2 (Steady-State Informativeness Given Mobility) The sequence of signal realisations {Wt}t>0 follows a time-homogeneous Markov process. If p(1) < 1, the process is irreducible and, hence, has a unique stationary distribution characterised by a constant probability π that the better school wins, π = Pr(Wi|ωi) for i ∈ {0, 1}, which solves $$\begin{eqnarray} \pi = & p\left(h\left(\widehat{m},s\right)\right)\pi +p\left(1-h\left(\widehat{m},s\right)\right)\left(1-\pi \right) \end{eqnarray}$$(A1) Hence, $$\begin{eqnarray} \pi \left(h\left(\widehat{m},s\right)\right)=\frac{p\left(1-h\left(\widehat{m},s\right)\right)}{1-p\left(h\left(\widehat{m},s\right)\right)+p\left(1-h\left(\widehat{m},s\right)\right)} \end{eqnarray}$$(A2) By Bayes’ rule and by the symmetry of the setting: for i, j ∈ {0, 1} and j ≠ i, $$\begin{eqnarray} Pr\left(\omega ^{i}|W^{i}\right)= & \displaystyle\frac{\pi \left(h\left(\widehat{m},s\right)\right)Pr\left(\omega ^{i}\right)}{\pi \left(h\left(\widehat{m},s\right)\right)Pr\left(\omega ^{i}\right)+\left(1-\pi \left(h\left(\widehat{m},s\right)\right)\right)Pr\left(\omega ^{j}\right)}=\pi \left(h\left(\widehat{m},s\right)\right). \end{eqnarray}$$(A3) Hence, |$\pi \left(h\right)\gt \frac{1}{2}$| for all h given (2). By Definition 2, |$I\left(\widehat{m}\right)=2\pi \left(h\left(\widehat{m},s\right)\right)-1$|⁠. Hence, |$I\left(\widehat{m}\right)\gt 0$|⁠. In addition, |$(dI)/(d\widehat{m})=(d\pi )/(dh)\cdot (dh)/(d\widehat{m})\ge 0$| since |$(dh)/(d\widehat{m})=s/2\ge 0$| and $$\begin{eqnarray} \frac{d\pi }{dh}\ge 0\Leftrightarrow \left[1-p\left(h\left(\widehat{m},s\right)\right)+p\left(1-h\left(\widehat{m},s\right)\right)\right]\frac{dp\left(h\left(\widehat{m},s\right)\right)}{dh}\ge 0, \end{eqnarray}$$(A4) where p( · ) ∈ [0, 1] and (dp(h))/(dh) ≥ 0 by (1). A.2. Proposition 2 (Convergence) I0 = 0 because the posterior beliefs of students in period 0 equal their prior beliefs. In addition, the equilibrium sequence satisfies (13), since for i, j ∈ {0, 1} and j ≠ i by Bayes’ rule it follows that $$\begin{eqnarray} I_{t}\equiv & Pr\left(\omega ^{i}|W_{t-1}^{i}\right)-Pr\left(\omega ^{j}|W_{t-1}^{i}\right)=2Pr\left(W_{t-1}^{i}|\omega ^{i}\right)-1, \end{eqnarray}$$(A5) and since the distribution of rankings in period t − 1 depends on the distribution of rankings in period t − 2 as follows $$\begin{eqnarray} Pr\left(W_{t-1}^{i}|\omega ^{i}\right)= & p\left(h\left(m_{t-1},s\right)\right)Pr\left(W_{t-2}^{i}|\omega ^{i}\right)+p\left(1-h\left(m_{t-1},s\right)\right)\left(1-Pr\left(W_{t-2}^{i}|\omega ^{i}\right)\right), \end{eqnarray}$$ and since (6) holds. The sequence {It}t≥0 is increasing by the following induction argument. Define $$\begin{eqnarray} Z\left(I_{t-1}\right)= & \left[p\left(h\left(m_{t-1},s\right)\right)-p\left(1-h\left(m_{t-1},s\right)\right)\right]I_{t-1} \\ & +p\left(h\left(m_{t-1},s\right)\right)-\left(1-p\left(1-h\left(m_{t-1},s\right)\right)\right), \end{eqnarray}$$(A6) where mt−1 = F(V · It−1). Then $$\begin{eqnarray} \displaystyle\frac{d}{dI_{t-1}}Z\left(I_{t-1}\right)= & \left[p\left(h\left(m_{t-1},s\right)\right)-p\left(1-h\left(m_{t-1},s\right)\right)\right]+2\left[\displaystyle\frac{d}{dI_{t-1}}p\left(h\left(m_{t-1},s\right)\right)\right]. \end{eqnarray}$$(A7) Since mt−1 ≥ 0, we have h(mt−1, s) ≥ 1/2. Given h(mt−1, s) ≥ 1/2 and (1), p(h(mt−1, s)) − p(1 − h(mt−1, s)) ≥ 0. In addition, $$\begin{eqnarray} \frac{d}{dI_{t-1}}p\left(h\left(m_{t-1},s\right)\right)=\frac{dp\left(h\right)}{dh}\frac{dh\left(m_{t-1},s\right)}{dm_{t-1}}\frac{dm_{t-1}}{dI_{t-1}}\ge 0, \end{eqnarray}$$(A8) since F( · ) is positive and increasing, V > 0, It−1 ≥ 0, (dh(mt−1, s))/(dmt−1) = s/2 ≥ 0, and (1) holds. Hence, it follows that Z(It−1) increases in It−1. In addition, by (2), I1 = Z(I0) = p(1/2) − (1 − p(1/2)) ≥ I0 = 0 and due to Z(It−1) being increasing in It−1, it follows that It = Z(It−1) ≥ Z(It−2) = It−1. Since {It}t≥0 is increasing, it converges to its least upper bound. This least upper bound is given by the smallest fixed point I1* for the following reason: suppose I1* was not the least upper bound. Then there would be some |$\widetilde{I}\in \left[0,1\right]$| such that |$\widetilde{I}\lt I^{1*}$| and |$Z\left(\widetilde{I}\right)\gt I^{1*}$|⁠. Since I1* is a fixed point, this implies |$Z\left(\widetilde{I}\right)\gt Z\left(I^{1*}\right)$|⁠. But this contradicts the fact that Z( · ) is increasing. Given (6), V > 0 and F( · ) being increasing, mt increases in It. Hence, as {It}t≥0 converges so does {mt}t≥0. Further, the smallest equilibrium level of informativeness I1* corresponds to the smallest equilibrium level of mobility m1*. A.3. Theorem 1 (Comparative Statics) Define $$\begin{eqnarray} \varGamma \left(I,s,F\left(\cdot \right),p\left(\cdot \right),V\right)=\frac{p\left(h\left(F\left(V\cdot I\right),s\right)\right)-\left(1-p\left(1-h\left(F\left(V\cdot I\right),s\right)\right)\right)}{1-p\left(h\left(F\left(V\cdot I\right),s\right)\right)+p\left(1-h\left(F\left(V\cdot I\right),s\right)\right)}. \end{eqnarray}$$(A9) For any I ∈ [0, 1], |$(d\varGamma )/(dI)=(d\varGamma )/(dF)\cdot (dF)/(dI)\ge 0$|⁠, since |$(d\varGamma )/(dF)\ge 0$| holds given (9), and since (dF)/(dI) ≥ 0 holds given I ≥ 0, V > 0 and F( · ) being increasing. 1. For any I ∈ [0, 1], |$(d\varGamma )/(ds)=(d\varGamma )/(dh)\cdot (dh)/(ds)\ge 0$|⁠, since |$(d\varGamma )/(dh)\ge 0\Leftrightarrow (d\pi )/(dh)\ge 0$| and (dπ)/(dh) ≥ 0 given (A4), and since (dh)/(ds) = F(V · I)/2 ≥ 0. After Corollary 1 in Milgrom and Roberts (1994), this implies that the smallest fixed point of |$\varGamma \left(I,s,F\left(\cdot \right),p\left(\cdot \right),V\right)$|⁠, denoted by I1*(s, F( · ), p( · ), V), is increasing in s. Since m1* = F(V · I1*), V > 0 and F( · ) is increasing, m1* also increases in s. 2. For any I ∈ [0, 1], and any F( · ) and |$\widetilde{F}\left(\cdot \right)$|⁠, such that F( · ) first-order stochastically dominates |$\widetilde{F}\left(\cdot \right)$|⁠, it holds that |$F\left(V\cdot I\right)\le \widetilde{F}\left(V\cdot I\right).$| By (9), this implies that for any I ∈ [0, 1], $$\begin{eqnarray} \varGamma \left(I,s,F\left(\cdot \right),p\left(\cdot \right),V\right)\le \varGamma \left(I,s,\widetilde{F}\left(\cdot \right),p\left(\cdot \right),V\right). \end{eqnarray}$$(A10) After Corollary 1 in Milgrom and Roberts (1994), this implies that the smallest fixed point satisfies |$I^{1*}\left(s,F\left(\cdot \right),p\left(\cdot \right),V\right)\le I^{1*}\left(s,\widetilde{F}\left(\cdot \right),p\left(\cdot \right),V\right)$|⁠. In addition, since m1* = F(V · I1*), V > 0 and F( · ) is increasing: |$m^{1*}\left(s,F\left(\cdot \right),p\left(\cdot \right),V\right)\le m^{1*}\left(s,\widetilde{F}\left(\cdot \right),p\left(\cdot \right),V\right)$|⁠. A.4. Proposition 3 (Planner’s Optimal Allocation) Let |$\overline{c}$| be the transport cost of the marginal high-ability student assigned to their non-local school. If the majority of high-ability students are assigned to the winning (losing) school, then |$h=(1+F\left(\overline{c}\right))/2$| (⁠|$h=(1-F\left(\overline{c}\right))/2$|⁠). Hence, |$\overline{c}=F^{-1}\left(\left|2h-1\right|\right)$|⁠. Let |$C\left(\left|2h-1\right|\right)=\int _{0}^{F^{-1}\left(\left|2h-1\right|\right)}cF\left(c\right)$| be the total expenditure on transport costs, which is comprised in equal parts of the cost of high-ability students with |$c\le \overline{c}$| travelling to school i and low-ability students with |$c\le \overline{c}$| travelling to school j, where i, j ∈ {0, 1} and i ≠ j. Suppose δ ∈ [1, ∞). For any h > 1/2, $$\begin{eqnarray} \frac{\partial U\left(h,\delta \right)}{\partial h}=V\left(1-\delta \right)\left[2\mu \left(h\right)-1+\frac{\partial \mu \left(h\right)}{\partial h}\left(2h-1\right)\right]-\frac{\partial }{\partial h}C\left(\left|2h-1\right|\right), \end{eqnarray}$$(A11) is strictly negative since μ(h) > 1/2 and (∂μ(h))/(∂h) ≥ 0 by Lemma 2. By Proposition 1, h* ≤ 1/2 ≤ h(m*, s). Suppose δ ∈ (0, 1]. Then the following inequality holds for any h < 1/2: $$\begin{eqnarray} U\left(h,\delta \right) \lt U\left(\frac{1}{2},\delta \right) \\ \Leftrightarrow V\cdot \left\lbrace \mu \left(h\right)\left[h+\left(1-h\right)\delta \right]+\left(1-\mu \left(h\right)\right)\left[1-h+h\delta \right]\right\rbrace -C\left(\left|2h-1\right|\right) \lt V\cdot \left(\frac{1}{2}+\frac{1}{2}\delta \right) \\ \Leftrightarrow \mu \left(h\right)\left[h+\left(1-h\right)\delta -\left(\frac{1}{2}+\frac{1}{2}\delta \right)\right]-\left(1-\mu \left(h\right)\right)\left[1-h+h\delta -\left(\frac{1}{2}+\frac{1}{2}\delta \right)\right] \lt \frac{C\left(\left|2h-1\right|\right)}{V} \\ \Leftrightarrow \left(h-\frac{1}{2}\right)\left(1-\delta \right) \lt \frac{C\left(\left|2h-1\right|\right)}{V}. \end{eqnarray}$$(A12) Hence, h* ≥ 1/2. For h ∈ (1/2, 1], (A11) decreases in δ given μ(h) > 1/2 and (∂μ(h))/(∂h) ≥ 0 by Lemma 2. Hence, by Topkis (1978), |$\text{argmax }_{h\in \left[1/2,1\right]}U\left(h,\delta \right)$| is monotone non-increasing in δ (in the sense of strong set order). By Theorem 1, a higher s or a lower τ, increase the equilibrium level of mobility and hence, the equilibrium share of high-ability students at the winning school, but have no impact on U(h, δ). A.5. Example 1 (Planner’s Optimal Allocation with Complements) Applying Proposition 1, yields |$m^{1*}=(1-\sqrt{1-s})/s$| and, hence, |$h\left(m^{1*},s\right)=(2-\sqrt{1-s})/2$|⁠. Suppose δ ∈ (0, 1]. By Proposition 3, h* ≥ 1/2 and, hence, |$C\left(\left|2h-1\right|\right)=\int _{0}^{2h-1}cdc=\left(2h-1\right)^{2}/2$|⁠. $$\begin{eqnarray} \max _{h\in \left[\frac{1}{2},1\right]}U\left(h,\delta \right)=\frac{1+2\delta \left(1-h\right)}{3-2h}-\frac{\left(2h-1\right)^{2}}{2}. \end{eqnarray}$$(A13) Then for h > 1/2 $$\begin{eqnarray} \frac{\partial U\left(h,\delta \right)}{\partial h}=\frac{2\left(1-\delta \right)}{\left(3-2h\right)^{2}}-2\left(2h-1\right) \end{eqnarray}$$(A14) and $$\begin{eqnarray} \frac{\partial ^{2}U\left(h,\delta \right)}{\partial h^{2}}=\frac{8\left(1-\delta \right)}{\left(3-2h\right)^{3}}-4, \end{eqnarray}$$(A15) (A14) is decreasing in h for |$h\lt 1/2\left(3-\left(2\left(1-\delta \right)\right)^{\frac{1}{3}}\right)$|⁠, and increasing in h otherwise. For any δ ∈ (0, 1), (A14) is strictly positive at h = 1/2 and strictly negative at h = 1. Hence, h* is unique and (A14) is equal to 0 at h*. As δ → 1, h* → 1/2 and as δ → 0, |$h^{*}\rightarrow 1/4\left(5-\sqrt{5}\right)$|⁠. The statement follows since h* decreases continuously with δ and |$1/2\lt (2-\sqrt{1-s})/2\lt 1/4\left(5-\sqrt{5}\right)$| for s ∈ [0, 1/2]. A.6. Remark 1 (Welfare across Equilibria) The proof of Proposition 3 can be applied to $$\begin{eqnarray} \max _{h\in \left\lbrace h\left(m^{1*},s\right),h\left(m^{2*},s\right)\right\rbrace }U\left(h,\delta \right), \end{eqnarray}$$(A16) where h(m1*, s), h(m2*, s) ≥ 1/2 by Proposition 1. Suppose F(c) = c4, V = 1.51, s = 1/2 and p(h) = (1 + h)/2. Applying Proposition 1, yields m1* ≈ 0.71 and m2* ≈ 0.9, hence, h(1/2, m1*) ≈ 0.68 and h(1/2, m2*) ≈ 0.72. Since h* ≥ 1/2, |$C\left(2h-1\right)=\int _{0}^{2h-1}cf\left(c\right)dc=\int _{0}^{2h-1}4c^{4}dc=4\left(2h-1\right)^{5}\!/5$|⁠. Hence, $$\begin{eqnarray} U\left(h,\delta \right)=1.51\frac{1+2\delta \left(1-h\right)}{3-2h}-\frac{4\left(2h-1\right)^{5}}{5}. \end{eqnarray}$$(A17) Then δ′ ∈ (0, 1) since ∂/(∂δ)[U(h(m1*, 1/2), δ) − U(h(m2*, 1/2), δ)] > 0 and since limδ → 0[U(h(m1*, 1/2), δ) − U(h(m2*, 1/2), δ)] < 0 and limδ → 1[U(h(m1*, 1/2), δ) − U(h(m2*, 1/2), δ)] > 0. Additional Supporting Information may be found in the online version of this article: Online Appendix Notes The author wishes to thank Martin Cripps (the Editor) and an anonymous referee for comments that greatly improved the article. I am very grateful to Meg Meyer and to Pawel Gola for discussions and feedback, as well as to Ricardo Alonso, Leonie Baumann, Inga Deimen, Francesc Dilmé, Matt Elliott, Peter Esö, Johannes Hörner, Kohei Kawamura, Gilat Levy, Marco Ottaviani, Ines Moreno de Barreda, Sujoy Mukerji, Collin Raymond, Anna Sanktjohanser, Dezsö Szalay, Alex Teytelboym, and conference and seminar participants at Econometric Society EWM, Econometric Society World Congress, Royal Economic Society Conference, York Symposium for Game Theory, Bonn, Cambridge, Cologne, Edinburgh and Oxford. Funding by the Royal Economic Society and German Research Foundation (DFG) through CRC TR 224 (Project B04) is gratefully acknowledged. Footnotes 1 Similarly, treatment outcomes for medical procedures are published so that those seeking treatment can compare the quality of health care providers. Yet, treatment outcomes also depend on the prior health conditions of past patients. 2 Estimates of value added have been published, but they do not eliminate the inference problem (Kane et al., 2002; Dranove et al., 2003; Wilson and Piebalga, 2008). In addition, estimates of schools’ value added are rarely used by students (Coldron et al., 2008; Imberman and Lovenheim, 2016). 3 For example, see Noden et al. (2014). 4 For example, see Burgess and Allen (2010), p.10. 5 This allocation arises if applications strategies in period 0 are symmetric with respect to schools’ identities. 6 In the article, I focus on a steady state in which the application strategy profile of students is constant across periods. To construct students’ posterior beliefs in such a steady state, it is not necessary to reason through the choices of students in each previous period as in the example above. Instead, it is possible to directly derive the stationary probability that the better school ranks high and then construct students’ posterior beliefs about schools’ relative quality. 7 Only about half of students in England attend their nearest school (Burgess et al., 2006). 8 If the state changes with some exogenously given probability |$g\in \left[0,\frac{1}{2}\right)$| each period and such changes are unobserved, the results of this article remain qualitatively unchanged (see Subsection 6.2). 9 Hence, if s = 0, intake ability will be equal across schools, irrespective of students’ application choices. 10 The fact that schools select on ability is not critical. The crucial feature is that an oversubscribed school admits at least as large a share of high-ability applicants as the other school, as discussed in Subsection 6.3. 11 School quality refers to features of the school that affect its performance for a given intake, e.g., teaching and leadership. For evidence that these features have a large impact on performance, see, e.g., Bloom et al. (2015). 12 For evidence that there is residual noise in rankings, see Kane et al. (2002). 13 Note that I do not assume that the better school’s probability of winning increases more than the worse school’s for a given increase in the share of high-ability students admitted. 14 Results are not affected by what information students have about their ability or by what students observe about other students’ types as long as the aggregate distribution of types is known. 15 The insights still apply if students observed a longer window of rankings, as long as they do not have access to all rankings available to students in previous periods (see Subsection 6.1). The most recent ranking is clearly the most easily accessible, e.g., in England this is the one circulated by the media. 16 Off the equilibrium path, It ∈ [−1, 1] and if It < 0 then |$\overline{m}_{t}=F\left(|V\cdot I_{t}|\right)$| would refer to the share of non-local students who apply to the most recent loser. 17 In the worst case, his application is rejected and he enrols at the other school, which results in the same expected payoff as though he had applied there. 18 Note that a non-local low-ability student is indifferent between applying to either school, but for all other types it is a strictly dominant strategy to apply to the school that offers a higher expected payoff conditional on enrolment. 19 Note that I assume that the worse school never wins with probability 1, which implies that the worse school winning is never an absorbing state. For a discussion about how results are affected when this assumption is relaxed, see Subsection 6.1. 20 For any time-invariant mobility level, the sequence of levels of informativeness converges. However, it may not converge to a steady-state equilibrium level. 21 Performance is measured by clinical outcomes (survival/readmission) and quality is measured by the adherence to clinical guidelines. 22 That access to performance information can increase applications to well-performing schools has been shown by Hastings and Weinstein (2008). 23 This reason is similar to the one for why steady-state informativeness increases in mobility. See Subsection 2.2. 24 To maximise equilibrium informativeness, such inertias should be made as strong as possible. However, if school qualities change exogenously over time, a trade-off arises: with unchanged qualities, a longer window of past performance provides a more informative ranking, but with changing qualities, recent past performance is more likely than earlier past performance to have been generated by the current school qualities. By contrast, if the ranking is based on last period’s performance, a decrease in transport costs and or a rise in the share of non-local high-ability applicants admitted by an oversubscribed school always raises equilibrium informativeness (see Subsection 6.2). 25 The last term of (14) already incorporates that the expenditure on transport costs is minimised for a given h by assigning those students to non-local schools who incur the lowest transport costs within each ability group. 26 Posterior beliefs in steady state satisfy (15) by the proof of Lemma 2. Beliefs in steady state are used to reflect that the planner internalises how the assignment rule in any given period affects the informativeness of future rankings. 27 Note that the equilibrium allocation h(m*, s) derived in Section 2 is independent of δ ∈ (0, ∞) because the allocation is driven only by the share of non-local high-ability students applying to the winning school. 28 Relatedly, in a static setting, (Barseghyan et al.,2019) study schools' incentives to exert effort when students care not only about schools' effort but also about their peers. For work on competition between hospitals see, e.g., (Kessler and McClellan, 2000; Gravelle and Sivey, 2010). 29 It is unrealistic to assume that every intervention weakly improves school quality and, in addition, if this were the case school quality would be certain to improve over time irrespective of which schools come under pressure. 30 The distribution of the new quality could be dependent on the quality level it replaces. The more likely it is that bad quality improves and the more likely it is that good quality deteriorates with an intervention, the more overall school quality improves when bad schools rather than good schools are selected for replacement. 31 Since I focus on a symmetric steady-state equilibrium, it is irrelevant how the relative performance of schools of the same quality is determined. 32 Note that γ = 0 does not recover the baseline model because there is a likelihood that both schools are good or both are bad. However, the qualitative insights of the baseline model apply if γ = 0 because optimal mobility still only varies with the difference between the posterior belief that the winning school is better and the posterior belief that the winning school is worse. 33 For any given time-invariant mobility level |$\widehat{m}$|⁠, γ only affects how quickly the joint distribution of school qualities and rankings converges to its stationary distribution, but not the stationary distribution itself. 34 There may be other reasons outside this model for an admission rule that selects a larger share of applicants based on ability being undesirable, e.g., one may worry that if oversubscribed schools get to select a larger share of their intake based on ability, these schools will invest more effort into screening applicants and will divert effort away from other tasks that would improve their students’ education. 35 The model of this article can be thought of as capturing situations in which there is sufficiently high differentiation between schools such that intakes will not become too unequal across schools, or situations in which students’ abilities are relatively homogeneous so that the performance advantage from taking on more able students is not too large. 36 In the terminology of the social learning literature, a herd will arise. 37 If a high-ranked school were more likely to maintain or improve its quality than a low-ranked school, e.g., because it can attract more capable teachers, then a high rank would also serve as a predictor for better relative quality in the future. Students would then find it even more attractive to attend a high-ranked school at any given belief about schools’ past qualities. As a consequence, rankings would become even more informative about schools’ past qualities. 38 Empirical evidence shows that students of higher socio-economic status are more likely to seek out better-performing schools (e.g., Hastings et al., 2005; Allen et al., 2014) and higher socio-economic status is correlated with more parental investment in education and higher expected attainment (e.g., Machin et al., 2013; Richards et al., 2016; Shaw et al., 2017). 39 I assume VH sufficiently low such that not all high-ability students apply to the most recent winner. 40 See Hoxby (2000) and Rothstein (2006) on Tiebout choice. 41 See Fiva and Kirkebøen (2011) and Hussain (2020) for analyses of how house prices change with the release of school quality indicators. 42 Dependening on the matching algorithm used, families may find it optimal to express a preference for a school to which their child is likely to be admitted rather than for the school with the highest perceived quality (Calsamiglia and Güell, 2018). 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This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)

Jehiel, Philippe; Steiner, Jakub

doi: 10.1093/ej/uez068pmid: N/A

Abstract A memoryless agent can acquire arbitrarily many signals. After each signal observation, she either terminates and chooses an action, or she discards her observation and draws a new signal. By conditioning the probability of termination on the information collected, she controls the correlation between the payoff state and her terminal action. We provide an optimality condition for the emerging stochastic choice. The condition highlights the benefits of selective memory applied to the extracted signals. Implications—obtained in simple examples—include (i) confirmation bias, (ii) speed-accuracy complementarity, (iii) overweighting of rare events, and (iv) salience effect. Economic agents often acquire information about the state of the economy before making their decisions. The information is typically modelled as a signal that helps the agent refine the distribution of the state and improve the decision-making. Often, signals come over time and agents can absorb only a small number of them. We capture this information-processing friction by assuming that agents receive as many signals as they wish but can remember only a finite number of them when making their choices. In the simplest setting we analyse, the agent can only remember one signal. A key strategic variable that we consider is to allow the agent to ignore some signals with positive probability and restart the signal extraction process. We allow agents to employ an arbitrary stationary decision process that specifies for each possible signal realisation a probability with which the agent restarts the process as well as the chosen action in case of termination. We do not impose time constraints and costs in the basic formulation so that the friction comes solely from the limited information-storing capacity of the agent. We ask ourselves: Should the agent optimally make her choice as soon as she receives the first signal whatever the realisation of it is, or could she be better off by rerunning the very same information-acquisition process? Can hesitation—selective repetition of a fixed stochastic decision procedure—be welfare-enhancing? A general insight is that selective rerunning of the primitive decision procedure is typically optimal. To document this most generally, we provide a simple necessary condition satisfied by the optimal rerunning strategy. The result is an interim indifference condition imposed on the agent who has concluded her decision-making with a plan to choose a particular action. Given the recommended action, the agent’s posterior expected payoff from implementing this action must be the same as the posterior expected payoff from rerunning the whole decision-making—the whole selective repetitions of the primitive signal extraction—and implementing whichever action the second run of the decision-making will recommend. We refer to this as to the second-thought-free condition. For illustration, consider a binary decision of whether to make an investment of a fixed size. The agent receives payoff 1 if she invests in the good state of the economy, payoff −1 if she invests in the bad state, and receives 0 when she does not invest whatever the state. One of the two states is a priori more likely; for sake of concreteness, let the prior probability of the good state be 2/3. Both states give rise to a population of good and bad signals, with the share of the good signals at 90% in the good state and 10% in the bad state. The agent draws possibly several signal realisations in sequence but remembers only the last one when making her investment choice. As follows from simple optimisation considerations, assume she invests if and only if the last remembered signal was good. Observe that the decision rule generated by the immediate termination upon the first signal that comes in does not generate a second-thought-free choice rule: An agent whose first observed signal was bad prefers to rerun the decision process, since the new run will either lead to not investing again or will give rise to the signal realisation that conflicts with the first observation and will lead to investing. Since, conditional on two conflicting signals, the a priori more common state is more likely, investing is preferred in this contingency. The agent benefits from having second thoughts when the first observed signal is surprising. We interpret the probability of terminating the decision process after receiving a particular signal as a search intensity targeting this particular signal. A higher probability of termination at a given information set inflates the likelihood that the agent makes the terminal choice at the set. We show that the failure of the second-thought-free condition with uniform search intensity in the above investment decision example indicates that relative to the uniform search, the agent benefits from decreasing the search intensity for the bad attribute. More generally, the second-thought-free condition follows from the first-order condition imposed on the optimal search intensities. The model provides microfoundations to a range of behavioural stylised facts. The unifying principle of our behavioural insights is the intuition that the agent targets her search towards the type of evidence that would provide her with more valuable posteriors under the uniform search. This principle generates confirmation bias in the context of the above example, since evidence that confirms the agent’s prior leads to more informed posterior than does evidence that contradicts the prior. An optimally targeted information search also generates speed-accuracy complementarity in the same setting; that is, accuracy of choice declines with the response time. The effect is generated by the confirmation bias: The agent encountering evidence contradicting her prior is likely to disregard the evidence and to have a second thought. Hence, long response times indicate a surprising state of the world, and the constrained-optimal choice rule commits errors in the surprising state relatively often. Overweighting of rare events occurs in a related setting in which the agent’s task is to form a probability belief about an event that is known to be rare, such as a flight accident, by observing a random flight outcome. Since observing a flight accident is far more informative about the probability of future accidents than observing an uneventful flight, the agent optimally biases her search towards eventful flights. In the last behavioural application, we show in a setting with multiple states that distinct states of the world are salient in the sense that they attract the agent’s attention (i.e., trigger higher termination rates in our framework). The effect arises because an indistinct perception stimulus that can be generated by several similar states is less informative than a distinct perception stimulus that is most likely generated by a specific distinct state. Hence, the optimal information search targets stimuli indicating distinct states. Our leading interpretation of the model is in terms of a single-person with information storage limitations but perfect ability to adjust optimally her termination strategies as a function of what she remembers. These adjustments can be viewed as a result of a successful trial and error process or as a result of evolutionary pressures in which case the adjustments may not be fine-tuned to each specific problem.1 Alternatively, one may think of the termination strategies and the final decisions as being chosen by different persons and only the one in charge of the final decision would be subject to information storage limitations, thereby allowing the termination strategies to be optimally determined. There is a wide range of studies that propose different modelling of optimisation over information structures. Relative to rational inattention models (Sims, 2003), we provide a procedural micro-foundation of our set of the feasible information structures (which must be obtained through variations of the termination strategies and as such can straightforwardly be related to the time dimension of the decision process). Perhaps surprisingly, our memoryless agent shares some of the flexibility in her choice of information structures with the sequential-sampling model of Wald (1945) in which there is perfect information aggregation. But, our approach allows for a simple derivation of the speed-accuracy complementarity, which is less immediate to obtain with sequential-sampling models (see however Fudenberg et al., 2018). Relative to studies based on finite automata (Hellman and Cover, 1970; Wilson, 2014; Basu and Chatterjee, 2015), our approach yields a simple necessary condition for the optimal choice rule, the second-thought-free condition. This condition arises because our agent chooses the probability of termination at each of her information sets. Such a termination optimisation is absent from the related models with finite automata in which the termination is exogenous (or the objective involves asymptotic performance as time diverges). The second-thought-free condition allows us to characterise the optimal choice rule in the binary settings. This article belongs to a growing economic literature that explains behavioural stylised facts as the constrained-optimal behaviour of decision-makers facing information processing frictions. For instance, Robson (2001), Rayo and Becker (2007), Netzer (2009), and Khaw et al. (2017) provide microfoundations for risk attitudes; Gabaix and Laibson (2017) endogenise discounting; and Wilson (2014), Compte and Postlewaite (2012), and Leung (2020) establish constrained-optimal ignorance of weakly informative news.2 1. Model An agent faces a decision under uncertainty. She chooses an action a ∈ A and receives a payoff u(a, θ) in the fixed payoff state θ ∈ Θ drawn from an interior prior π ∈ Δ(Θ). The sets Θ and A are finite. The agent chooses a Blackwell experiment p, where p is a family of conditional signal distributions p(x∣ θ) that depend on θ ∈ Θ. The experiment generates a signal realisation x from a finite space X. The conditional signal distributions are fully mixed: p(x∣ θ) > 0 for all x, θ. We allow the agent to choose among possibly several such experiments and we let |$\mathcal {P}$| denote the exogenous set of experiments from which she chooses. We impose no restrictions on |$\mathcal {P}$| (other than the full-support of each p). The agent can repeat the selected experiment arbitrarily many times, but she is unable to aggregate the information across the repetitions. Each run of the experiment is a cognition that exhausts the agent’s capacity dedicated to the problem being solved. Once the agent hits the constraint at the end of the experiment, she can continue only after she unclogs her capacity by amnesia. We model this as follows. The agent can condition the repetition of the experiment on the last observed signal realisation. She chooses a vector β = (βx)x∈X ∈ B = [0, 1]|X|∖{(0, …, 0)} of termination probabilities βx for each signal realisation x; we call β a termination strategy. The agent runs the experiment p for the first time, receives signal realisation x(1) with probability p(x(1) ∣ θ) and terminates the reasoning with probability |$\beta _{x^{(1)}}$|⁠. She restarts with the complementary probability |$1-\beta _{x^{(1)}}$|⁠, and receives a signal realisation x(2) from a new run of the process p with probability p(x(2) ∣ θ), terminates with probability |$\beta _{x^{(2)}}$| or restarts with probability |$1-\beta _{x^{(2)}}$|⁠, and continues until she terminates after a random number of repetitions of p; see Figure 1. When the agent chooses having distinct βx for different x, then she implements the familiar idea of selective memory; some facts and observations are easily forgotten whereas others are remembered and they trigger choice. After the agent terminates the reasoning with a terminal signal realisation x, she selects an action a = σ(x) according to an action strategy|$\sigma :X\longrightarrow A$|⁠.3 Let S be the set of all mappings from X to A. Fig. 1. Open in new tabDownload slide For each |$(p, \beta , \sigma )$|⁠, the decision process is a Markov chain evolving on the agent’s states of mind, with transition probabilities that depend on the payoff state |$\theta$|⁠. The chain begins in the state of mind O and transits to states x ∈ X = {x1, x2} with probabilities |$p(x\mid \theta )$|⁠. The process returns to O with probability |$1- \beta _x$|⁠, or terminates with choice of |$a= \sigma (x)$| with probability |$\beta _x$|⁠. Fig. 1. Open in new tabDownload slide For each |$(p, \beta , \sigma )$|⁠, the decision process is a Markov chain evolving on the agent’s states of mind, with transition probabilities that depend on the payoff state |$\theta$|⁠. The chain begins in the state of mind O and transits to states x ∈ X = {x1, x2} with probabilities |$p(x\mid \theta )$|⁠. The process returns to O with probability |$1- \beta _x$|⁠, or terminates with choice of |$a= \sigma (x)$| with probability |$\beta _x$|⁠. By excluding the termination strategy (0, …, 0) we force the agent to make a decision a ∈ A. Since β ≠ (0, …, 0) and each feasible experiment p generates all signal values with a positive probability in each state, the decision process almost surely eventually terminates. The outcomes of distinct runs of p are conditionally independent. Thus, the probability that the agent terminates after t repetitions of the experiment p resulting in the signal history |$\mathbf {x}^t=(x^{(1)},\dots ,x^{(t)})$| is $$\begin{eqnarray} \rho \left(\mathbf {x}^t\mid \theta ;p,\beta \right)= \beta _{x^{(t)}}p(x^{(t)}\mid \theta )\prod _{l=1}^{t-1} \left(1-\beta _{x^{(l)}}\right)p\left(x^{(l)}\mid \theta \right). \end{eqnarray}$$(1) We let $$\begin{eqnarray} r(a\mid \theta ;p,\beta ,\sigma )=\sum _{t=1}^\infty \sum _{\mathbf {x}^t:\sigma (x^{(t)})=a}\rho \left(\mathbf {x}^t\mid \theta ;p,\beta \right) \end{eqnarray}$$(2) denote the probability that the agent who employs the experiment p, the termination strategy β, and action strategy σ terminates with action a in state θ. We call r(p, β, σ) ≔ (r(a ∣ θ; p, β, σ))a∈A,θ∈Θ the choice rule. The set of feasible choice rules is |$\mathcal {R}(\mathcal {P} )=\lbrace r(p,\beta ,\sigma ):p\in \mathcal {P},\beta \in B, \sigma \in S\rbrace$|⁠. Sometimes we abuse notation, omit p, β, σ and write r(a∣ θ) for the probability of a in state θ under the rule constructed by some p, β, σ. The repeated-cognition problem is to select, for a given prior π, utility function u and set |$\mathcal {P}$|⁠, a feasible choice rule r that maximises the expected payoff: $$\begin{eqnarray} \max _{r\in \mathcal {R}(\mathcal {P})}\sum _{\theta \in \Theta ,a\in A}\pi _{\theta }r(a\mid \theta )u(a,\theta ). \end{eqnarray}$$(3) The optimisation in (3) can be an outcome of selective pressures that favour successful decision procedures via cultural or biological evolution, or via competition of firms differing in their internal procedures. There are no costs to delaying the decision in our model but incorporating such costs would not affect our qualitative insights when these are not too big. We address agents with less severe memory constraints and with exponential time discounting preferences in Section 6. 2. Optimal Cognition Biases We now derive a necessary optimality condition that the choice rule solving the repeated-cognition problem must satisfy. Generically, the condition requires the agent to engage in selective information processing—that is, to ignore some signals more often than others. 2.1. Second-Thought-Free Choice Rules We start with a definition of second-thought-free choice rules. If the agent’s decision process generates such a rule, then she has no incentive to rerun the process regardless of the action recommendation with which the process terminates. Our main result below states that the optimal rule is second-thought-free. Let r be a generic stochastic choice rule that specifies conditional probabilities r(a ∣ θ) of each action a ∈ A in each state θ ∈ Θ. Definition 1. The choice rule r is second-thought-free with respect to the utility u and prior π if the agent prefers each action recommended by the rule to a new run of the rule r. That is, for each action a chosen with positive probability, $$\begin{eqnarray} \operatorname{E}_{\alpha }[u(a_1,\theta )\mid a_{1}=a]\ge \operatorname{E}_{\alpha }[u(a_{2},\theta )\mid a_{1}=a], \end{eqnarray}$$(4)where the expectations are with respect to the random variables θ and a2, and α(θ, a1, a2) = πθr(a1∣ θ)r(a2∣ θ) is the joint distribution of the state and two actions consecutively generated by r. The definition requires the agent who terminates with an action plan a to weakly prefer a to forgetting a and choosing whichever action a new run of the decision process will recommend. Although the definition allows for the strict preference against having a second thought, the next lemma shows that if a choice rule is second-thought-free, then the agent is indifferent between terminating and the second thought. Lemma 1. If r is second-thought-free, then(4)is met with equality for each action a chosen with positive probability: $$\begin{eqnarray} \operatorname{E}_\alpha [u(a_1,\theta )\mid a_1=a]=\operatorname{E}_\alpha [u(a_2,\theta )\mid a_1=a]. \end{eqnarray}$$(5) We refer to (5) as the second-thought-free condition. Proof. If (4) holds with strict inequality for some a chosen with positive probability, then $$\begin{eqnarray} \operatorname{E}_\alpha \left[u(a_1,\theta )\right] =\operatorname{E}_\alpha \left[\operatorname{E}_\alpha \left[u(a_1,\theta )\mid a_1\right] \right] \gt \operatorname{E}_\alpha \left[\operatorname{E}_\alpha \left[u(a_2,\theta )\mid a_1\right] \right]=\operatorname{E}_\alpha \left[u(a_2,\theta )\right], \end{eqnarray}$$ which contradicts that a1 and a2 are conditionally iid. 2.2. Optimality Condition We provide here a general necessary optimality condition imposed on the stochastic choice rule. Proposition 1. If a choice rule solves the repeated-cognition problem (3), then it is second-thought-free and satisfies (5). To understand the statement, consider the optimal choice rule r* generated by a process that consists of a random number of repetitions of a primitive cognition p. Once these repetitions of p terminate with a signal realisation x and the agent is about to take an action a = σ(x), then, according to the proposition, she must be indifferent between a, and running the process associated with r* from scratch, where the new run of r* would involve new repetitions of p. To prove Proposition 1, we introduce an effective experiment s(p, β). While the primitive experiment p(x ∣ θ) specifies the probability that its one run results in signal x, we define s(x∣ θ; p, β) to be the probability that selective repetitions of p according to the termination strategy β terminate with x. Relative to p(x ∣ θ), the effective probabilities s(x ∣ θ; p, β) are inflated for those x at which the agent terminates with a high probability βx. Lemma 2. An agent who employs a primitive experiment p and a termination strategy β terminates with x in state θ with probability: $$\begin{eqnarray} s(x\mid \theta ;p,\beta )=\frac{\beta _{x}p(x\mid \theta )}{\sum _{x^{\prime }\in X}\beta _{x^{\prime }}p\left( x^{\prime }\mid \theta \right) }. \end{eqnarray}$$(6) Proof. Experiment s(p, β) satisfies the recursive formula $$\begin{eqnarray} s(x\mid \theta ;p,\beta )=\beta _x p(x\mid \theta )+\sum _{x^{\prime }\in X} \left(1-\beta _{x^{\prime }}\right)p\left(x^{\prime }\mid \theta \right) s(x\mid \theta ;p,\beta ). \end{eqnarray}$$ The first summand is the probability that the agent terminates with signal x after the first run of the experiment p. The second summand is the probability that the agent continues after the first run and terminates with x later. Solving for s(x∣ θ; p, β) gives (6). The lemma implies that s(p, β) and hence also r(p, β, σ) are homogeneous of degree zero with respect to β. Thus, since we abstract from the delay costs, for any optimal termination strategy β*, αβ* for α ∈ (0, 1) is optimal too, and it generates the same optimal choice rule r* as β*. This multiplicity of implementation of the optimal choice rule would disappear in a natural approximation of our model with exponential discount factor approaching 1. Such approximation would select the quickest available decision process that implements the optimal feasible rule r*; that is, it would impose that maxx∈Xβx = 1. Proof of Proposition 1. Using (6), we rewrite the objective as follows. $$\begin{eqnarray} \max _{p\in \mathcal {P},\beta \in B,\sigma \in S}\sum _{\theta \in \Theta ,x\in X}\pi _{\theta }\frac{\beta _{x}p(x\mid \theta )}{\sum _{x^{\prime }\in X}\beta _{x^{\prime }}p\left( x^{\prime }\mid \theta \right) }u(\sigma (x),\theta ). \end{eqnarray}$$(7) Let rule r(p*, β*, σ*) solve the repeated-cognition problem. Consider an action a chosen with a positive probability and x such that σ*(x) = a and |$\beta ^*_x\gt 0$|⁠. The constraint βx ≥ 0 is not binding for this x, and the first-order condition of (7) with respect to βx is: $$\begin{eqnarray} \sum _{\theta \in \Theta } \pi _\theta \frac{s\left(x\mid \theta ;p^*,\beta ^*\right)}{\beta ^*_x} u(a,\theta ) - \sum _{\theta \in \Theta ,x^{\prime }\in X} \pi _\theta s\left(x^{\prime }\mid \theta ;p^*,\beta ^*\right)\frac{s\left(x\mid \theta ;p^*,\beta ^*\right)}{\beta ^*_x} u\left(\sigma ^*(x^{\prime }),\theta \right) &=& \\ \sum _{\theta \in \Theta } \pi _\theta \frac{s\left(x\mid \theta ;p^*,\beta ^*\right)}{\beta ^*_x} u(a,\theta ) - \sum _{\theta \in \Theta ,a^{\prime }\in A} \pi _\theta r\left(a^{\prime }\mid \theta ;p^*,\beta ^*,\sigma ^*\right)\frac{s\left(x\mid \theta ;p^*,\beta ^*\right)}{\beta ^*_x} u\left(a^{\prime },\theta \right) &\ge &0. \end{eqnarray}$$ Multiplication by |$\beta ^*_x$|⁠, summation over all x such that σ*(x) = a, and division by ∑θπθr(a ∣ θ; p*, β*, σ*) gives (4). Thus, the terminating agent weakly prefers termination to continuation. Lemma 1 implies the indifference (5). Since the objective function in (7) is homogenous of degree zero with respect to β, we can restrict β to the simplex over the signal set X. This simplex is compact, the objective function in (7) is continuous in β and the p(x∣ θ), hence the repeated-cognition problem has a solution whenever the set of the primitive experiments |$\mathcal {P}$| is compact. 2.2.1. Comment Our agent can be viewed as having imperfect recall in the sense of Piccione and Rubinstein (1997). Our approach corresponds to their ex ante approach, and the insight of Proposition 1 can be related to the observation in their absent-minded driver example that the ex ante optimal solution is also a (modified) multi-self equilibrium in which the decision problem is viewed as a team composed of multiple selves all sharing the decision-maker’s objective. 3. Analytical Solution of the Binary Setting The action and state sets are binary: A = Θ = {0, 1}. To avoid a trivial case, we assume that neither action is dominant. Then, without loss of generality, u(a, θ) = uθ > 0 if a = θ and u(a, θ) = 0 otherwise. State θ is drawn from an interior prior π ∈ Δ(Θ). The exogenous set |$\mathcal {P}$| of the feasible statistical experiments is finite, and each |$p\in \mathcal {P}$| delivers a signal x from a finite signal space X with probability p(x ∣ θ). The agent chooses |$p\in \mathcal {P}$|⁠, the termination strategy β = (βx)x∈X and action strategy |$\sigma :X\longrightarrow A$| to maximise the expected payoff. The first result states that there exists a solution in which the agent ignores all but two signal realisations of the chosen experiment p. That is, she always repeats the experiment upon encountering all but two signals. Roughly, the result follows because it is advantageous to consider only the most informative signal realisations.4 Lemma 3. There exists a solution in which the termination probability βxis positive for at most two signal values x ∈ X. See Appendix for the proofs omitted in the main text. Based on the lemma, we can, without loss of generality, restrict the signal space X to be binary, and identify it with the action and state spaces, X = A = Θ. Again without loss of generality, we choose signal labels in each experiment in such a way that each experiment |$p\in \mathcal {P}$| satisfies the monotone likelihood ratio property: p(1 ∣ θ)/p(0 ∣ θ) increases in θ. We continue to assume that p(x∣ θ) > 0 for all x and θ. Define σI to be the identity function, and let the agent employ the binary experiment p and the action strategy σI. The next lemma characterises the set |$\mathcal {R}_{p,\sigma _{I}}=\lbrace r(p,\beta ,\sigma _{I}):\beta \in B\rbrace$| of the feasible choice rules that such an agent has access to. To characterise this set, we introduce a parameter that we dub perceptual distance between states 0 and 1 under the experiment p: $$\begin{eqnarray} d_{p}=\frac{p(1\mid 1)p(0\mid 0)}{p(0\mid 1)p(1\mid 0)}. \end{eqnarray}$$ The perceptual distance is a summary statistic of the experiment p. The larger it is, the more p reliably discriminates between the two states. The monotone likelihood property of each p implies that dp > 1. The next lemma states that the perceptual distance is preserved under any termination strategy β. Lemma 4. |$\mathcal {R}_{p,\sigma _I}=\lbrace r:r(1\mid 1)r(0\mid 0)=d_p r(1\mid 0)r(0\mid 1)\rbrace$|⁠. That is, a rule r can be constructed from p if and only if it preserves the perceptual distance: |$\frac{r(1\,\mid \,1)r(0\,\mid \,0)}{r(0\,\mid \,1)r(1\,\mid \,0)}=d_{p}$| (or if it always selects a same action). By controlling the termination strategy β, the agent trades off the likelihoods r(0 ∣ 0; p, β, σI) and r(1 ∣ 1; p, β, σI) of the correct choice in the states 0 and 1, respectively. See Figure 2. The set |$\mathcal {R}_{p,\sigma _{I}}$| of rules accessible from p is compact. Fig. 2. Open in new tabDownload slide Each point in |$[0, 1]^2$| on this graph corresponds to a choice rule. The depicted curves are the sets |$\mathcal {R}_{p, \sigma _I}$| of the choice rules constructible from experiments p and action strategy σI. The thick curve corresponds to the experiment |$\overline{p}$| with the maximal perceptual distance |$\overline{d}$|⁠. Since the objective is linear in the choice rule, the indifference curves are downward sloping lines. The dashed line is the indifference curve tangential to |$\mathcal {R}_{\overline{p}, \sigma _I}$|⁠. The dot depicts the solution of the repeated-cognition problem. Fig. 2. Open in new tabDownload slide Each point in |$[0, 1]^2$| on this graph corresponds to a choice rule. The depicted curves are the sets |$\mathcal {R}_{p, \sigma _I}$| of the choice rules constructible from experiments p and action strategy σI. The thick curve corresponds to the experiment |$\overline{p}$| with the maximal perceptual distance |$\overline{d}$|⁠. Since the objective is linear in the choice rule, the indifference curves are downward sloping lines. The dashed line is the indifference curve tangential to |$\mathcal {R}_{\overline{p}, \sigma _I}$|⁠. The dot depicts the solution of the repeated-cognition problem. Fig. 3. Open in new tabDownload slide Confirmation bias with discounting. Action 1 is a priori more attractive: |$\pi _1u_1=5\times \pi _0u_0$|⁠. The primitive experiment is symmetric: |$\mathit{ p}(1 \mid 1) = \mathit{ p}(0 \mid 0) = 0.9$|⁠. The agent terminates immediately when she observes signal value 1, |$\beta ^*_1=1$|⁠. When |$\delta \gt 0.71$|⁠, then the agent is biased towards state 1: when she encounters signal value 0, then she terminates the decision-process with a probability only |$\beta ^*_0( \delta )\lt 1$| (the full curve). The dotted line is |$\beta ^*_0/ \beta ^*_1$| from the baseline model without discounting. Fig. 3. Open in new tabDownload slide Confirmation bias with discounting. Action 1 is a priori more attractive: |$\pi _1u_1=5\times \pi _0u_0$|⁠. The primitive experiment is symmetric: |$\mathit{ p}(1 \mid 1) = \mathit{ p}(0 \mid 0) = 0.9$|⁠. The agent terminates immediately when she observes signal value 1, |$\beta ^*_1=1$|⁠. When |$\delta \gt 0.71$|⁠, then the agent is biased towards state 1: when she encounters signal value 0, then she terminates the decision-process with a probability only |$\beta ^*_0( \delta )\lt 1$| (the full curve). The dotted line is |$\beta ^*_0/ \beta ^*_1$| from the baseline model without discounting. Thanks to the chosen labelling of the signals, the agent can equate her choice to the observed signal without a loss: Lemma 5. For any rule r(p, β, σ)there exists β′ such that the rule r(p, β′, σI) achieves at least as high expected payoff as r(p, β, σ) where σIis the identity function. The solution to the repeated-cognition problem in the binary setting exists since the objective is continuous in the choice rule and the agent optimises on the compact set |$\bigcup _{p\in \mathcal {P}}\mathcal {R}_{p,\sigma _I}$| of the rules. Let |$\overline{p}$| be the experiment with the maximal perceptual distance: |$\overline{p}\in \arg \max _{p\in \mathcal {P}}d_{p}$|⁠, and let |$\overline{d} =\max _{p\in \mathcal {P}}d_{p}$|⁠. In line with the intuition that the agent should go for the most informative experiment, we establish: Lemma 6. There exists a solution to the repeated-cognition problem in which the agent employs the experiment|$\overline{p}$|with the maximal perceptual distance. The last lemma implies that all details of the set |$\mathcal {P}$| relevant for the solution are summarised in the one-dimensional statistic |$\overline{d}$| that is independent of the payoff function u.5 We are now ready to solve the binary setting. The optimal effective choice rule |$r^*(a\mid \theta )=r(a\mid \theta ;\overline{p}, \beta ^*,\sigma _I)$| consists of four unknown probabilities and it is determined by four conditions: the second-thought-free condition (5), the feasibility condition from Lemma 4, and two normalisation conditions. Let parameter |$R=\frac{\pi _1u_1}{\pi _0u_0}$| measure the relative a priori attractiveness of action 1. Proposition 2. When|$R\ge \overline{d}$|⁠, then the agent always chooses action 1; when|$R\le 1/\overline{d}$|⁠, then the agent always chooses action 0; when|$R\in (1/\overline{d},\overline{d})$|⁠, then the agent chooses both actions with positive probabilities and $$\begin{eqnarray} r^{\ast }(1\mid 1)=\frac{\overline{d}R-\sqrt{\overline{d}R}}{(\overline{d} -1)R}\mbox{, }r^{\ast }(0\mid 0)=\frac{\overline{d}-\sqrt{\overline{d}R}}{ \overline{d}-1}, \end{eqnarray}$$(8) $$\begin{eqnarray} \frac{\beta _{1}^{\ast }}{\beta _{0}^{\ast }}=\frac{\overline{d}R-\sqrt{ \overline{d}R}}{\sqrt{\overline{d}R}-R}\frac{\overline{p}(0\mid 1)}{\overline{p}(1\mid 1)}. \end{eqnarray}$$(9) When the ex ante attractiveness of one of the actions is too strong relative to the perceptual distance of the two states, then the agent always chooses the ex ante attractive action. The decision process is non-trivial for intermediate incentives: the agent engages in repeated cognition and she chooses both actions with positive probabilities. 4. Behavioural Applications This section presents three behavioural effects illustrated in the binary setting from Section 3: confirmation bias, speed-accuracy complementarity, and overweighting of rare events. 4.1. Confirmation Bias Psychologists and economists distinguish at least three mechanisms leading to confirmation bias: (i) People search for evidence selectively, targeting the evidence type in accord with their priors, e.g., Nickerson (1998), (ii) they selectively memorise and recall the data supporting their priors, e.g., Oswald and Grosjean (2004), and (iii) they selectively interpret ambiguous evidence, e.g., Rabin and Schrag (1999) and Fryer et al. (2018). We focus on the first two mechanisms and interpret them in light of our optimal repeated-cognition result. Corollary 1. When action|$1$|is a priori more attractive, |$R \in (1, d)$|⁠, and the unique primitive binary experiment is symmetric, |$p(1 \mid 1) = p(0 \mid 0) > 1/2$|, then the agent searches relatively more intensively for signal value|$1$|⁠: |$\beta ^*_1\gt \beta ^*_0$|⁠. Proof. Since |$\beta ^*_1/\beta ^*_0$| increases in R, it suffices to show that |$\beta ^*_1/\beta ^*_0=1$| when R = 1 and the primitive experiment p is symmetric. Indeed, when R = 1, then by (9), $$\begin{eqnarray} \frac{\beta ^*_1}{\beta ^*_0}=\sqrt{d}\frac{p(0\mid 1)}{ p(1\mid 1)}=\sqrt{\frac{p(0\mid 0)p(0\mid 1)}{p(1\mid 1) p(1\mid 0)}}=1, \end{eqnarray}$$ where |$d=\frac{p(0\,\mid \,0)p(1\,\mid \,1)}{p(1\,\mid \,0)p(0\,\mid \,1)}$| and the last equality follows from the symmetry of p. To see the connection to confirmation bias, consider, like in our introductory example, an agent whose task is to announce the realised state of the world: she receives reward u1 = u0 = 1 if she makes the correct announcement and 0 otherwise. The agent finds the state θ = 1 a priori more likely than the state 0, π1 > π0. Consider the decision process that terminates immediately after the first run of the experiment and chooses the action equal to the observed signal value: β0 = β1 = 1, σ = σI. To establish that such an unbiased process is suboptimal it suffices to show that it does not satisfy the second-thought-free condition. To see this, we examine the agent who has received the a priori unlikely signal 0 and argue that she benefits from the second thought. Such a surprised agent is better off by restarting instead of terminating with action 0, since if the new run of the process concludes with signal 0 again, then the second thought will have been inconsequential. If, however, the new run of the process concludes with signal and action 1, then the induced switch from action 0 to 1 is beneficial. This is because when the experiment p is symmetric, then, conditional on two conflicting signals, the a priori more common state 1 is relatively more likely. The agent benefits from second thought whenever she receives the surprising recommendation, and thus will deviate from the uniform search in favour of the a priori likely signal value 1. The optimal strategy resembles the natural process in which the selective memory gives rise to confirmation bias. Consider the fastest optimal strategy, letting |$\beta _{1}^{\ast }=1$|⁠. When the agent observes signal 1 that confirms her prior belief, then she terminates and immediately announces the state 1. But if she is surprised, observing signal 0 that contradicts her prior, then she discards the signal with positive probability |$\beta _{0}^{\ast }$| and repeats the experiment. Although finding the exact optimal value |$\beta _{0}^{\ast }$| may be difficult, the fact that double-checking one’s own reasoning when one arrives at a surprising conclusion is a common practice suggests that people are able to deviate from the unbiased information-acquisition process in the payoff improving direction. 4.1.1. Comments (1) The above insight can receive an alternative political economy interpretation. The two states θ represent left vs right wing policy. Consider a right-wing newspaper that targets the right-wing readers viewed as having a prior belief in favour of the right-wing policy. Readers can only absorb one piece of information (the analog of our information storage constraint) and the newspaper has to decide which piece of information x as generated by p(x ∣ θ) to choose as its headline. Our model explains why such journals would target their search toward evidence favouring the right-wing policy.6 (2) Meyer (1991) studies optimal biases in a sequential-learning problem of an agent who receives a sequence of signals and, unlike our agent, can aggregate the sequence. Meyer’s main insight is that some asymmetries in the signal structure are optimal. Although optimal asymmetries arise both in her and our frameworks, the two papers study distinct optimisations. While our agent controls termination probabilities in a stationary decision process, Meyer’s agent controls the choice of a Blackwell experiment in each round of a non-stationary process. 4.2. Speed-Accuracy Complementarity Our model generates the speed-accuracy complementarity effect—a stylised fact stating that delayed choices tend to be less accurate than speedy choices; see the psychology studies of Swensson (1972) and Luce (1986). We establish this effect in the setting from the previous subsection. Let φ(θ, a, t) be the joint probability distribution of the state θ, chosen action a, and the reaction time t generated by the solution (p, β*, σI) of the repeated-cognition problem. Corollary 2. When action |$1$| is a priori more attractive, |$R \in (1, d)$|⁠, and the unique primitive binary experiment is symmetric, |$p(1 \mid 1) = p(0 \mid 0) > 1/2$|, then the probability|${{\rm {Pr}}}_{\varphi }(a=\theta \mid t)$|of the correct choice decreases with response time t. Due to the stationarity of the decision process, the probability of the correct choice conditional on the payoff state is independent of the reaction time: |$\Pr _{\varphi }(a=\theta \mid \theta ,t)=\Pr _{\varphi }(a=\theta \mid \theta )$|⁠. At optimum, this conditional probability of the correct choice is larger in the a priori more attractive state 1 than in the state 0, reflecting the relative weights of the two states in the objective. Overall, unconditionally on the payoff state, the probability Prφ(a = θ ∣t) of the correct choice depends on the response time because t correlates with θ. A long response time indicates that the agent has repeatedly encountered the signal value 0 and has hesitated to terminate. Hence, conditional on large t, the likelihood of the unattractive state 0 becomes high. The longer the agent has hesitated, the more likely it is that she is facing the unattractive state in which she is making more mistakes. Proof. |$\beta ^*_1\gt \beta ^*_0$| by Corollary 1. We let |$f_\theta =\beta ^*_1 p(1\mid \theta )+\beta ^*_0p(0\mid \theta )$| denote the probability of termination per each round in state θ. The response time t in the state θ is geometrically distributed with the decision rate fθ: |$\Pr _\varphi (t\mid \theta )= f_\theta (1-f_\theta )^t$| for t = 0, 1, …. Since p(1 ∣ 1) = p(0 ∣ 0) > p(1 ∣ 0) = p(0 ∣ 1) and |$\beta ^*_1\gt \beta ^*_0$|⁠, the decision rate is higher in state 1 than in state 0: f1 > f0. Thus, the likelihood ratio |$\Pr _\varphi (t\mid \theta =1)/\Pr _\varphi (t\mid \theta =0)$| decreases with t, and hence |$\Pr _\varphi (\theta =1\mid t)$| decreases in t. The fact that |$\beta ^*_1\gt \beta ^*_0$|⁠, and the symmetry of p implies that the probability of the correct choice is larger in state 1 than in state 0: $$\begin{eqnarray} r\left(1\mid 1;p,\beta ^*,\sigma _I\right)&=& \frac{\beta ^*_1 p(1\mid 1)}{\beta ^*_0p(0\mid 1)+\beta ^*_1p(1\mid 1)}\gt \frac{\beta ^*_0p(0\mid 0)}{\beta ^*_0 p(0\mid 0)+\beta ^*_1p(1\mid 0)} \\ &=& r\left(0\mid 0;p,\beta ^*,\sigma _I\right). \end{eqnarray}$$ Since |$\Pr _\varphi (a=\theta \mid t)= \Pr _\varphi (\theta =1\mid t)r(1\mid 1;p,\beta ^*,\sigma _I)+\Pr _\varphi (\theta =0\mid t)r(0\mid 0;p,\beta ^*,\sigma _I)$|⁠, the result obtains. 4.2.1. Comment The predictions of our model are in line with the evidence on state recognition problems reported in Ratcliff and McKoon (2008) according to which: (i) the posterior probability of correct recognition is higher when announcing the a priori more likely state, and (ii) late announcements are relatively less precise. This is in contrast to the prediction of the traditional Wald model (see Fudenberg et al. (2018) for an elaboration of Wald model in which the stakes attached to the correct recognition are a priori unknown). 4.3. Overweighting of Rare Events We consider a state-recognition task in which the two actions are a priori equally attractive, R = π0u0/π1u1 = 1, and π0 = π1 = 1/2. In contrast to previous applications, the distribution of the signal values x = 0, 1 is asymmetric across states. Specifically, the probability of x = 1 in state θ is ρθ ∈ (0, 1) and the probability of x = 0 is 1 − ρθ. We assume, essentially without loss of generality, that ρ0 < ρ1 < 1 − ρ0.7 The a priori probability of event x = 1 is (ρ0 + ρ1)/2 < 1/2, and thus the event x = 1 is relatively rarer than x = 0. The next result states that at the optimum, the agent is relatively more likely to discard the more common event x = 0 in agreement with Kahneman and Tversky (1979), who observe that agents tend to overweight rare events. Corollary 3. When the two actions are a priori equally attractive, |$R = 1$|, then the agent is biased in favour of the event|$x = 1$|⁠: |$\beta _{1}^{\ast }\gt \beta _{0}^{\ast }\gt 0$|(and her guess of the state equals the observed signal realisation, i.e., σ = σI). Proof. This task is a special case of our binary setting with the primitive experiment p(x ∣ θ) = ρθ if x = 1, p(x ∣ θ) = 1 − ρθ if x = 0 and with equally a priori attractive actions, R = 1. Since ρ0 < ρ1, the labelling of the signals satisfies the monotone likelihood property. Since R = 1 ∈ (1/d, d), Proposition 2 implies that the agent’s behaviour is stochastic, both |$\beta ^*_0$| and |$\beta ^*_1$| are positive, and the ratio of the search intensities |$\beta ^*_1/\beta ^*_0$| satisfies (9). Since R = 1, (9) simplifies to $$\begin{eqnarray} \frac{\beta ^*_1}{\beta ^*_0}=\sqrt{d}\frac{p(0\mid 1)}{p(1\mid 1)}=\sqrt{\frac{ p(0\mid 1) p(0\mid 0)}{ p(1\mid 1)p(1\mid 0)}}= \sqrt{\frac{(1-\rho _1)(1-\rho _0)}{\rho _1\rho _0}}. \end{eqnarray}$$ The inequality |$\beta ^*_1\gt \beta ^*_0$| follows from ρ1 < 1 − ρ0. For illustration, consider a formation of belief over the probability of a flight accident. The accident probability per flight in the safe state of the world is 10−6, whereas it is 10−5 in the dangerous state of the world, and both states are a priori equally likely. The agent can sequentially observe arbitrarily many past flight outcomes, but cannot aggregate the information, and recalls only the last observed flight. She guesses that the state of the world is dangerous if and only if the last observed flight is eventful. Consider first an agent who always terminates right after the observation of the first data-point. Such an agent benefits from a ‘second thought' whenever she observes an uneventful flight: either the second observed flight will be uneventful, in which case the second thought will have been inconsequential, or the redrawn flight will be eventful and the agent will switch her assessment from the safe to the dangerous state. Such a switch is beneficial since conditional on two contradicting data-points the dangerous state is relatively more likely. Thus, relative to the immediate termination strategy, the agent will benefit from discarding the uneventful flight observations with positive probability. 5. A Tractable Setting with Multiple States We now present a class of settings with multiple payoff states that admits a simple analytical solution in the form of a system of linear equations for the optimal termination probabilities. Subsection 5.1 applies this solution in a stylised example that explains salience of perceptually distinct states as a second-best adaptation. The agent faces a perceptual task that requires her to announce a realisation of the state θ ∈ Θ drawn from a fully mixed prior π ∈ Δ(Θ), where 2 < |Θ| < ∞. She is endowed with a primitive perception technology that generates a perceived value θ′ of the state. The primitive perception is informative but noisy: the perceived value θ′ equals the true state θ with a high probability, but mistakes, θ′ ≠ θ, occur sometimes. We view the primitive perception technology as a black-box model of a physiological sensor that generates a noisy impression θ′ of the true state θ. The agent can use the sensor repeatedly but is not able to aggregate the information. She conditions the repetition of the sensor’s use on the most recent perception and announces the terminal perception. We formalise this perception task as follows. The agent makes an announcement a ∈ A = Θ, where 2 < |Θ| < ∞, and receives payoff u(a, θ) = uθ > 0 if her announcement is correct, a = θ, and u(a, θ) = 0 if a ≠ θ. Each use of the agent’s sensor generates a signal value/perception θ′ ∈ X = Θ, with conditional probabilities p(θ′ ∣ θ) > 0. The set |$\mathcal {P}$| is the singleton {p}. We make the following assumption. Symmetry: p(θ′ ∣ θ) = p(θ ∣ θ′). The symmetry assumption leads to a significant simplification of the second-thought-free condition described in Lemma 9 in Appendix. Additionally, we make a simplifying assumption that the agent uses the identity action strategy σI; she announces the state equal to her last perception. We also make the assumption that the optimal termination probabilities βx are positive for all x ∈ Θ.8 Let r* = r(p, β*, σI) be the optimal feasible choice rule. Proposition 3. The optimal termination probabilities satisfy the system of linear equations, $$\begin{eqnarray} \sum _{\tilde{\theta }\in \Theta }\beta ^*_{\tilde{\theta }}\frac{p(\tilde{\theta }\mid \theta )}{\left(\pi _\theta u_\theta p(\theta \mid \theta )\right)^{1/2}}= \sum _{\tilde{\theta }\in \Theta }\beta ^*_{\tilde{\theta }}\frac{p(\tilde{\theta }\mid \theta ^{\prime })}{\left(\pi _{\theta ^{\prime }} u_{\theta ^{\prime }} p(\theta ^{\prime } \mid \theta ^{\prime })\right)^{1/2}} \mbox{ for all }\theta ,\theta ^{\prime }\in \Theta . \end{eqnarray}$$(10) The proposition implies that the decision rate |$f_\theta =\sum _{\tilde{\theta }}\beta ^*_{\tilde{\theta }}p(\tilde{\theta }\mid \theta )$| in each state θ is proportional to (πθuθp(θ ∣ θ))1/2 and thus is high in those states that are reliably identified by the primitive experiment and in which the ex ante expected reward for the correct state recognition is high. 5.1. Salience Bordalo et al. (2012) interpret salience as directed attention focus. They quote the popular work by Daniel Kahneman (2011): ‘Our mind has a useful capability to focus on whatever is odd, different or unusual.' The quote states a causal relation between the two features of the salient phenomena: these are: (i) odd, different or unusual, and because of (i), people benefit from (ii) focusing their attention on such phenomena. Here, we confirm Kahneman’s intuition within our proposed framework. Our microfoundation of the salience effect is related to the insight emerging in psychological research on visual salience. Itti (2007) conceptualises the visual salience effect as attention allocation to a subset of the visual field that is ‘sufficiently different from its surroundings to be worthy of [one’s] attention'. Similarly, in our model, a payoff state is salient if it stands out sufficiently from similar states to be worthy of the focus of the agent’s information search. For two states θ1 and θ2, we say that θ1 is more distinct than θ2 if for each other state θ3 ≠ θ1, θ2, p(θ1 ∣ θ3) < p(θ2 ∣ θ3). Suppose for illustration that the perceptual task involves recognition of a color from a set {azure, indigo, red}. Intuitively, the red color stands out of this set, and this is captured by the above definition. Assume that the two shades of blue are similar in that the agent’s first impression confuses them in 10% of cases, p(azure ∣ indigo) = p(indigo ∣ azure) = 0.1, but p(θ ∣ red) = p(red ∣ θ) = 0.01 for θ ∈ {azure, indigo}. Then, the red color is more distinct according to our definition than either of the two blue shades. We focus on the effect stemming from the agent’s differential ability to perceptually discriminate between the states, and thus we abstract from the differences in the ex ante rewards across states; we assume that πθuθ is constant across all states. Additionally, we impose the following assumption: 5.1.1. Sufficient Precision p(θ ∣ θ) > p(θ′ ∣ θ) for all θ ≠ θ′. Proposition 4. If state|$\theta_1$|is more distinct than state|$\theta_2$|⁠, then the agent’s terminal perception is biased in favour of the more distinct state|$\theta_1$|at the expense of the less distinct state|$\theta_2$|⁠: $$\begin{eqnarray} r^{\ast }(\theta _{1}\mid \theta _{2})\gt r^{\ast }(\theta _{2}\mid \theta _{1}). \end{eqnarray}$$ Since the primitive perception technology p is symmetric by assumption, the asymmetry in favour of the distinct state of the optimal terminal perception r* is driven solely by the optimisation of the termination strategy. To gain the intuition for the salience of the distinct states, consider a state θ* that is similar to many other states and an agent who always terminates the process after the first round: |$\beta =\mathbf {1}$|⁠. This agent is relatively uninformed whenever she forms perception θ*, since the true state differs from θ* with a sizeable probability. The agent with this indistinct perception θ* would thus benefit from ‘having a second thought'—i.e., from running the primitive perception formation process once again. The optimal termination strategy involves repeating the primitive process with relatively high probability whenever the agent forms a perception of an indistinct state, and this shifts the terminal perception in favour of the distinct states. 6. Extensions In the first subsection, we discuss how our model can accommodate agents with more general memory constraints. Subsection 6.2 accommodates agents who discount future payoffs at an exponential rate. 6.1. Sophisticated agents To demonstrate the flexibility of the general model, we now discuss two specific settings. They feature sophisticated agents with non-trivial memory that can be used to aggregate information over several observed signal realisations. Perhaps surprisingly, we show that those settings can in fact be interpreted as special cases of our general model that on its face value allows only for trivial memory. We show that such accommodation of non-trivial memory is possible via expansion of the set |$\mathcal {P}$| of the primitive experiments. This allows us to establish the generality of the second-thought-free condition. Moreover, when the state and action spaces are binary, then the setting with sophisticated agents boils down to the simple binary setting as formulated in Section 3, except for the determination of the perceptual-distance parameter |$\overline{d}$|⁠, which is now endogenously determined by the agent’s ability to process information. Example 1 (imperfect information aggregation). This setting relaxes the agent’s inability to aggregate information across the repetitions of her reasoning by endowing her with a finite set of memory states that she can use to represent the signal histories. The setting of this example builds on Hellman and Cover (1970) and Wilson (2014). The agent can repeatedly sample from a single statistical experiment that generates signal realisations from a finite signal space. Additionally, the agent is endowed with a finite set of memory states. After each run of the experiment, the agent randomises between terminating and continuation of the decision process, where in the latter case, she may transition to a new memory state. The termination decisions and the transitions among memory states follow a stationary mixed strategy that conditions on the current memory state and the last observed signal. Once the agent terminates, she maps the last memory state and the last observed signal value to a chosen action. The feasible statistical experiment and the set of memory states specify a set of constructible choice rules, from which the agent chooses the one that maximises her ex ante expected payoff. The formal specification of this example follows. The agent is endowed with one Blackwell experiment μ(x∣θ) with a finite signal space X and, additionally, with a finite set M of memory states m. After each run of the experiment μ, the agent either terminates or continues with decision-making. If the agent continues, then she transitions from the current memory state to a new memory state and reruns the statistical experiment μ(x ∣ θ). That is, the agent selects a (generalisation of the) termination strategy: |$\gamma :M\times X\longrightarrow \Delta \left( M\cup \lbrace \mathfrak {t}\rbrace \right)$|⁠, where γ(m′ ∣m, x) is the probability that the agent in memory state m who has observed signal realisation x in the last run of the experiment μ continues with the decision-making and transitions to memory state m′, and |$\gamma (\mathfrak {t}\mid m,x)$| is the probability that such an agent terminates. The terminating agent chooses action σ(m, x) that depends both on the current memory state and on the signal realisation observed in the last run of μ. The agent starts the decision-making in the memory state m0. A pair γ, σ induces a θ-dependent Markov chain over the memory states that eventually terminates with choice σ(m, x), where m is the last memory state and x is the last signal realisation observed. Let p(a ∣ θ; γ, σ) be the probability that the agent terminates with the choice a in state θ, and let |$\mathcal {P}_{iia}$| be the set of all stochastic choice rules p that this agent can construct. She selects the choice rule from |$\mathcal {P}_{iia}$| that maximises her ex ante expected payoff. We now demonstrate that this example is a special case of our baseline model. Consider the baseline model with the signal space X = A and the set of the feasible primitive experiments |$\mathcal {P}=\mathcal {P}_{iia}$|⁠. The set |$\mathcal {R}(\mathcal {P}_{iia}) =\lbrace r(p,\beta ,\sigma ):p\in \mathcal {P} _{iia},\beta \in B, \sigma \in S\rbrace$| is then the set of stochastic choice rules that can be constructed as follows. The agent runs any process |$p\in \mathcal {P}_{iia}$|⁠, and observes a signal value/action recommendation a with probability p(a ∣ θ). She terminates with probability βa, according to the termination strategy β = (βa)a∈A, and upon the termination chooses an action a′ = σ(a), where σ ∈ S is any mapping |$A\longrightarrow A$|⁠. She reruns the process p with probability 1 − βa, observes a new action recommendation generated by p, et cetera, until she terminates after a stochastic number of repetitions of the process p. As it turns out, no new choice rules beyond those from |$\mathcal {P}_{iia}$| can be constructed by these selective repetitions. This follows because the repetitions of the rule |$p\in \mathcal {P}_{iia}$| with the termination strategy β can always be replicated with an appropriate choice of a different rule in |$\mathcal {P}_{iia}$| that whenever p would terminate with a restarts the process from scratch with probability 1 − βa. Formally: Lemma 7. |$\mathcal {R}(\mathcal {P} _{iia})=\mathcal {P}_{iia}$|⁠. According to the lemma, Example 1 is a special case of our baseline model with |$\mathcal {P}=\mathcal {P}_{iia}$| and X = A, since in such a specification of the baseline model, the set of feasible rules coincides with those in Example 1. In particular, the optimal choice rule |$p^*\in \mathcal {P}_{iia}$| solving Example 1 coincides with the optimal rule |$r^*\in \mathcal {R}(\mathcal {P}_{iia})$| solving this specification of the baseline model. The repeated-cognition problem with |$\mathcal {P}=\mathcal {P}_{iia}$| is purely formal in that the optimal termination probabilities |$\beta ^*_x=1$| for all x ∈ X = A, and thus the agent conducts the optimal process |$p^*\in \mathcal {P}_{iia}$| only once and terminates. Nevertheless, the observation that p* solves the repeated-cognition problem has an important implication. Corollary 4. The choice rule that solves Example 1 (imperfect information aggregation) is second-thought-free. Wilson (2014) differs from this example mainly in that she assumes exogenous termination probabilities. By adding optimisation over the terminations to the model of Wilson, we gained the partial characterisation of the optimal choice rule with no need to fully solve the problem: one can conclude that the optimal choice rule is second-thought-free without analysing the optimal use of the memory states. Example 2 (partial forgetting). The agent of this example can remember up to a fixed finite number of signal realisations generated by a single statistical experiment. In each round of her decision process, she can discard a subset of the currently remembered signals values, extract a new signal realisation, or terminate, where each of these decisions is determined by a stationary mixed strategy that conditions on the currently remembered stock of the signal values. The statistical experiment and the maximal number of signals that the agent can remember determine the set of stochastic choice rules that she can construct, from which she chooses the rule that maximises her ex ante expected payoff. We first formalise this example as follows. Let H be the set of signal histories h of length |h| ≤ N. The agent at a history h can (i) terminate her decision-making, (ii) discard some of the information accumulated, or (iii), if |h| < N, acquire a new signal realisation. (i) An agent terminating at h chooses action σ(h). (ii) An agent who discards some information transitions to a truncation h′ of her current history h.9 (iii) An agent who acquires a new signal realisation transitions to a history hx, where x is the new signal realisation drawn from μ(x∣ θ). The decision-making is governed by a pair of mappings |$\gamma :H\times \Theta \longrightarrow \Delta \left(H\cup \lbrace \mathfrak {t}\rbrace \right)$| and |$\sigma :H\longrightarrow A$|⁠, where γ(h′ ∣h, θ) stands for the probability that the agent at history h in state θ continues decision-making and transitions to h′, and |$\gamma (\mathfrak {t}\mid h,\theta )$| is the probability of termination at history h in state θ. The mapping γ is constrained to satisfy (1) γ(h′ ∣h, θ) is independent of θ if h′ is a truncation of h, (2) |$\gamma (\mathfrak {t}\mid h,\theta )$| is independent of θ, (3) |$\frac{\gamma (hx\,\mid \,h,\theta )}{ \gamma (hx^{\prime }\,\mid \,h,\theta )}=\frac{\mu (x\,\mid \,\theta )}{\mu (x^{\prime }\,\mid \,\theta )}$|⁠, (4) γ(h′ ∣h, θ) = 0 unless h′ is a truncation of h, or h′ = hx for some x ∈ X and |hx| ≤ N. Constraints 1 and 2 require the agent to condition the decision to discard information or to terminate only on her current history independently of the state. Constraint 3 allows the agent to expand her information set only by running the experiment μ(x∣ θ). Constraint 4 restricts each step of information acquisition to one draw from μ(x ∣ θ) or to a partial discarding of the accumulated information. Let p(a ∣ θ; γ, σ) be the probability that the agent who employs (γ, σ) terminates with action a in the state θ. The agent chooses γ and σ to maximise her ex ante expected payoff. As with the previous example, let |$\mathcal {R}(\mathcal {P}_{pf})$| be the set of feasible choice rules in our baseline model with the set of feasible primitive experiments |$\mathcal {P}$| identified with |$\mathcal {P} _{pf}$|⁠. Lemma 8. |$\mathcal {R}(\mathcal {P}_{pf})= \mathcal {P}_{pf}$|⁠. Thus, again, the rule |$p^*\in \mathcal {P}_{pf}$| solving this example, and the optimal rule |$r^*\in \mathcal {R}(\mathcal {P}_{pf})$| coincide, and thus the rule solving the example must be second-thought-free. Corollary 5. The choice rule that solves Example 2 (partial forgetting) is second-thought-free. Additionally, when the state and action sets are binary, Proposition 2 applies to both examples with |$\overline{d}=\frac{ p^*(1\,\mid \,1)p^*(0\,\mid \,0)}{p^*(0\,\mid \,1)p^*(0\,\mid \,1)}$|⁠, and thus, relative to the baseline setting in which the agent remembers only one signal, the examples have the same solution except for the determination of the endogenous parameter |$\overline{d}$|⁠. Thus, for instance, if the state 1 is a priori more attractive than state 0, then the agent is more likely to make the correct choice in state 1 than in state 0; r*(1 ∣ 1) > r*(0 ∣ 0). Like in Subsection 4.1, the optimal decision procedure favours the evidence supporting the a priori attractive state. 6.2. Impatient Agents Our baseline model abstracts from the cost of time in that the agent is only concerned with how the repetitions of the signal extraction affect the correlation of the signal with the state. We now incorporate discounting. We continue to study the baseline model from Section 1, except that the agent discounts future payoffs exponentially with the discount factor δ ∈ (0, 1). To accommodate discounting, we redefine the choice rule induced by the experiment p, the termination strategy β and the action strategy σ as follows. $$\begin{eqnarray} r_{\delta }(a\mid \theta ;p,\beta ,\sigma )=\sum _{t=1}^\infty \sum _{\mathbf {x} ^{t}:\sigma (x_{t})=a}\delta ^{t}\rho \left( \mathbf {x}^{t}\mid \theta ;p,\beta \right) , \end{eqnarray}$$(11) where |$\rho \left( \mathbf {x}^{t}\mid \theta ;p,\beta \right)$| defined in (1) is the conditional probability of the signal history |$\mathbf {x}^{t}$|⁠. That is, rδ(a∣ θ; p, β, σ) is the discounted probability of the choice of action a in the state θ. When δ = 1, then (11) coincides with our baseline definition of the choice rule. The set of feasible discounted rules is |$\mathcal {R}_{\delta }(\mathcal {P} )=\lbrace r_{\delta }(p,\beta ,\sigma ):p\in \mathcal {P},\beta \in B,\sigma \in S\rbrace$|⁠. The discounted repeated-cognition problem is to select a feasible rule rδ that maximises the expected payoff: $$\begin{eqnarray} \max _{r_{\delta }\in \mathcal {R_{\delta }}(\mathcal {P})}\sum _{\theta \in \Theta ,a\in A}\pi _{\theta }r_{\delta }(a\mid \theta )u(a,\theta ), \end{eqnarray}$$(12) where discounting is incorporated in the definition of the feasible rules. The next result generalises the second-thought-free condition. Let |$r^*_\delta =r_\delta (p^*,\beta ^*,\sigma ^*)$| be the choice rule solving the discounted repeated-cognition problem (12). Proposition 5. If the termination strategy|$\beta ^*_x\in (0,1)$|is interior for all x such that|$\sigma^*(x) = a$|⁠, then $$\begin{eqnarray} \sum _{\theta \in \Theta }\pi _\theta u(a,\theta ) r^*_\delta (a\mid \theta )= \delta \sum _{\theta \in \Theta ,a^{\prime }\in A} \pi _\theta u(a^{\prime },\theta )r^*_\delta (a^{\prime }\mid \theta )r^*_\delta (a\mid \theta ). \end{eqnarray}$$(13) The condition has the same interpretation as the second-thought-free condition in the absence of discounting. The left-hand side is the payoff for following the optimal decision process |$r^*_\delta$| summed up across all contingencies that terminate with choice of a. The right-hand side is the payoff that the agent would get across the same contingencies if she restarted the decision process |$r^*_\delta$| instead of the termination. For illustration, we now revisit the confirmation bias application from Subsection 4.1 with an impatient agent. We find that, unless discounting is too strong, the impatient agent chooses qualitatively the same strategy as the patient one, although the impatient agent speeds up her decision-making by choosing larger termination probabilities. The setting is as follows. The agent chooses a ∈ {0, 1} and receives u(a, θ) = uθ > 0 if a = θ, and zero reward otherwise. Action 1 is a priori more attractive than action 0; π1u1 > π0u0. The agent has access to a single primitive experiment p that generates signal values in X = {0, 1}. The experiment is symmetric with probabilities p(1 ∣ 1) = p(0 ∣ 0) = α > 1/2. We impose a sufficient-informativeness condition that the signal is sufficiently precise relative to the ex ante attractiveness of action 1: |$\frac{\alpha }{1-\alpha }\gt \frac{\pi _1u_1}{\pi _0u_0}$|⁠. Proposition 6. The agent chooses the action equal to the last observed signal realisation. She terminates her decision-making immediately after she encounters signal realisation|$1$|⁠: |$\beta _{1}^{\ast }=1$|⁠. When |$\delta \in \big( \frac{1}{\alpha +(1-\alpha )R} ,1\big]$|⁠, then the agent who observes |$x = 0$|terminates with an interior probability|$\beta _{0}^{\ast }\in (0,1)$|that decreases in δ. When|$\delta \in \big( 0,\frac{1}{\alpha +(1-\alpha )R}\big)$|⁠, then the agent terminates immediately:|$\beta _{0}^{\ast }=\beta _{1}^{\ast }=1$|⁠. 7. Summary Agents, who cannot comprehend all facts available to them, benefit from selective attention. We show that agents can implement a targeted information search in a process that resembles the natural phenomenon of hesitation. Like a hesitant person, the agent can, conditional on the action contemplated, decide whether she implements the action or whether she will have a second thought, and run the cognition process once more. Such hesitation can be productive, despite consisting of repetitions of the same stochastic cognition process. By conditioning the probability of the repetition on the conclusion of the reasoning, the agent controls the correlation of her terminal conclusion and the payoff state. The optimal decision process arising in our model exhibits natural hesitation patterns: the agent will have second thoughts—that is, she will repeat her cognition—whenever the expected payoff for the currently favoured choice is inferior to the expected payoff for continuing decision-making. At optimum, the agent terminating the decision-making must be indifferent between terminating with the currently contemplated action, and repeating the process. In a sense, the condition formalises the concept of a reasonable doubt. Abstracting from many considerations such as information aggregation across the jury members, a jury deciding a trial under common law should be, if using the optimal decision procedure, indifferent between declaring a verdict and announcing a hung jury and initiate retrial. Let us conclude by reviewing the limitations of our main result. The central assumption—the ability of the agent to freely repeat her decision process—may fail for several reasons. One reason is that the agent may only have access to a limited data set that constrains her to a finite number of repetitions of the primitive decision process, making the optimal termination strategy non-stationary. Another complication arises if the outcomes of distinct runs of the same cognition process are not conditionally independent as assumed in our model; this may arise if some cognition errors are systematic and are likely to emerge in distinct repetitions of the cognition. We conjecture that the second-thought-free condition holds in such a case, with the agent internalising the correlations between the cognition runs. Appendix A A.1. Proofs for Section 3 Proof of Lemma 3. Assume that there exists a solution with βx positive for n > 2 signals x ∈ X. We show that then there exists a solution with n − 1 positive signals. The proposition follows from the induction on n. Let us prove the induction step. Fix the primitive experiment p employed by the agent, let β be an optimal termination strategy for the given p, and let X′ be the set of signals with positive βx, and write shortly s(x∣ θ) for the effective experiment s(x ∣ θ; p, β) induced by p and β. Let us abuse notation by letting s(x) = ∑θπθs(x ∣ θ) stand for the unconditional effective probability of x. For x ∈ X′ let qx ∈ Δ(Θ) be the posterior belief upon terminating with x: qx(θ) = πθs(x ∣ θ)/s(x). Since |X′| > 2 and the state space Θ is binary, there exists a signal x* ∈ X′ such that |$q_{x^*}$| is in the convex hull of the posteriors qx, x ∈ X′∖{x*}. Let μx be the coefficients that decompose |$q_{x^*}$| into qx, x ∈ X′∖{x*}. That is, μ ∈ Δ(X′∖{x*}) such that |$q_{x^*}(\theta )=\sum _{x\in X^{\prime }\setminus \lbrace x^*\rbrace }\mu _x q_x(\theta )$| for all θ ∈ Θ. We will construct an alternative feasible effective experiment |$\tilde{s}(x\mid \theta )$| with unconditional probabilities of x denoted by |$\tilde{s}(x)$| and the posteriors |$\pi _\theta \tilde{s}(x\mid \theta )/\tilde{s}(x)$| denoted by |$\tilde{q}_x(\theta )$| such that: $$\begin{eqnarray} \tilde{s}(x)= \left\lbrace \begin{array}{@{}l@{\quad }l@{}}s(x)+s(x^*)\mu _x \mbox{ if }x\in X^{\prime }\setminus \lbrace x^*\rbrace ,\\ 0 \mbox{ otherwise,} \end{array}\right. \end{eqnarray}$$(A1) and $$\begin{eqnarray} \tilde{q}_x(\theta )=q_x(\theta ) \mbox{ for all }x\in X^{\prime }\setminus \lbrace x^*\rbrace ,\theta \in \Theta . \end{eqnarray}$$(A2) Since the experiment |$\tilde{s}$| is more informative than s (in the sense of the Blackwell comparison), there exists a solution with this alternative feasible effective experiment |$\tilde{s}$|⁠, as needed for the induction step. It remains to construct |$\tilde{s}$|⁠. Note that if an effective experiment |$s(x\mid \theta ;p,\beta )=\frac{\beta _x p(x\,\mid \,\theta )}{\sum _{x^{\prime }}\beta _{x^{\prime }}p(x^{\prime }\,\mid \,\theta )}$| is induced by some p and β, then for any vector of probabilities |$\tilde{\beta }_x$|⁠, the experiment $$\begin{eqnarray} \tilde{s}(x\mid \theta )= \frac{\tilde{\beta }_x s(x\mid \theta ;p,\beta )}{\sum _{x^{\prime }\in X}\tilde{\beta }_{x^{\prime }} s(x^{\prime }\mid \theta ;p,\beta )}= \frac{\tilde{\beta }_x\beta _x p(x\mid \theta )}{\sum _{x^{\prime }\in X}\tilde{\beta }_{x^{\prime }}\beta _{x^{\prime }}p(x^{\prime }\mid \theta )} \end{eqnarray}$$ is also feasible, since it is induced by p and |$\beta ^{\prime }=(\tilde{\beta }_{x}\beta _x)_{x\in X}$|⁠. We claim that if $$\begin{eqnarray} \tilde{\beta }_x= \left\lbrace \begin{array}{@{}l@{\quad }l@{}}c\left(1+\displaystyle\frac{s(x^*)\mu _x}{s(x)}\right) \mbox{ if }x\in X^{\prime }\setminus \lbrace x^*\rbrace ,\\ 0 \mbox{ otherwise,} \end{array}\right. \end{eqnarray}$$ where c is a constant such that |$\tilde{\beta }_x\in (0,1)$| for all x ∈ X, then the resulting |$\tilde{s}$| satisfies the properties (A1) and (A2). Let us check: $$\begin{eqnarray} \tilde{s}(x\mid \theta ) &=& \displaystyle\frac{\tilde{\beta }_x s(x\mid \theta )}{\sum _{x^{\prime }\in X^{\prime }\setminus \lbrace x^*\rbrace }\tilde{\beta }_{x^{\prime }}s(x^{\prime }\mid \theta )} \\ &=& \displaystyle\frac{\tilde{\beta }_x s(x\mid \theta )}{c\left(\sum _{x^{\prime }\in X^{\prime }\setminus \lbrace x^*\rbrace }s(x^{\prime }\mid \theta ) +\sum _{x^{\prime }\in X^{\prime }\setminus \lbrace x^*\rbrace }\displaystyle\frac{s(x^*)\mu _{x^{\prime }}}{s(x^{\prime })}s(x^{\prime }\mid \theta )\right)}\\ &=& \displaystyle\frac{\tilde{\beta }_x s(x\mid \theta )}{c\left(\sum _{x^{\prime }\in X^{\prime }\setminus \lbrace x^*\rbrace }s(x^{\prime }\mid \theta ) +\sum _{x^{\prime }\in X^{\prime }\setminus \lbrace x^*\rbrace }\displaystyle\frac{s(x^*)\mu _{x^{\prime }}}{\pi _\theta }q_{x^{\prime }}(\theta )\right)}\\ &=& \displaystyle\frac{\tilde{\beta }_x s(x\mid \theta )}{c\left(\sum _{x^{\prime }\in X^{\prime }\setminus \lbrace x^*\rbrace }s(x^{\prime }\mid \theta ) +\displaystyle\frac{s(x^*)}{\pi _\theta }q_{x^*} (\theta )\right)}\\ &=& \displaystyle\frac{\tilde{\beta }_x s(x\mid \theta )}{c\left(\sum _{x^{\prime }\in X^{\prime }\setminus \lbrace x^*\rbrace }s(x^{\prime }\mid \theta ) +s(x^*\mid \theta )\right)}\\ &=&\displaystyle\frac{\tilde{\beta }_x s(x\mid \theta )}{c}\\ &=& \left(1+\displaystyle\frac{s(x^*)\mu _x}{s(x)}\right) s(x\mid \theta ). \end{eqnarray}$$ The property (A1) holds since for all x ∈ X′∖{x*}: $$\begin{eqnarray} \tilde{s}(x)=\left(1+\frac{s(x^*)\mu _x}{s(x)}\right)s(x)=s(x)+s(x^*)\mu _x. \end{eqnarray}$$ To establish the property (A2), check that for all x ∈ X′∖{x*} and all θ ∈ Θ: $$\begin{eqnarray} \tilde{q}_x(\theta )=\displaystyle\frac{\pi _\theta \tilde{s}(x\mid \theta )}{\sum _{\theta ^{\prime }\in \Theta }\tilde{s}(x\mid \theta ^{\prime })}=\displaystyle\frac{\pi _\theta \left(1+\displaystyle\frac{s(x^*)\mu _x}{s(x)}\right) s(x\mid \theta )}{\sum _{\theta ^{\prime }\in \Theta }\left(1+\displaystyle\frac{s(x^*)\mu _x}{s(x)}\right) s(x\mid \theta ^{\prime })}=\displaystyle\frac{\pi _\theta s(x\mid \theta )}{\sum _{\theta ^{\prime }\in \Theta } s(x\mid \theta ^{\prime })} =q_x(\theta ). \end{eqnarray}$$ Proof of Lemma 4. For any positive β, $$\begin{eqnarray} \displaystyle\frac{r(1\mid 1;p,\beta ,\sigma _I)r(0\mid 0;p,\beta ,\sigma _I)}{r(0\mid 1;p,\beta ,\sigma _I)r(1\mid 0;p,\beta ,\sigma _I)} = \displaystyle\frac{ \displaystyle\frac{\beta _1 p(1\mid 1)}{\sum _x\beta _x p(x\mid 1)} \displaystyle\frac{\beta _0 p(0\mid 0)}{\sum _x\beta _x p(x\mid 0)} }{ \displaystyle\frac{\beta _0 p(0\mid 1)}{\sum _x\beta _x p(x\mid 1)} \displaystyle\frac{\beta _1 p(1\mid 0)}{\sum _x\beta _x p(x\mid 0)} } = \displaystyle\frac{p(1\mid 1)p(0\mid 0)}{p(0\mid 1)p(1\mid 0)}= d_p. \end{eqnarray}$$ Thus, every |$r\in \mathcal {R}_{p,\sigma _I}$| either always selects a same action, or satisfies |$\frac{r(1\,\mid \,1)r(0\,\mid \,0)}{r(0\,\mid \,1)r(0\,\mid \,1)}=d_p$|⁠. Vice versa, if a rule r′ satisfies |$\frac{r^{\prime }(1\,\mid \,1)r^{\prime }(0\,\mid \,0)}{r^{\prime }(0\,\mid \,1)r^{\prime }(0\,\mid \,1)}=d_p$|⁠, then it belongs to |$\mathcal {R}_{p,\sigma _I}$|⁠. To see this, let ra denote the rule that always selects action a. Consider positive β0, and note that r(p, (β0, β1), σI) is continuous in β1, and converges to r1 and r0 as β1 approaches 1 and 0. Thus, there exists β such that r′(1 ∣ 1) = r(1 ∣ 1; p, β, σI). Moreover, there is a unique rule |$\tilde{r}$| that satisfies |$\tilde{r}(1\mid 1)=r^{\prime }(1\mid 1)$| and |$\frac{\tilde{r}(1\,\mid \,1)\tilde{r}(0\,\mid \,0)}{\tilde{r}(0\,\mid \,1)\tilde{r}(0\,\mid \,1)}=d_p$|⁠. Thus, r′ must be r(p, β, σI) and hence constructible from p.10 Proof of Lemma 5. The statement is trivial when r(p, β, σ) chooses an action a′ with probability 1, since then we can set |$\beta ^{\prime }_{a^{\prime }}=1$| and |$\beta ^{\prime }_{x}=0$| for x ≠ a′. Accordingly, assume that both actions are chosen with positive probabilities under the rule r(p, β, σ) and σ(x) = 1 − x. For the sake of contradiction, assume that r(p, β, σ) achieves a higher payoff than all rules constructible with p and σI. Then, the payoff difference between the rule r(p, β, σ) and the choice rule that always selects a = 1 must be positive: $$\begin{eqnarray} \pi _0u_0r(0\mid 0;p,\beta ,\sigma )+\pi _1u_1r(1\mid 1;p,\beta ,\sigma )-\pi _1u_1 &=& \\ \pi _0u_0r\left(1\mid 0;p,\beta ,\sigma _I\right)+\pi _1u_1r\left(0\mid 1;p,\beta ,\sigma _I\right)-\pi _1u_1 &=& \\ \pi _0u_0r\left(1\mid 0;p,\beta ,\sigma _I\right) - \pi _1u_1r\left(1\mid 1;p,\beta ,\sigma _I\right) &\gt & 0, \end{eqnarray}$$ where we have used r(a ∣ θ; p, β, σI) = r(1 − a ∣ θ; p, β, σ) for the first equality. Similarly, the payoff difference between the rule r(p, β, σ) and the rule that always selects a = 0 must be positive: $$\begin{eqnarray} \pi _0u_0r(0\mid 0;p,\beta ,\sigma )+\pi _1u_1r(1\mid 1;p,\beta ,\sigma )-\pi _0u_0 &=&\\ \pi _0u_0r\left(1\mid 0;p,\beta ,\sigma _I\right)+\pi _1u_1r\left(0\mid 1;p,\beta ,\sigma _I\right)-\pi _0u_0 &=&\\ \pi _1u_1r(0\mid 1;p,\beta ,\sigma _I)-\pi _0u_0 r(0\mid 0;p,\beta ,\sigma _I) &\gt & 0. \end{eqnarray}$$ The last two inequalities imply $$\begin{eqnarray} \frac{r(1\mid 1;p,\beta ,\sigma _I)}{r(1\mid 0;p,\beta ,\sigma _I)} \lt \frac{\pi _0u_0}{\pi _1u_1}\lt \frac{r(0\mid 1;p,\beta ,\sigma _I)}{r(0\mid 0;p,\beta ,\sigma _I)}, \end{eqnarray}$$ which establishes contradiction because by Lemma 4, the rule r(a ∣ θ; p, β, σI) satisfies $$\begin{eqnarray} \frac{r(1\mid 1;p,\beta ,\sigma _I)r(0\mid 0;p,\beta ,\sigma _I)}{r(1\mid 0;p,\beta ,\sigma _I)r(0\mid 1;p,\beta ,\sigma _I)}=\frac{p(1\mid 1)p(0\mid 0)}{p(1\mid 0)p(0\mid 1)}, \end{eqnarray}$$ and therefore it inherits the monotone likelihood ratio property from p. Proof of Lemma 6. Consider the choice rule r(p, β, σI) constructed from the experiment p with perceptual distance dp = d, and fix the probability r(0 ∣ 0; p, β, σI) = α of the correct choice in state 0 to a value α ∈ (0, 1). Then, by Lemma 4, the probability r(1 ∣ 1; p, β, σI) of the correct choice in state 1 satisfies $$\begin{eqnarray} \frac{r(1\mid 1;p,\beta ,\sigma _I)\alpha }{(1-r(1\mid 1;p,\beta ,\sigma _I))(1-\alpha )}=d. \end{eqnarray}$$ For each α, the solution for r(1 ∣ 1; p, β, σI) of this equation increases in d. Proof of Proposition 2. The agent’s objective is linear with respect to the choice rule r(p, β, σ). Thus, the optimal rule is the point of tangency of the set |$\mathcal {R}_{\overline{p},\sigma _I}$| of the feasible rules and of an indifference line; see Figure 2. The slope |$\frac{d r\left(0\,\mid \,0;\overline{p},\beta ,\sigma _I\right)}{d r\left(1\,\mid \,1;\overline{p},\beta ,\sigma _I\right)}$| is decreasing in |$r\left(1\mid 1;\overline{p},\beta ,\sigma _I\right)$| and attains value |$-1/\overline{d}$| for |$r\left(1\mid 1;\overline{p},\beta ,\sigma _I\right)=0$|⁠, and value |$-\overline{d}$| for |$r\left(1\mid 1;\overline{p},\beta ,\sigma _I\right)=1$|⁠. Thus, when |$R\lt 1/\overline{d}$| or |$R\gt \overline{d}$|⁠, then the problem has the corner solution as specified in statements 1 and 2 of the proposition. When |$R\in \left(1/\overline{d},\overline{d}\right)$|⁠, then the optimal choice rule |$r^*=r\left(\overline{p},\beta ^*,\sigma _I\right)$| satisfies the feasibility condition |$\frac{r^*(1\,\mid \,1)r^*(0\,\mid \,0)}{r^*(0\,\mid \,1)r^*(0\,\mid \,1)}=\overline{d}$|⁠, the second-thought-free condition (5) (applied to action a = 1): $$\begin{eqnarray} \pi _1u_1r^*(1\mid 1)=\pi _0u_0r^*(0\mid 0)r^*(1\mid 0) + \pi _1u_1r^*(1\mid 1)r^*(1\mid 1), \end{eqnarray}$$ and two normalisation conditions ∑ar*(a∣ θ) = 1, for θ ∈ {0, 1}. These four conditions jointly imply the explicit solution for the optimal choice rule in (8). The expression (9) for |$\beta ^*_1/\beta ^*_0$| follows from (8) and the condition |$\frac{r^*(1\,\mid \,\theta )}{r^*(0\,\mid \,\theta )}= \frac{\beta _1^*\overline{p}(1\,\mid \,\theta )}{\beta _0^*\overline{p}(0\,\mid \,\theta )}$|⁠. A.2. Proofs for Section 5 The next result is an auxiliary lemma used in the proof of Proposition 4. Lemma 9. The optimal effective choice rule r* satisfies for any pair of states θ, θ′ ∈ Θ: $$\begin{eqnarray} \pi _\theta u_\theta r^*(\theta \mid \theta )r^*(\theta ^{\prime }\mid \theta )=r^*(\theta \mid \theta ^{\prime })\pi _{\theta ^{\prime }} u_{\theta ^{\prime }} r^*(\theta ^{\prime }\mid \theta ^{\prime }). \end{eqnarray}$$(A3) Condition (A3) is a strengthening of the second-thought-free condition (5). It requires that the agent who has terminated the decision process with perception θ, and knows that the second run of the process r* terminates with a value θ′ is indifferent between θ and θ′. This condition is stronger than the second-thought-free condition (5), since (5) requires (A3) to hold only on average across all θ′. This strengthening holds for the special case of a symmetric experiment p. Proof of Lemma 9. The optimal effective choice rule satisfies the second-thought-free condition (5), equivalent to: $$\begin{eqnarray} \pi _\theta u_\theta r^*(\theta \mid \theta )=\sum _{\theta ^{\prime }\in \Theta }\pi _{\theta ^{\prime }} u_{\theta ^{\prime }} r^*(\theta \mid \theta ^{\prime })r^*(\theta ^{\prime }\mid \theta ^{\prime })\mbox{ for all }\theta \in \Theta , \end{eqnarray}$$ which after two algebraic steps gives: $$\begin{eqnarray} \pi _\theta u_\theta r^*(\theta \mid \theta )\big (1-r^*(\theta \mid \theta )\big )=\sum _{\theta ^{\prime }\ne \theta }\pi _{\theta ^{\prime }}u_{\theta ^{\prime }} r^*(\theta \mid \theta ^{\prime })r^*(\theta ^{\prime }\mid \theta ^{\prime })\mbox{ for all }\theta \in \Theta , \end{eqnarray}$$ $$\begin{eqnarray} \sum _{\theta ^{\prime }\ne \theta }\pi _\theta u_\theta r^*(\theta \mid \theta )r^*(\theta ^{\prime }\mid \theta )=\sum _{\theta ^{\prime }\ne \theta }\pi _{\theta ^{\prime }}u_{\theta ^{\prime }} r^*(\theta ^{\prime }\mid \theta ^{\prime })r^*(\theta \mid \theta ^{\prime })\mbox{ for all }\theta \in \Theta . \end{eqnarray}$$ The last system of equations is formally equivalent to the system of balance conditions for a Markov chain. To see this, consider an ergodic Markov chain with transition probabilities from θ to θ′ equal to r*(θ′ ∣ θ). The balance condition for the stationary distribution μ(θ) of this chain is $$\begin{eqnarray} \sum _{\theta ^{\prime }\ne \theta }\mu (\theta )r^*(\theta ^{\prime }\mid \theta )=\sum _{\theta ^{\prime }\ne \theta }\mu (\theta ^{\prime })r^*(\theta \mid \theta ^{\prime })\mbox{ for all }\theta \in \Theta , \end{eqnarray}$$ and thus, for each state θ, πθuθr*(θ ∣ θ) is proportional to the ergodic probability μ(θ) of the state θ for the chain with transition probabilities r*(θ′ ∣ θ). Recall that if a Markov chain with transition probabilities m(θ′ ∣ θ) is reversible, then its stationary distribution μ(θ) satisfies detailed balance conditions $$\begin{eqnarray} \mu (\theta )m(\theta ^{\prime }\mid \theta )=\mu (\theta ^{\prime })m(\theta \mid \theta ^{\prime })\mbox{ for all } \theta \ne \theta ^{\prime }. \end{eqnarray}$$ Thus, it suffices to prove that the probabilities r*(θ′ ∣ θ) constitute a reversible Markov chain. Recall that a Markov chain m(θ′ ∣ θ) is reversible if and only if it satisfies the Kolmogorov criterion, which requires for all sequences of states θ1, θ2, …, θn, $$\begin{eqnarray} \frac{m(\theta _2\mid \theta _1)m(\theta _3\mid \theta _2)\dots m(\theta _n\mid \theta _{n-1}) m(\theta _1\mid \theta _n)}{ m(\theta _n\mid \theta _1)m(\theta _{n-1}\mid \theta _n)\dots m(\theta _2\mid \theta _{3}) m(\theta _1\mid \theta _2)}=1. \end{eqnarray}$$(A4) The Markov chain with transition probabilities p(θ′ ∣ θ) given by the primitive experiment p satisfies the Kolmogorov criterion (A4) since p is symmetric by assumption. Finally, for any positive termination strategy β, the effective choice rule r(θ′ ∣ θ; p, β, σI) satisfies the Kolmogorov criterion too. This is because |$r(\theta ^{\prime }\mid \theta ;p,\beta ,\sigma _I)=\frac{\beta _{\theta ^{\prime }}p(\theta ^{\prime }\,\mid \,\theta )}{\sum _{\tilde{\theta }}\beta _{\tilde{\theta }}p(\tilde{\theta }\,\mid \,\theta )}$|⁠, and when the expressions for r(θ′ ∣ θ; p, β, σI) are substituted into (A4), then the terms |$\beta _{\theta ^{\prime }}$| and the denominators cancel out, and hence $$\begin{eqnarray} && \frac{r(\theta _2\mid \theta _1;p,\beta \sigma _I)r(\theta _3\mid \theta _2;p,\beta ,\sigma _I)\dots r(\theta _1\mid \theta _n;p,\beta ,\sigma _I)}{ r(\theta _n\mid \theta _1;p,\beta ,\sigma _I)r(\theta _{n-1}\mid \theta _n;p,\beta ,\sigma _I)\dots r(\theta _1\mid \theta _2;p,\beta ,\sigma _I)} \\ && \qquad = \frac{p(\theta _2\mid \theta _1)p(\theta _3\mid \theta _2)\dots p(\theta _1\mid \theta _n)}{ p(\theta _n\mid \theta _1)p(\theta _{n-1}\mid \theta _n)\dots p(\theta _1\mid \theta _2)}=1, \end{eqnarray}$$ as needed. Proof of Proposition 3. Lemma 9 implies for all pairs θ, θ′ ∈ Θ: $$\begin{eqnarray} \pi _\theta u_\theta r^*(\theta \mid \theta )r^*(\theta ^{\prime }\mid \theta )=r^*(\theta \mid \theta ^{\prime })\pi _{\theta ^{\prime }} u_{\theta ^{\prime }} r^*(\theta ^{\prime }\mid \theta ^{\prime }). \end{eqnarray}$$ By Lemma 2, we can substitute |$r^*(\theta ^{\prime }\mid \theta )=\frac{\beta ^*_{\theta ^{\prime }}p(\theta ^{\prime }\,\mid \,\theta )}{\sum _{\tilde{\theta }}\beta ^*_{\tilde{\theta }}p\left(\tilde{\theta }\,\mid \,\theta \right)}$|⁠, which gives $$\begin{eqnarray} \frac{\beta ^*_{\theta }\beta ^*_{\theta ^{\prime }}\pi _\theta u_\theta p(\theta \mid \theta )p(\theta ^{\prime }\mid \theta )}{\left(\sum _{\tilde{\theta }}\beta ^*_{\tilde{\theta }}p(\tilde{\theta }\mid \theta )\right)^2} = \frac{\beta ^*_{\theta }\beta ^*_{\theta ^{\prime }}p(\theta \mid \theta ^{\prime })\pi _{\theta ^{\prime }} u_{\theta ^{\prime }} p(\theta ^{\prime }\mid \theta ^{\prime })}{\left(\sum _{\tilde{\theta }}\beta ^*_{\tilde{\theta }}p(\tilde{\theta }\mid \theta ^{\prime })\right)^2}. \end{eqnarray}$$ Using the symmetry of p we get $$\begin{eqnarray} \frac{\sum _{\tilde{\theta }}\beta ^*_{\tilde{\theta }}p(\tilde{\theta }\mid \theta ^{\prime })}{\sum _{\tilde{\theta }}\beta ^*_{\tilde{\theta }}p(\tilde{\theta }\mid \theta )} = \left(\frac{\pi _{\theta ^{\prime }} u_{\theta ^{\prime }}p(\theta ^{\prime }\mid \theta ^{\prime })}{\pi _\theta u_\theta p(\theta \mid \theta )}\right)^{1/2}, \end{eqnarray}$$(A5) which gives (10) after rearrangement. Proof of Proposition 4. To compare r*(θ1 ∣ θ2) and r*(θ2 ∣ θ1), we write $$\begin{eqnarray} \displaystyle\frac{r^*(\theta _1\mid \theta _2)}{r^*(\theta _2\mid \theta _1)} = \displaystyle\frac{\displaystyle\frac{\beta ^*_{\theta _1} p(\theta _1\mid \theta _2)}{\sum _{\tilde{\theta }} \beta ^*_{\tilde{\theta }} p(\tilde{\theta }\mid \theta _2) }}{\displaystyle\frac{\beta ^*_{\theta _2} p(\theta _2\mid \theta _1)}{\sum _{\tilde{\theta }} \beta ^*_{\tilde{\theta }} p(\tilde{\theta }\mid \theta _1)}} = \displaystyle\frac{\displaystyle\frac{\beta ^*_{\theta _1} p(\theta _1\mid \theta _2)}{\left(\pi _{\theta _2} u_{\theta _2}p(\theta _2\mid \theta _2)\right)^{1/2}}}{\displaystyle\frac{\beta ^*_{\theta _2} p(\theta _2\mid \theta _1)}{\left(\pi _{\theta _1}u_{\theta _1}p(\theta _1\mid \theta _1)\right)^{1/2}}} = \displaystyle\frac{\beta ^*_{\theta _1}p^{1/2}(\theta _1\mid \theta _1)}{\beta ^*_{\theta _2}p^{1/2}(\theta _2\mid \theta _2)}, \end{eqnarray}$$ where we have used (A5) in the second step, and the symmetry of p and equality of πθuθ across θ in the last step. Define |$\hat{\beta }_{\theta }=\beta ^*_{\theta }p^{1/2}(\theta \mid \theta )$|⁠. We need to prove that if θ1 is more distinct than θ2, then |$\hat{\beta }_{\theta _1}\gt \hat{\beta }_{\theta _2}$|⁠. By (A5), |$\big (\hat{\beta }_{\theta }\big )_\theta$| satisfy the system of linear equations: $$\begin{eqnarray} \sum _{\theta ^{\prime }}D_{\theta ^{\prime }\theta }\hat{\beta }_{\theta ^{\prime }}=1 \mbox{ for all } \theta , \end{eqnarray}$$ where . We claim that if θ1 is more distinct than θ2, then |$D_{\theta _3\theta _1}\lt D_{\theta _3\theta _2}$| for all θ3 ≠ θ1, θ2. This follows from p(θ3 ∣ θ1) < p(θ3 ∣ θ2) and from the symmetry of p: $$\begin{eqnarray} p(\theta _1\mid \theta _1)&=&1-p(\theta _2\mid \theta _1)-\sum _{\theta _3\ne \theta _1,\theta _2}p(\theta _3\mid \theta _1) \gt 1-p(\theta _1\mid \theta _2)-\sum _{\theta _3\ne \theta _1,\theta _2}p(\theta _3\mid \theta _2) \\ &&=p(\theta _2\mid \theta _2), \end{eqnarray}$$ and therefore, $$\begin{eqnarray} D_{\theta _3\theta _1}= \frac{p(\theta _1\mid \theta _3)}{p^{1/2}(\theta _1\mid \theta _1)p^{1/2}(\theta _3\mid \theta _3)} \lt \frac{p(\theta _2\mid \theta _3)}{p^{1/2}(\theta _2\mid \theta _2)p^{1/2}(\theta _3\mid \theta _3)}=D_{\theta _3\theta _2}. \end{eqnarray}$$ Thus, $$\begin{eqnarray} D_{\theta _1\theta _1}\hat{\beta }_{\theta _1}+D_{\theta _2\theta _1}\hat{\beta }_{\theta _2}=1-\sum _{\theta _3\ne \theta _1,\theta _2}D_{\theta _3\theta _1}\hat{\beta }_{\theta _3} \gt 1-\sum _{\theta _3\ne \theta _1,\theta _2}D_{\theta _3\theta _2}\hat{\beta }_{\theta _3}= D_{\theta _2\theta _2}\hat{\beta }_{\theta _2}+D_{\theta _1\theta _2}\hat{\beta }_{\theta _1}. \end{eqnarray}$$ Using that Dθθ = 1 and |$D_{\theta \theta ^{\prime }}=D_{\theta ^{\prime }\theta }$|⁠, we have $$\begin{eqnarray} \hat{\beta }_{\theta _1}+D_{\theta _2\theta _1}\hat{\beta }_{\theta _2} \gt \hat{\beta }_{\theta _2}+D_{\theta _2\theta _1}\hat{\beta }_{\theta _1}. \end{eqnarray}$$ The assumption of sufficient precision of p and symmetry of p imply that |$D_{\theta _2\theta _1}\lt 1$|⁠, and thus |$\hat{\beta }_{\theta _1}\gt \hat{\beta }_{\theta _2}$|⁠, as needed. A.3. Proofs of the Results from Section 6 Proof of Lemma 7. All rules feasible in |$\mathcal {P}_{iia}$| are feasible in |$\mathcal {R}(\mathcal {P}_{iia})$|⁠: |$\mathcal {R}(\mathcal {P}_{iia})\supset \mathcal {P}_{iia}$|⁠. This is immediate since when βa = 1 for all a ∈ A, then r(p, β, σI) = p for all |$p\in \mathcal {P}_{iia}$|⁠. It remains to show |$\mathcal {R}(\mathcal {P}_{iia})\subset \mathcal {P}_{iia}$|⁠. Consider |$p(\gamma ,\sigma )\in \mathcal {P}_{iia}$| constructed in the setting of Example 1 by the use of the generalised termination strategy γ(m, x), and the action strategy σ(m, x). Recall that |$r(p(\gamma ,\sigma ),\beta ,\hat{\sigma })$| is the choice rule constructed by repetitions of the rule p(γ, σ) according to the termination strategy β = (βa)a∈A and by applying the action strategy |$\hat{\sigma }:A\longrightarrow A$| upon the termination. We need to show that there exists γ′ and σ′ such that |$r(p(\gamma ,\sigma ),\beta ,\hat{\sigma })=p(\gamma ^{\prime },\sigma ^{\prime })$|⁠. This is indeed so when the termination probability |$\gamma ^{\prime }(\mathfrak {t}\mid m,x)=\gamma (\mathfrak {t}\mid m,x)\beta _{\sigma (m,x)}$| for m ≠ m0, the transition probability to the original memory state m0 is |$\gamma ^{\prime }(m_0\mid m,x)=\gamma (m_0\mid m,x)+ \gamma (\mathfrak {t}\mid m,x)\left(1-\beta _{\sigma (m,x)}\right)$|⁠, which is the sum of the probabilities that the original process γ transits to m0 and that the decision process |$r(p(\gamma ,\sigma ),\beta ,\hat{\sigma })$| restarts after termination of p(γ, σ). Additionally, for all |$\tilde{m}\ne m_0$|⁠, |$\gamma ^{\prime }(\tilde{m}\mid m,x)=\gamma (\tilde{m}\mid m,x)$|⁠. The above choice of γ′ implies that the process p(γ′, σ′) replicates the Markov process over the memory states under |$r(p(\gamma ,\sigma ),\beta ,\hat{\sigma })$|⁠. Finally, to replicate the choices upon terminations, we set the action strategy |$\sigma ^{\prime }(m,x)=\hat{\sigma }(\sigma (m,x))$| for all (m, x). Proof of Lemma 8. Again, trivially, |$\mathcal {R}(\mathcal {P}_{pf})\supset \mathcal {P}_{pf}$|⁠, since r(p, (1, …, 1), σI) = p for all |$p\in \mathcal {P}_{pf}$|⁠. Additionally, |$\mathcal {R}(\mathcal {P}_{pf})\subset \mathcal {P}_{pf}$|⁠. This is indeed so because for any β = (βa)a∈A and any |$\hat{\sigma }:A\longrightarrow A$|⁠, |$r(p(\gamma ,\sigma ),\beta ,\hat{\sigma })=p(\gamma ^{\prime },\sigma ^{\prime })$| where the termination probability |$\gamma ^{\prime }(\mathfrak {t}\mid h,\theta )=\gamma (\mathfrak {t}\mid h,\theta )\beta _{\sigma (h)}$|⁠, the transition probability to the empty signal history ∅ is set to |$\gamma ^{\prime }(\emptyset \mid h,\theta )=\gamma (\emptyset \mid h,\theta )+ \gamma (\mathfrak {t}\mid h,\theta )\left(1-\beta _{\sigma (h)}\right)$|⁠, and for all |$\tilde{h} \ne \emptyset$|⁠, |$\gamma ^{\prime }(\tilde{h}\mid h,\theta )=\gamma (\tilde{h}\mid h,\theta )$|⁠. Finally, the action strategy is set to |$\sigma ^{\prime }(h)=\hat{\sigma }(\sigma (h))$| for all histories h. Proof of Proposition 5. We extend the definition of the effective experiment to the setting with discounting. Let $$\begin{eqnarray} s_\delta (x\mid \theta ;p,\beta )=\sum _t\sum _{\mathbf {x}^t:x_t=x}\delta ^t\rho \left(\mathbf {x}^t\mid \theta ;p,\beta \right), \end{eqnarray}$$ where |$\rho \left(\mathbf {x}^t\mid \theta ;p,\beta \right)$| is the probability of the signal history |$\mathbf {x}^t$| defined in (1). Thus, sδ(x∣ θ; p, β) is the discounted probability that the agent’s last observed signal value is x. It satisfies the recursion: $$\begin{eqnarray} s_\delta (x\mid \theta ;p,\beta )=\beta _x p(x\mid \theta )+\delta \sum _{x^{\prime }\in X}\left(1-\beta _{x^{\prime }} p\left(x^{\prime }\mid \theta \right)\right) s_\delta (x\mid \theta ;p,\beta ), \end{eqnarray}$$(A6) where the first summand is the probability that the decision process terminates with x in the first round and the second summand is the discounted probability that the process terminates with x later. Solving (A6) for sδ gives $$\begin{eqnarray} s_\delta (x\mid \theta ;p,\beta )=\frac{\beta _x p(x\mid \theta )}{1-\delta +\delta \sum _{x^{\prime }\in X}\beta _{x^{\prime }} p(x^{\prime }\mid \theta )}. \end{eqnarray}$$ The discounted repeated-cognition problem (12) is thus equivalent to $$\begin{eqnarray} \max _{p\in \mathcal {P},\beta \in B,\sigma \in S}\sum _{\theta \in \Theta ,x\in X} \pi _\theta \frac{\beta _x p(x\mid \theta )}{1-\delta +\delta \sum _{x^{\prime }\in X}\beta _{x^{\prime }} p(x^{\prime }\mid \theta )} u(\sigma (x),\theta ). \end{eqnarray}$$(A7) Consider x with an interior termination probability |$\beta ^*_x\in (0,1)$| and let a = σ*(x). The first-order condition of the problem (A7) with respect to βx is: $$\begin{eqnarray} \sum _{\theta \in \Theta } \pi _\theta \frac{s_\delta (x\mid \theta ;p^*,\beta ^*)}{\beta ^*_x} u(a,\theta ) - \delta \sum _{\theta \in \Theta ,x^{\prime }\in X} \pi _\theta s_\delta (x^{\prime }\mid \theta ;p^*,\beta ^*)\frac{s_\delta (x\mid \theta ;p^*,\beta ^*)}{\beta ^*_x} u(\sigma ^*(x^{\prime }),\theta ) &=& \\ \sum _{\theta \in \Theta } \pi _\theta \frac{s_\delta (x\mid \theta ;p^*,\beta ^*)}{\beta ^*_x} u(a,\theta ) - \delta \sum _{\theta \in \Theta ,a^{\prime }\in A} \pi _\theta r^*_\delta (a^{\prime }\mid \theta ;p^*,\beta ^*,\sigma ^*)\frac{s_\delta (x\mid \theta ;p^*,\beta ^*)}{\beta ^*_x} u(a^{\prime },\theta ) &= &0, \end{eqnarray}$$ where we have summed over all x′ such that σ*(x′) = a′ in the second line. Multiplication by |$\beta ^*_x$| and summation over all x such that σ*(x) = a gives (13). Proof of Proposition 6. Due to the condition that α/(1 − α) > R, any (β, σ) that leads to a selection of only one action with certainty is dominated by the decision process that terminates after the first round and chooses an action equal to the observed signal value. Thus, both |$\beta ^*_0$| and |$\beta ^*_1$| are positive, and the action strategy is σ*(x) = x or σ*(x) = 1 − x. Let us show that the action strategy σ* must be the identity function σI. Assume for contradiction that σ*(x) = 1 − x. The payoff difference between the rule rδ(p, β*, σ*) and the choice rule that always selects a = 1 must be positive, since the latter is dominated: $$\begin{eqnarray} \pi _0u_0r_\delta (0\mid 0;p,\beta ^*,\sigma ^*)+\pi _1u_1r_\delta (1\mid 1;p,\beta ^*,\sigma ^*)-\pi _1u_1 &=& \\ \pi _0u_0r_\delta (1\mid 0;p,\beta ^*,\sigma _I)+\pi _1u_1r_\delta (0\mid 1;p,\beta ^*,\sigma _I)-\pi _1u_1 &\ge &\\ \pi _0u_0r_\delta (1\mid 0;p,\beta ^*,\sigma _I)-\pi _1u_1r_\delta (1\mid 1;p,\beta ^*,\sigma _I) \gt 0, & & \end{eqnarray}$$ where the first inequality follows from the fact that any discounted choice rule satisfies ∑arδ(a ∣ θ; p, β, σ) ≤ 1. Similarly, the payoff difference between the rule rδ(p, β*, σ*) and the rule that always selects a = 0 must be positive: $$\begin{eqnarray} \pi _0u_0r_\delta (0\mid 0;p,\beta ^*,\sigma ^*)+\pi _1u_1r_\delta (1\mid 1;p,\beta ^*,\sigma ^*)-\pi _0u_0 &=&\\ \pi _0u_0r_\delta (1\mid 0;p,\beta ^*,\sigma _I)+\pi _1u_1r_\delta (0\mid 1;p,\beta ^*,\sigma _I)-\pi _0u_0 &\ge &\\ \pi _1u_1r_\delta (0\mid 1;p,\beta ^*,\sigma _I)-\pi _0u_0 r_\delta (0\mid 0;p,\beta ^*,\sigma _I) \gt 0. & & \end{eqnarray}$$ The last two inequalities imply: $$\begin{eqnarray} \frac{r_\delta (0\mid 1;p,\beta ^*,\sigma _I)}{r_\delta (0\mid 0;p,\beta ^*,\sigma _I)}\gt \frac{\pi _0u_0}{\pi _1u_1}\gt \frac{r_\delta (1\mid 1;p,\beta ^*,\sigma _I)}{r_\delta (1\mid 0;p,\beta ^*,\sigma _I)}. \end{eqnarray}$$ This establishes contradiction because as shown in the proof of Proposition 5, |$r_\delta (x\mid \theta ;p,\beta ^*,\sigma _I)=s_\delta (x\mid \theta ;p,\beta ^*)=\frac{\beta ^*_x p(x\,\mid \,\theta )}{1-\delta +\delta \sum _{x^{\prime }}\beta ^*_{x^{\prime }}p(x^{\prime }\,\mid \,\theta )}$|⁠, and thus $$\begin{eqnarray} \frac{r_\delta (1\mid 1;p,\beta ^*,\sigma _I)r_\delta (0\mid 0;p,\beta ^*,\sigma _I)}{r_\delta (0\mid 1;p,\beta ^*,\sigma _I)r_\delta (1\mid 0;p,\beta ^*,\sigma _I)} =\frac{p(1\mid 1)p(0\mid 0)}{p(0\mid 1)p(1\mid 0)}\gt 1. \end{eqnarray}$$ Further, it must hold that |$\beta ^*_0=1$| or |$\beta ^*_1=1$|⁠. Otherwise, if both |$\beta ^*_0\lt 1$| and |$\beta ^*_1\lt 1$|⁠, then the agent can increase both |$\beta ^*_x$| by a same factor. This preserves the conditional action distribution in each state θ and increases the decision rates in both states, and thus it is a profitable deviation. Additionally, it must be that |$\beta ^*_1=1$|⁠: using the expressions for sδ(θ ∣ θ; p, β) = rδ(θ ∣ θ; p, β, σI), the payoff for σI and (β0, β1) = (β, 1) is $$\begin{eqnarray} \pi _0u_0\frac{\beta \alpha }{1-\delta +\delta (\beta \alpha +1-\alpha )}+\pi _1u_1\frac{\alpha }{1-\delta +\delta (\alpha +\beta (1-\alpha ))}, \end{eqnarray}$$(A8) and payoff for σI and (β0, β1) = (1, β) is $$\begin{eqnarray} \pi _0u_0\frac{\alpha }{1-\delta +\delta (\alpha +\beta (1-\alpha ))}+\pi _1u_1\frac{\beta \alpha }{1-\delta +\delta (\beta \alpha +1-\alpha )}. \end{eqnarray}$$(A9) The assumptions that π1u1 > π0u0 and that α > 1/2 imply that, for any β ∈ (0, 1), (A8) exceeds (A9), as needed. It therefore remains to find |$\beta ^*_0 \in (0,1]$|⁠. If the optimal value is interior, then it satisfies (13) with a = 0: $$\begin{eqnarray} \pi _0u_0r_\delta (0\mid 0,p,\beta ^*,\sigma _I) &=& \delta \left(\pi _0u_0r^2_\delta (0\mid 0;p,\beta ^*,\sigma _I)\right. \\ && \left. +\pi _1u_1r_\delta (1\mid 1;p,\beta ^*,\sigma _I)r_\delta (0\mid 1;p,\beta ^*,\sigma _I) \right). \end{eqnarray}$$ After the substitution of |$r_\delta (x\mid \theta ;p,\beta ,\sigma _I)=\frac{\beta _xp(x\,\mid \,\theta )}{1-\delta +\delta \sum _{x^{\prime }}\beta _{x^{\prime }}p(x^{\prime }\,\mid \,\theta )}$|⁠, this condition simplifies into a quadratic equation for |$\beta ^*_0$|⁠. When |$\delta \lt \frac{1}{\alpha + (1-\alpha )R}$|⁠, then this condition does not have an interior solution and the derivative of the value (A8) with respect to β0 at β0 = 1 is positive. Thus, in this case, the unique |$\beta ^*_0$| satisfying the first-order condition is |$\beta ^*_0=1$|⁠. When |$\delta \gt \frac{1}{\alpha + (1-\alpha )R}$|⁠, then the condition has an interior solution and the derivative of the value (A8) with respect to β0 at β0 = 1 is negative. Thus, for this range of parameters, the unique |$\beta ^*_0$| satisfying the first-order condition is the interior value that solves the quadratic equation, solution of which decreases in δ. Notes This paper has been previously circulated under the title: ‘On Second Thoughts, Selective Memory, and Resulting Behavioral Biases.’ We thank Mark Dean, Andrew Ellis, Alessandro Pavan, Philip Reny, Larry Samuelson, Colin Stewart, Balazs Szentes, colleagues at the University of Edinburgh, the audiences at Bocconi, Queen Mary, Columbia, Ecole Polytechnique, Zurich and St Andrews universities, workshops and conferences in Erice, Alghero, Faro, Gerzensee, New York, Cambridge, Vancouver, and Barcelona, the editor (Gilat Levy), and the two referees for helpful comments. Ludmila Matysková and Jan Šedek provided excellent research assistance. Deborah Nováková and Laura Straková have helped with English. Jakub Steiner has received financial support from the Czech Science Foundation grant 16-00703S and from the ERC grant 770652. Philippe Jehiel thanks the ERC grant n○ 742816 for funding. Footnotes 1 In the latter case, while the second-thought free conditions need not be satisfied for each problem in isolation, we would still derive that some degree of selective hesitation is optimal. 2 Somewhat less related is a literature that explores how exogenous analogy-based and extrapolation-driven errors in learning lead to behavioural biases; see coarse learning in Jehiel (2005) and its application to overoptimism in Jehiel (2018). By contrast, in our approach, the agent optimises the error distribution given the constraints. 3 We do not allow for mixed action strategies since the optimum can always be achieved with a pure action strategy. 4 This insight exploits the assumption of perfect patience, since impatient agents would trade off informativeness against delay costs. We conjecture that when exponential discounting is considered, then the result that the agent ignores all but two signal realisations continues to hold for sufficiently patient agents and generic signal structures. 5 Such summary statistic of |$\mathcal {P}$| continues to exist when 2 < |X| < ∞. For any pair of signal realisations (x, x′) and an experiment p, let |$d_{x,x^{\prime },p}=\frac{p(x\,\mid \,0)p(x^{\prime }\,\mid \,1)}{p(x\,\mid \,1)p(x^{\prime }\,\mid \,0)}$|⁠. Then, |$\overline{d}$| is the maximum of |$d_{x,x^{\prime },p}$| over all ordered pairs (x, x′) and experiments p. 6 This is to be contrasted with the reputation-based explanation of Gentzkow and Shapiro (2006). See also Calvert (1985), Suen (2004), and Che and Mierendorff (2019) for constrained-optimal media-bias models. 7 We can always achieve this by relabelling the states θ and the signals values x, unless ρ0 = ρ1 or ρ0 = 1 − ρ1. 8 These two assumption are satisfied when p(θ ∣ θ) is sufficiently close to one for each θ. 9 A truncation is obtained by deleting one or more last elements in h. 10 Rules ra that always select an action a can be trivially constructed from p and σI by using βa = 1 and βx = 0 for x ≠ a. References Basu P. , Chatterjee K. ( 2015 ). ‘ On interim rationality, belief formation and learning in decision problems with bounded memory ’, Unpublished. OpenURL Placeholder Text WorldCat Bordalo P. , Gennaioli N., Shleifer A. 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Google Scholar Crossref Search ADS WorldCat © The Author(s) 2019. Published by Oxford University Press on behalf of Royal Economic Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. © The Author(s) 2019. Published by Oxford University Press on behalf of Royal Economic Society.

Mengel,, Friederike

doi: 10.1093/ej/ueaa035pmid: N/A

Abstract Gender differences in networking have been cited as an important reason behind gender earnings and promotion gaps. Despite this fact there is comparatively little evidence on whether such differences exist or what they look like. We conduct a series of experiments to gain insight into these questions. The experiments are designed to understand differences in the strategic use of networks, when both men and women have the same opportunities to network. While we do find evidence of gender earnings and promotion gaps in the lab, we do not find evidence of gender differences in network formation, except for the fact that men display more homophily than women. Women and men do, however, not systematically differ in terms of the number of links formed or received nor in terms of their centrality in the network. Earnings and promotion gaps appear partly because male decision makers are more likely to reward their (predominantly male) network neighbours with increased earnings as well as promotion. Persistent gender earnings and promotion gaps have attracted much attention in research and policy debates in recent years (see Goldin and Rouse, 2000; Niederle and Vesterlund, 2007; Black et al., 2008; Bagues and Esteve-Volart, 2010 or Sandberg, 2013 among many others).1 Potential explanations for gender earnings and promotion gaps include differences in competitiveness and career ambition, differences in child-rearing responsibilities, cultural pressures but also outright gender discrimination. One of the most commonly cited explanations for gender earnings and promotion gaps are gender differences in networking (Saloner, 1985; Gersick et al., 2000; Sandberg, 2013). Since Granovetter (1973) a number of authors have pointed out the importance of social connections for obtaining jobs and job-related advantages (Montgomery, 1991; Hwang and Kim, 2009; Renneboog and Zhao, 2011; Beaman and Magruder, 2012). Gender differences in obtaining and using such connections via networking have been named a key factor to limits women’s success in labor markets. Consequently, the amount of resources spent on women’s networking events, designed to address presumed differences in networking is enormous.2 Despite these facts there is little evidence as to whether gender differences in networking exist or what they look like.3 The principal aim of this paper is to test for the existence of gender differences in networking and to better understand their nature. Identifying gender differences in networking in the field presents a number of difficulties. First, real-life networks often cannot be observed. Even if networks can be elicited, it is often hard to distinguish types of relationships. It is also difficult to measure failed attempts at linking and to observe how the network (and networking efforts) change with incentives. Finally, the position a person occupies in a network will be endogenous to her as well as others’ characteristics and past decisions, a fact that makes identification of gender differences difficult (McDowell et al., 2005).4 All these difficulties can be overcome in a lab experiment. Some important features of real-life interactions are, however, absent in the lab. Obstacles to networking for women often include factors, such as childcare duties, which prevent women from spending time networking after work (Campbell, 1988). In the field it is difficult to disentangle such lack of opportunities from preferences or strategic choices (Moore, 1990). In the lab opportunities are the same for men and women. Hence we can identify whether there are gender differences in how men and women form and use networks strategically if both have the same opportunity in doing so. In our experiment participants first performed a real effort task. The second stage was the networking stage. In the third stage one group member was selected to be ‘decision maker’ and to allocate the overall surplus among all group members. All three stages (task, networking and allocation of surplus) were repeated ten times. Treatments differed in two dimensions. Our first treatment variation concerns the networking stage. Networking can have many functions including joint production, coordination, forming agreements, acquiring or passing on information. A minimal networking variation focuses on the information aspect of networking. If i forms a link to j, then j is informed about i’s score but not vice versa. Hence under this variation, forming a link allows participants to pass on information, but not to acquire information.5 Under the second variation, if i forms a link to j, a chat window opens and i and j can chat for three minutes. This open communication variation hence allows participants to network in a less restrictive format and it allows participants both to pass on but also to acquire information, to explicitly discuss and reach agreements, etc. Our second treatment variation changes how the decision maker is selected. We focus on three different environments, which differ in how promotion—defined as being selected as a decision maker—is determined. In the first environment, it is determined by performance. In the second, by the number of incoming connections. In the third, by designation by others. Understanding in which of these settings networking differences appear (if at all) can help us understand the origin of networking differences. It also has consequences for organisational design if one of the aims is to reduce gender gaps.6 We find substantial gender earnings and promotion gaps in our experimental treatments. Men earn between 12% and 30% more than women in three treatments. They are between 9% and 10% more likely to be promoted in two treatments. Only in two of our six treatments did we find neither earnings nor promotion gaps. In terms of networking, we find few differences in how networks are formed. Men’s networks display more homophily than women’s in almost all treatments.7 In two treatments men also have a somewhat higher out-degree (more outgoing links) compared to women. Otherwise there are no gender differences in network formation. Neither homophily, nor out-degree are, however, systematically related to earnings or promotion on average across both genders. In line with a conjecture by Ibarra (1993) we find, though, that men benefit from homophilous ties while women don’t. We also find gender differences in how networks are used. While neither women nor men discriminate between genders per se, men have a tendency to favour their network neighbours. In particular, men are |$\approx 40 \%$| of a standard deviation more likely to designate network neighbours to succeed them as decision makers. They tend to reward network neighbours by |$\approx 16 \%$| higher earnings in the treatments where earnings gaps have been identified. Neither men nor women receive preferential treatment in either of these dimensions per se. However, as most neighbours of male decision makers are male, the fact that men, but not women, reward their network neighbours can explain a substantial part of the earnings and promotion gaps we observe. This fact also explains why men benefit from homophily while women don’t. Our paper contributes to the literature on gender differences in networking by providing what is to our knowledge the first experimental study of gender differences in strategic networking. Gender differences in networking has been an active research area in organisational behaviour and sociology (Eder and Hallinan, 1978; Campbell, 1988; Burt, 1995; 1998; Ibarra, 1992; 1993). In the context of his seminal work on structural holes Burt (1998) has shown that early promotion correlates to network properties in opposite directions for men and women. For men it is better to have diverse contacts. Women get promoted earlier, the more their relations are directly or indirectly concentrated in a single contact. Particularly interesting in our context is work by Ibarra (1993) who studies personal networks of women and minorities in management. She develops two hypotheses related to homophily within this context: (i) women will have a smaller percentage of same-sex ties; and (ii) homophily and positional power of network contacts will be negatively associated for women, but not for (white) men.8 Despite the fact that there are no pre-existing structural asymmetries between men and women in our experiment, our results are in line with both these hypotheses. Our results also shed light on a number of other conjectures on the origin of networking differences that have been circulated in existing popular as well as academic literature. Roughly speaking, these conjectures can be divided into three categories. The first category claims that networking is not as useful for women as it is for men, either because women can expect less positive reciprocity than men (Heilman and Chen, 2005; Aguiar et al., 2009), because there are fewer women in powerful positions or because networking women are perceived as less likeable (McGinn and Tempest, 2000; Sandberg, 2013). Our evidence partly supports these conjectures. Women do less often benefit from positive reciprocity in our experiment. The reason is, however, not that men or women would discriminate against women per se. Instead men (and only men) do substantially reward their network neighbours and those neighbours happen to be predominantly men. Conditional on who they are linked to, men and women benefit equally from positive reciprocity. The second category of explanations claims that women network less effectively, because they use networks less strategically (Rudman, 1998). We find little evidence supporting this conjecture when it comes to network formation. Women in our experiment form equally many links as men in almost all treatments and their networking activities depend on achievements (performance) in the same way as men’s. A third category of explanations focuses on differences in opportunities such as the fact that women have less time to engage in networking activities because they are more involved with, e.g., childcare (Campbell, 1988). As discussed above, such differences are outside the scope of our experiment. While this means that some aspects of networking cannot be studied in this paper, it also means that we are able to isolate differences in the strategic use of networks under ex ante equal opportunities. Our study is also related to research on gender differences in the workplace more generally (Delfgaauw et al., 2013). There is an empirical literature studying how referrals from current employees (the ‘old boys’ network’) can reduce employer uncertainty about worker productivity (Simon and Warner, 1992). These papers do not usually focus on gender differences in networking. Exceptions include Marmaros and Sacerdote (2002) who study how college seniors use social networks to obtain their first jobs or Lalanne and Seabright (2014) who find that salaries of male, but not female executive board members are an increasing function of influential people they have met in the past. Because of the difficulties with field data described above, neither of these studies can identify networking differences. The findings by Lalanne and Seabright (2014), in particular, are however consistent with our finding that men tend to favour network neighbours. This can lead to earnings gaps if there is homophily in networks. The effect of homophily could be compounded if, unlike in our experimental setting, there are more men in powerful positions to start with. Zeltzer (2020) shows that part of the Medicare physician pay gap can be explained by gender homophily in referral networks, illustrating how gender homophily can contribute to occupational inequalities. Also Ibarra (1992) has demonstrated the existence of homophily in a study conducted in an advertising firm. She concluded that men appeared to reap greater network returns from homophilous relationships. As discussed above, this is in line with our evidence.9 Several other researchers have documented gender differences in existing networks (Moore, 1990; Benenson, 1993; Buechel et al., 2018; Lindenlaub and Prummer, 2014). This research has produced rich accounts of women and men’s positions in networks, though the evidence on what the differences are is a bit mixed. Such differences in existing networks of men and women could come about via differences in networking, but also via differences in preferences, abilities or organisational and social constraints. Our study contributes to this literature by providing experimental variation on incentives to network. Because we are able to observe strategic formation of networks starting from a fully symmetric situation, we are able to show what type of differences in existing networks are likely due (or not due) to gender differences in strategic networking. The finding that predominantly men tend to favour network neighbours contributes a new aspect to the gift exchange and reciprocity literature (Fehr et al., 1993; 1998). This literature has focused on documenting how people exchange favours in work settings (typically trading effort for fixed wages). Our paper identifies another dimension of work interactions in which gift exchange plays an important role. Predominantly men reward their network neighbours through earnings and promotions, which can contribute to gender earnings and promotion gaps. Finally we also contribute to the literature that documents and discusses reasons behind gender earnings and promotion gaps, which are not directly related to networking differences. Some researchers have, for example, documented gender biases in performance evaluations (Goldin and Rouse, 2000; Krawczyk and Smyk, 2016; Boring, 2017; Mengel et al., 2019), in education (Mondschein et al., 2000; Halim and Ruble, 2010) or gender differences in preferences (Gneezy et al., 2003; Niederle and Vesterlund, 2007). All of these can be additional channels leading to earnings and promotion gaps. In this sense our paper complements this evidence. The paper is organised as follows. In Section 1 we describe the experimental design as well as the results from our control treatment. Section 2 shows our evidence on earnings and promotion gaps, Section 3 discusses gender differences in networking and Section 4 discusses some mechanisms and additional results. Section 5 concludes. More information about the sample, experimental instructions as well as additional tables and figures can be found in the Online Appendix. 1. Design and Procedures In this section we describe the experimental sample (Subsection 1.1), design and procedures (Subsection 1.2) and discuss evidence from our control treatment (Subsection 1.3). At the end of the section we summarise the research questions and give a road map for the rest of the paper (Subsection 1.4). 1.1. Sample We describe some characteristics of our sample. More details are provided in Online Appendix A. Our participants have signed up at Essex Lab at the University of Essex to participate in social sciences experiments. Most participants are university students, but there is a non-negligible share (12%) of non-students participating in the experiment. The sample is overall gender balanced: 50.88% of participants are male in the minimal treatments and exactly 50% in the treatments with chats. Online Appendix Figure A.4 shows the distribution of group compositions in terms of gender. The typical group in the experiment was gender balanced with three male and three female participants. There were no exclusively male or female groups, but several groups with either 33% or 66% women and some groups with only one woman (or one man). The age distribution among male and female participants is plotted in Online Appendix Figure A.1. Women were on average 22.39 (22.38 in the treatments with chats) years old ranging from 18 to 62 (18 to 69). Men were on average 22.71 (23.28) years old with a range from 18 to 54 (18 to 77). Online Appendix Figures A.2 and A.3 show the distribution of participants’ nationalities. Most participants are from Europe (non-UK), followed by the UK and South- and East-Asian countries. Finally, Online Appendix Table A.1 reports balancing tests, which shows no statistically significant differences across treatments according to the sample characteristics we elicited. 1.2. Design All of our treatments consist of ten repetitions of the following game of three stages: (i) first participants solve a task and receive a score reflecting their performance (task stage); (ii) they can form links to others (networking stage); and (iii) one group member allocates the group’s surplus (allocation stage). These three stages are meant to represent highly stylised work environments, where first work is produced and then networking is used to achieve work-related benefits, such as pay increases or promotion. We will describe the three stages in turn. First, however, we will describe how gender identity was communicated in the experiment. Gender identity: at the start of the experiment participants were asked to enter some basic demographic information, such as age, gender, nationality, student status. Afterwards participants were informed on the screen that they were assigned an avatar which was shown to them on the screen. They were also informed that ‘All women have been assigned a female ‘avatar’ and all men a male ‘avatar’. Other than that the pictures have no connection to the information provided by you.’ Hence they were informed that behind a female (male) avatar is always a female (male) participant, but this information was framed in the context of an assurance of their anonymity. When filling in the demographics participants did not know yet that there would be avatars in the experiment.10 We used 24 different female and male avatars to reduce the risk that particular facial features might trigger responses by others.11 With this design we hoped to credibly communicate gender identity while at the same time minimise the risk that participants consider this an experiment about gender or wonder why gender information is given.12 Participants were then randomly assigned into groups of six participants and remained in these groups throughout the experiment. We chose repeated interaction as it is often described as an essential part of an environment for networking to be effective (Jones et al., 1997). We now describe the three stages of the experiment: the task, networking and allocation stage. The stages were repeated ten times in the same groups. Task stage: we asked participants to count the number of ‘1’ entries in a Boolean 20 × 20 matrix with only 0 and 1 entries (Abeler et al., 2011). Participants had 75 seconds to enter their count. A screenshot of the task can be found in Online Appendix Figure C.3. Denote by Δi the absolute value of the difference between the true number of ‘1’ entries in the matrix and participant i’s count.13 Participant i then receives a score SCi which equals $$\begin{eqnarray} SC_{i}= \left\lbrace \begin{array}{@{}l@{\quad }l@{}}20-\Delta _{i} & \text{if } \Delta _{i} \le 20 \\ 0 & \text{else} \\ \end{array}\right. \end{eqnarray}$$ The group score is the sum of the scores of all group members and hence ranges between {0, ..., 120}. After the task, participants were informed about their own score and their rank in the group of six. Ties were broken randomly by the flip of a fair coin. Participants were also informed about the group score, but not about the individual scores of other group members.14 Networking stage: in this stage participants could form links to other group members. Links last only for the current rounds, i.e., have to be renewed in each period. Participants received an endowment of ten tokens in each period and each link costs two tokens. Only the participant initiating the link had to pay for it. Remaining endowments from the network stage were converted into GBP at a rate of 1:1 and added to participants’ earnings at the end of the experiment. There are two treatment variations on the networking stage both focused on information transmission.15 Under the first participants learned the individual scores of the group members who established a link to them. Online Appendix Figures C.4 and C.5 show screenshots of the linking stage and the associated information stage. This minimal networking condition, where a link initiated by i only reveals i’s score to j could reflect networking activities such as passing one’s CV or newest research paper or communicating another achievement to a target person. While this condition allows us to have full control about which information participants hold at any given time, it may be too restrictive to capture what ‘networking’ is about for our participants. We hence also study an open communication variation which allows participants to network in a less restrictive format. Under this second treatment variation, if either participant i established a link to j or vice versa, then a bilateral chat window opened in which participants i and j could chat for three minutes. If participants held multiple links at the same time, all chats happen simultaneously on a split screen.16 This treatment variation hence also breaks the tight link between transmitting information about performance and networking which is present under the first variation. Instead it allows participants to communicate, make agreements or transmit information in whichever way they wanted. We label the treatments with this open form of communication with a suffix -COMM. Allocation stage: after the networking stage the group score was converted into pounds (GBP) at a rate of 1:1 and a decision maker allocated the earnings among the six group members (in any way s/he likes). The allocation of earnings hence took place in a multi-person dictator game with the decision maker being the dictator.17 At the end of each round, participants were informed about the group score, their own score, who was decision maker, how much the decision maker allocated to them and their payoff in this round (allocation by the decision maker plus remaining endowment from the networking stage). Treatments also differed in how the decision maker is determined. In treatments PERF and PERF-COMM the best-performing group member (with the highest score SCi) becomes decision maker. In treatments DESIG and DESIG-COMM one participant is randomly chosen to be the decision maker in period 1. In all subsequent periods the current decision maker designates the next period decision maker. Participants cannot designate themselves. In treatments NET and NET-COMM the group member with the highest in-degree in the network (i.e., who most others linked to) becomes decision maker. These three conditions highlight three aspects of typical ‘promotions’: performance, designation and networking. Comparing these treatments will help us understand to what extent networking differences depend on the role networking is given in the institutional environment. See Subsection 1.4 for more details and research questions. We also ran a control condition (CONTROL) which we will describe in Subsection 1.3. Table 1 summarises the number of observations and the gender distribution for each treatment. While the aim of the paper is not to test predictions of standard game theory, theoretical predictions for the different treatments can be found in Online Appendix E.18 Table 1. Number of Observations, Clusters (i.e., Groups of Six Participants) and Gender Distribution in Different Treatments. . Observations . Gender distribution . . Observations . Groups (clusters) . Women . Men . PERF 600 10 29 31 NET 600 10 30 30 DESIG 660 11 31 35 PERF-COMM 720 12 36 36 NET-COMM 720 12 38 34 DESIG-COMM 600 10 28 32 CONTROL 220 – 10 12 . Observations . Gender distribution . . Observations . Groups (clusters) . Women . Men . PERF 600 10 29 31 NET 600 10 30 30 DESIG 660 11 31 35 PERF-COMM 720 12 36 36 NET-COMM 720 12 38 34 DESIG-COMM 600 10 28 32 CONTROL 220 – 10 12 Open in new tab Table 1. Number of Observations, Clusters (i.e., Groups of Six Participants) and Gender Distribution in Different Treatments. . Observations . Gender distribution . . Observations . Groups (clusters) . Women . Men . PERF 600 10 29 31 NET 600 10 30 30 DESIG 660 11 31 35 PERF-COMM 720 12 36 36 NET-COMM 720 12 38 34 DESIG-COMM 600 10 28 32 CONTROL 220 – 10 12 . Observations . Gender distribution . . Observations . Groups (clusters) . Women . Men . PERF 600 10 29 31 NET 600 10 30 30 DESIG 660 11 31 35 PERF-COMM 720 12 36 36 NET-COMM 720 12 38 34 DESIG-COMM 600 10 28 32 CONTROL 220 – 10 12 Open in new tab Other details: at the end of the experiment one period was selected randomly for payment. Participants’ earnings are the show-up fee of £3, the remaining amount from their endowment in the networking stage as well as the share of the group score the decision maker allocated to them. Earnings ranged between 4 GBP and 124 GBP with an average of 22.90 GBP. The experiments were conducted at Essex Lab at the University of Essex in March 2014 using the software z-tree (Fischbacher, 2007). Participants were recruited using the recruitment system hRoot. More detailed description of the sample as well as balancing tests can be found in Online Appendix A. Ethical approval was obtained by the FEC (Faculty Ethics Committee) at the University of Essex under Annex B. 1.3. Control Condition The control condition was conducted to see whether there are substantial performance differences between men and women in this task in the absence of a networking or allocation stage. In the control condition participants performed the task ten times repeatedly and were paid simply their score SCi from a randomly drawn period (in addition to the show-up fee). Table 2 shows that the performance of men and women in the control treatment is very similar. This is true both for accuracy (their score) and speed (how long it took them to enter the score). The median score for women is 15.9 and for men 15.5 points meaning that they were off by about 4.1 to 4.5 numbers in their count on average across the ten matrices they faced. The number of different women in the CONTROL condition with the maximal score of 20 is ten, and the number of men seven. Hence more than 70% of participants reach the maximal score at least once. The distribution of individual average scores (across the ten rounds) is not different between men and women according to a rank-sum test (p = 0.6680).19Online Appendix Figure H.1 (Panel (a)) shows the cumulative distribution of all scores for both men and women. The figure shows that, while there are somewhat more zero scores among men, the distribution of scores is otherwise very similar.20 Table 2. Performance Differences in CONTROL. In Columns (1) and (2) the Table Shows Summary Statistics for Individual Scores Averaged Across Participants and Matrices. Columns (3) and (4) Show Summary Statistics on the Average Time Taken to Complete a Task. . Accuracy . Speed . . Female . Male . Female . Male . Mean 15.19 13.43 70.38 68.04 Median 15.9 15.5 70.7 68.65 SD 2.97 5.36 5.00 5.85 0–25 13.8 11.8 69.25 63.8 75–100 17.6 17.7 74.8 74.5 Rank-sum test p = 0.6680 p = 0.3199 Participants 12 10 12 10 Observations 120 100 120 100 . Accuracy . Speed . . Female . Male . Female . Male . Mean 15.19 13.43 70.38 68.04 Median 15.9 15.5 70.7 68.65 SD 2.97 5.36 5.00 5.85 0–25 13.8 11.8 69.25 63.8 75–100 17.6 17.7 74.8 74.5 Rank-sum test p = 0.6680 p = 0.3199 Participants 12 10 12 10 Observations 120 100 120 100 Open in new tab Table 2. Performance Differences in CONTROL. In Columns (1) and (2) the Table Shows Summary Statistics for Individual Scores Averaged Across Participants and Matrices. Columns (3) and (4) Show Summary Statistics on the Average Time Taken to Complete a Task. . Accuracy . Speed . . Female . Male . Female . Male . Mean 15.19 13.43 70.38 68.04 Median 15.9 15.5 70.7 68.65 SD 2.97 5.36 5.00 5.85 0–25 13.8 11.8 69.25 63.8 75–100 17.6 17.7 74.8 74.5 Rank-sum test p = 0.6680 p = 0.3199 Participants 12 10 12 10 Observations 120 100 120 100 . Accuracy . Speed . . Female . Male . Female . Male . Mean 15.19 13.43 70.38 68.04 Median 15.9 15.5 70.7 68.65 SD 2.97 5.36 5.00 5.85 0–25 13.8 11.8 69.25 63.8 75–100 17.6 17.7 74.8 74.5 Rank-sum test p = 0.6680 p = 0.3199 Participants 12 10 12 10 Observations 120 100 120 100 Open in new tab In terms of the time taken to enter their decision (speed), both men and women are relatively close to the time out of 75 seconds. On average (across the ten matrices faced) they enter their count about five seconds before that. Online Appendix Figure H.1 (Panel (b)) shows the cumulative distribution of time taken in all rounds separately for men and women. It can be seen that the screen times out for men and women in about 50% of the cases; 70% of both men and women finish the task with fewer than ten seconds to spare. Among those that make relatively quick decisions (between 55 and 65 seconds) men are a bit faster than women. Taken together the evidence suggest that the task was easy, but not trivial for participants. There are no substantial gender differences neither in terms of accuracy nor in terms of speed, i.e., time taken to enter the count. 1.4. Research Questions Before we start presenting our main results in the next section, we summarise our research questions and hypotheses. The presentation of our results will then follow the structure outlined in this section. First we briefly discuss the motives to network in the different treatments. In treatment PERF the only clear reason to network is to communicate one’s own performance to a potential future decision maker. This could serve as a signal of one’s ability or effort. As the group score is known in addition it also serves as a (noisy) signal of others’ effort or ability. The COMM-variation adds an element of persuasion to this motive where participants can explicitly ask for a certain share of the earnings as a result of their performance. According to standard game theory there are, however, no incentives to network in these treatments (Online Appendix E). A direct and explicit impact of networking on promotion is added in treatment NET where the network explicitly determines who becomes decision maker via a form of popularity contest. Hence, in this treatment, there is a potential motive for favour exchange as each link formed to a person helps them to reach power (become decision maker). The COMM-variation allows for explicit discussion of linking strategies and explicit coordination on who to link to. The favour exchange element is reinforced in treatments DESIG where there is an equilibrium in which two participants form a coalition and share power among themselves (see Online Appendix E). While such agreements have to be reached tacitly in DESIG, in DESIG-COMM open communication allows reaching such agreements explicitly. There can be non-tangible reasons for forming a link as well, such as establishing likeability or ‘connection’ in a vague sense. These non-tangible elements are present in all treatments. However, we would expect them to be stronger in the COMM-treatments with open communication. For all our research questions we will ask how the extent to which the institutional environment creates a space for informal arrangements and favour exchange affects gender differences. We now state our research questions and the road map for the following sections. As much of our motivation comes from the role networking plays for earnings and promotion gaps, we first ask whether there are earnings and/or promotion gaps in our experiment. We also ask how the answer to this question depends on the role networking is given in the institutional environment. Q1 Are there gender earnings and promotion gaps and do they depend on the role networking is given in the institutional environment? Research question Q1 will be addressed in Section 2. The second question relates to gender differences in networking, specifically to identifying differences in network formation. Q2 Are there gender differences in networking and do they depend on the role networking is given in the institutional environment? Answering this question comprehensively also tests a set of conjectures discussed in the Introduction. If women network less effectively as they are more reluctant to communicate achievements (Rudman, 1998), then we should see women forming fewer links (have a lower out-degree) in PERF compared to men, particularly among the group of high performers. If women network less effectively as they use networks less strategically, then this can lead to multiple differences in network formation we should detect. In PERF women’s networking activities should react less to performance than men’s, in DESIG we should see fewer reciprocal links etc. We should also detect larger gender differences in the treatments where networks have more of a strategic role. Research question Q2 will be addressed in Subsection 3.2. Our third question relates to how network are used. Q3 Are there gender differences in how networks are used and do they depend on the role networking is given in the institutional environment? In addressing this question we will give special attention to the question of favour exchange. Hence we will ask whether there are gender differences in the extent to which women and men use networks to exchange favours. Differences in how networks are used can impact on how beneficial it is for men and women to network and hence can shed light on Heilman and Chen (2005)’s conjecture that women may network less because they are less likely to benefit from reciprocity (see also Aguiar et al., 2009). Research question Q3 will be addressed in Subsection 3.3. We now turn to our main results. 2. Gender Earnings and Promotion Gaps We ask whether there are earnings and promotion gaps in our experiment starting with earnings gaps. To answer this question we focus on average earnings from periods 6–10 of the experiment disregarding show-up fees and remaining endowments from the networking stage. We focus on periods 6–10 to capture mature behaviour after some learning has taken place and we disregard show-up fees and remaining endowments for this analysis to capture as closely as possible the type of monetary earnings differences typically referred to as ‘earnings gaps’. Differences in networking and associated costs will be studied further below. Earnings, thus defined, can differ across genders for three reasons. First, the frequency with which women and men are decision makers can differ (promotion gap). Second, the amount of money male and female decision makers allocate to themselves could differ and third the amount decision makers allocate to males and females who are not decision makers could differ. The second difference is maybe best interpreted as differences in altruism or generosity between men and women in this setting.21 For the purpose of defining earnings gaps in this paper, we are interested in the third difference. We hence define the earnings gap as the percentage gap between earnings of male and female participants who are not decision maker. Panel (a) in Figure 1 shows the earnings gap for the Base treatments, where networking involves only minimal communication (i.e., passing on information about one’s score). Conditional on not being decision maker in treatment NET men earn 11.00 pounds on average which is 25% more than women who earn 8.83 pounds in that case. In treatment PERF and DESIG there are no statistically significant gender differences in earnings. Panel (b) in Figure 1 shows the earnings gap for the COMM treatments. Men earn substantially more than women in all treatments with open communication. The earnings gap is almost 30% in PERF-COMM and |$\approx 10\%$| in NET-COMM. In DESIG-COMM, the difference between female and male earnings is not statistically significant at conventional levels. Fig. 1. Open in new tabDownload slide Percentage Gap between Earnings of Male and Female Participants Who Are Not Decision Maker. Positive Differences Mean Men Earn More and Negative Differences Mean Women Earn More. Stars Indicate Significance Levels According to Two-Sided Rank-Sum Tests|$(^{***} 1\%, $||$^{**} 5\%, $||$^{*} 10\%)$|. Fig. 1. Open in new tabDownload slide Percentage Gap between Earnings of Male and Female Participants Who Are Not Decision Maker. Positive Differences Mean Men Earn More and Negative Differences Mean Women Earn More. Stars Indicate Significance Levels According to Two-Sided Rank-Sum Tests|$(^{***} 1\%, $||$^{**} 5\%, $||$^{*} 10\%)$|. Table 3 reports the results of regressions where we regress the earnings of participants who are not decision makers on a gender dummy (=1 if the participant is male) and their performance (score) in the task as well as some controls. It can be seen that a higher performance increases earnings in all treatments, albeit not significantly so in DESIG. In treatments NET, PERF-COMM and NET-COMM there is an additional effect of gender. Men earn ≈1.50−3.40 GBP more than women even after performance is controlled for (columns (3), (4) and (6)). After accounting for mean performance of men and women the earnings gap ranges between 12% and 30%.22 Table 3. Earnings as a Function of Gender Dummy and Performance (Score) in the Task. . Earnings gap . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . Male −0.233 −1.254 1.556* 3.408*** 2.422 2.151** (1.357) (1.363) (0.810) (0.865) (2.587) (0.878) Score 0.127** 0.030 0.290*** 0.245*** 0.202*** 0.340*** (0.049) (0.034) (0.069) (0.074) (0.051) (0.055) Observations 250 275 250 300 250 300 Number of participants 60 66 59 72 60 71 . Earnings gap . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . Male −0.233 −1.254 1.556* 3.408*** 2.422 2.151** (1.357) (1.363) (0.810) (0.865) (2.587) (0.878) Score 0.127** 0.030 0.290*** 0.245*** 0.202*** 0.340*** (0.049) (0.034) (0.069) (0.074) (0.051) (0.055) Observations 250 275 250 300 250 300 Number of participants 60 66 59 72 60 71 Notes: Random effects OLS regressions based on data from periods 6–10 of the experiment. Standard errors are clustered at the (matching) group level and account for auto-correlation at the individual level. Controls for age, nationality and session fixed effects are included. Earnings regressions include only participants not as decision maker. Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab Table 3. Earnings as a Function of Gender Dummy and Performance (Score) in the Task. . Earnings gap . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . Male −0.233 −1.254 1.556* 3.408*** 2.422 2.151** (1.357) (1.363) (0.810) (0.865) (2.587) (0.878) Score 0.127** 0.030 0.290*** 0.245*** 0.202*** 0.340*** (0.049) (0.034) (0.069) (0.074) (0.051) (0.055) Observations 250 275 250 300 250 300 Number of participants 60 66 59 72 60 71 . Earnings gap . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . Male −0.233 −1.254 1.556* 3.408*** 2.422 2.151** (1.357) (1.363) (0.810) (0.865) (2.587) (0.878) Score 0.127** 0.030 0.290*** 0.245*** 0.202*** 0.340*** (0.049) (0.034) (0.069) (0.074) (0.051) (0.055) Observations 250 275 250 300 250 300 Number of participants 60 66 59 72 60 71 Notes: Random effects OLS regressions based on data from periods 6–10 of the experiment. Standard errors are clustered at the (matching) group level and account for auto-correlation at the individual level. Controls for age, nationality and session fixed effects are included. Earnings regressions include only participants not as decision maker. Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab Promotion gap: Table 4 focuses on promotions, in particular on the probability to become decision maker. Performance increases participants’ chances to become decision maker only in treatments PERF and PERF-COMM, where, by design, the highest-scoring group members become decision maker. There is no significant effect of performance on the chances to become decision maker in any of the other treatments. There are possibly gender gaps in treatments NET and DESIG-COMM. Men are between 9% and 10% more likely to become decision makers in these treatments (columns (3) and (5)). However, those are either only marginally significant at the 10% level (NET) or just outside of 10% statistical significance (DESIG-COMM). Table 4. Promotion as a Function of Gender Dummy and Performance (Score) in the Task. . Promotion gap . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . Male −0.086 0.033 0.092* 0.025 0.102 −0.078 (0.059) (0.042) (0.050) (0.055) (0.074) (0.081) Score 0.014*** 0.001 −0.002 0.015*** −0.002 0.000 (0.002) (0.002) (0.003) (0.002) (0.003) (0.002) Observations 300 330 300 360 300 360 Number of participants 60 66 60 72 60 72 . Promotion gap . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . Male −0.086 0.033 0.092* 0.025 0.102 −0.078 (0.059) (0.042) (0.050) (0.055) (0.074) (0.081) Score 0.014*** 0.001 −0.002 0.015*** −0.002 0.000 (0.002) (0.002) (0.003) (0.002) (0.003) (0.002) Observations 300 330 300 360 300 360 Number of participants 60 66 60 72 60 72 Notes: Random effects OLS regressions based on data from periods 6–10 of the experiment. Standard errors are clustered at the (matching) group level and account for auto-correlation at the individual level. Controls for age, nationality and session fixed effects are included. Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab Table 4. Promotion as a Function of Gender Dummy and Performance (Score) in the Task. . Promotion gap . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . Male −0.086 0.033 0.092* 0.025 0.102 −0.078 (0.059) (0.042) (0.050) (0.055) (0.074) (0.081) Score 0.014*** 0.001 −0.002 0.015*** −0.002 0.000 (0.002) (0.002) (0.003) (0.002) (0.003) (0.002) Observations 300 330 300 360 300 360 Number of participants 60 66 60 72 60 72 . Promotion gap . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . Male −0.086 0.033 0.092* 0.025 0.102 −0.078 (0.059) (0.042) (0.050) (0.055) (0.074) (0.081) Score 0.014*** 0.001 −0.002 0.015*** −0.002 0.000 (0.002) (0.002) (0.003) (0.002) (0.003) (0.002) Observations 300 330 300 360 300 360 Number of participants 60 66 60 72 60 72 Notes: Random effects OLS regressions based on data from periods 6–10 of the experiment. Standard errors are clustered at the (matching) group level and account for auto-correlation at the individual level. Controls for age, nationality and session fixed effects are included. Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab How does the institutional environment affect gender earnings and promotions gaps? We conjectured in Subsection 1.4 that environments that create more space for informal arrangements and favour exchange could lead to bigger gender differences in earnings and promotion. We find some support for this conjecture, as in our basic treatment variations we find earnings or promotion gaps only in treatment NET. In the -COMM variations, by contrast, we identify earnings gaps also in PERF-COMM, possibly because with chats favour exchange is also possible in this environment. We analyse chat content in Subsection 4.3. Robustness: Online Appendix G reports a few robustness checks and additional results. Online Appendix Table G.1 reports some descriptive statistics. Online Appendix Tables G.2 and G.3 explicitly show all controls used in Tables 3 and 4. We also conducted our regressions with avatar fixed effects. The problem with this exercise is that each avatar exists only in one gender. Male avatars can hence jointly absorb the effect of the male dummy. Still results are robust under such exercises and, importantly, no single avatar receives systematically higher or lower earnings than others (see also Figures C.6 and C.7 in Online Appendix B). 3. Networking To study whether earnings and promotion gaps can be (at least partially) explained by differences in networking, we first ask whether certain network positions are positively related to earnings and promotion (Subsection 3.1). We then ask whether women and men differ in how they form networks and in terms of the network positions they occupy (Subsection 3.2). Finally, we ask whether women and men differ in how they use existing networks (Subsection 3.3). As before we focus on mature behaviour in the second half of the experiment, i.e., across periods 6–10. 3.1. Importance of Network Position for Earnings and Promotion A network is defined as a collection of nodes |$\mathcal {N}=\lbrace 1,...,6\rbrace$| and a set of edges (links between the nodes) defined as |$\Xi ^{} \subseteq \lbrace (i,j) | i\ne j \in \mathcal {N}\rbrace$|⁠, where an element (i, j) indicates that i has established a link to j. Note that (i, j) ∈ Ξ does not imply (j, i) ∈ Ξ reflecting the fact that the network is directed, as (i) only the agent who establishes the link bears the cost; and (ii) in the treatments with minimal communication information along (i, j) flows only from i to j. We consider the following network characteristics. Agent i’s out-degree summarises how many links s/he has formed in the network, i.e., counts the number of edges (i, j) ∈ Ξ. Among network characteristics out-degree is probably the closest measure of ‘networking’ as it measures how active an agent is in terms of forming links. Out-degree is also the only network characteristic that agents have full control over, i.e., it does not depend on decisions of others. In-degree, by contrast, is defined as the number of others linked to an agent, i.e., it counts edges (j, i) ∈ Ξ. In-degree, just as out-degree, ranges between 0 to 5. We would not think of in-degree as a good measure of networking, as it cannot be controlled (directly) by the agent. However it can be seen as a measure of popularity and is in treatments NET and NET-COMM mechanically related to promotion, as those with the highest in-degree become decision maker in these treatments. A variable that has been linked to networking success in the sociological literature is homophily. Homophily is the principle that a contact between similar people occurs at a higher rate than among dissimilar people, where similarity can be race, gender or any other dimension (McPherson et al., 2001). In our context (gender-based) homophily measures the share of actual within-gender links relative to the share implied by random linking. More precisely we define homophily as follows. Denote by sg the share of same-gender links of a person of gender g and by ωgk the share of people of gender g in group k. The homophily index we then use is Currarini et al. (2009)’s inbreeding homophily index defined as $$\begin{eqnarray} \frac{s_{g}-\omega _{gk}}{1-\omega _{gk}} \end{eqnarray}$$ Homophily takes the value 0 if the share of within-gender links equals the share implied by random linking. If it exceeds 0, participants establish disproportionately more links within gender. If it is negative, they establish disproportionately more links across gender (heterophily).23 Homophily (in-degree) reports this measure for an agent’s in-degree and homophily (out-degree) for an agent’s out-degree, by measuring sg among participants’ incoming and outgoing links, respectively. Note that it is in principle both possible (i) for one gender to display more homophily than the other gender in terms of out- and in-degree as well as (ii) for one gender to display more homophily in in-degree while the other gender displays more homophily in out-degree. Online Appendix Figure H.3 illustrates this point. It has been argued in the literature that having homophilous networks is beneficial for men, but not for women (Ibarra, 1993). This is a conjecture we will test below. Eigenvector centrality is a measure of how central a person is in the network. It reports an agent’s eigenvector centrality in the undirected adjacency matrix.24 Unlike the degree measures eigenvector centrality not only accounts for how many people one is linked to, but also who these people are, i.e., how important they are in terms of their network position. Eigenvector centrality is considered important in the literature on diffusion of information in social networks (Jackson, 2015). Online Appendix Figures H.4 and H.5 show the distributions for these different network characteristics across treatments. The figures show that there is substantial variation in all five network characteristics. They also show that there are very few treatment differences in homophily and eigenvector centrality. It can be seen, however, that more links are formed and received in the NET treatments compared to the PERF and DESIG environments.25 We now ask how network position affects earnings and promotion in the experiment. To this end we estimate the following equation for each condition and network characteristic separately $$\begin{eqnarray} y_{i}^{t}=\alpha + \beta _{1} \tt {male}_{i} + \beta _{2} \tt {score}_{i}^{t}+\beta _{3} \tt {NW-characteristic}_{i}^{t}+ \epsilon _{i}^{t}, \end{eqnarray}$$(1) where yi is our outcome of interest, i.e., either earnings (Table 5) or promotion (Table 6), and NW-characteristic is one of the following network characteristics: in-degree, out-degree, eigenvector centrality, homophily (in-degree) and homophily (out-degree). We chose not to control for these network characteristics at the same time as they tend to be strongly correlated. Tables 5 and 6 report β3 for each network characteristic. Table 5. Effect of Network Position on Earnings. . Effect of network position on earnings (coefficientsβ3) . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . In-degree 1.195 0.630 0.577 1.273 3.476** 0.742 (0.759) (0.682) (0.460) (1.015) (1.074) (0.514) Out-degree 0.549* 0.976** −0.008 0.752 0.020 −0.037 (0.283) (0.404) (0.232) (0.590) (0.374) (0.202) EV centrality 4.574 7.603* 0.976 5.697 31.638** 15.297*** (3.555) (3.866) (2.844) (3.711) (11.254) (4.073) Homophily (in) −0.034 0.706 −0.404 −1.448 0.200 0.609 (0.401) (0.540) (0.386) (1.005) (0.820) (0.505) Homophily (out) −0.016 0.846 0.058 −0.355 0.631 1.070 (0.490) (1.270) (0.651) (0.940) (1.024) (0.624) Observations 250 275 250 300 250 300 . Effect of network position on earnings (coefficientsβ3) . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . In-degree 1.195 0.630 0.577 1.273 3.476** 0.742 (0.759) (0.682) (0.460) (1.015) (1.074) (0.514) Out-degree 0.549* 0.976** −0.008 0.752 0.020 −0.037 (0.283) (0.404) (0.232) (0.590) (0.374) (0.202) EV centrality 4.574 7.603* 0.976 5.697 31.638** 15.297*** (3.555) (3.866) (2.844) (3.711) (11.254) (4.073) Homophily (in) −0.034 0.706 −0.404 −1.448 0.200 0.609 (0.401) (0.540) (0.386) (1.005) (0.820) (0.505) Homophily (out) −0.016 0.846 0.058 −0.355 0.631 1.070 (0.490) (1.270) (0.651) (0.940) (1.024) (0.624) Observations 250 275 250 300 250 300 Notes: Coefficients β3from different OLS regression of earnings on gender dummy, score and one network characteristics based on data from periods 6–10 of the experiment. Standard errors clustered at the matching group (network) level are in parentheses. All regressions include controls for age and nationality and session fixed effects. Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab Table 5. Effect of Network Position on Earnings. . Effect of network position on earnings (coefficientsβ3) . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . In-degree 1.195 0.630 0.577 1.273 3.476** 0.742 (0.759) (0.682) (0.460) (1.015) (1.074) (0.514) Out-degree 0.549* 0.976** −0.008 0.752 0.020 −0.037 (0.283) (0.404) (0.232) (0.590) (0.374) (0.202) EV centrality 4.574 7.603* 0.976 5.697 31.638** 15.297*** (3.555) (3.866) (2.844) (3.711) (11.254) (4.073) Homophily (in) −0.034 0.706 −0.404 −1.448 0.200 0.609 (0.401) (0.540) (0.386) (1.005) (0.820) (0.505) Homophily (out) −0.016 0.846 0.058 −0.355 0.631 1.070 (0.490) (1.270) (0.651) (0.940) (1.024) (0.624) Observations 250 275 250 300 250 300 . Effect of network position on earnings (coefficientsβ3) . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . In-degree 1.195 0.630 0.577 1.273 3.476** 0.742 (0.759) (0.682) (0.460) (1.015) (1.074) (0.514) Out-degree 0.549* 0.976** −0.008 0.752 0.020 −0.037 (0.283) (0.404) (0.232) (0.590) (0.374) (0.202) EV centrality 4.574 7.603* 0.976 5.697 31.638** 15.297*** (3.555) (3.866) (2.844) (3.711) (11.254) (4.073) Homophily (in) −0.034 0.706 −0.404 −1.448 0.200 0.609 (0.401) (0.540) (0.386) (1.005) (0.820) (0.505) Homophily (out) −0.016 0.846 0.058 −0.355 0.631 1.070 (0.490) (1.270) (0.651) (0.940) (1.024) (0.624) Observations 250 275 250 300 250 300 Notes: Coefficients β3from different OLS regression of earnings on gender dummy, score and one network characteristics based on data from periods 6–10 of the experiment. Standard errors clustered at the matching group (network) level are in parentheses. All regressions include controls for age and nationality and session fixed effects. Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab Table 6. Effect of Network Position on Promotion. . Effect of network position on promotion (coefficientsβ3) . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . In-degree −0.006 0.067* 0.157*** 0.053** 0.068** 0.185*** (0.017) (0.030) (0.017) (0.019) (0.023) (0.017) Out-degree −0.062*** 0.012 −0.016 −0.000 0.005 −0.002 (0.012) (0.009) (0.015) (0.024) (0.010) (0.009) EV centrality −0.507* 0.448* 1.229*** 0.187 0.786*** 1.059*** (0.241) (0.229) (0.214) (0.163) (0.204) (0.202) Homophily (in) −0.019 0.037 0.044 −0.097** 0.015 0.008 (0.023) (0.025) (0.039) (0.033) (0.032) (0.021) Homophily (out) 0.013 −0.054 0.028 −0.032 −0.022 −0.076** (0.024) (0.033) (0.018) (0.032) (0.035) (0.029) Observations 300 330 300 360 300 360 . Effect of network position on promotion (coefficientsβ3) . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . In-degree −0.006 0.067* 0.157*** 0.053** 0.068** 0.185*** (0.017) (0.030) (0.017) (0.019) (0.023) (0.017) Out-degree −0.062*** 0.012 −0.016 −0.000 0.005 −0.002 (0.012) (0.009) (0.015) (0.024) (0.010) (0.009) EV centrality −0.507* 0.448* 1.229*** 0.187 0.786*** 1.059*** (0.241) (0.229) (0.214) (0.163) (0.204) (0.202) Homophily (in) −0.019 0.037 0.044 −0.097** 0.015 0.008 (0.023) (0.025) (0.039) (0.033) (0.032) (0.021) Homophily (out) 0.013 −0.054 0.028 −0.032 −0.022 −0.076** (0.024) (0.033) (0.018) (0.032) (0.035) (0.029) Observations 300 330 300 360 300 360 Notes: Coefficients β3from different OLS regression of promotion on gender dummy, score and one network characteristics based on data from periods 6–10 of the experiment. Standard errors clustered at the matching group (network) level are in parentheses. All regressions include controls for age and nationality and fixed effects for the number of male group members and session fixed effects. Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab Table 6. Effect of Network Position on Promotion. . Effect of network position on promotion (coefficientsβ3) . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . In-degree −0.006 0.067* 0.157*** 0.053** 0.068** 0.185*** (0.017) (0.030) (0.017) (0.019) (0.023) (0.017) Out-degree −0.062*** 0.012 −0.016 −0.000 0.005 −0.002 (0.012) (0.009) (0.015) (0.024) (0.010) (0.009) EV centrality −0.507* 0.448* 1.229*** 0.187 0.786*** 1.059*** (0.241) (0.229) (0.214) (0.163) (0.204) (0.202) Homophily (in) −0.019 0.037 0.044 −0.097** 0.015 0.008 (0.023) (0.025) (0.039) (0.033) (0.032) (0.021) Homophily (out) 0.013 −0.054 0.028 −0.032 −0.022 −0.076** (0.024) (0.033) (0.018) (0.032) (0.035) (0.029) Observations 300 330 300 360 300 360 . Effect of network position on promotion (coefficientsβ3) . . (1) . (2) . (3) . (4) . (5) . (6) . . PERF . DESIG . NET . PERF-COMM . DESIG-COMM . NET-COMM . In-degree −0.006 0.067* 0.157*** 0.053** 0.068** 0.185*** (0.017) (0.030) (0.017) (0.019) (0.023) (0.017) Out-degree −0.062*** 0.012 −0.016 −0.000 0.005 −0.002 (0.012) (0.009) (0.015) (0.024) (0.010) (0.009) EV centrality −0.507* 0.448* 1.229*** 0.187 0.786*** 1.059*** (0.241) (0.229) (0.214) (0.163) (0.204) (0.202) Homophily (in) −0.019 0.037 0.044 −0.097** 0.015 0.008 (0.023) (0.025) (0.039) (0.033) (0.032) (0.021) Homophily (out) 0.013 −0.054 0.028 −0.032 −0.022 −0.076** (0.024) (0.033) (0.018) (0.032) (0.035) (0.029) Observations 300 330 300 360 300 360 Notes: Coefficients β3from different OLS regression of promotion on gender dummy, score and one network characteristics based on data from periods 6–10 of the experiment. Standard errors clustered at the matching group (network) level are in parentheses. All regressions include controls for age and nationality and fixed effects for the number of male group members and session fixed effects. Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab In terms of the impact of network position on earnings (Table 5), there are only two network characteristic for which β3 has the same sign across all treatments. Those are in-degree and eigenvector centrality. Both of them are consistently associated with higher earnings. However this effect is statistically significant in only one treatment for in-degree and in three treatments for eigenvector centrality. Out-degree and homophily do not seem to have a consistent effect on earnings or promotion. It should also be noted that earnings gaps remain even after network characteristics are controlled for. In the three treatments, where statistically significant earnings gaps have been identified (NET,NET-COMM and PERF-COMM), the coefficient β1 is in the same range as in the original regression and always statistically significant.26 This suggests that network position cannot explain the differences in earnings we observe. The results are similar with respect to promotion gaps. Promotion gaps remain even after network characteristics are controlled for. Now in-degree is positively associated to promotion in all treatments, but treatment PERF. In NET and NET-COMM we would expect this association by construction. There it is hence a purely mechanical effect. As in-degree measures the number of links received, this positive association could also reflect an attempt by participants to link to others who they believe are likely going to be decision maker. No other network characteristic shows a consistent sign of β3 across all treatments, but eigenvector centrality has a statistically significant and positive relation to promotion in four out of six treatments. In particular also homophily has no consistent sign and is never statistically significant on average, i.e., across both genders. This is the case for both earnings and promotion. According to a conjecture by Ibarra (1993), however, homophily should have a positive effect for men and a negative effect for women. Indeed we do find some evidence for such an effect. On average across the treatments without chats, we find that homophily in out-degree is positively associated with earnings and promotion for men (β3 = 1.370 for earnings and β3 = 0.935*** for promotion), but not for women (β3 = 0.379 for earnings and β3 = −0.103 for promotion). For the COMM variations we find that homophily has a positive effect on earnings for men (on average across the three decision environments) with raw coefficients β3 = 1.197 for men’s earnings and β3 = 0.030 for promotion. For women, by contrast, both these coefficients are negative with β3 = −0.123 for earnings and β3 = −0.059** for promotion. While not all these coefficients are statistically significant, it seems that forming links within gender (homophily) might indeed be beneficial for men, but not for women, as conjectured by Ibarra (1993). Robustness checks: we also conducted a number of robustness checks and additional analyses. Tables G.4 and G.5 show results separately for majority-female, gender-balanced and majority-male groups with no differential patterns across these groups. Tables G.6 and G.7 in Online Appendix G show the results of running regression (1) on past average network characteristics, i.e., earnings or promotion at time t are explained via the mean of NW-characteristic across periods 1, ..., t instead of simply by NW-characteristic|$_{i}^{t}$|⁠. This exercise hence allows for the fact that earnings or promotion may be affected by the network position of agents over a longer horizon rather than just their position in the current round. Table G.6 shows results that are very similar under this exercise. The only network characteristic that reliably affects earnings is eigenvector centrality. Earnings gaps appear in the same treatments as in the regressions focused on current network characteristics. They are also of the same magnitude. Table G.7 shows that the effect of past eigenvector centrality is weaker and in most treatments not statistically significant, suggesting that current rather than past eigenvector centrality matters more for promotion. Past in-degree is mostly statistically insignificant in line with the idea that some of the effect of current in-degree might not be causal. 3.2. Gender Differences in Network Formation In this section we ask whether there are gender differences in network formation, in particular whether men and women end up with different network positions. Of course we will be particularly interested in those network characteristics that seem to systematically affect earnings and promotion. Table 7 shows the mean value of all network characteristics discussed in Subsection 3.1 for both men and women and across our six main treatments. The table also shows gender difference in these characteristics measured by the β coefficient in an OLS regression $$\begin{eqnarray} y_{i}=\alpha + \beta \tt {male}_{i}+\epsilon _{i}, \end{eqnarray}$$ where yi is the network characteristic of interest.27 Table 7. Network Characteristics. . . . . PERF . DESIG . NET . . PERF . DESIG . NET . COMM . COMM . COMM . . W . M . W . M . W . M . W . M . W . M . W . M . In-degree 1.468 1.534 1.141 0.982 1.853 1.866 0.383 0.566 1.142 1.006 1.594 1.594 β 0.066 −0.159 0.013 0.183* −0.136 −0.000 Out-degree 1.448 1.252 1.109 0.948 1.580 2.140 0.388 0.655 0.971 1.418 1.431 2.252 β −0.196 −0.161 0.560* 0.266 0.447 0.821** EV centrality 0.176 0.159 0.155 0.176 0.162 0.170 0.149 0.182 0.167 0.165 0.155 0.179 β −0.018 0.020 0.007 0.033 −0.001 0.023 Homophily (in) −0.181 0.081 −0.331* 0.073 −0.635*** 0.066 −0.163 0.084 −0.447 0.122 −0.609* 0.111 β 0.262 0.405* 0.702*** 0.248 0.569* 0.720* Homophily (out) −0.114 0.022 −0.245* 0.089* −0.327** 0.087 −0.179 0.082 −0.254 0.094 −0.243 0.035* β 0.136 0.334** 0.415*** 0.261** 0.349** 0.278* . . . . PERF . DESIG . NET . . PERF . DESIG . NET . COMM . COMM . COMM . . W . M . W . M . W . M . W . M . W . M . W . M . In-degree 1.468 1.534 1.141 0.982 1.853 1.866 0.383 0.566 1.142 1.006 1.594 1.594 β 0.066 −0.159 0.013 0.183* −0.136 −0.000 Out-degree 1.448 1.252 1.109 0.948 1.580 2.140 0.388 0.655 0.971 1.418 1.431 2.252 β −0.196 −0.161 0.560* 0.266 0.447 0.821** EV centrality 0.176 0.159 0.155 0.176 0.162 0.170 0.149 0.182 0.167 0.165 0.155 0.179 β −0.018 0.020 0.007 0.033 −0.001 0.023 Homophily (in) −0.181 0.081 −0.331* 0.073 −0.635*** 0.066 −0.163 0.084 −0.447 0.122 −0.609* 0.111 β 0.262 0.405* 0.702*** 0.248 0.569* 0.720* Homophily (out) −0.114 0.022 −0.245* 0.089* −0.327** 0.087 −0.179 0.082 −0.254 0.094 −0.243 0.035* β 0.136 0.334** 0.415*** 0.261** 0.349** 0.278* Notes: Mean across periods 6–10 by gender as well as β from panel OLS regression |$y_{i}=\alpha + \beta \tt {male}_{i}$|⁠, where yi is the outcome (network characteristic) of interest. Standard errors are clustered at the matching group level. Stars on means of homophily measures indicate significance levels from F-test of α = 0 for women and α + β = 0 for men, respectively. Open in new tab Table 7. Network Characteristics. . . . . PERF . DESIG . NET . . PERF . DESIG . NET . COMM . COMM . COMM . . W . M . W . M . W . M . W . M . W . M . W . M . In-degree 1.468 1.534 1.141 0.982 1.853 1.866 0.383 0.566 1.142 1.006 1.594 1.594 β 0.066 −0.159 0.013 0.183* −0.136 −0.000 Out-degree 1.448 1.252 1.109 0.948 1.580 2.140 0.388 0.655 0.971 1.418 1.431 2.252 β −0.196 −0.161 0.560* 0.266 0.447 0.821** EV centrality 0.176 0.159 0.155 0.176 0.162 0.170 0.149 0.182 0.167 0.165 0.155 0.179 β −0.018 0.020 0.007 0.033 −0.001 0.023 Homophily (in) −0.181 0.081 −0.331* 0.073 −0.635*** 0.066 −0.163 0.084 −0.447 0.122 −0.609* 0.111 β 0.262 0.405* 0.702*** 0.248 0.569* 0.720* Homophily (out) −0.114 0.022 −0.245* 0.089* −0.327** 0.087 −0.179 0.082 −0.254 0.094 −0.243 0.035* β 0.136 0.334** 0.415*** 0.261** 0.349** 0.278* . . . . PERF . DESIG . NET . . PERF . DESIG . NET . COMM . COMM . COMM . . W . M . W . M . W . M . W . M . W . M . W . M . In-degree 1.468 1.534 1.141 0.982 1.853 1.866 0.383 0.566 1.142 1.006 1.594 1.594 β 0.066 −0.159 0.013 0.183* −0.136 −0.000 Out-degree 1.448 1.252 1.109 0.948 1.580 2.140 0.388 0.655 0.971 1.418 1.431 2.252 β −0.196 −0.161 0.560* 0.266 0.447 0.821** EV centrality 0.176 0.159 0.155 0.176 0.162 0.170 0.149 0.182 0.167 0.165 0.155 0.179 β −0.018 0.020 0.007 0.033 −0.001 0.023 Homophily (in) −0.181 0.081 −0.331* 0.073 −0.635*** 0.066 −0.163 0.084 −0.447 0.122 −0.609* 0.111 β 0.262 0.405* 0.702*** 0.248 0.569* 0.720* Homophily (out) −0.114 0.022 −0.245* 0.089* −0.327** 0.087 −0.179 0.082 −0.254 0.094 −0.243 0.035* β 0.136 0.334** 0.415*** 0.261** 0.349** 0.278* Notes: Mean across periods 6–10 by gender as well as β from panel OLS regression |$y_{i}=\alpha + \beta \tt {male}_{i}$|⁠, where yi is the outcome (network characteristic) of interest. Standard errors are clustered at the matching group level. Stars on means of homophily measures indicate significance levels from F-test of α = 0 for women and α + β = 0 for men, respectively. Open in new tab As discussed above out-degree is the only network characteristic that is fully under the participant’s control and arguably the best measure of networking. We hence focus on this measure first. Overall, the fewest number of links are formed in treatment PERF-COMM (about one link every other period) and most links are formed in NET and NET-COMM with about 1.5 links formed and received by women and about two links formed and received by men. These are also the only treatments where men are somewhat more active than women in networking, forming 0.56 or 0.821 links more on average per period.28 In all other treatments men and women form and receive about the same number of links across all treatments. As one of the reasons to form links could be to signal performance, we checked for gender differences in how participants’ propensity to form links reacts to performance in more detail. To do this we regressed out-degree (number of links formed) on score and ask whether men or women’s out-degree reacts more strongly to score. In the minimal communication treatments we see some (small) positive association of out-degree with score, which is only in statistically significant for men in DESIG and NET (see Online Appendix Table G.8). In the COMM-variation out-degree does not react to score neither for men nor for women. Here all coefficients are close to zero. Crucially, however, there is no statistically significant gender difference in how out-degree reacts to score in any of the treatments. If we split the sample by score we also find no gender differences in out-degree neither for ‘low achieving’ (ranked 4–6) nor ‘high achieving’ (ranked 1–3) participants. Hence there is no evidence that women network less or are more reluctant to communicate achievements in our context. Panel (a) in Figure 2 illustrates the mean out-degree of men and women over time in the six treatments. Fig. 2. Open in new tabDownload slide Average Network Characteristics of Men and Women over Time. Top Panel Shows Treatments PERF,DESIG and NET. Bottom Panel Shows Treatments PERF-COMM,DESIG-COMM and NET-COMM. Black Solid Line Are Women, Grey Dashed Line Men. Fig. 2. Open in new tabDownload slide Average Network Characteristics of Men and Women over Time. Top Panel Shows Treatments PERF,DESIG and NET. Bottom Panel Shows Treatments PERF-COMM,DESIG-COMM and NET-COMM. Black Solid Line Are Women, Grey Dashed Line Men. Most gender differences arise in terms of homophily. Men display homophily in all treatments (α + β > 0) both in terms of in- and out-going links, i.e., they link more to men and receive more links from men compared to what gender-blind linking would suggest. Women, by contrast display heterophily in all treatments (α < 0). Except for treatment PERF the gender difference in homophily is always statistically significant for out-degree and it is statistically different in four out of six treatments for in-degree.29 These differences are illustrated in Figure 3. As homophily is positively related to earnings for men and negatively for women (Subsection 4.1), this difference is in line with both genders following earnings-maximising strategies. Fig. 3. Open in new tabDownload slide Average Degree of Homophily (In- and Out-Degree) of Men and Women over Time. Top Panel Shows Treatments PERF,DESIG and NET(from Left to Right). Bottom Panel Shows Treatments PERF-COMM,DESIG-COMM and NET-COMM (from Left to Right). Black Solid Line Are Women, Grey Line Men. The Reference Line Shows the Case of Zero Homophily Implied by Random Linking. Above the Reference Line Networks Display Homophily, i.e., Over-proportional Linking within Gender. Below the Reference Line Networks Display Heterophily, i.e., Under-proportional Linking within Gender. Fig. 3. Open in new tabDownload slide Average Degree of Homophily (In- and Out-Degree) of Men and Women over Time. Top Panel Shows Treatments PERF,DESIG and NET(from Left to Right). Bottom Panel Shows Treatments PERF-COMM,DESIG-COMM and NET-COMM (from Left to Right). Black Solid Line Are Women, Grey Line Men. The Reference Line Shows the Case of Zero Homophily Implied by Random Linking. Above the Reference Line Networks Display Homophily, i.e., Over-proportional Linking within Gender. Below the Reference Line Networks Display Heterophily, i.e., Under-proportional Linking within Gender. Apart from homophily, we find few differences between how women and men form networks. Importantly, differences between women’s and men’s eigenvector centrality are small and statistically insignificant. Panel (b) in Figure 2 illustrates mean eigenvector centrality of men and women over time in the six treatments illustrating that they are virtually identical and statistically no different in any of the treatments. 3.3. Strategic Use of Networks In the previous section we saw that differences in network formation (and resulting network positions) are not able to explain earnings and promotion gaps by themselves. In this subsection we will try to understand whether there are differences in how men and women use networks in their decisions and whether and how such differences can be part of the explanation for gender earnings and promotion gaps. In particular, we will focus on decision makers in this subsection and ask whether there are any differences between how male and female decision makers use networks in their decisions regarding earnings and promotion. To these ends we run the following regression $$\begin{eqnarray} y_{ij}^{t}&=&\alpha +\beta _{1} \tt {score share}_{j}^{t} + \beta _{2} \tt {network share}_{j}^{t} + \beta _{3} \tt {female}_{j}^{t} \\ && +\, \gamma _{1} \tt {score share}_{j}^{t} \times \tt {male}_{i}^{t} + \gamma _{2} \tt {network share}_{j}^{t} \times \tt {male}_{i}^{t} \\ &&+\, \gamma _{3} \tt {female}_{j}^{t} \times \tt {male}_{i}^{t} + \epsilon _{ij}^{t} \end{eqnarray}$$(2) where |$x_{ij}^{t}$| denotes the amount decision maker i allocates to j in round t and |$y_{ij}^{t}=\frac{x_{ij}^{t}}{\sum _{k \ne i} x_{ik}^{t}}$| hence denotes the share of the group score remaining (after i has allocated some to herself) that decision maker i allocates to j in period t. We exclude agent i from all measures in the regression because we are interested in how i treats j compared to other group members and not in, e.g., how much i keeps to herself.30 Since each agent has five group members, yij = 0.2, ∀j if i treats all group members equally. |$y_{ij}^{t}$| is regressed on (i) network share|$\sum _{\tau =1}^{t-1}\frac{\tt {link}_{ij}^{\tau }}{\sum _{k \ne i} \tt {link}_{ik}^{\tau }}$|⁠: the share j occupies in i’s network (i.e., which share of i’s incoming links in past periods stem from agent j) and (ii) score share|$\frac{\tt {score}_{j}^{t}}{\sum _{k \ne i} \tt {score}_{k}^{t}}$|⁠: the share that j’s performance (scorej) contributed to the group score exclusive of i’s performance. If the denominator in any of these variables (⁠|$y_{ij}^{t}$|⁠, score share or network share) is zero, then we set the value of the variable to 0.2 reflecting the fact that all five group members are equal. The dummy femalej indicates whether the recipient j is female or not. All three variables are then also interacted with decision maker gender indicated by the dummy male. Table 8 shows the results of this regression for the minimal communication treatments. In columns (1)–(4) the outcome is earnings and in columns (5)–(6) it is promotion. Columns (5)–(6) exist only for treatment DESIG, as it is only in this treatment that decision makers make decisions regarding promotion. Table 8. OLS Regression Shown in Equation (2) with ‘Decision Maker Gender Interactions’. . Minimal communication treatments . . (1) . (2) . (3) . (4) . (5) . (6) . Variables . All . PERF . DESIG . NET . DESIG . DESIG . Score share (β1) 0.286*** 0.267* 0.353* 0.233** 0.190 0.327 (0.082) (0.139) (0.165) (0.094) (0.237) (0.247) Network share (β2) −0.023 −0.000 −0.045 −0.022 −0.142* −0.144 (0.024) (0.039) (0.034) (0.025) (0.077) (0.084) Female (β3) 0.017 0.035 0.001 0.012 0.117 0.132 (0.014) (0.020) (0.036) (0.007) (0.071) (0.078) Score share × male DM (γ1) −0.084 −0.142 −0.160 0.044 0.053 −0.212 (0.071) (0.112) (0.146) (0.073) (0.214) (0.202) Network share × male DM (γ2) 0.088* 0.054 0.129 0.054 0.526*** 0.506*** (0.046) (0.084) (0.073) (0.034) (0.144) (0.153) Female × male DM (γ3) −0.001 0.051 −0.011 −0.028 −0.208* −0.201* (0.029) (0.068) (0.054) (0.024) (0.098) (0.103) Past DM −0.056 (0.086) Past DM × male DM 0.284** (0.106) Constant 0.136*** 0.126** 0.136*** 0.149*** 0.062 0.038 (0.019) (0.037) (0.029) (0.023) (0.043) (0.041) β1 + γ1 0.202** 0.117 0.194* 0.276** 0.241 0.114 β2 + γ2 0.069** 0.061 0.084* 0.032 0.385*** 0.362*** β3 + γ3 0.016 0.091 −0.010 −0.016 −0.091* −0.069 Observations 775 250 275 250 275 275 R2 0.034 0.056 0.038 0.061 0.073 0.111 . Minimal communication treatments . . (1) . (2) . (3) . (4) . (5) . (6) . Variables . All . PERF . DESIG . NET . DESIG . DESIG . Score share (β1) 0.286*** 0.267* 0.353* 0.233** 0.190 0.327 (0.082) (0.139) (0.165) (0.094) (0.237) (0.247) Network share (β2) −0.023 −0.000 −0.045 −0.022 −0.142* −0.144 (0.024) (0.039) (0.034) (0.025) (0.077) (0.084) Female (β3) 0.017 0.035 0.001 0.012 0.117 0.132 (0.014) (0.020) (0.036) (0.007) (0.071) (0.078) Score share × male DM (γ1) −0.084 −0.142 −0.160 0.044 0.053 −0.212 (0.071) (0.112) (0.146) (0.073) (0.214) (0.202) Network share × male DM (γ2) 0.088* 0.054 0.129 0.054 0.526*** 0.506*** (0.046) (0.084) (0.073) (0.034) (0.144) (0.153) Female × male DM (γ3) −0.001 0.051 −0.011 −0.028 −0.208* −0.201* (0.029) (0.068) (0.054) (0.024) (0.098) (0.103) Past DM −0.056 (0.086) Past DM × male DM 0.284** (0.106) Constant 0.136*** 0.126** 0.136*** 0.149*** 0.062 0.038 (0.019) (0.037) (0.029) (0.023) (0.043) (0.041) β1 + γ1 0.202** 0.117 0.194* 0.276** 0.241 0.114 β2 + γ2 0.069** 0.061 0.084* 0.032 0.385*** 0.362*** β3 + γ3 0.016 0.091 −0.010 −0.016 −0.091* −0.069 Observations 775 250 275 250 275 275 R2 0.034 0.056 0.038 0.061 0.073 0.111 Notes: Standard errors are clustered at the (matching) group level and account for autocorrelation at the individual level. For each period 6–10 and each group each regression contains five datapoints indicating how much each decision maker allocated to each group member (columns (1)–(4)) and whether or not a group member was designated to be the next decision maker (columns (5)–(6)). Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab Table 8. OLS Regression Shown in Equation (2) with ‘Decision Maker Gender Interactions’. . Minimal communication treatments . . (1) . (2) . (3) . (4) . (5) . (6) . Variables . All . PERF . DESIG . NET . DESIG . DESIG . Score share (β1) 0.286*** 0.267* 0.353* 0.233** 0.190 0.327 (0.082) (0.139) (0.165) (0.094) (0.237) (0.247) Network share (β2) −0.023 −0.000 −0.045 −0.022 −0.142* −0.144 (0.024) (0.039) (0.034) (0.025) (0.077) (0.084) Female (β3) 0.017 0.035 0.001 0.012 0.117 0.132 (0.014) (0.020) (0.036) (0.007) (0.071) (0.078) Score share × male DM (γ1) −0.084 −0.142 −0.160 0.044 0.053 −0.212 (0.071) (0.112) (0.146) (0.073) (0.214) (0.202) Network share × male DM (γ2) 0.088* 0.054 0.129 0.054 0.526*** 0.506*** (0.046) (0.084) (0.073) (0.034) (0.144) (0.153) Female × male DM (γ3) −0.001 0.051 −0.011 −0.028 −0.208* −0.201* (0.029) (0.068) (0.054) (0.024) (0.098) (0.103) Past DM −0.056 (0.086) Past DM × male DM 0.284** (0.106) Constant 0.136*** 0.126** 0.136*** 0.149*** 0.062 0.038 (0.019) (0.037) (0.029) (0.023) (0.043) (0.041) β1 + γ1 0.202** 0.117 0.194* 0.276** 0.241 0.114 β2 + γ2 0.069** 0.061 0.084* 0.032 0.385*** 0.362*** β3 + γ3 0.016 0.091 −0.010 −0.016 −0.091* −0.069 Observations 775 250 275 250 275 275 R2 0.034 0.056 0.038 0.061 0.073 0.111 . Minimal communication treatments . . (1) . (2) . (3) . (4) . (5) . (6) . Variables . All . PERF . DESIG . NET . DESIG . DESIG . Score share (β1) 0.286*** 0.267* 0.353* 0.233** 0.190 0.327 (0.082) (0.139) (0.165) (0.094) (0.237) (0.247) Network share (β2) −0.023 −0.000 −0.045 −0.022 −0.142* −0.144 (0.024) (0.039) (0.034) (0.025) (0.077) (0.084) Female (β3) 0.017 0.035 0.001 0.012 0.117 0.132 (0.014) (0.020) (0.036) (0.007) (0.071) (0.078) Score share × male DM (γ1) −0.084 −0.142 −0.160 0.044 0.053 −0.212 (0.071) (0.112) (0.146) (0.073) (0.214) (0.202) Network share × male DM (γ2) 0.088* 0.054 0.129 0.054 0.526*** 0.506*** (0.046) (0.084) (0.073) (0.034) (0.144) (0.153) Female × male DM (γ3) −0.001 0.051 −0.011 −0.028 −0.208* −0.201* (0.029) (0.068) (0.054) (0.024) (0.098) (0.103) Past DM −0.056 (0.086) Past DM × male DM 0.284** (0.106) Constant 0.136*** 0.126** 0.136*** 0.149*** 0.062 0.038 (0.019) (0.037) (0.029) (0.023) (0.043) (0.041) β1 + γ1 0.202** 0.117 0.194* 0.276** 0.241 0.114 β2 + γ2 0.069** 0.061 0.084* 0.032 0.385*** 0.362*** β3 + γ3 0.016 0.091 −0.010 −0.016 −0.091* −0.069 Observations 775 250 275 250 275 275 R2 0.034 0.056 0.038 0.061 0.073 0.111 Notes: Standard errors are clustered at the (matching) group level and account for autocorrelation at the individual level. For each period 6–10 and each group each regression contains five datapoints indicating how much each decision maker allocated to each group member (columns (1)–(4)) and whether or not a group member was designated to be the next decision maker (columns (5)–(6)). Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab Across all treatments both women and men tend to allocate more to group members with better performance, i.e., to those whose score contributes more to the group score. Increasing the contribution to the group score from 0.2 (median) to 0.3 leads to an |$\approx 3 \%$| increase in the share of the group score allocated to that person. Given the median group score and allocations this implies that improving the score by one will increase earnings by between 7 and 20 pence..31 Male decision makers reward performance in similar ways as female decision makers. γ1 is small, changing in sign and statistically insignificant across all the treatments. Higher performance has an additional reward in treatment DESIG. In this treatment decision makers reward high performers by nominating them to be the next decision makers (column (5)), even though the effect is not statistically significant. Apart from rewarding performance, female decision makers seem to treat all group members equally when it comes to allocating the group score. In particular they do not discriminate against nor favour women and they do not react to network share, i.e., they neither discriminate against nor favour those who establish more links to them. Also male decision makers do not discriminate against nor favour women, certainly not in terms of earnings, though there may be an effect with respect to promotions (columns (5)). Unlike women, however, men reward those who establish more links to them. The effect is sizeable. In terms of earnings, a 1% higher frequency to be among the decision makers’ neighbours leads to an |$\approx 0.07 \%$| increase in the share allocated to that person (column (1)). This coefficient size is about one-third compared to that associated with a 1% increase in performance. The effect is even bigger when it comes to promotions (γ2 = 0.526 in column (5)). This coefficient is |$\approx 275\%$| bigger compared to the coefficient associated with an increase in performance (score share). Column (6) explores an additional factor which is that decision makers in DESIG can use arrangements to designate each other in turn as decision makers.32 In column (6) we include a dummy variable ‘past DM’ which indicates whether j was decision maker in t − 1 and hence designated i to be the decision maker in t. A positive coefficient on this dummy indicates reciprocal favour exchange in terms of designations. Column (6) shows that female decision makers do not seem to reciprocate in this manner and tend to designate others (e.g., those with high scores) as decision makers. Male decision makers do, however, engage in such reciprocal designations as indicated by the interaction ‘past DM × male DM’. We will study the role of such reciprocal arrangements in more detail in Subsection 4.1. Results for the COMM-treatments are reported in Table 9. Again both men and women reward better performance, though in most treatments the effect is not statistically significant and in treatment DESIG-COMM it is even negative. Hence with open communication (and hence possibilities for explicit discussion and agreements) performance seems less important a factor in allocating earnings. Also here neither men nor women discriminate against or favour one gender per se. Men again reward their network neighbours with higher earnings in treatments PERF-COMM and NET-COMM (β2 + γ2). Interestingly, now also women reward their network neighbours with increased promotion in DESIG-COMM (column (5)). Column (6) shows that reciprocal designations play a very important role under this communication structure for both female and male decision makers, though the effect is more than twice as big for male decision makers. In Subsection 4.1 we study designation patterns and show that indeed the open communication structure is much more conducive to reciprocal designations. Table 9. OLS Regression Shown in Equation (2) with ‘Decision Maker Gender Interactions’. COMM Treatments. . Comm treatments . . (1) . (2) . (3) . (4) . (5) . (6) . Variables . All . PERF . DESIG . NET . DESIG . DESIG . Score share (β1) 0.181 0.104 −0.208 0.368* −0.287 −0.059 (0.118) (0.163) (0.194) (0.178) (0.314) (0.266) Network share (β2) −0.008 −0.010 0.063 −0.055** 0.186** 0.192*** (0.017) (0.023) (0.040) (0.018) (0.081) (0.068) Female (β3) −0.017 0.040 −0.053 −0.043** −0.107 −0.066 (0.023) (0.032) (0.063) (0.019) (0.073) (0.061) Score share × male DM (γ1) −0.025 0.215 0.104 −0.186* 0.336 0.146 (0.098) (0.164) (0.162) (0.086) (0.306) (0.262) Network share × male DM (γ2) 0.008 0.042 −0.095 0.081*** −0.253** −0.265*** (0.026) (0.036) (0.053) (0.020) (0.099) (0.083) Female × male DM (γ3) −0.010 −0.143* 0.066 0.036 0.083 0.049 (0.037) (0.066) (0.071) (0.025) (0.089) (0.074) Past DM 0.243*** (0.078) Past DM × male DM 0.364*** (0.098) Constant 0.177*** 0.171*** 0.233*** 0.157*** 0.187*** 0.060 (0.019) (0.029) (0.016) (0.033) (0.064) (0.055) β1 + γ1 0.155** 0.318* −0.010 0.182 0.048 0.086 β2 + γ2 0.000 0.032* −0.030 0.035* 0.439*** −0.072 β3 + γ3 −0.027 −0.010* 0.010 −0.016 −0.024 −0.017 Observations 850 300 250 300 250 250 R2 0.025 0.099 0.026 0.167 0.030 0.330 . Comm treatments . . (1) . (2) . (3) . (4) . (5) . (6) . Variables . All . PERF . DESIG . NET . DESIG . DESIG . Score share (β1) 0.181 0.104 −0.208 0.368* −0.287 −0.059 (0.118) (0.163) (0.194) (0.178) (0.314) (0.266) Network share (β2) −0.008 −0.010 0.063 −0.055** 0.186** 0.192*** (0.017) (0.023) (0.040) (0.018) (0.081) (0.068) Female (β3) −0.017 0.040 −0.053 −0.043** −0.107 −0.066 (0.023) (0.032) (0.063) (0.019) (0.073) (0.061) Score share × male DM (γ1) −0.025 0.215 0.104 −0.186* 0.336 0.146 (0.098) (0.164) (0.162) (0.086) (0.306) (0.262) Network share × male DM (γ2) 0.008 0.042 −0.095 0.081*** −0.253** −0.265*** (0.026) (0.036) (0.053) (0.020) (0.099) (0.083) Female × male DM (γ3) −0.010 −0.143* 0.066 0.036 0.083 0.049 (0.037) (0.066) (0.071) (0.025) (0.089) (0.074) Past DM 0.243*** (0.078) Past DM × male DM 0.364*** (0.098) Constant 0.177*** 0.171*** 0.233*** 0.157*** 0.187*** 0.060 (0.019) (0.029) (0.016) (0.033) (0.064) (0.055) β1 + γ1 0.155** 0.318* −0.010 0.182 0.048 0.086 β2 + γ2 0.000 0.032* −0.030 0.035* 0.439*** −0.072 β3 + γ3 −0.027 −0.010* 0.010 −0.016 −0.024 −0.017 Observations 850 300 250 300 250 250 R2 0.025 0.099 0.026 0.167 0.030 0.330 Notes: Standard errors are clustered at the (matching) group level and account for autocorrelation at the individual level. For each period 6–10 and each group each regression contains five datapoints indicating how much each decision maker allocated to each group member (columns (1)–(4)) and whether or not a group member was designated to be the next decision maker (columns (5)–(6)). Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab Table 9. OLS Regression Shown in Equation (2) with ‘Decision Maker Gender Interactions’. COMM Treatments. . Comm treatments . . (1) . (2) . (3) . (4) . (5) . (6) . Variables . All . PERF . DESIG . NET . DESIG . DESIG . Score share (β1) 0.181 0.104 −0.208 0.368* −0.287 −0.059 (0.118) (0.163) (0.194) (0.178) (0.314) (0.266) Network share (β2) −0.008 −0.010 0.063 −0.055** 0.186** 0.192*** (0.017) (0.023) (0.040) (0.018) (0.081) (0.068) Female (β3) −0.017 0.040 −0.053 −0.043** −0.107 −0.066 (0.023) (0.032) (0.063) (0.019) (0.073) (0.061) Score share × male DM (γ1) −0.025 0.215 0.104 −0.186* 0.336 0.146 (0.098) (0.164) (0.162) (0.086) (0.306) (0.262) Network share × male DM (γ2) 0.008 0.042 −0.095 0.081*** −0.253** −0.265*** (0.026) (0.036) (0.053) (0.020) (0.099) (0.083) Female × male DM (γ3) −0.010 −0.143* 0.066 0.036 0.083 0.049 (0.037) (0.066) (0.071) (0.025) (0.089) (0.074) Past DM 0.243*** (0.078) Past DM × male DM 0.364*** (0.098) Constant 0.177*** 0.171*** 0.233*** 0.157*** 0.187*** 0.060 (0.019) (0.029) (0.016) (0.033) (0.064) (0.055) β1 + γ1 0.155** 0.318* −0.010 0.182 0.048 0.086 β2 + γ2 0.000 0.032* −0.030 0.035* 0.439*** −0.072 β3 + γ3 −0.027 −0.010* 0.010 −0.016 −0.024 −0.017 Observations 850 300 250 300 250 250 R2 0.025 0.099 0.026 0.167 0.030 0.330 . Comm treatments . . (1) . (2) . (3) . (4) . (5) . (6) . Variables . All . PERF . DESIG . NET . DESIG . DESIG . Score share (β1) 0.181 0.104 −0.208 0.368* −0.287 −0.059 (0.118) (0.163) (0.194) (0.178) (0.314) (0.266) Network share (β2) −0.008 −0.010 0.063 −0.055** 0.186** 0.192*** (0.017) (0.023) (0.040) (0.018) (0.081) (0.068) Female (β3) −0.017 0.040 −0.053 −0.043** −0.107 −0.066 (0.023) (0.032) (0.063) (0.019) (0.073) (0.061) Score share × male DM (γ1) −0.025 0.215 0.104 −0.186* 0.336 0.146 (0.098) (0.164) (0.162) (0.086) (0.306) (0.262) Network share × male DM (γ2) 0.008 0.042 −0.095 0.081*** −0.253** −0.265*** (0.026) (0.036) (0.053) (0.020) (0.099) (0.083) Female × male DM (γ3) −0.010 −0.143* 0.066 0.036 0.083 0.049 (0.037) (0.066) (0.071) (0.025) (0.089) (0.074) Past DM 0.243*** (0.078) Past DM × male DM 0.364*** (0.098) Constant 0.177*** 0.171*** 0.233*** 0.157*** 0.187*** 0.060 (0.019) (0.029) (0.016) (0.033) (0.064) (0.055) β1 + γ1 0.155** 0.318* −0.010 0.182 0.048 0.086 β2 + γ2 0.000 0.032* −0.030 0.035* 0.439*** −0.072 β3 + γ3 −0.027 −0.010* 0.010 −0.016 −0.024 −0.017 Observations 850 300 250 300 250 250 R2 0.025 0.099 0.026 0.167 0.030 0.330 Notes: Standard errors are clustered at the (matching) group level and account for autocorrelation at the individual level. For each period 6–10 and each group each regression contains five datapoints indicating how much each decision maker allocated to each group member (columns (1)–(4)) and whether or not a group member was designated to be the next decision maker (columns (5)–(6)). Robust SE in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Open in new tab To sum up, while both female and male decision makers reward performance in most treatments and neither favours one or the other gender per se, there is a difference when it comes to how network neighbours are treated. In particular male decision makers reward network neighbours with higher earnings and they engage to a much larger extent in reciprocal designations compared to female decision makers. Network neighbours are rewarded by men irrespective of their performance and their gender. How many of these network neighbours are women? In treatment DESIG 39% of the neighbours of male decision makers are female, while in treatments DESIG-COMM and NET-COMM 37% or 48%, respectively are female. Hence in all treatments, where network neighbours seem to be rewarded women are a minority of such neighbours. As a result of this men will over-proportionately reward men when they reward their network neighbours simply because more of their neighbours are men. As it is predominantly men who reward their network neighbours, one of the implications of these findings is that homophily should be associated with higher earnings and increased promotion chances for men, while the opposite should be true for women (Ibarra, 1992). We have seen above (Subsection 3.2) that this is indeed the case. A second implication of this finding is that earnings gaps should arise mostly if decision makers are male. We also find some evidence for this. In treatment NET men earn |$41\%$| more than women if the decision maker is male (p < 0.01) and |$10\%$| more if she is female. In PERF-COMM men earn |$67\%$| more if the decision maker is male (p < 0.01) and |$21\%$| if s/he is female (p < 0.05). In treatment DESIG-COMM men are |$33\%$| more likely to be promoted compared to a woman if the decision maker is male and |$11\%$| more likely if the decision maker is female. In all other treatments there are no statistically significant differences in earnings or promotion gaps depending on decision maker gender. 4. Discussion In this section we present additional results and uncover in somewhat more detail some of the patterns identified above. Subsection 4.1 focuses on designation patterns in treatments DESIG and DESIG-COMM. Subsection 4.2 asks to what extent network formation is in line with incentives provided by the behaviour of decision makers. Subsection 4.3 contains an analysis of chats. 4.1. Designation Networks This section takes a closer look at ‘designation networks’, i.e., the directed networks illustrating who nominates who to be decision maker in treatments DESIG and DESIG-COMM. Figure 4 shows such designation networks. Men are represented by black nodes and women by white nodes. A directed link from node i to j means that i has designated j to be decision maker in the following period. The figure, as the rest of the analysis focuses on periods 6–10. A first glance, the figure illustrates a striking effect of open communication. While in DESIG designation networks involve between 3–4 different nodes (Panel (a)), in DESIG-COMM six out of ten networks involve only two nodes who designate each other in turn to be decision maker (Panel (b)). Fig. 4. Open in new tabDownload slide Designation Networks Across Periods 6–10. Black Nodes Represent Men and White Nodes Women. Fig. 4. Open in new tabDownload slide Designation Networks Across Periods 6–10. Black Nodes Represent Men and White Nodes Women. In DESIG networks (d) and (i) come closest to a pattern where two participants keep nominating each other in turns. Most networks are more inclusive, involving more participants. There are three exclusively male networks ((a), (d) and (h)) and one exclusively female network ((e)). A striking feature of designation networks is the extent of homophily they display. Men are 50% more likely to designate a man, while women are 25% more likely to designate a woman compared to what chance would suggest. This is consistent with the evidence seen in the previous section. Men tend to reward their network neighbours with designations and these tend to over-proportionately be men. As a consequence designation networks display substantial homophily. In terms of other gender differences, we find that men have a higher degree than women. This simply reflects the fact that men are decision makers more often, i.e., that there is a gender promotion gap.33 In DESIG-COMM there is more reciprocation: 75% of nodes in fully reciprocal designation networks are men and 61% of nodes in designation networks involving some reciprocation are men (across DESIG and DESIG-COMM). This contrasts with only 53% of participants being male.34 Such reciprocation could possibly explain an additional part of the observed promotion gaps. There seems to be more such reciprocity in the COMM-variations, possibly because it allows participants to explicitly agree on such arrangements. Text analysis suggests that participants do indeed discuss such arrangements (Subsection 4.3). Given the importance of reciprocity in the designation treatments, one may wonder whether those who are not decision makers in the first half of the experiment stop forming links in later rounds. There is some evidence that this might be the case, but conditional on the level of activity in first rounds differences between those who were and were not decision maker in the first half of the experiment are small and not statistically significant. There are also no gender differences in these reactions. 4.2. Incentives to Network In this section we briefly discuss incentives to network and to what extent they are in line with what we observe. We first describe the subgame perfect Nash equilibria of the induced ten-period games under standard game theoretic assumptions. Under such assumptions, networking does not have any benefits in treatments PERF and DESIG. As it does come with a cost, equilibrium networks should be empty in these treatments. This is different in treatment NET, where the networking game is a game of coalition formation. In equilibrium we should see a coalition of n ≥ 3 players who are linked in a complete graph. Each of these players becomes decision maker with probability |$\frac{1}{n}$|⁠. In all treatments there is an equilibrium where all players provide high effort. In treatment PERF decision makers will keep all the surplus to themselves according to the game theoretic prediction. High effort is provided simply to maintain one’s chances of becoming a decision maker. In both DESIG and NET, incentives to provide high effort are maintained by the allocation choices of decision makers. Participants outside the coalition of decision makers are paid the minimal amount needed to incentivise high effort. Decision makers claim the rest to themselves. For details and underlying assumptions, see Online Appendix E. Standard (gender-blind) assumptions of course do not imply any gender differences in networking, nor can they explain the presence of homophily or earnings or promotion gaps. In line with these equilibrium predictions, we do however see that more links are formed per person and round in treatments NET and NET-COMM (≈1.8) compared to the remaining treatments (≈0.9) where equilibrium networks are empty (Table 7). The standard game theoretic predictions summarised above rely on particular assumptions, that we had no particular prior to be satisfied and find empirically refuted. Still, these predictions can provide a useful benchmark for understanding incentives. Can alternative assumptions explain our findings? One modelling alternative would allow for alternative sharing rules among dictators, e.g., motivated by altruism or other factors. This might explain some of the allocations we find, but could not explain gender differences in earnings or promotions in our experiment, unless we assume that women or men differ in some way in their sharing rules (combined with homophily). Empirically we can refute two such assumptions, namely that (i) women or men differ in how much they reward performance (see coefficient γ1 in Tables 8 and 9) and (ii) that women or men differ in how altruistic they are (see footnote 21). Another possibility would be to consider gender differences in reciprocity. We do find that men both tend to reward network neighbours more than women (Subsection 3.3) and that they are more often involved in reciprocal designation networks (Subsection 4.1). However, these differences seem specific to the networking context rather than reflecting a general tendency of men to be more reciprocal. In trust games, commonly used to elicit positive reciprocity, it is typically found that, if at all, women are more reciprocal than men (Croson and Buchan, 1999). What are incentives to network conditional on the empirically observed behaviour by decision makers? To answer this question we first use our evidence from Subsection 3.3 and ask how much can be gained from being linked to a male/female decision maker? In treatment NET, for example, male decision makers reward their network neighbours by an increased share of earnings allocated to other group members of 0.032 (coefficient β2 + γ2 in Table 8). Multiplied with the mean amount allocated to other group members of ≈45 this yields a gain of ≈1.44 GBP from being linked to a male decision maker. This means that on average the gain from such a link is just slightly below its cost of £2. Similar calculations yield a gain of 1.12 GBP in PERF-COMM and a gain of 1.92 in NET-COMM on top of any gains from increased chances of becoming decision maker oneself.35 Since female decision makers do not reward neighbours with increased earnings in most treatments, a rational reaction would be to link predominantly to men, i.e., display homophily in out-degrees for men and heterophily for women. We do indeed see this (Table 7), suggesting that participants do at least partially react to these incentives. 4.3. Chat Analysis In the last subsection we analyse the chats from the COMM-treatments to understand what participants discussed with their connections. The five topics we focus on are (i) performance, (ii) networks, (iii) agreements or deals among participants (as, e.g., those described in Subsection 4.1), (iv) the behaviour of other participants or (v) gender.36 We categorise chat content in two ways. First, we study the proportion of chats which mechanically contain certain keywords for each topic (see Table 10 for the keywords for each category). Second, we sent a random sample of 75 chats (25 per treatment) to external raters using an international online survey company and ask them what they thought the chat was about. We allowed them to pick multiple from eight possible answers (see Online Appendix Figure F.1). For each topic, we are then interested in the percentage of chats that were classified as being about this topic by at least (90%, 50%, 10%) of external raters. There were 56, 56 and 54 raters respectively across the three treatments PERF-COMM, DESIG-COMM and NET-COMM. Raters were UK nationals, but otherwise the sample was not restricted.37 Participants were paid 1 GBP for answering all 25 questions, but were not paid if they failed an attention check or answered the 25 questions in under two minutes.38 If both the mechanical method and the method using external raters yield similar results we are confident that we have identified key patterns in the chats. Table 10 shows the results. Performance is discussed in most chats. Between 68% and 72% of chats contain one of our key words and most chats are classified by a majority of raters as being about performance. There are no statistically significant treatment differences in these proportions. Networks is the second most discussed topic according to both the mechanical analysis and the external raters. Here we do detect treatment differences with higher proportions of chats being about networks in NET-COMM (32%) and DESIG-COMM (20%) compared to PERF-COMM (8%). Some level of discussion about agreements is picked up by external raters with the highest percentage in treatment DESIG-COMM followed by NET-COMM and PERF-COMM. These are not picked up as much by our mechanical analysis, possibly because our choice of words was not rich enough to capture these discussions. In line with the evidence from Subsection 4.1 the discussion of agreements in DESIG-COMM is also the only topic where we detect some gender differences. Men discuss agreements more often compared to women, but the difference is only marginally statistically significant (two-sided rank-sum test, p < 0.1). Finally, we also detect some level of discussion about other participants. External raters also pick up some discussion about gender, but this is not at all backed up by our mechanical analysis. Note also that apart from performance none of the topics is picked up by a large percentage of external raters. This could partly be due to the fact that many chats that are about networks or agreements are also about performance and not all raters tick multiple options even though this was possible. Table 10. Analysis of Chat Content. . PERF-COMM . DESIG-COMM . NET-COMM . Performance |$\ge 90\%$| of raters 0.16 0.20 0.12 |$\ge 50\%$| of raters 0.68 0.52 0.76 |$\ge 10\%$| of raters 0.96 0.96 0.96 Words: score, rank(ed), count(ed) 0.68 0.68 0.72 Networks |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.04 0.08 0.00 |$\ge 10\%$| of raters 0.16 0.36 0.28 Words: link(s), connection(s), linking 0.08 0.20 0.32 Agreements |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.04 0.08 0.00 |$\ge 10\%$| of raters 0.16 0.36 0.28 Words: agree, deal, arrangement, split 0.00 0.16 0.04 Others |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.00 0.04 0.04 |$\ge 10\%$| of raters 0.16 0.28 0.20 Words: labels of other participants 0.28 0.16 0.12 Gender |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.08 0.04 0.04 |$\ge 10\%$| of raters 0.16 0.20 0.28 Words: male, men, man, women, woman, female 0.00 0.00 0.00 . PERF-COMM . DESIG-COMM . NET-COMM . Performance |$\ge 90\%$| of raters 0.16 0.20 0.12 |$\ge 50\%$| of raters 0.68 0.52 0.76 |$\ge 10\%$| of raters 0.96 0.96 0.96 Words: score, rank(ed), count(ed) 0.68 0.68 0.72 Networks |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.04 0.08 0.00 |$\ge 10\%$| of raters 0.16 0.36 0.28 Words: link(s), connection(s), linking 0.08 0.20 0.32 Agreements |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.04 0.08 0.00 |$\ge 10\%$| of raters 0.16 0.36 0.28 Words: agree, deal, arrangement, split 0.00 0.16 0.04 Others |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.00 0.04 0.04 |$\ge 10\%$| of raters 0.16 0.28 0.20 Words: labels of other participants 0.28 0.16 0.12 Gender |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.08 0.04 0.04 |$\ge 10\%$| of raters 0.16 0.20 0.28 Words: male, men, man, women, woman, female 0.00 0.00 0.00 Open in new tab Table 10. Analysis of Chat Content. . PERF-COMM . DESIG-COMM . NET-COMM . Performance |$\ge 90\%$| of raters 0.16 0.20 0.12 |$\ge 50\%$| of raters 0.68 0.52 0.76 |$\ge 10\%$| of raters 0.96 0.96 0.96 Words: score, rank(ed), count(ed) 0.68 0.68 0.72 Networks |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.04 0.08 0.00 |$\ge 10\%$| of raters 0.16 0.36 0.28 Words: link(s), connection(s), linking 0.08 0.20 0.32 Agreements |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.04 0.08 0.00 |$\ge 10\%$| of raters 0.16 0.36 0.28 Words: agree, deal, arrangement, split 0.00 0.16 0.04 Others |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.00 0.04 0.04 |$\ge 10\%$| of raters 0.16 0.28 0.20 Words: labels of other participants 0.28 0.16 0.12 Gender |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.08 0.04 0.04 |$\ge 10\%$| of raters 0.16 0.20 0.28 Words: male, men, man, women, woman, female 0.00 0.00 0.00 . PERF-COMM . DESIG-COMM . NET-COMM . Performance |$\ge 90\%$| of raters 0.16 0.20 0.12 |$\ge 50\%$| of raters 0.68 0.52 0.76 |$\ge 10\%$| of raters 0.96 0.96 0.96 Words: score, rank(ed), count(ed) 0.68 0.68 0.72 Networks |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.04 0.08 0.00 |$\ge 10\%$| of raters 0.16 0.36 0.28 Words: link(s), connection(s), linking 0.08 0.20 0.32 Agreements |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.04 0.08 0.00 |$\ge 10\%$| of raters 0.16 0.36 0.28 Words: agree, deal, arrangement, split 0.00 0.16 0.04 Others |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.00 0.04 0.04 |$\ge 10\%$| of raters 0.16 0.28 0.20 Words: labels of other participants 0.28 0.16 0.12 Gender |$\ge 90\%$| of raters 0.00 0.00 0.00 |$\ge 50\%$| of raters 0.08 0.04 0.04 |$\ge 10\%$| of raters 0.16 0.20 0.28 Words: male, men, man, women, woman, female 0.00 0.00 0.00 Open in new tab In summary our content analysis shows that in PERF-COMM most chats are about performance and some are about other participants’ behaviour. No other topic is consistently identified by both methods to matter in more than 10% of chats. Also in DESIG-COMM performance is the most common topic, but here networking, agreements and other participants’ behaviour are also consistently identified as important topics (discussed in more than 10% of chats according to both classification methods). In NET-COMM performance is the most important topic, but also networking and other participants’ behaviour is frequently discussed. These results are intuitive. The more importance the environment gives for agreements or networking, the more often these are discussed in chats. 5. Conclusions We conducted an experiment to understand gender differences in networking and how they contribute to gender earnings and promotion gaps. In our experiment participants interacted in environments, where promotion and earnings depend on performance, networking or designation in different treatments. We do find evidence of gender earnings and promotion gaps. However, with the exception of homophily we do not find much evidence of gender differences in networking. In particular women and men do not systematically differ in terms of their in- or out-degree nor in terms of their centrality in the network. Earnings and promotion gaps appear, because male decision makers reward their network neighbours with increased earnings as well as promotion and these network neighbours happen to be predominantly male. It is useful to remember at this stage that our experiment was gender balanced. In many real-life situations, where gender earnings and promotion gaps can be observed the share of women is well below 50% overall and even lower among decision makers. In such situations the combined effect of homophily and men rewarding network neighbours could have even bigger consequences. Similarly in bigger groups with more levels of hierarchy, these effects could accumulate if they are found at every level of the hierarchy. To the extent that our results prove to have external validity, there are potentially actionable consequences in terms of measures to address gender networking differences. Such measures should not focus as much on presumed strategic networking differences, for which we found little evidence, but rather on opportunities and factors that limit the benefit of networking for women. One possibly important factor outside of the scope of this study is the fact that there may be limited opportunities for women which, rather than strategic differences in networking, could cause gender differences in networks outside the lab. Our findings also have implications for the design of work environments in view of reducing gender earnings and promotion gaps. While networking increases information flows and seems to lead to less rent extraction by decision makers, work environments where designation and networking play important roles can lead to larger gender differences in earnings and promotion. This could be particularly the case in areas that are ex ante characterised by large gender imbalances. In areas that are more gender balanced interventions could include the encouraging of mixing between male and female workers to reduce homophily. Future research could be aimed at testing the effectiveness of such interventions in the field. Another direction for future research is to study the strength and type of links more explicitly in a lab design. Ibarra (1993) finds, for example, that women have more supportive relationships while men form a greater number of instrumental relationships. Related to that it would also be interesting to study settings where networking has different functions, such as producing joint output or acquiring human capital. It would be interesting to see if the effects we identified in this paper are also observed in these contexts. In this paper we made the choice that ties can be formed unilaterally. Participants can unilaterally choose to start a conversation with someone or provide them with some information. As in many real-life interactions the recipient cannot prevent others from sending information (e.g., via e-mail outside the lab) or starting a conversation, however they can choose how much attention to pay to the information and whether to engage or not in the conversation.39 There could be other situations where link formation is bilateral, i.e., where the consent of both parties is needed to initiate a link. This is another direction for future research. Finally, it should be kept in mind that this paper speaks to networking differences given ex ante equal opportunities. Gender differences in networking that arise, e.g., because women are more involved with childcare and hence have less time for after-work activities are outside the scope of this paper, but potentially very important in contributing to gender earnings and promotion gaps. Additional Supporting Information may be found in the online version of this article: Online Appendix Replication Package Notes The data and codes for this paper are available on the Journal website. They were checked for their ability to replicate the results presented in the paper. I thank Andrea Galeotti, Rachel Kranton, Joshua Miller, Steve Pudney, Carmit Segal, Martin Strobel, Nick Vriend, Ro’i Zultan, two anonymous reviewers and seminar participants in Essex, Frankfurt, Geneva (EEA 2016), Hamburg, London (experimental workshop 2015), Munich (workshop on decisions, groups and networks), Norwich (BiNoMa Networks workshop 2016), Sussex (RES conference 2016) and the BEE-Lab meeting in Maastricht for helpful comments, Sara Godoy for assistance in running the experiments and Edward Ruchevits for programming. Financial support from Dutch Science Foundation (NWO, VENI grant 016.125.040) is gratefully acknowledged. Footnotes 1 Academia is no exception. While in some fields of academia gender promotion and earnings gaps have converged, this is not true in others. Economics is one of the fields where promotion and earnings gaps are particularly persistent and cannot be easily explained (Ceci et al., 2014). Earnings gaps among US full professors in economics wereen higher in 2010 than they were in 1995 with female full professors earning less than 75% of their male counterparts (Ceci et al., 2014). 2 A Google search of women’s networking events returns more than 21 million results (google.co.uk, May 2015). The UK’s Daily Telegraph (http://www.telegraph.co.uk/women/womens-business/10129034/Women-only-events-Does-anyone-else-have-networking-fatigue.html) asks ‘does anyone else have networking fatigue’ in the light of so many ‘women only’ networking events? BBC Radio 4 has a programme called Networking Nation (http://www.bbc.co.uk/programmes/b04l0gdl) and organisations like the Women in Business Network (wibn.co.uk), Enterprising Women (www.enterprising.women.org) or Forward Ladies (forwardladies.com) hold regular networking events. 3 Literature is reviewed in detail below. 4 The example studied in McDowell et al. (2005) are co-authorship networks in academia. Findings that women tend to co-author less than men (have fewer links in co-authorship networks) could be due, among others, to lower productivity or propensity to publish, but also to selection into different research areas, etc. 5 This minimal networking condition could reflect networking activities such as passing one’s CV or newest research paper, e-mailing colleagues highlighting one’s contribution to a project or communicating another achievement to a target person. 6 Typical work environments have features of all three. If we think, e.g., about promotions in an academia, performance (in terms of publications, teaching evaluations, etc.) clearly matters. However, there is also an element of designation as typically those who are already at a higher level of the hierarchy, e.g., full professors, decide on promotions of those at a lower level, e.g., associate or assistant professors. And finally networking is seen by many to play an important role as colleagues share information about their work. How important each of these components is will differ across different work environments. 7 Throughout the paper we will use the term ‘homophily’ to refer to the mere statistical fact that men are over-proportionately connected to men and women with women (McPherson et al., 2001). 8 Those are hypotheses 1 and 3 in Ibarra (1993). 9 Gender differences in the formation of friendship networks have been studied by Mayer and Puller (2008). While there will likely be some common elements in friendship and professional network formation, the latter serves different aims and many of the elements discussed above (share of women in powerful positions, likeability of networking women, etc.) will not be present or substantially weakened in friendship networks. 10 The instructions do not make any mention of avatars, so participants learn that avatars exist only after they have filled in the demographic information (see the instructions in Online Appendix B). Demographic information was cross-validated by an experimenter (see Online Appendix C for details). 11 Figures C.6 and C.7 in Online Appendix C show all avatars with their average score and earnings. 12 Text analysis suggests that this was successful. Participants refer to others in the chat as he/she depending on the gender of the avatar used. When referring to another participant in the chat such gendered words are used 96% of the time. 13 The number of ‘1’ entries in these matrices across rounds was (135; 129; 167; 145; 182; 117; 235; 151; 142; 190) in this order. 14 Giving participants information about individual scores could be interesting when there are benefits to linking with participants with higher performance (e.g., if network neighbours engaged in joint production where performance matters). This is not the case here. Note, though, that participants can still hold information about past scores as well as past roles (decision maker or not) of others. See Subsection 1.2 (‘Networking stage’ and ‘Allocation stage’). 15 As discussed in the Introduction, networking can have other functions as well, such as acquiring human capital or producing a joint output. In order not to make the design too complex, we decided to focus on one function of networking only, which is sharing of information. 16 This places a cognitive constraint on how many conversations participants can entertain. Comparison with the minimal treatments, however, suggests that this constraint was rarely binding. More importantly, even if the constraint was binding, this presumably would be the same for both genders. 17 Dictator games following real effort tasks have been studied by Ruffle (1998) and Oxoby and Spraggon (2008) among others. Heinz et al. (2012) find that female dictators tend to reward performance more than male dictators. Ruffle (1998) and Oxoby and Spraggon (2008) do not explicitly study and report gender differences. 18 Broadly speaking, since in treatments PERF and DESIG, networking does not have any benefits under standard game theoretic assumptions, but does come with a cost, we should not observe any networking in these treatments and equilibrium networks should be empty. This is different in treatment NET, where the networking game is a game of coalition formation. In equilibrium we should see a coalition of n ≥ 3 players who are linked in a complete graph. Each of these players becomes decision maker with probability |$\frac{1}{n}$|⁠. See Online Appendix E for details and underlying assumptions. 19 If we do not average across individuals, giving the rank-sum test greater power to detect differences, the difference is still not significant (p = 0.3231). 20 In Online Appendix H we also illustrate performance differences in the main treatments (Figure H.2) and show that there are no substantial gender differences in these treatments either. 21 While gender differences in altruism are not the focus of this paper, they could—combined with a promotion gap—create additional imbalances in earnings. Hence it is worthwhile pointing out that we do not detect statistically significant gender differences. Female decision makers allocate on average (64%, 52%, 46%, 47%, 32% and 33%, respectively, of the pie to themselves in treatments (PERF,DESIG, NET, PERF-COMM, DESIG-COMM and NET-COMM)), while for male decision makers the same numbers are (61%, 51%, 48%, 44%, 28% and 32%). While there are no gender differences, there are two noticeable patterns in these shares. First, participants allocate more to themselves in treatments PERF and PERF-COMM, where the decision maker has the highest performance and hence the highest contribution to the group earnings. Second, participants allocate less to themselves in the COMM-treatments, where they can be directly challenged by others for their allocation decisions in the chats. 22 The mean score of men is 14.94, 12.68 and 13.00 in NET, PERF-COMM and NET-COMM, respectively (15.02, 13.06 and 13.68 for women). 23 Consider, for example, a group of four women and two men. Random linking would imply that 60% of a woman’s links in this group are to other women (since she can’t link to herself) and 40% to men. If now a woman in this group has two links, one to a woman and one to a man, the homophily index would be (0.5−0.6)|$/$|(1−0.6)=−0.25 indicating heterophily. See e.g. Currarini et al. (2009). 24 Loosely speaking, eigenvector centrality measures how many others an agent connects to, where connections to other ‘important’ agents contribute more to the influence of the agent in question than equal connections to ‘unimportant’ others. Hence it is a recursively defined measure (see Online Appendix D for the precise definition). Google’s PageRank is a variant of the eigenvector centrality measure. 25 We also considered two further well-known network characteristics: betweenness centrality and clustering. We find that neither of them has any significant impact neither on earnings nor promotion. Because there is very little variation for these measures in our networks, these null results are not too meaningful. As a consequence we chose to omit these measures from our analysis. 26 For NET it ranges between 1.699* and 3.107**, for PERF-COMM between 3.799*** and 5.110*** and for NET-COMM between 1.959* and 2.010**. 27 Other network characteristics, such as clustering or betweenness centrality do not deliver significant gender differences. These measures, however, lack variation and include many zeros. Hence it is hard to interpret these distributions. 28 Remember that in these treatments those with the highest in-degree are more likely to become decision maker. Hence forming many links here (high out-degree) c.p. reduces one’s chances of becoming decision maker, as it increases those of other group members. 29 Note that it is in principle both possible (i) for one gender to display more homophily than the other gender in terms of out- and in-degree as well as (ii) for one gender to display more homophily in in-degree while the other gender displays more homophily in out-degree. Online Appendix Figure H.3 illustrates this point. 30 Gender difference in altruism is an interesting and much studied topic (see, e.g., the survey by Croson and Gneezy, 2009 and the discussion in footnote 21). Here we are interested, however, in whether and how networking contributes to gender differences in earnings and promotion gaps. 31 We averaged the coefficients for men and women to do this computation. Score has a mean of 14.4 in treatment PERF (15.27 in NET) with a standard deviation of 6.8 (6.5 in NET). The amount allocated to others has a standard deviation of 6.24 in PERF and 7.92 in NET. See Online Appendix Table G.1. 32 Such strategies can be part of Nash equilibrium in this treatment. See Online Appendix E. 33 Path dependence does not seem to be a big issue. Out of the randomly selected decision makers in period 1, 47% were female and the remainder male. 34 Note that reciprocity here is instrumental. As such it is different from the type of positive reciprocity (trustworthiness) identified in trust games, where sometimes women have been found to be more trustworthy (Croson and Buchan, 1999; Alesina and LaFerrara, 2002). See also the survey by Croson and Gneezy (2009). 35 These calculations are oversimplified as coefficients reported are based on the network share not just one given link. They hence correspond to the thought experiment where one link is formed in a situation where no other group member has links to the decision maker. If there are more links, then any given link will be worth less. 36 We also conducted some analysis on basic chat characteristics, in particular the length of chats and the percent of chats where the person who initiates the chat does not receive a reply. Those are reported in Online Appendix Table F.1. 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