The Economic Journal

Shin, Hyun, Song

doi: 10.1111/j.1468-0297.2008.02239.xpmid: N/A

Abstract A widespread opinion before the credit crisis of 2007/8 was that securitisation enhances financial stability by dispersing credit risk. After the credit crisis, securitisation was blamed for allowing the ‘hot potato’ of bad loans to be passed to unsuspecting investors. Both views miss the endogeneity of credit supply. Securitisation enables credit expansion through higher leverage of the financial system as a whole. Securitisation by itself may not enhance financial stability if the imperative to expand assets drives down lending standards. The ‘hot potato’ of bad loans sits in the financial system on the balance sheets of large banks rather than being sold on to final investors, since the aim of financial intermediaries is to expand lending in order to utilise slack in balance sheet capacity. There are two pieces of received wisdom concerning securitisation – one old and one new. The old view (prevalent before outbreak of the credit crisis of 2007/8) emphasised the positive role played by securitisation in dispersing credit risk, thereby enhancing the resilience of the financial system to defaults by borrowers. The subsequent credit crisis has somewhat tarnished this positive image.1 In its place, there is a new received wisdom which emphasises the distorted incentives that developed at all stages of the securitisation process, and which allowed the ‘hot potato’ of bad loans to pass through the financial system to be held finally in the hands of unsuspecting final investors. Although both views of securitisation (old and new, positive and negative) are appealing at a superficial level, they both neglect the endogeneity of credit supply. Financial intermediaries manage their balance sheets actively in response to shifts in measured risks. The supply of credit is the outcome of such decisions, and depends sensitively on key attributes of intermediaries’ balance sheets. Three attributes merit special mention – equity, leverage and funding source. The equity of a financial intermediary is its risk capital that can absorb potential losses. Leverage is the ratio of total assets to equity and is a reflection of the constraints placed on the financial intermediary by its creditors on the level of exposure for each dollar of its equity. Finally, the funding source matters for the total credit supplied by the financial intermediary sector as a whole to the ultimate borrowers. At the aggregate sector level (i.e. once the claims and obligations between leveraged entities have been netted out), the lending to ultimate borrowers must be funded either from the equity of the intermediary sector or by borrowing from creditors outside the intermediary sector. For any fixed profile of equity and leverage across the banks, the supply of credit to ultimate borrowers is larger when the banks borrow more from creditors outside the banking system. In a traditional banking system that intermediates between retail depositors and ultimate borrowers, the total quantity of deposits represents the obligation of the banking system to creditors outside the banking system. However, securitisation opens up potentially new sources of funding for the banking system by tapping new creditors. The new creditors are those who buy mortgage‐backed securities (MBSs), claims that are written on MBSs such as collateralised debt obligations (CDOs), and (one step removed) those who buy the asset‐backed commercial paper (ABCP) that are ultimately backed by CDOs and MBSs.2 The new creditors who buy the securitised claims include pension funds, mutual funds and insurance companies, as well as foreign investors such as foreign central banks. Indeed, we will see shortly that foreign central banks have been an important funding source for residential mortgage lending in the US. We will also examine some more partial evidence for the UK from the balance sheet of Northern Rock, the UK mortgage bank which failed in 2007. Although securitisation may facilitate greater credit supply to ultimate borrowers at the aggregate level, the choice to supply credit is taken by the constituents of the banking system taken as a whole. For a financial intermediary, its return on equity is magnified by leverage. To the extent that it wishes to maximise its return on equity, it will attempt to maintain the highest level of leverage consistent with limits set by creditors (for instance, through the ‘haircuts’ on repurchase agreements) or self‐imposed risk constraints. As measured risk fluctuates, so will leverage itself. In benign financial market conditions when measured risks are low, financial intermediaries expand balance sheets as they increase leverage. Although the intermediary could increase leverage in other ways – for instance, returning equity to shareholders, buying back equity by issuing long‐term debt – the evidence suggests that they tend to keep equity intact and adjust the size of total assets; see Adrian and Shin (2007, 2008a). As balance sheets expand, new borrowers must be found. When all prime borrowers have a mortgage but balance sheets still need to expand, then banks have to lower their lending standards in order to lend to subprime borrowers. The seeds of the subsequent downturn in the credit cycle are thus sown. When the downturn arrives, the bad loans are either sitting on the balance sheets of the large financial intermediaries, or they are in special purpose vehicles (SPVs) that are sponsored by them. This is so, since the bad loans were taken on precisely in order to utilise the slack on their balance sheets. Although final investors such as pension funds and insurance companies will suffer losses, too, the large financial intermediaries are more exposed in the sense that they face the danger of seeing their capital wiped out. The severity of the credit crisis of 2007/8 lies precisely in the fact that the bad loans were not all passed on to final investors. Instead, the ‘hot potato’ sits inside the financial system, on the balance sheet of the largest and most sophisticated financial intermediaries. The outline of this article is as follows. I begin with some background on securitisation, and construct an accounting framework of the financial system as a network of inter‐linked balance sheets. When this accounting framework is combined with a model of leverage based on value at risk (VaR), it is possible to model a lending boom fuelled by declines in measured risks. I conclude with a discussion of the implications for financial stability. 1. Background Securitisation has played a key role in the growth of residential mortgage lending, especially in the US. Figure 1 plots the total outstanding US home mortgage assets held by various classes of financial institutions from 1980. Fig. 1. Open in new tabDownload slide US Home Mortgage Assets (1980Q1–2008Q1): Flow of Funds, US Federal Reserve Fig. 1. Open in new tabDownload slide US Home Mortgage Assets (1980Q1–2008Q1): Flow of Funds, US Federal Reserve Even as recently as the early 1980s, banks and savings institutions held the bulk of home mortgages. Since then, the mortgage pools of the government sponsored enterprises (GSEs) such as Fannie Mae and Freddie Mac have become the largest holder of residential mortgages. Also noticeable are the securitisation vehicles classified under asset backed securities (ABS) issuers. The ABS issuers hold mortgages that do not conform to the GSE standards, hence including the subprime mortgages as well as large mortgages (‘jumbo’ mortgages) that exceed the upper threshold on the GSE conforming mortgages. Figure 2 is an aggregate series that distinguishes the ‘bank‐based’ holdings of residential mortgages from the ‘market‐based’ holdings. The latter is the sum of the holdings of the government sponsored enterprises, the GSE mortgage pools and the private label ABS issuers. The bank‐based series is the sum of the remaining three categories. The market‐based series overtook the bank‐based series in 1990 and now accounts for two thirds of approximately 11 trillion dollars’ worth of residential mortgages outstanding. Fig. 2. Open in new tabDownload slide Bank‐based and Market‐based Home Mortgage Holdings (1980Q1–2008Q1): Flow of Funds, US Federal Reserve Fig. 2. Open in new tabDownload slide Bank‐based and Market‐based Home Mortgage Holdings (1980Q1–2008Q1): Flow of Funds, US Federal Reserve Securitisation had long been seen as a positive development for the resilience of the financial system by enabling the dispersion of credit risk. However, since the onset of the credit crisis of 2007/8, a less sympathetic view of securitisation has gained support that emphasises the multi‐layered agency problems that took hold at every stage of the securitisation process, starting with the origination of the loan to the sale, warehousing and securitisation as well as the role of the credit rating agencies in the process.3 We could dub this less charitable view the ‘hot potato’ hypothesis, which has figured frequently in speeches given by policy makers on the credit crisis.4 The motto would be that there is always a greater fool in the chain who will buy the bad loan. At the end of the chain, according to this view, is the hapless final investor who ends up holding the hot potato and suffers the eventual loss. A celebrated anonymous cartoon strip has circulated widely on the internet5 depicting a hapless official from a Norwegian municipality in conversation with a broker after suffering losses on subprime mortgage securities. There is also mounting empirical evidence that lending standards had been lowered progressively in the run‐up to the credit crisis of 2007; see Demyanyk and van Hemert (2007), Mian and Sufi (2007) and Keys et al. (2007). It is clear that final investors who buy claims backed by bad assets will suffer losses. However, it is important to draw a distinction between selling a bad loan down the chain and issuing liabilities backed by bad loans. By selling a bad loan, you get rid of the bad loan from your balance sheet. In this sense, the hot potato is passed down the chain to the greater fool next in the chain. However, the second action has a different consequence. By issuing liabilities against bad loans, you do not get rid of the bad loan. The hot potato is sitting in the financial system, on the books of the special purpose vehicles (SPVs). Although the special purpose vehicles are separate legal entities from the large financial intermediaries that sponsor them, the finanical intermediaries have exposures to them from liquidity enhancements and various forms of retained interest; see Gorton and Souleles (2006). Thus, far from passing the hot potato down the chain to the greater fool next in the chain, the large financial intermediaries end up keeping the hot potato. In effect, the large financial intermediaries are the last in the chain. They are the greatest fool. While the final investors such as the famed Norwegian municipality will end up losing money, the financial intermediaries that sponsored the SPVs are in danger of larger losses. Since the intermediaries are leveraged, they are in danger of having their equity wiped out. Indeed, Greenlaw et al. (2008) report that of the approximately 1.4 trillion dollar total exposure to subprime mortgages, around half of the potential losses are borne by US leveraged financial institutions, such as commercial banks, investment banks and hedge funds. When foreign leveraged institutions are included, the total rises to two thirds. Gorton (2008) also argues against the hot potato hypothesis by noting that financial intermediaries have borne a large share of the total losses. Hence, we are faced with the following important question. Why did apparently sophisticated banks act as the ‘greatest fool’? In the rest of the article, I outline a framework that addresses this question. 2. An Accounting Framework Financial intermediaries play a role both as a lender and also as a borrower. In what follows, I describe an accounting framework to take account of the interlocking claims and obligations. There are n + 1 entities in financial system, where n of them are leveraged institutions (referred to as ‘banks’ for convenience) and one unleveraged sector (indexed by n + 1), which aggregates the balance sheets of unleveraged institutions such as insurance companies, pension funds and mutual funds, as well as household investors or foreign central banks. There is also an ‘end‐user’ sector who are the ultimate borrowers. For these purposes, the ultimate borrowers may be considered as households who buy a house financed with a mortgage. Denote by the face value of claims held by bank i against such end‐user borrowers. As well as the end‐user loans, there are also claims between members of the financial system. The liability of one party in the system will be the asset of another party. Denote by the face value of the obligation of bank i, and by πij the share of bank i ’s obligations that are held by bank j. Then, denoting by the notional value of equity of bank i, the balance sheet identity of bank i in terms of face values is: (1) The left‐hand side of (1) is the total assets of bank i in notional values, consisting of the loans made to end‐users , and the claims held against the other leveraged entities (the ‘banks’) in the financial system, . The right‐hand side of (1) gives the total liabilities of bank i in notional values and consists of the total promised repayment by bank i plus the notional equity that equates the two sides of the balance sheets. The interlocking claims and obligations can be depicted in terms of the following table, where denotes the notional value of bank i ’s obligations to bank j. Summing the ith row of the matrix gives the total liabilities of bank i, since it sums the obligations of bank i to other banks and to the long‐only investors (sector n + 1). The sum of the entries in the ith column of the matrix gives the total notional assets of bank i, since it sums the claims that bank i has on all other banks in the system, plus the loans it has made to the end‐users. The total notional assets of bank i are denoted as . 2.1. Credit Risk To begin with, suppose there are two dates, date 0 and date 1. Loans are made at date 0 and are repaid at date 1. The loans made to the end‐users are risky and banks face credit risk. Credit risk follows the familiar Vasicek (2002) one factor model, which is widely used and has been adopted as the backbone of the Basel II capital regulations.6 Under the Vasicek one factor model, the end‐user borrower j of bank i repays the loan when the realisation of random variable Zij is non‐negative, where Zij is defined as (2) where Φ(·) is the c.d.f. of the standard normal, Y and {Xij} are mutually independent standard normal random variables, and ρ and pi are constants. Y has the interpretation of the common risk factor and Xij is the idiosyncratic risk factor. The probability of default of any borrower j of bank i is pi since Conditional on the common factor Y, defaults are independent across borrowers, and the parameter ρ gives the ex ante correlation in defaults between any two loans made by bank i. Suppose that bank i ’s portfolio includes N loans to end‐users each with face value . But letting N become large, the loan portfolio to end‐users consists of many small loans whose defaults are independent conditional on the realisation of Y. By the law of large numbers, the repayment wi on the loan book of face value then becomes a determinstic function of Y. In other words, The c.d.f. over the repayment on bank i ’s loan book is thus 3 Note the following features. A change in pi (the probability of default on a particular loan made by bank i) implies a first degree stochastic dominance shift in the repayment density. A fall in pi pushes down the c.d.f., implying a first‐degree stochastic shift to the right in repayments. When pi is fixed, the mean repayment remains unchanged. However, a change in the parameter ρ keeping pi fixed implies a second degree stochastic dominance shift in the repayment density. An increase in ρ is associated with a mean‐preserving spread of the repayment density, making the loan book more risky. 2.2. Realised Values of Debt The realised value of repayment on the loans to end‐users will determine the realised value of the claims held between the banks, since the ability of one bank to fulfil its promise will depend on the resources it has to meet its obligations. Let us use the hat notation ‘’ to denote realised values at date 1. Thus, is the realised repayment on bank i ’s loans to end‐users, is the realised repayment by bank i and so on. Assume that all debt is of equal seniority, so that if , then bank j receives share πij of . Creditors receive the full value of the assets of the bank if the realised value of the assets fall short of the face value. Hence, realised values of debt satisfy (4) where is the profile of realised values of debt. There is non‐decreasing function F(·) that maps realised asset values to the realised asset values that result when debts are settled. The ex post allocation is a fixed point of the mapping F(·). Eisenberg and Noe (2001) showed that under mild regularity conditions, there is a unique fixed point of this mapping F(·); see Shin (2008a) for a simple exposition. Moreover, given the unique fixed point of F(·), the realised value of bank i ’s debt can be written as a function of the realised repayments from the loans to end‐users . Since the realised values are determinstic functions of Y, I can write the realised value of the assets of bank i as a deterministic function of the common factor Y. Hence, (5) Moreover, the comparative statics result on lattices due to Milgrom and Roberts (1994, theorem 3) ensures that the unique fixed point of the mapping F(·) is increasing in the realised repayments , so that each is an increasing function of see Eisenberg and Noe (2001). In this way, for each bank i, the realised value of its assets is a well‐defined, increasing function of Y. 2.3. Market Values Market values are defined as the expected values (seen from date 0) of the possible realised values at date 1 where the expectations is taken with respect to the distribution of loans losses given by the Vasicek model. I use the notation yi (without any hats or bars) to denote the market value of bank i ’s loans to end‐users. Similarly, xi is the market value of bank i ’s debt, given by the expected value of realised debt values at date 1. The total marked‐to‐market value of assets of bank i can then be written as (6) The balance sheet identity for bank i in market values is (7) The left‐hand side is the market value of assets and the right‐hand side is the market value of the liabilities side of the balance sheet, where ei denotes the market value of equity of bank i. The matrix of claims and obligations between banks can then be written in market values, as below. The ith row of the matrix can be summed to give the market value of debt of bank i, while the ith column of the matrix can be summed to give the market value of total assets of bank i. From the balance sheet identity (7), I can express the vector of debt values across the banks as follows, where Π is the n × n matrix where the (i, j)th entry is πij. (8) or more succinctly as (9) Equation (9) shows the recursive nature of debt in a financial system. Each bank’s debt value is increasing in the debt value of other banks. Solving for y, Define the leverage of bank i as the ratio of the market value of assets to the market value of its equity. Denote leverage by λi. Then, leverage is defined as (10) Since xi/ei = λi − 1, x = e(Λ−I), where Λ is the diagonal matrix whose ith diagonal entry is λi. Thus (11) Thus, the profile of total lending by the n banks to the end‐user borrowers depends on the interaction of three features of the banking system – the distribution of equity e in the banking system, the profile of leverage Λ and the structure of the financial system given by Π. Total lending to end users is increasing in equity and in leverage, as one would expect. More subtle is the role of the financial system, as given by the matrix Π. Define the vector z as (12) where so that . In other words, zi is the proportion of bank i ’s debt held by the outside claimholders – the sector n + 1. Then, total lending to end‐user borrowers ∑iyi can be obtained by post‐multiplying (11) by u so that (13) Equation (13) is the balance sheet identity for the financial sector as a whole, where all the claims and obligations between banks have been netted out. The left‐hand side is the total lending to the end‐user borrowers. The first term on the right‐hand side of (13) is the total equity of the banking system, and the second term is the total funding to the banking sector provided by the outside claimholders (note that the second term can be written as ). Thus, the importance of the structure of the financial system for the supply of credit is clear from (13). Ultimately, credit supply to end‐users must come either from the equity of the banking system or the funding provided by non‐banks. 2.4. Financial System Leverage A given degree of leverage for the financial system as a whole is consistent with a wide range of leverage levels for the individual banks. This is true both in terms of the face values of claims, as well as market values. First consider face values. A financial system in face values can be represented as the array that satisfies the balance sheet identity: (14) Then, for positive constant φ, we can construct a financial system where the aggregate equity, lending and leverage are all unchanged but where the debt to equity ratio of all individual banks is φ times as large. Specifically, consider the financial system where and Π′ is any matrix of interbank claims whose ith row sum to 1 − zi/φ. Finally, is defined as (15) Then, aggregate lending is given by Hence, aggregate notional leverage in both financial systems is . However, by construction, the debt to equity ratio of all individual banks is φ times larger in the second financial system. The only restriction on the constant φ comes from the feature that the ith row of Π′ sums to 1 − zi/φ. So, φ should not be so small that 1 − zi/φ < 0 for some i. This puts a lower bound on φ. But there is no upper bound. I can construct a financial system where aggregate notional leverage is unchanged but where individual bank notional leverage can be as high as we want. The intuition is that the banks can lend and borrow from each other in large amounts so that their leverage can be raised, without altering the aggregate relationship between the banking sector with the ultimate creditors. The construction presented above can also be made for the balance sheet quantities expressed in market values but with one difference. It is still true that two financial systems can have the same aggregate market leverage and where the individual market leverage for the banks differ by a positive factor φ. However, for market leverage, the constant factor φ cannot be chosen arbitrarily large. This is because the market value of debt xi cannot be larger than the market value of assets ai, and the market value of assets is underpinned by the value of fundamental assets {yk}. Thus, there is an upper bound in choosing the constant factor φ. Subject to this condition, the construction follows the exactly analogous process. The leverage of the aggregate banking sector itself is related to the leverage of individual banks in the following way. If I denote the leverage of the banking sector as a whole by L, I can write it as 16 where (16) follows from (13). Thus, other things being equal, the leverage of the banking sector as a whole is increasing in the amount of funding obtained from outside claimholders, as given by the quantities {zi}. Proposition 1. For any given profile of leverage for individual banks, the leverage of the financial intermediary sector as a whole is increasing in the proportion of funding obtained from creditors outside the financial intermediary sector. 3. Value at Risk Up to this point, I have confined myself to manipulating balance sheet identities. I now turn to the decision rule followed by the banks so that I can address comparative statics questions on how lending to end‐users depends on the underlying parameters that drive credit risk (see Figure 3). For this purpose, I employ the notion of value at risk. For bank i its value at risk at confidence level c relative to the face value of its assets , is the smallest non‐negative number Vi such that 17 Fig. 3. Open in new tabDownload slide Value at Risk Fig. 3. Open in new tabDownload slide Value at Risk Value at risk Vi is the ‘approximately’ worst case loss that can be suffered by the bank, where ‘approximately worst case’ is defined so that anything worse happens with probability smaller than the benchmark 1 − c. The concept of value at risk has been adopted widely, both by the private sector and regulators, and is the bedrock of the capital regulations adopted by Basel regulations. The 1996 Market Risk Amendment of the original 1988 Basel Accord is based on the notion of value at risk, and the Basel II regulations have further built on the notion of value at risk. There is an important open question of how well grounded is the notion of value at risk from a microeconomic perspective. Adrian and Shin (2008a) provide one possible approach in terms of a model of a contracting problem in which value at risk can be shown to arise as part of the optimal contract between a bank and its creditors in a repurchase agreement. For the exercise here, let us simply assume that banks behave according to the prescriptions that flow from the notion of value at risk and investigate the consequences of such actions. In particular, assume that bank i aims to set market equity ei to its value at risk Vi, so that (18) 3.1. Decrease in Default Probability In this context, let us examine consequences of more favourable macroeconomic conditions as reflected in the decline of default probabilities {pi} in the Vasicek one‐factor model. For simplicity, let pi = p for all i, and we suppose that p has fallen. Recall that the c.d.f. for realised repayments on bank i ’s loans to end‐users is given by (19) Notice that when the default probability pi for bank i declines, there is a rightwards shift in the density over the realised loan values in the sense of first degree stochastic dominance. Moreover, since the value of interbank claims are increasing in the aggregate factor Y, a fall in p entails a first‐degree stochastic dominance shift in the density over realised values of interbank assets held by bank i. Hence, there is a first‐degree stochastic dominance shift in the density over bank i ’s total asset value . Figure 4 illustrates the shift. Fig. 4. Open in new tabDownload slide Value at Risk and Leverage Fig. 4. Open in new tabDownload slide Value at Risk and Leverage The market value of assets following the fall in p is given by , and the market equity is given by . We have , since the ex post value of equity at the terminal date is increasing in the realised values , and there is a first‐degree stochastic dominance shift in . At the same time, there is a decline in the value at risk of bank i. This is because the c.d.f. over asset values shifts lower following the fall in p. Therefore, the (1 − c) quantile of the realised asset value shifts upward. The value at risk is smaller than before, and is given by . Thus, following the decline in p, we have (20) so that . Hence, bank i has surplus equity in the sense that its market equity is too large relative to the equity that is required to meet its value at risk. The surplus equity could, in principle, be remedied by paying a dividend to shareholders, or by buying back equity by issuing more debt. However, in practice, the evidence points to banks remedying surplus equity by raising the size of total balance sheets instead, rather than paying out the surplus equity.7 Consistent with this evidence, we assume that if bank i has surplus equity, it expands its balance sheet by increasing the notional value of debt and using the proceeds to take on more assets. Assumption 1. Whenafter the decline in p, bank i increases the face value of its debt. As banks raise new debt, they will acquire assets with the proceeds. The interbank claims matrix Π will therefore change. Since our focus here is on the effect on aggregate lending, the exact way in which the interbank claims matrix changes is not of direct interest. Suppose the new interbank claims matrix is given by Π* after the adjustment of face values and the profile of market value of debt is given by x* after the adjustment of face values. The comparative statics result due to Milgrom and Roberts (1994, theorem 3) for the fixed point of increasing functions on complete lattices implies that when the face value of bank i ’s debt increases, the market values of debt is increasing for all banks.8 Hence, given Assumption 1, we have (21) Let us make one further assumption. As banks increase their borrowing in response to the appearance of surplus equity, they will search for new sources of funding. If financial innovation through securitisation is available, the banks may tap new sources of funding by borrowing from the outside creditor sector–sector n + 1 in my notation. I therefore make the following assumption. Assumption 2. When banks increase notional debt in response to a fall in p, the proportion of funding raised from the outside creditor sector is non‐decreasing. This assumption places a restriction on the new interbank claims matrix Π* so that the sum of the ith row of Π* is no larger than the sum of the i ’s row of the initial interbank matrix Π. In other words, (22) We will see shortly some empirical evidence that bears on Assumption 2. Proposition 2. When p falls, the value of aggregate lending to end‐users increases, both in notional values and in market values. The argument for this Proposition starts with the balance sheet identities before and after the change in face values of debt. The balance sheet identities in face values are (23) where * indicates variables after the change. The face value of equity remains unchanged (), so that the change in aggregate notional lending is given by (24) The first term on the right‐hand side is positive from our assumption that banks react to surplus equity by expanding their balance sheets, while the second term on the right‐hand side is positive from our assumption (22) that an increasing proportion of the funding comes from the outside sector. Thus, , so that total lending to end‐user borrowers in terms of notional values increases. The argument for the increase in the market value of loans to end‐users following the decline in p is similar. The balance sheet identities in market values before and after the change are (25) The change in the market value of loans to end‐users is (26) Equation (26) differs from the analogous one for face values in that the banks’ balance sheets now reflect the capital gain on their loan portolio as given by (e* − e)u, where e* = e′, where e′ is the value given in (20). The increased equity is an additional funding source when loans are valued at market values. All three terms on the right‐hand side of (26) are positive, and so (y* − y)u > 0. 4. Lending Boom I can now sketch the scenario for a lending boom by using the results derived so far. The first ingredient is the relationship between the probability of default p on the loan book and the aggregate lending to end‐user borrowers, who may be interpreted as being households who borrow in order to buy a house. Proposition 1 gives a declining function that maps p to total lending. Figure 5 depicts the negative relationship between total (notional) lending and p, where the total lending appears on the horizontal axis. The arrows indicate that for each level of p, there is an associated level of total lending . Fig. 5. Open in new tabDownload slide Aggregate Lending is Decreasing in p Fig. 5. Open in new tabDownload slide Aggregate Lending is Decreasing in p If I further suppose that there is a macroeconomic feedback going from total lending to the probability of default, then I may expect amplifications that result from the interplay between strengthening balance sheets and increased lending.9 If increased loan supply feeds through to more buoyant aggregate conditions, it is possible to sketch a scenario for a lending boom. Thus, for the purpose of illustration, suppose there is a mapping g which maps aggregate lending to the probability of default p. To be consistent with the interpretation of higher credit supply leading to more buoyant conditions, the function g(·) should be decreasing. Figure 6 superimposes the function g(·) on Figure 5. Now consider the scenario where the advent of securitisation shifts the mix between internal and external funding that banks use toward greater use of funding from outside creditors. We may interpret this scenario as a decline in the entries of the interbank matrix Π such that the proportion of funding raised from outside creditors increases. As argued in the previous Section, such a development increases the aggregate lending to the end‐user borrowers even if the leverage of individual banks (and their value at risk) is unchanged. In terms of the diagram, the shift to greater use of outside funding can be represented as a shift to the right of the credit supply function. Figure 7 depicts the shift in credit supply that results and the consequences of such a shift. Fig. 7. Open in new tabDownload slide Lending Boom Fig. 7. Open in new tabDownload slide Lending Boom Fig. 6. Open in new tabDownload slide Initial Point Fig. 6. Open in new tabDownload slide Initial Point The initial shock from the greater use of outside funding results in a rightwards shift in the supply of credit curve. The new intersection point is to the bottom right‐hand side of the initial point, associated with a lower probability of default p and greater total lending to the end‐user sector. Although there are no explicit dynamics in our framework, it is illuminating to trace out the step‐wise adjustment resulting from the one‐off shift in the use of outside funding. The initial shift is a rightwards shift in the credit supply curve which results in higher aggregate lending for a fixed p . However, the macro feedback effect of greater loan supply then kicks in, resulting in a decrease in the probability of default. This adjustment is depicted by the first downward sloping arrow in Figure 7. However, the fall in p results in greater lending according to the argument for Proposition 1. Greater lending then feeds to lower p and so on. The new settling point given in Figure 7 is associated with a substantially lower probability of default as well as a large stock of lending. 4.1. Subprime Lending At the cost of some additional complexity, it would be possible to incorporate subprime lending into the story. Suppose that the population of prime borrowers is small relative to the expansion of total lending as implied by the new crossing point between the credit supply curve and the macro feedback function g(·) in Figure 7. Then, once all the prime borrowers have been granted a mortgage, the banking system has to find additional means of creating assets. One way would be for the banks to lend to each other. However, as discussed earlier, the aggregate lending of the banking system to mortgage borrowers must equal the sum of the equity and the borrowing from outside creditors. Since it is the borrowing from the outside creditors which is increasing, the funding must ultimately find its way to an end‐user borrower. Once all the prime borrowers in the population have a mortgage, the banks must find new borrowers in order to expand their balance sheets. The only way they can do this is to lower their lending standards. Subprime borrowers will then start to receive funding. The mechanical nature of our framework in which banks simply choose their balance sheet size masks important questions concerning the short‐termist nature of such lending to subprime borrowers. The answer as to why banks would lower their lending standards in order to lend to subprime borrowers must appeal to other frictions within the banking institutions that allows such short‐termism. Distorted incentives and shortened decisions horizons induced by agency problems within the bank would be part of the overall story. See Rajan (2005) and Kashyap et al. (2008) for discussion of such incentives. 5. Empirical Evidence Aggregate lending to end‐user borrowers by the banking system must be financed either by the equity in the banking system or by borrowing from creditors outside the banking system. The empirical counterpart to the sector described as the ‘banking system’ is the whole of the leveraged financial sector, which includes the traditional commercial banking system, but also encompasses the market‐based financial system that plays a role in extending credit to banks and non‐banks by borrowing from outside creditors. In this sense, the leveraged financial sector should be conceived broadly to include all leveraged institutions, such as investment banks, hedge funds and (in the US especially) the government sponsored enterprises (GSEs) such as Fannie Mae and Freddie Mac. 5.1. Evidence from US GSE Mortgage‐backed Securities A complete disaggregation of the funding source for the leveraged financial sector is not possible due to the lack of detailed breakdowns in the data between funding from leveraged and unleveraged creditors. A partial picture can be obtained, however, by examining the holding of US agency and GSE‐backed securities. Figure 8 plots the total holding of US agency and GSE‐backed securities broken down into the identity of the creditor at the end of each year from 2001 to 2007. The data are from the US Flow of Funds accounts compiled by the Federal Reserve (table L.210). Leveraged financial institutions include commercial banks, broker dealers and other securitisation vehicles. The non‐leveraged financial institutions include mutual funds, insurance companies and pension funds. The ‘non‐financial sector’ includes household, corporate and government sectors. Finally, the ‘rest of the world’ category indicates foreign creditors, especially foreign central banks or other official sector holders. Figure 9 charts the holders by percentage holdings. Fig. 9. Open in new tabDownload slide Holding of GSE‐backed Securities (percentages) Fig. 9. Open in new tabDownload slide Holding of GSE‐backed Securities (percentages) Fig. 8. Open in new tabDownload slide Holding of GSE‐backed Securities Fig. 8. Open in new tabDownload slide Holding of GSE‐backed Securities The key series for our purposes is the proportion held by other leveraged financial institutions. We see that US leveraged institutions have been holding a declining proportion of the total. At the end of 2002, leveraged financial institutions held 48.4% of the total but by the end of 2007 that percentage had dropped to 36.7%. There has been a consequent increase in the funding provided by the non‐leveraged sector. In terms of the model, this translates to an increase in the z vector of proportions raised from outside the ‘banking sector’ of the model. Notably, the holdings of the ‘rest of the world’ category (which itself is mostly accounted for by foreign central banks) has more than tripled from $504 billion at the end of 2001 to $1,540 billion at the end of 2007. Recall that the increased proportion of the funding coming from outside the banking system plays a key role in the development of the lending boom scenario of the previous Section. We see that the assumption has some empirical support. 5.2. Evidence from the UK The increased importance of securitisation can be found also in the UK, from the balance sheet series of Northern Rock, the UK bank that failed in 2007. Northern Rock was a building society (i.e. a mutually owned savings and mortgage bank) until its decision to go public and float its shares on the stock market in 1997. In the nine years from June 1998 (the first year after demutualisation) to June 2007 (on the eve of its crisis), Northern Rock’s total assets grew from 17.4 billion pounds to 113.5 billion pounds (a constant equivalent annual growth rate of 23.2%). By the eve of its crisis, Northern Rock was the fifth largest bank in the UK by mortgage assets. Northern Rock’s liabilities reflect both the funding constraints it faced, as well as the way it overcame those constraints. Figure 10 charts the composition of Northern Rock’s liabilities from June 1998 to June 2007. Fig. 10. Open in new tabDownload slide Northern Rock Annual and Interim Reports Fig. 10. Open in new tabDownload slide Northern Rock Annual and Interim Reports Traditional deposit funding did not keep pace with total assets and the gap was made up primarily by securitised notes and other forms of non‐retail funding. The ‘other liabilities’ category includes interbank funding, short‐term notes and covered bonds. Covered bonds are long‐term liabilities written against segregated mortgage assets. The breakdown between leveraged and non‐leveraged holders of these liabilities is not available, but two points are worthy of mention. First, the securitised notes were of long maturity, with the maturity being around two years; see Shin (2008b). Thus, it is quite plausible that a substantial part of these notes were held by non‐leveraged financial institutions. If this is the case, then Figure 10 would be an illustration of the increased funding obtained from creditors outside the banking sector. 5.3. Liquidity Crisis The consequences of the increased funding of assets by creditors from outside the banking sector are felt most acutely when the lending boom turns to bust. The framework sketched so far is a static one in which loans are made at date 0 and repaid at date 1. This assumption masks the maturity mismatch that can build up in the aggregate balance sheet when the loans to the end‐user borrowers are long term, while the debt is short term. In the expansion stage, the maturity mismatch does not show up but the mismatch makes the contraction stage more painful due to the irreversibility of long‐term loans. The contraction stage must make reference to more than two dates. The simplest extension would be to have three dates, 0, 1 and 2, where loans are granted at date 0, and are repaid at date 2 but then banks experience an increase in the probability of default p in the Vasicek credit risk model at date 1. Then, value at risk increases following the parameter shift, while the market value of equity decreases. Indeed, there is the chain of inequalities: (27) which is the mirror image of the inequalities (20) that hold during the boom. The counterpart to Assumption 1 would be that the banks attempt to reduce their total balance sheet size by reducing the size of their notional debt level . However, if the loans to end‐users are long term, then banks are not free to reduce the size of their balance sheets flexibly. The constraint will bind harder if the proportion of assets of this type constitute a large fraction of total assets. In aggregate, the total long‐term lending to end‐users is mirrored by the size of the funding obtained from lenders from outside the banking sector. Thus, at an aggregate level, the increased use of securitisation is associated with a tighter constraint against rapid reductions in balance sheet size. When value at risk increases, banks must cut back the size of their balance sheets. Some banks will be able to reduce their balance sheets flexibly by not rolling over short‐term assets and short‐term liabilities. But not every bank can do this, since the financial system as a whole holds long‐term illiquid assets financed by short‐term liquid liabilities. There will be ‘pinch points’ that are thus exposed when value at risk increases. These pinch point banks will suffer a liquidity crisis. Northern Rock is a good example of such a pinch point. Its assets were almost all long‐term residential mortgages. Thus, it had very little scope to reduce its balance sheet in a flexible way once the crisis struck. Crucially, Northern Rock was vulnerable to the tick‐up in value at risk due to its high leverage. Figure 11 plots the leverage series from June 1998 to December 2007 according to three different measures of equity. In the early years, there was no distinction between total equity, shareholder equity and common equity. All equity was common equity. However, in 2005, the total equity series included for the first time 736.5 million pounds worth of subordinated debt, as well as 299.3 million pounds worth of reserve notes. Both of these items had been issued much earlier (in 2001) but they were included in the equity series in the annual report for the first time in 2005.10 The inclusion of these subordinated debt items introduced a jump up in the equity series for Northern Rock, and accounts for the sharp jump down in the leverage series in June 2005 in Figure 11. However, as we can see also from Figure 11, when the subordinated debt items are excluded, and equity is construed just as shareholder equity, the leverage series continues to move up in 2005. On the eve of its crisis in 2007, the leverage ratio on common equity stood at almost 60. This made Northern Rock particularly vulnerable among UK banks to the credit crisis that erupted in August 2007.11 Fig. 11. Open in new tabDownload slide Northern Rock’s Leverage June 1998 – December 2007 Fig. 11. Open in new tabDownload slide Northern Rock’s Leverage June 1998 – December 2007 Although the conventional notion of equity in bank regulation is as a buffer against losses to depositors, the relevant equity measure for funding constraints is the stake held by those who control the assets – i.e. the common equity holders. The distinction is seen most clearly for repurchase agreements (repos), where the haircuts applied by creditors determine the permitted leverage; see Adrian and Shin (2008a). Thus, even though the Basel‐style leverage ratios were kept low by issuing subordinated debt and preferred equity, the effective leverage for funding purposes was climbing very rapidly in the case of Northern Rock. Its run in the summer of 2007 should be seen in this context. 6. Related Literature and Conclusions The importance of securitisation for financial stability derives from the ability of the shadow banking system to increase total supply of credit to end‐users. When there is a decline in the riskiness of fundamental assets (in our case, through a fall in the parameter p), the risk‐taking capacity of the shadow banking system increases. The idea that the changes in the lender’s balance sheet is important in determining the supply of credit has also figured in an earlier literature that has emphasised the liquidity structure of the banks’ balance sheets (Bernanke and Blinder, 1988; Kashyap and Stein, 2000), or the cushioning effect of the banks’ regulatory capital (Van den Heuvel, 2002). The supply‐side mechanism for the growth of credit should be distinguished from the larger literature on the fluctuations in credit due to the shifts in the demand for credit, as emphasised for instance by Bernanke and Gertler (1989) and Kiyotaki and Moore (1998, 2001). The key to the demand‐side explanations of the fluctuation of credit is the changing strength of the borrower’s balance sheet and the resulting change in the creditworthiness of the borrower. The mechanism proposed here for the origin of the subprime crisis has more in common with the supply side explanation. The greater risk‐taking capacity of the shadow banking system leads to an increased demand for new assets to fill the expanding balance sheets and an increase in leverage. The picture is of an inflating balloon which fills up with new assets. As the balloon expands, the banks search for new assets to fill the balloon. They look for borrowers that they can lend to. However, once they have exhausted all the good borrowers, they need to scour for other borrowers – even subprime ones. The seeds of the subsequent downturn in the credit cycle are thus sown. According to the picture painted here, the subprime crisis has its origin in the increased supply of loans – or equivalently, in the imperative to find new assets to fill the expanding balance sheets. In this way, it is possible to explain two features of the subprime crisis – first, why apparently sophisticated financial intermediaries continued to lend to borrowers of dubious creditworthiness and, second, why such sophisticated financial intermediaries held the bad loans on their own balance sheets, rather than passing them on to other unsuspecting investors. Both facts are explained by the imperative to use up slack in balance sheet capacity during an upturn in the credit cycle. Footnotes 1 " See BIS (2008), Brunnermeier (forthcoming), Greenlaw et al. (2008) or IMF (2008) for an account of the credit crisis of 2007/8. 2 " See Gorton and Souleles (2006) for a description of special purpose vehicles involved in the securitisation process in the US. 3 " A comprehensive survey of the securitisation process for subprime mortgages is given by Ashcraft and Schuermann (2008) who details the specific agency problems at seven points in the securitisation chain. 4 " See, for instance, Gieve (2008) and Mishkin (2008) among others. 5 " For instance, http://bigpicture.typepad.com/comments/2008/02/how‐subprime‐re.html 6 " See also Alizalde and Repullo (2006) for an application of the Vasicek model in a model of banking competition. 7 " See Adrian and Shin (2007, 2008a). 8 " See Eisenberg and Noe (2001). 9 " Adrian and Shin (2008b) exhibit evidence that expansions of intermediary balance sheets help explain future growth of GDP components such as housing investment and durable good consumption. 10 " See Shin (2008a). 11 " See Yorulmazer (2008) for an empirical analysis of UK banks at the time of the Northern Rock crisis. 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(forthcoming). ‘De‐ciphering the credit crisis of 2007’ , Journal of Economic Perspectives . OpenURL Placeholder Text WorldCat Demyanyk , Y. and Van Hemert , O. ( 2007 ). ‘Understanding the subprime mortgage crisis’ , working paper, New York University, Stern School of Business . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Eisenberg , L. and Noe , T. H. ( 2001 ). ‘Systemic risk in financial systems’ , Management Science , vol. 47 , pp. 236 – 49 . Google Scholar Crossref Search ADS WorldCat Gieve , J. ( 2008 ). ‘The return of the credit cycle: old lessons in new markets’ , speech at the Euromoney bond investors congress , February 27, available at http://www.bankofengland.co.uk/publications/speeches/2008/speech338.pdf Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Gorton , G. ( 2008 ). ‘The panic of 2007’ , paper for the Federal Reserve Bank of Kansas City Symposium at Jackson Hole . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Gorton , G. and Souleles , N. ( 2006 ). ‘Special purpose vehicles and securitization’, in ( R. Stulz and M. Carey, eds), The Risks of Financial Institutions , pp. 549 – 97 , Chicago: University of Chicago Press . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Greenlaw , D. , Hatzius , J., Kashyap , A. and Shin , H. S. ( 2008 ). ‘Leveraged losses: lessons from the mortgage market meltdown’ , Report of the US Monetary Monetary Form , No. 2, available at http://www.chicagogsb.edu/usmpf/docs/usmpf2008confdraft.pdf Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC International Monetary Fund ( 2008 ). Global Financial Stability Report , April, Washington DC: IMF . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Kashyap , A. , Rajan , R. and Stein , J. ( 2008 ). ‘Rethinking capital regulation’ , paper for the Federal Reserve Bank of Kansas City Symposium at Jackson Hole . Kashyap , A. and Stein , J. ( 2000 ). ‘What do a million observations on banks say about the transmission of monetary policy?’ , American Economic Review , vol. 90 , pp. 407 – 28 . Google Scholar Crossref Search ADS WorldCat Keys , B. , Mukherjee , T., Seru , A. and Vig , V. ( 2007 ). ‘Did securitization lead to lax screening? Evidence from subprime loans’ , working paper, University of Chicago GSB . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Kiyotaki , N. and Moore , J. ( 1998 ). ‘Credit chains’ , LSE working paper, available at http://econ.lse.ac.uk/staff/kiyotaki/creditchains.pdf. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Kiyotaki , N. and Moore , J. ( 2001 ) ‘Liquidity and asset prices’ , LSE working paper, available at http://econ.lse.ac.uk/staff/kiyotaki/liquidityandassetprices.pdf. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Mian , A. and Sufi , A. ( 2007 ). ‘The consequences of mortgage credit expansion: evidence from the 2007 mortgage default crisis’ , working paper, University of Chicago GSB . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Milgrom , P. and Roberts , J. ( 1994 ). ‘Comparing equilibria’ , American Economic Review , vol. 84 , pp. 441 – 59 . OpenURL Placeholder Text WorldCat Mishkin , F. ( 2008 ). ‘On leveraged losses: lessons from the mortgage market meltdown’ , discussion at 2nd US Monetary Policy Forum, New York, February 27, available at http://www.federalreserve.gov/newsevents/speech/mishkin20080229a.htm Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Rajan , R. ( 2005 ). ‘Has financial development made the world riskier?’ , Proceedings of the Federal Reserve Bank of Kansas City Symposium at Jackson Hole, available at http://www.kc.frb.org/publicat/sympos/2005/sym05prg.htm Shin , H. S. ( 2008a ). ‘Risk and liquidity in a system context’ , Journal of Financial Intermediation , vol. 17 , pp. 315 – 29 . Google Scholar Crossref Search ADS WorldCat Shin , H. S. ( 2008b ). ‘Reflections on Northern Rock: the bank run that heralded the global financial crisis’, Journal of Economic Perspectives , forthcoming. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Van den Heuvel , S. ( 2002 ). ‘The bank capital channel of monetary policy’ , working paper, Wharton School, University of Pennsylvania , available at http://finance.wharton.upenn.edu/~vdheuvel/BCC.pdf Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Vasicek , O. ( 2002 ). ‘The distribution of loan portfolio value ’, available at http://www.moodyskmv.com/conf04/pdf/papers/dist_loan_port_val.pdf Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Yorulmazer , T. ( 2008 ). ‘Liquidity, bank runs and bailouts: spillover effects during the Northern Rock episode’ , working paper, Federal Reserve Bank of New York . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Author notes " Presented as the EconomicJournal Lecture at the Royal Economic Society Conference in Warwick, March 17‐8, 2008. I am grateful to Frank Heinemann, Gara Minguez Afonso, Jean‐Charles Rochet and Andrew Scott for their comments on earlier versions and, especially, to Tobias Adrian for allowing me to draw on work from our on‐going collaboration. © The Author(s). Journal compilation © Royal Economic Society 2009

Fehr,, Ernst;Brown,, Martin;Zehnder,, Christian

doi: 10.1111/j.1468-0297.2008.02240.xpmid: N/A

Abstract We study the impact of reputational incentives in markets characterised by moral hazard problems. Social preferences have been shown to enhance contract enforcement in these markets, while at the same time generating considerable wage and price rigidity. Reputation powerfully amplifies the positive effects of social preferences on contract enforcement by increasing contract efficiency substantially. This effect is, however, associated with a considerable bilateralisation of market interactions, suggesting that it may aggravate price rigidities. Surprisingly, reputation in fact weakens the wage and price rigidities arising from social preferences. Thus, in markets characterised by moral hazard, reputational incentives unambiguously increase mutually beneficial exchanges, reduce rents, and render markets more responsive to supply and demand shocks. Severe moral hazard problems are pervasive in many labour, credit and goods markets. Reputational incentives are likely to play an important role in such markets (MacLeod, 2007) but empirical evidence on the role of reputation is still scarce. This article assesses empirically the impact of reputational incentives on contract enforcement, the distribution of gains from trade and the structure of interactions between contracting partners in a competitive environment with severe moral hazard problems. Our examination starts from a body of evidence indicating that heterogeneous preferences for fairness, equity, social image concerns, efficiency, or reciprocity generally have a non‐negligible impact on behaviour in such environments.1 For convenience, we summarise these different non‐pecuniary motives under the term ‘reciprocity’ because these motives typically imply some kind of ‘reciprocal behaviour’ in the principal–agent contexts we study. The evidence shows that reciprocity contributes to the enforcement of contracts in moral hazard situations but a considerable gap typically remains between the first best performance levels and the performance levels enforced by reciprocity. The efficiency enhancing effects of reciprocity on contract enforcement come at a cost, however – the payment of non‐competitive rents to the agents and an extremely high degree of price stickiness in response to supply and demand shocks. It is natural to ask how reputation formation affects the interactions between principals and agents because many relevant situations involve repeated interactions or situations where principals acquire information about agents’ past behaviour. In fact, repeated interactions are ubiquitous in labour, credit and goods markets. In view of the existence of a heterogeneous population of reciprocal and selfish individuals, reputational incentives inevitably interact with reciprocity in these environments. Therefore, focusing on the question of how reciprocity and reputation interact in the enforcement of contracts is indispensable in understanding the impact of reputational incentives because reciprocal individuals’ behaviour may generate strong reputation incentives for the selfish individuals to meet their contractual obligations. Our main insights can be summarised as follows. Reputation formation strongly amplifies the positive effect of reciprocity on contract efficiency. The intuitive reason behind this finding is that the opportunity for reputation formation implies that selfish agents also have an incentive to behave as if they were reciprocal. By mimicking reciprocal behaviour, selfish agents make the principal believe that they are (at least potentially) reciprocal. Such a reputation is valuable for selfish agents because the principal only pays non‐competitive rents to agents who have not yet been identified as selfish. As a consequence, reputational incentives imply that a relatively small fraction of reciprocal agents suffices to generate large efficiency gains. In fact, reputation effects can be sufficiently strong to sustain very high levels of efficiency, even when reciprocal behaviour alone cannot prevent a market collapse. While reputation formation enhances efficiency, it also fundamentally alters the nature of interactions in competitive markets with moral hazard. The absence of third party enforcement of contracts give rise to a strong bilateralisation of trades, that is, a large share of all trades takes place in long‐term relations between trading partners in which reciprocity and reputation sustain high performance levels. In fact, we can show that bilateral relations prevail even when public information about agents’ past behaviour would provide adequate information for sustaining reputation incentives outside of such relations. One might conjecture that the strong bilateralisation of market interactions could foster rent‐sharing and the stickiness of prices with regard to supply and demand shocks because pairs of traders might develop social ties that render fairness concerns more prominent. However, we find the opposite to be true. Reputational incentives lead to a substantial reduction in price stickiness relative to a situation in which only reciprocity can enforce contracts. This finding enables us to identify a main source for sticky prices, namely the absence of third party contract enforcement and the resulting reliance on reciprocity as a contact enforcement device. Reputational incentives mitigate this price stickiness but they do not remove it completely: a substantial amount of price stickiness remains even in the presence of reputational incentives. The remainder of the article is structured as follows: Section 1 provides a short review of laboratory and field evidence on reciprocity as a contract enforcement device in one‐shot interactions. Section 2 documents how reputation formation amplifies the positive impact of reciprocity on contract efficiency and how it affects market interactions in a thorough way. Section 3 provides new evidence indicating that reputation significantly mitigates the price rigidity that is generated by the absence of third party enforcement of contracts. Section 4 concludes. 1. Reciprocity, Contract Enforcement and Price Rigidity Recognising how moral hazard problems affect the principals’ and the agents’ behaviour when neither explicit nor implicit (i.e., reputational) incentives are present is necessary for understanding the effects of reputation. Under these circumstances, reciprocity is the only remaining contract enforcement device. We thus provide a short review of the impact of reciprocity on contract enforcement and price rigidity, which sets the stage for studying the impact of reputation. A convenient tool for studying the impact of social preferences on contract enforcement and wage/price rigidity is the gift‐exchange game (Fehr et al., 1993). This game models a one‐shot transaction in which explicit incentives are absent and the agent’s performance (i.e. effort or product quality) is not legally enforceable. The most natural interpretations of this game are employment contracts in which the worker’s effort is not contractible, or sales contracts for experience goods, when inspection cannot determine quality. The structure of the game is as follows: the principal suggests a contract to the agent, specifying a fixed payment and a requested performance level. While the payment to the agent is enforceable, the agent’s performance is not. If the agent rejects the contract offer, he receives an outside option. If he accepts, he can choose his performance level independent of the requested level; higher performance generates higher revenues for the principal but also higher costs for the agent. The principal’s profit is equal to the revenue generated by the agent’s performance minus the fixed payment. The agent’s payoff, in turn, is calculated as the fixed payment minus the cost of his performance. The parameters of the cost and revenue function are usually chosen in such a way that the efficient outcome is achieved when the agent chooses the maximum performance level. If all players were purely self‐interested, a very inefficient outcome would result in this game. Since higher levels of performance are associated with higher costs, selfish agents are never willing to provide more than the minimum performance level. Rational principals anticipate this behaviour and offer a payment that compensates the worker for his outside‐option and the cost of the minimum performance level. However, if there is a sufficiently large share of reciprocal agents who are willing to reward high fixed payments with high performance, it may be profitable for the principal to pay the agent a rent. A large number of laboratory studies report evidence from one‐shot gift‐exchange experiments in which reputation formation cannot play a role (Fehr et al., 1993; Fehr and Falk, 1999; Gaechter and Falk, 2002; Hannan et al., 2002; Charness, 2004; Charness et al., 2004; Brown et al., 2004; List, 2006; Englmaier and Leider, 2008). The results of these papers can be summarised as follows: a non‐negligible share of agents choose non‐minimal performance levels when offered a payment that gives them a rent. Moreover, these reciprocal agents typically reward higher payments with higher performance. There are also many agents, however, who choose the minimal performance irrespective of the offered payment. On average, principals make payments that provide agents with a positive rent leading to downwards wage rigidity relative to the competitive wage level. However, due to the substantial share of selfish agents, many principals refrain from making payments high enough to induce maximum performance. As a consequence, average performance is usually significantly higher than the minimum, but still substantially lower than the efficient level.2 The gap between the efficient effort level and the actual effort provided in a simple gift exchange, in which only the agent can reciprocate, can be reduced if the principal is also given an opportunity to reciprocate (Fehr et al., 1997; Fehr et al., 2007). For example, if the principal can reward or punish the agent ex post in a one‐shot game, a significant increase in the effort level relative to the effort in a simple gift exchange can be achieved. This increase stems from the fact that reciprocal principals provide an incentive for selfish agents to provide non‐minimal performance. However, even if the principal can reciprocate, the agents’ average effort is typically still far from the first best level.3 While laboratory experiments have the great advantage of providing the researcher with a high degree of control, it is possible that findings identified in laboratory settings may not carry over to field environments. Fortunately, several researchers have addressed this question with field experiments implementing gift‐exchange situations in natural environments. In order to study gift exchange in the field, experimenters have exogenously manipulated the fixed wage paid to workers in natural work environments with a one‐shot character. The workers in these experiments perform tasks such as data entry (Gneezy and List, 2006; Kube et al., 2006; Englmaier and Leider, 2008), stuffing envelopes (Al‐Ubaydli et al., 2008), newspaper promotion (Cohn et al., 2007) and planting trees (Bellemare and Shearer, 2007). In general, these studies confirm the existence of reciprocal responses in the field. If the wage is cut relative to the promised or expected payment, the workers’ output decreases substantially (Kube et al., 2006), indicating the relevance of negative reciprocity in the field. Positive effects of wage increases on workers’ performance are also present in field settings. However, the average impact of a pure wage increase on effort has been small in several of the above mentioned studies; see Fehr et al. (2008) for a more detailed discussion. One reason why in several field studies the effect of wage increases is small may be that the fairness increasing effect of a wage increase is not transparent: workers are simply paid a higher wage relative to what they were told when hired but no explanation is given for the increase.4 The gift‐exchange hypothesis predicts that wage variations that are associated with fairness or kindness variations will lead to variations in performance; if wage variations do not affect workers’ fairness or kindness perceptions, no performance effect is predicted. Support for this view comes from Cohn et al. (2007) and Kube et al. (2008). Cohn et al. (2007) show that only those workers who view the previous wage as unfairly low respond significantly positive with their effort to a wage increase, while workers who perceived the previous wage as fair do not increase their effort level. Kube et al. (2008) show that workers who receive a non‐monetary gift in gift wrap paper, which renders the kindness of the gift salient, exhibit a large effort increase, while a surprise wage increase by the amount of the value of the gift leads only to a small effort increase. Taken together, the findings of laboratory and field experiments provide empirical support for the efficiency enhancing effect of reciprocity in situations of contractual incompleteness where principals face a moral hazard problem. However, in simple gift exchanges, in which only agents have a chance to reciprocate, the effects of monetary wage gifts on efficiency are not overwhelming. Moreover, this efficiency enhancing effect is associated with considerable downwards wage rigidity, i.e., rent payments to the workers. The question then is how reputational incentives affect efficiency, prices and trading patterns in an environment characterised by moral hazard that is already partially solved by reciprocal interactions between principals and agents. 2. Reputation – a Powerful Amplifier of the Efficiency Enhancing Effect of Reciprocity In real‐world markets with moral hazard, market participants often have the opportunity to transact repeatedly. If the same principals and agents interact repeatedly or if the principal has information about the agent’s behaviour in previous transactions with other principals, the principal can condition the current contract terms on the agent’s past behaviour. This may motivate the agent to perform, because if he satisfies the principal today, his future contract terms are more attractive. There is a large theoretical literature showing that these reputational forces may solve moral hazard problems even if all traders are completely selfish; see Klein et al. (1978) and Klein and Leffler (1981) for early discussions of this problem; later papers include Shapiro and Stiglitz (1984); Bull (1987); MacLeod and Malcomson (1989, 1998); Baker et al. (1994, 2002). However, we already know from dozens of laboratory experiments and from the recent wave of field experiments that not all agents are selfish. Thus, an empirical assessment of reputation incentives must take possible interactions between reciprocity and reputation into account. One way to study these interactions is to implement laboratory games with a finite time horizon. In some cases, a finite time horizon is an empirically realistic approximation of real world phenomena. For example, there is a mandatory retirement age in many countries, making the end of one’s employment relation is perfectly foreseeable. However, we use finitely repeated games in our context mainly as a work horse for studying interactions between reciprocal and selfish individuals because a commonly known final period enables us to identify the selfish individuals: selfish individuals will never provide non‐minimal performance levels in the final period. The seminal paper by Kreps et al. (1982) shows that the mere belief in the existence of reciprocal players may sustain cooperative play for a large number of periods in a finitely repeated prisoners’ dilemma game. Their argument begs the question where such a belief should come from. However, this becomes obvious in view of the strong evidence for the existence of reciprocal individuals. In the presence of reciprocal agents, selfish agents may have incentives to provide high performance if their principal treats them kindly. The reason is that such behaviour makes the principal believe that these agents are (at least potentially) reciprocal. Such a reputation is valuable for selfish agents because finite repetition implies that the principal only makes attractive offers to agents who have not yet been identified as selfish. This is due to the principal’s anticipation that selfish agents will always shirk in the final period. By backward induction, this expectation unravels all incentives to make kind offers in any period of the interaction. The presence of a share of reciprocal agents may motivate the principal to make a generous offer to an agent of unknown type even in the last period. If principals are willing to make generous offers, this implies that workers can earn rents. However, selfish agents need to hide their type and imitate the behaviour of reciprocal agents in order to have access to these rents. Since not only the truly reciprocal agents but the selfish ones as well are willing to perform in response to generous offers in non‐final periods, generous offers are then even more attractive to principals. In the following we show that reputational incentives indeed discipline the selfish types among the agents. Consequently, these incentives greatly increase the gains from trade and the frequency of trading between principals and agents in markets with moral hazard. 2.1. Reputation in Relational Contracts Brown et al. (2004) examine gift exchange in a laboratory market in which the parties can choose their trading partners. There are 7 principals and 10 agents. Each market participant can conclude a maximum of one contract per period so that there is an excess supply of agents. The matching between principals and agents takes place in a one‐sided continuous posted‐offer auction. Principals can make as many contract offers as they wish during a period, stipulating their payment and the desired performance. Moreover, principals can choose whether to make the contract offer public, in which case all market participants see the offer and any agent can accept. Alternatively, a contract offer can be made privately to one agent, who is the only person who can see and accept the offer. After an agent has accepted a contract offer, he chooses his performance. The experiment lasts 15 periods, which is common knowledge among participants. The main condition in this experiment is the incomplete contracts with fixed identities (ICF) treatment. In this treatment, contracts are not third‐party enforceable, i.e. the agent can freely choose his performance, irrespective of the principal’s requests in his contract offer. Also, all principals and agents have fixed identification numbers for the whole duration of the experiment. This feature enables principals and agents to engage in long‐term relationships. Moreover, it allows principals within these relationships to condition their contract offers on the agent’s past behaviour, so that reputation effects can emerge endogenously. The authors compare the outcome of this main treatment to two control treatments. In the incomplete contracts with random identities (ICR) treatment, everything is identical to the ICF except that subjects’ identification numbers are randomly reassigned in every period. Thus, reputation formation and relational contracting is ruled out in this treatment, and reciprocity is the sole contract enforcement device. The second control treatment is the complete contracts (C) treatment in which contracts are third‐party enforceable: agents must provide the performance desired by the principal in the accepted contract in this treatment. While identification numbers of market participants are fixed throughout the experiment and long‐term relationships are thus possible, they are not necessary to enforce performance. Figure 1(a) shows that reputation opportunities lead to a substantial increase in the average performance level. This effect is indicated by the large performance difference between the ICF and the ICR. In addition, the reputation effect is already significant in periods 1 and 2, consistent with the view that many subjects immediately understand the logic of reputational incentives. Figure 1(b) shows that reputational incentives indeed discipline selfish subjects. This Figure shows each agent’s average performance in periods 1–14 and in period 15. The selfish individuals chose the minimal performance of 1 in period 15 but many of them chose rather high performance levels in the non‐final periods, indicating the disciplining effect of reputational incentives. In contrast, the reciprocal subjects also chose high performance levels in the final period. In fact, their final period performance was sufficiently high to render the payment of rents in this period profitable for the principal. Fig. 1. Open in new tabDownload slide Endogenous Reputation Formation in Markets. (a) Reputation and Average Contract Efficiency over Time; (b) Performance of Selfish and Reciprocal Subjects in the Incomplete Contracts Treatment with Fixed Identities (ICF); (c) Cumulative Share of Trades in Relationships of Various Lengths
Notes. In the ICF treatment, contracts are not third party enforceable and long‐term relations (bilateral reputation building) are possible. Contracts in the ICR treatment are not third party enforceable, and long‐term relations are ruled out. Contracts are third party enforceable and long‐term relations are possible in the C treatment. Public reputation mechanisms are however common in many markets plagued by moral hazard. In the modified ICF treatment contracts are not third party enforceable and long‐term relations as well as public reputation building is possible. Fig. 1. Open in new tabDownload slide Endogenous Reputation Formation in Markets. (a) Reputation and Average Contract Efficiency over Time; (b) Performance of Selfish and Reciprocal Subjects in the Incomplete Contracts Treatment with Fixed Identities (ICF); (c) Cumulative Share of Trades in Relationships of Various Lengths
Notes. In the ICF treatment, contracts are not third party enforceable and long‐term relations (bilateral reputation building) are possible. Contracts in the ICR treatment are not third party enforceable, and long‐term relations are ruled out. Contracts are third party enforceable and long‐term relations are possible in the C treatment. Public reputation mechanisms are however common in many markets plagued by moral hazard. In the modified ICF treatment contracts are not third party enforceable and long‐term relations as well as public reputation building is possible. The principals disciplined the agents in the non‐final periods by practising a contingent renewal policy: If an agent provided high performance in period t, the principal offered him a new contract in t + 1. This contract was characterised by a high payment that implied a substantial rent for the agent. If an agent performed poorly, the principal offered him, with a very high probability, no contract at all in t + 1. In turn, many agents provided high performance as long as principals offered them contracts which involved substantial rents. The principals’ contingent renewal policy led to a considerable bilateralisation of market interactions because the principals frequently made private offers to their incumbents. Of the offers in the ICF 44% are private offers to the incumbent agent, while this only occurs in 10% of the cases in the C treatment, in which contract enforcement is exogenous. The differences in actual trades (accepted offers) are even more striking. Of actual trades in the ICF 52% are renewed contracts with the last‐period agent. In contrast, only 8% of trades in the C treatment are contract renewals and 76% of the trades are initiated by public offers. Thus, the principals’ contingent renewal policy in the ICF together with the associated performance increase led to long‐term relations. Figure 1(c) documents this by showing the cumulative share of trades that took place in relationships of various lengths. For example, while 90% of all trades in the C treatment took place in one‐shot or two‐shot interactions, 51% of all trades in the ICF occurred in relationships that lasted 4 or more periods. 2.2. Public Reputation in Relational Contracts The above evidence suggests that the provision of reputational incentives may fundamentally alter the nature of market interactions. If third parties enforce contracts, one‐shot interactions prevail and incumbent workers receive no special treatment, whereas information about past behaviour becomes important if a moral hazard problem exists, thus transforming competitive markets into bilateral trading islands. There is indeed a considerable body of field evidence for the prevalence of repeated bilateral interactions in many markets. Important examples are long‐term employment relationships (Hall, 1982; Auer and Cazes, 2000), lending relationships between banks and small businesses (Berger and Udell, 1995) and long‐term exchange relationships between providers and consumers of experience goods (Kollock, 1994). Unfortunately, however, the field evidence does not reveal whether these repeated interactions emerge due to potential moral hazard and the provision of reputational incentives. The problem is that distinguishing reputational incentive effects from other reasons for repeated interaction, such as transaction costs of switching or insurance considerations (Azariadis 1975), is very difficult in the available field data. The laboratory experiments solve this problem, thus providing evidence that contracting problems cause repeated bilateral trading. However, the bilateralisation of market interactions observed in Brown et al. (2004) may be a consequence of the fact that the agents could only acquire reputation in a bilateral interaction with a principal. Principals in this experiment only observed ‘their’ agents’ past performance but not that of the other agents in the market, rendering the acquisition of a public reputation impossible. While public reputation plays little or no role at all in many labour and service markets, there are also markets where agents can acquire a public reputation. Public reputation mechanisms may be institutionalised – such as credit bureaus in credit markets – or they may arise informally – such as reference letters in the labour market. The question therefore arises whether the addition of public reputation removes or diminishes the bilateralisation of market interactions. Falk et al. (2004) addressed this question by adding a public reputation formation opportunity to the ICF treatment described above. All principals could observe all past wage and effort levels of all agents in the market in this modified ICF treatment. The authors observe that public reputation opportunities indeed reduce the bilateralisation of the market somewhat because the percentage of trades that takes place in long‐term relations is significantly higher in the ICF than in the treatment with public reputation. However, public reputation has a surprisingly small effect because a large number of trades still take place in bilateral, long‐term relations. This fact becomes transparent in Figure 1(c)if one compares the C treatment with the modified ICF treatment with public reputation. While roughly 40% of all trades in the public reputation treatment take place in relationships lasting 4 or more periods, almost all interactions in the C treatment occur in one or two‐shot interactions. Thus, despite the fact that public reputation somewhat crowds out relational contracting, the principals still rely on contingent contract renewal of relational contracts as a discipline device to a large extent. The addition of public reputation to the ICF also leads to an increase in performance, bringing it closer to its efficient level. In fact, the agents’ average performance for an extended number of periods (period 7–13) is roughly 9 (on a scale between 1–10), only one unit below the efficient level. In particular, public reputation increases performance levels in case of lower wage offers, rendering the principal less dependent on reciprocity as a contract enforcement device.5 2.3. Competition and Relational Contracts The threat of firing in case of low performance disciplines selfish agents in Brown et al. (2004); those who are fired face the risk of unemployment due to the excess supply of agents. What happens, however, if there is no risk of unemployment because there is an excess demand for agents? Are relational contracts that enforce high performance still possible in this environment, and if so, what are the terms of these contracts? How can selfish agents be disciplined if finding another principal who hires them is easy? Models of labour and credit markets (Carmichael, 1984; MacLeod and Malcomson 1998; Boot and Thakor 1994) show that relational contracts can, in principle, sustain high performance by agents even when these are in high demand. In order to do so, however, incumbent principals must offer contracts which involve quasi‐rents for agents: Once the agents are in a relationship with a principal, the future value of this relationship must be higher than potential value of switching to an ‘outside’ principal. In a recent paper, Brown et al. (2008) examine the principals’ performance enforcement strategies when there is strong competition for agents’ services. They modify their experiment from 2004 by implementing an excess demand for agents (10 principals and 7 agents). In the following we call this the high‐demand market, and refer to their 2004 experiment as the low‐demand market. The results of Brown et al. (2008) show that principals’ contract offers also provide reputational incentives for selfish players when there is an excess demand for agents. Those agents who provide high effort receive a wage offer in the next period from their incumbant principal which exceeds the wages they could get from outside principals in the market. In this way, principals in the high‐demand market reward high performance. As a result, the agents’ mean performance in the ICF treatment is significantly higher than in the ICR treatment of the high‐demand market (see Figure 2). Fig. 2. Open in new tabDownload slide Reputation and Reciprocity Effects on Performance under Excess Demand and Supply
Note.‘Low demand’ indicates excess supply of agents. ‘High demand’ indicates excess demand for agents. Only reciprocity can enforce contracts in the ICR treatments. Both reciprocity and reputational incentives, as well as their interaction, can enforce contracts in the ICF treatments. Fig. 2. Open in new tabDownload slide Reputation and Reciprocity Effects on Performance under Excess Demand and Supply
Note.‘Low demand’ indicates excess supply of agents. ‘High demand’ indicates excess demand for agents. Only reciprocity can enforce contracts in the ICR treatments. Both reciprocity and reputational incentives, as well as their interaction, can enforce contracts in the ICF treatments. However, the excess demand for agents leads to a lower incidence of long‐term relations. For example, relationships exceeding 6 periods are substantially less frequent in the market with high‐demand (24% of all trades) than in the market with low‐demand (45% of all trades). This suggests that strong competition for agents makes sustaining long‐term relations more difficult, as agents are more likely to abandon their incumbent principal. This conjecture is confirmed by comparing the break‐up of relationships in the ICF treatment under both market conditions. In the market with a high‐demand, principals are equally likely to make a renewed contract offer to their last‐period agent as in the market with low‐demand (80%). However, while agents only reject 2% of these offers in the market with low‐demand, 28% were rejected in the market with high‐demand. Does the lower frequency of long‐term relations in the market with high‐demand reduce agents’ performance relative to the market with low‐demand? Surprisingly, it does not. The agents’ mean performance by period evolves almost identically under both market conditions (compare ICF high‐demand with ICF low‐demand in Figure 2), leading to almost the same average performance under high‐demand (6.7) as under low‐demand (6.9). The identical performance in the two conditions, despite a lower incidence of long‐term relations in the high‐demand condition, is somewhat puzzling. There are two explanations for this finding: First, due to stronger competition for agents, wages are substantially higher under high‐demand than under low‐demand which induces higher performance by reciprocal agents (see Section 3 for a detailed discussion of wages in the high‐demand and low‐demand conditions). Thus in the market with high‐demand, reciprocity in combination with higher wages may play a larger role in performance provision. Support for the larger role of reciprocity under high‐demand is provided in Figure 2, which shows that mean performance is substantially higher in the high‐demand condition of the ICR than in the low‐demand condition of the ICR. Second, the authors find that in the high‐demand market reputational incentives are still strong in many relationships which break off early. As discussed above, many relationships in the high‐demand market are broken off by the agents after they have performed well and received a renewed contract offer. This suggests that agents provide a high level of effort for their current principal because the expected payments from ‘outside’ principals are lower than those of their current one. However, once in a while, outside principals make high wage offers which lure agents away from their current relationship. Indeed, the authors find that in the majority of cases (74%) in which relationships are broken off by the agent, the agent had received an outside offer which was at least as high as that of his current principal. Since agents sometimes terminate ongoing high performance relations after the arrival of a high outside offer in the high‐demand treatment, average performance in short‐ and medium‐term relations is substantially higher than in the low‐demand treatment where relationships are mostly broken off by unsatisfied principals. 2.4. Reputation Effects When Reciprocity Alone Fails In the previous subsections, we reported evidence showing that reputation formation amplifies the positive impact of reciprocity on agents’ performance levels. However, two important features facilitate contract enforcement in the previously reported experiments. First, the parameters of the experiments were chosen in such a way that the typically prevailing share of reciprocal subjects (40–60%) renders trading in a one‐shot environment viable. Thus, almost all feasible trades took place even in the absence of any reputational incentives, i.e., non‐minimal performance levels could be attributed to reciprocity alone. This raises the question of the effects of reputational incentives when reciprocity alone is too weak to maintain trading. Second, the principals in the previous subsections had perfect information about the incumbent agents’ past effort in the relationship. Thus, if an agent provided low effort, there was no ambiguity in interpreting this event: the agent did not want to provide a higher effort, providing a good signal about the agents’ type. However, random exogenous events may, in reality, be responsible for a low output. If the principal can only directly observe an agent’s output, but not his effort per se, low output ceases to be a precise indicator of low effort. Low output may then indicate bad luck or low effort; this ambiguity may mitigate the power of contingent renewal policies because future rewards can only be made contingent on a random output measure. In theory, reputational equilibria with high performance can also be sustained if principals cannot observe the agent’s effort perfectly and reciprocity alone fails to enable trade (Kreps and Wilson, 1982; Kreps et al., 1982; Camerer and Weigelt, 1988; Diamond, 1989; Brown and Zehnder, 2007; Fehr and Zehnder, 2008). However, little is known empirically about the impact of reputational incentives on contract offers and trading frequency in such a ‘hostile’ environment. Fehr and Zehnder (2008) conducted a credit market experiment which implements both features mentioned above. Two sources of moral hazard coexist in their credit market. First, the lender cannot observe the borrower’s project choice and, therefore, borrowers may choose inefficient high risk projects. Second, the absence of legal enforcement of repayments implies that borrowers may withhold their repayment even if they successfully realised their projects. The experimental credit market consists of 17 participants. Seven participants are lenders, the other ten are borrowers. Each borrower can realise one of two projects in each of the 20 periods: an efficient low risk project or an inefficient high risk project. Borrowers have no equity and need external funding from a lender to realise a project. Lenders can make as many contract offers as they wish in a one‐sided continuous posted‐offer auction. While the loan size is exogenously fixed, a contract offer determines the desired project and a desired repayment in case of project success. Contract offers can be public (every borrower can accept) or private (only a specific borrower can accept). Each lender and each borrower can conclude a maximum of one contract per period. Borrowers who have obtained credit can realise either the inefficient high‐risk project or the efficient low risk project; a random device determines whether the project is a success or a failure. Both the project choice and the realised project return are private information to the borrower. In case of a project failure, the project’s return is zero and the borrower cannot make a repayment. If the project turns out to be successful, the borrower is able the make a repayment up to the level of the project return. In the main treatment of Fehr and Zehnder (2008), lenders and borrowers have fixed identification numbers, enabling lenders to establish long‐term relationships with specific borrowers if they want to. Since this treatment is similar to the treatments with incomplete contracts and fixed identities in Brown et al. (2004, 2008) we also label it ICF. In the control treatment intentionally repeated interactions are excluded by randomly reassigning ID numbers at the beginning of every period – accordingly we call this treatment ICR. The more realistic setup, with stochastic outcomes and asymmetric information, makes reputation formation in the ICF treatment of this experiment much more difficult than in the experiments reported above. Since lenders can neither observe the project choice nor its outcome, they do not know whether a defaulting borrower is unable (because the project failed) or unwilling to repay his credit. Even an honest borrower who intends to repay and who chooses the efficient, low‐risk project may face a project failure, making him unable to repay his debt. The lender can therefore never know with certainty whether he faced an opportunistic borrower who did not intend to repay his debt or whether the borrower had just bad luck. The experimental results indicate that individual reputation formation in long‐term relations is still a powerful contract enforcement device even if the informational conditions make acquiring a good reputation very difficult. The lack of repayment incentives leads to a breakdown of trading in the credit market in the ICR, where reputation formation opportunities are absent. Although a considerable fraction of (reciprocal) borrowers repay credits, trading is, on average, not profitable for lenders. Figure 3 shows the fraction of realised contracts over time. While almost all lenders enter the credit market in the beginning, there is already a sharp decline in market trading in period 4 in the ICR. After period 4, trading gradually decreases until the frequency of market trading becomes very low. In the final period, only 17% of the feasible contracts are concluded. In contrast, a stable credit market emerges in the ICF where reputation formation is possible and borrowers can acquire a reputation. Figure 3 indicates that at least 74% of the available trades take place in each of the first 19 periods. Overall, 81% of the available contracts are concluded. In this treatment, lenders establish long‐term relations and condition future credit offers on the borrower’s past repayment behaviour so that the borrowers face incentives to choose the efficient low risk project and to repay their debt. As in Brown et al. (2004), this leads to a bilateralisation of the market: the majority of trades are concluded by pairs who interact at least five times with each other. Thus, reputation formation in endogenously formed long‐term credit relations strongly alleviates the double moral hazard problem in the credit market and allows for mutually beneficial trades between lenders and borrowers. Fig. 3. Open in new tabDownload slide Relational Contracts when Reciprocity Fails
Note. Long‐term relations between lenders and borrowers are possible in the ICF treatment, while long‐term relations are ruled out in the ICR treatment. In both treatments, a lender faces the same two moral hazard problems: choice of inefficient high risk projects and lack of credit repayment in case of project success. Fig. 3. Open in new tabDownload slide Relational Contracts when Reciprocity Fails
Note. Long‐term relations between lenders and borrowers are possible in the ICF treatment, while long‐term relations are ruled out in the ICR treatment. In both treatments, a lender faces the same two moral hazard problems: choice of inefficient high risk projects and lack of credit repayment in case of project success. 3. The Impact of Reputational Incentives on Price Rigidity A considerable body of evidence indicates that prices in goods markets (Blinder, 1991; Cechetti, 1986; Carlton, 1986), credit markets (Hannan and Berger, 1991; Neumark and Sharpe, 1992) and, particularly in labour markets, are rigid (Blinder and Choi, 1990; Akerlof et al., 1996; Altonji and Devereux, 2000; Smith, 2000; Nickell and Quintini, 2003; Fehr and Goette, 2005, Dickens et al., 2007). While there are many different explanations for price and wage rigidity in the literature, such as risk aversion (Azariadis, 1975), transaction costs (Mankiw, 1985; Salop, 1979), or imperfect information (Lucas, 1972), reciprocity has been suggested as one important source of rigidity in markets characterised by moral hazard (Akerlof and Yellen, 1990). The evidence from competitive gift‐exchange markets discussed in Section 1 confirms that subjects in the role of employees are typically paid substantially more than their reservation wages, implying that wage levels do not converge to competitive levels. In addition to the level rigidity of prices and wages identified in those papers, there is also another interesting type of rigidity: how wages and prices respond to shocks to supply and demand. Brandts and Charness (2004) suggest that such shocks exert little influence on prices in one‐shot gift‐exchange markets where reciprocity alone enforces agents performance. Does relational contracting, i.e. the provision of reputation incentives in bilateral repeated trades, strengthen or weaken wage and price rigidity? Repeated game models of labour markets (Shapiro and Stiglitz, 1984; MacLeod and Malcolmson, 1989, 1998) show that relational contracting may lead to the payment of non‐competitive rents in bilateral relationships. However, these models of relational contracting exhibit multiple equilibria which makes it impossible to predict how high these rents will be. Thus theory cannot tell us whether rents paid in relationships will be higher or lower than those which would prevail if repeated interaction were not feasible, and reciprocity alone would drive contract enforcement. The multiplicity of equilibria also makes it impossible to predict how market interactions and prices respond to exogenous shocks because for any set of exogenous parameters there exist many different equilibria with different behaviours and prices. The data in Brown et al. (2004, 2008) enable us to examine the role of reputational incentives in price rigidity. Their data allow us to study prices when reputation and reciprocity affect market outcome (ICF treatment), and compare these to prices when reciprocity alone affects the outcome (ICR treatment) or when contracts are third‐party enforced (C treatment). Moreover, we can study price variation across market conditions in each of these treatments by comparing prices under high‐demand (10 principals and 7 agents) and low‐demand (7 principals and 10 agents). As we showed above, mean performance levels differ strongly across these treatments. When we compare prices, and price rigidity, across treatments it is therefore important to account for different performance levels. What we are interested in, after all, is how much a principal must pay for a given (or expected) performance level. In the following we therefore compare prices paid for a given performance level.6Figure 4 displays the mean prices paid for performance levels 6–10 in each treatment.7 Fig. 4. Open in new tabDownload slide The Impact of Reciprocity and Reputation on Price Rigidity
Note.‘low demand’ indicates excess supply of agents. ‘high demand’ indicates excess demand for agents. Neither reciprocity nor reputation is needed for contract enforcement in the C treatments. In the ICR treatments, only reciprocity can enforce contracts. Both reciprocity and reputational incentives, as well as their interaction, can enforce contracts in the ICF treatments. Fig. 4. Open in new tabDownload slide The Impact of Reciprocity and Reputation on Price Rigidity
Note.‘low demand’ indicates excess supply of agents. ‘high demand’ indicates excess demand for agents. Neither reciprocity nor reputation is needed for contract enforcement in the C treatments. In the ICR treatments, only reciprocity can enforce contracts. Both reciprocity and reputational incentives, as well as their interaction, can enforce contracts in the ICF treatments. The Figure shows that prices respond strongly to supply and demand changes under third party enforcement (C treatments). At all performance levels prices are much higher in the high‐demand condition and at the most frequent performance level of 10 the price in the high‐demand condition is more than 40 units higher than in the low demand condition. Prices are much less responsive to changes in supply and demand in the ICR, indicating a remarkable degree of price stickiness in this environment and corroborating the results in Brandts and Charness (2004). Moreover, almost all interactions are one‐shot in the C treatments and all interactions are one‐shot by design in the ICR treatment. Therefore, the difference between the C and the ICR treatment cannot be due to differences in the duration of interactions within pairs but must, instead, be due to the absence of third party enforcement and the resulting reliance on reciprocity as a contract enforcement device. How does the introduction of reputational incentives in an environment without third party enforcement change the responsiveness of prices to shocks? Figure 4 shows that reputational incentives in the ICF increase the flexibility of prices considerably compared to the near absence of flexibility in the ICR condition. The formal tests reported in column 1 of Table 1 also support this result. The OLS regression shows that the price difference between excess demand and excess supply is roughly 10 units lower in the ICR treatment than in the ICF treatment. However, Figure 4 and Table 1 also show that reputational incentives do not completely restore price flexibility because price differences between high‐ and low‐demand condition are roughly 13 units larger in the C treatment than in the ICF treatment. Table 1 
Determinants of Price Rigidity . Price difference between low and high demand condition . Price in low demand condition . Price in high demand condition . Price in high and low demand condition . Effort −1.522 4.554 2.407 4.554 [0.649]** [0.205]*** [0.328]*** [0.201]*** C treatment 13.368 −17.895 11.341 −17.895 [4.547]*** [1.906]*** [2.495]*** [1.870]*** ICR treatment −9.717 0.412 −8.423 0.412 [4.031]** [1.428] [2.656]*** [1.400] High demand 29.453 [3.168]*** Effort × High demand −2.147 [0.380]*** C × High demand 29.235 [3.085]*** ICR × High demand −8.835 [2.964]*** Constant 26.553 8.681 38.134 8.681 [4.567]*** [1.449]*** [2.878]*** [1.422]*** Observations 27 1,459 1,561 3,020 R‐squared 0.54 0.61 0.64 0.74 Clustered at session level no yes yes yes . Price difference between low and high demand condition . Price in low demand condition . Price in high demand condition . Price in high and low demand condition . Effort −1.522 4.554 2.407 4.554 [0.649]** [0.205]*** [0.328]*** [0.201]*** C treatment 13.368 −17.895 11.341 −17.895 [4.547]*** [1.906]*** [2.495]*** [1.870]*** ICR treatment −9.717 0.412 −8.423 0.412 [4.031]** [1.428] [2.656]*** [1.400] High demand 29.453 [3.168]*** Effort × High demand −2.147 [0.380]*** C × High demand 29.235 [3.085]*** ICR × High demand −8.835 [2.964]*** Constant 26.553 8.681 38.134 8.681 [4.567]*** [1.449]*** [2.878]*** [1.422]*** Observations 27 1,459 1,561 3,020 R‐squared 0.54 0.61 0.64 0.74 Clustered at session level no yes yes yes Note. Column (1) shows an OLS regression of price differences between the low‐ and high‐demand conditions across the ICR, the ICF and the C treatment. The dependent variable is the mean price difference between the high‐demand and low‐demand conditions per effort level and treatment. Columns (2) and (3) show OLS regressions of prices in individual contracts on the C and the ICR treatments, with the ICF treatment as the omitted category. In the OLS regressions of column (4) individual prices in both the high and the low demand condition are the dependent variable and the ICF treatment in the low demand condition is the omitted category. Robust standard errors are in brackets in all regressions. ** indicates significance at the 5% level, *** at the 1% level. Open in new tab Table 1 
Determinants of Price Rigidity . Price difference between low and high demand condition . Price in low demand condition . Price in high demand condition . Price in high and low demand condition . Effort −1.522 4.554 2.407 4.554 [0.649]** [0.205]*** [0.328]*** [0.201]*** C treatment 13.368 −17.895 11.341 −17.895 [4.547]*** [1.906]*** [2.495]*** [1.870]*** ICR treatment −9.717 0.412 −8.423 0.412 [4.031]** [1.428] [2.656]*** [1.400] High demand 29.453 [3.168]*** Effort × High demand −2.147 [0.380]*** C × High demand 29.235 [3.085]*** ICR × High demand −8.835 [2.964]*** Constant 26.553 8.681 38.134 8.681 [4.567]*** [1.449]*** [2.878]*** [1.422]*** Observations 27 1,459 1,561 3,020 R‐squared 0.54 0.61 0.64 0.74 Clustered at session level no yes yes yes . Price difference between low and high demand condition . Price in low demand condition . Price in high demand condition . Price in high and low demand condition . Effort −1.522 4.554 2.407 4.554 [0.649]** [0.205]*** [0.328]*** [0.201]*** C treatment 13.368 −17.895 11.341 −17.895 [4.547]*** [1.906]*** [2.495]*** [1.870]*** ICR treatment −9.717 0.412 −8.423 0.412 [4.031]** [1.428] [2.656]*** [1.400] High demand 29.453 [3.168]*** Effort × High demand −2.147 [0.380]*** C × High demand 29.235 [3.085]*** ICR × High demand −8.835 [2.964]*** Constant 26.553 8.681 38.134 8.681 [4.567]*** [1.449]*** [2.878]*** [1.422]*** Observations 27 1,459 1,561 3,020 R‐squared 0.54 0.61 0.64 0.74 Clustered at session level no yes yes yes Note. Column (1) shows an OLS regression of price differences between the low‐ and high‐demand conditions across the ICR, the ICF and the C treatment. The dependent variable is the mean price difference between the high‐demand and low‐demand conditions per effort level and treatment. Columns (2) and (3) show OLS regressions of prices in individual contracts on the C and the ICR treatments, with the ICF treatment as the omitted category. In the OLS regressions of column (4) individual prices in both the high and the low demand condition are the dependent variable and the ICF treatment in the low demand condition is the omitted category. Robust standard errors are in brackets in all regressions. ** indicates significance at the 5% level, *** at the 1% level. Open in new tab Why do reputational incentives alleviate price stickiness? Reputation incentives may weaken downward price rigidity because they partially disburden prices from their function of motivating agents. Generous fixed payments are the only way to induce (reciprocal) agents to provide non‐minimal performance in a one‐shot gift‐exchange environment. In a setting with repeated interactions, selfish (and reciprocal) agents are concerned about the consequences of their current behaviour for their future earnings. In this environment, it is possible to motivate the performance of selfish (and reciprocal) agents with less generous fixed payments. Figure 4 informs us about how the downward rigidity of prices is influenced by reputation incentives. The prices in the C condition provide us with information about what prices the principals have to pay under competitive conditions with third party enforcement of contracts. Thus, by comparing prices in the C condition with those in the ICF and the ICR conditions, we can compute the rents paid in the latter two conditions. The agents in the ICR earn a considerable rent when there is a low demand for them. They receive prices that are roughly 17 units higher in the ICR than in the C treatment – a difference that is highly significant according to column 2 in Table 1. Prices are lower at any given performance level in the ICF treatment than in the ICR treatment. However, this price difference is small and insignificant (see ICR coefficient in column 2 of Table 1). Reputation incentives may also affect upward price rigidity in markets characterised by moral hazard problems. If principals in a one‐shot situation expect that only some agents behave reciprocally, the expected performance of agents is lower for any price offer compared to a situation in which contracts are enforceable. Therefore, the principals in the ICR will offer lower prices for any desired effort level compared to principals in the C treatment. The lower performance expectation in the ICR constrains the impact of competition for agents on agents’ wages. In the ICF reputation incentives increase the expected performance relative to the ICR and thus allow principals to compete more vigorously for agents by offering higher prices. However, as reputation incentives do not lead to perfect contract enforcement, the expected performance in the ICF is still lower than in the C treatment for any desired performance level. As a consequence, firms in the ICF are less willing to bid up prices in the high‐demand condition, implying a certain amount of upwards price rigidity relative to the C treatment. Figure 4 and column 3 of Table 1 document the upwards rigidity of prices in the high demand condition: In the ICF and ICR conditions wages are significantly lower than in C condition. In addition, prices in the ICF are significantly higher than in the ICR for each effort level. Comparing the first three columns of Table 1 there seems to be an interesting asymmetry in the effect of reputational incentives on price rigidity: in the high‐demand condition prices in the ICF are substantially and significantly higher than in the ICR while in the low‐demand condition prices in the ICF are almost identical to those in the ICR. Indeed, the coefficients of ICR in these columns suggest that the lower price responsiveness across demand conditions in the ICR compared to the ICF (9.7 points, see column 1) is mainly driven by reduced upward price rigidity in the high‐demand condition of the ICF (8.4 points, see column 3). This finding is confirmed in a pooled analysis of all six treatments reported in the final column of the Table. In this regression, the ICF condition of the low‐demand condition is the omitted category. Therefore, the ICR term captures the difference in prices between the ICR and ICF treatments for the low‐demand condition, which is identical to the corresponding coefficient in regression (2). As this coefficient is close to zero and insignificant we can conclude that the ICF does not alleviate downwards wage rigidity in the low‐demand condition. The coefficient for High demand measures the price increase in the ICF treatment relative to the low demand condition. The negative interaction term ICR × High demand indicates that the impact of the high‐demand condition (relative to the low‐demand condition) is significantly lower in the ICR relative to the ICF condition, i.e., the high‐demand condition raises prices considerably less in the ICR. This result suggests that the increased responsiveness of prices to demand shocks in the ICF (relative to the ICR) is mainly due to the higher average performance under reputational incentives which enables the principals to compete more strongly for scarce agents by offering them higher wages. 4. Summary and Conclusions We examine the impact of reputational incentives on contract enforcement, the terms of trade and trading patterns in competitive markets with moral hazard. The evidence indicates that reputation formation strongly amplifies the positive effect of reciprocity on contract efficiency. The opportunity for reputation formation gives selfish agents an incentive to mimic the reciprocal agents’ behaviour in order to improve the future contract offers they may receive from principals. As a consequence, reputation effects can be sufficiently strong to sustain high levels of efficiency, even when reciprocal behaviour alone cannot prevent a collapse of trading. While reputation formation does enhance efficiency, it also fundamentally alters the nature of market interaction. Long‐term trading in bilateral pairs replaces one‐shot interactions when third party enforcement of contracts is absent and reputation is a key force of enforcing contracts. In fact, bilateral relations play an important role in our experimental markets even if a public reputation can be acquired. Interestingly, we find that the bilateralisation of the market through relational contracting increases the responsiveness of prices to changes in supply and demand. We are able to identify the absence of third party enforcement and the subsequent reliance on reciprocity as an enforcement device as the key force behind the unresponsiveness of prices to shocks. Relational contracting increases price flexibility predominately by rendering the principals more willing to compete for scarce agents, that is, by alleviation upwards price rigidity. Our findings are a first step in understanding the relevance of relational contracts for price formation in labour, goods and credit markets. Future studies should disentangle the impact of contract enforcement problems on price rigidity from the role of alternative causes such as transaction costs, insurance considerations, imperfect information or imperfect competition. Moreover, field studies should examine whether the observed impact of moral hazard on wage rigidity in the labour market, is comparable to its impact on prices in goods markets and interest rates in credit markets. Understanding whether the rigidity of prices and interest rates are driven by imperfect competition or transaction costs, or are the result of inherent contract enforcement problems is not only of academic interest, but also of key importance to policy makers in central banks and to competition authorities. Footnotes 1 " The interested reader may consult reviews such as Fehr and Fischbacher (2002), chapter 3 of Camerer (2003) or the recent survey of Fehr et al. (2008). 2 " An illustrative example is the one‐shot condition in Brown et al. (2004), where the performance levels could be chosen on a scale from 1 to 10. While 10 would be the efficient level, the average performance ends up at a level of 3.3. 3 " In Fehr et al., (2007), for example, the principals have the option of paying a bonus ex post, that is, after observing the agents’ effort. The first best effort level is 10 (on a scale from 1 to 10) but the agents’ average effort is 5.2. 4 " Therefore, employees may come up with many different interpretations for why they are paid more than expected. Some may believe that the employers’ ability to pay is high enough. Others may believe that the initial wage promise was mistakenly low. Still others’ may self‐servingly attribute the wage increase as a reward for their ability. In all these cases, workers have no reason to believe that the wage increase constitutes a kind act and, therefore, the gift‐exchange hypothesis does not predict that effort should rise in these cases. 5 " Brown and Zehnder (2007) examine the impact of institutionalised information sharing between lenders on the behaviour of borrowers in the credit market. They find that in the absence of the possibility for repeated interaction, information sharing between lenders generates substantial reputation incentives for selfish borrowers to repay loans. When relationship formation is possible, they confirm the findings of Brown et al. (2004) and Falk et al. (2004). Bilateral relationships themselves motivate repayment, so that information sharing has little additional impact on borrower behaviour. Again, public information sharing only slightly reduces the formation of bilateral long‐term relationships. 6 " In the ICF and ICR treatments the principals were asked, after a contract was accepted, which effort level they expected from the agent. We replicated our analysis of price rigidity in Figure 4 and Table 1 controlling for this ‘expected’ performance rather than actual performance and observed qualitatively identical results. This is not surprising because actual performance levels and expected performance levels are highly correlated. 7 " There are almost no observations at performance levels below 6 in the C treatment, making a reliable comparison with the other treatments at these performance levels impossible. 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Cogley,, Timothy;Sargent, Thomas, J.

doi: 10.1111/j.1468-0297.2008.02237.xpmid: N/A

Abstract We study prices and allocations in a complete‐markets, pure‐exchange economy in which there are two types of agents with different priors over infinite sequences of the aggregate endowment. Aggregate consumption growth evolves exogenously according to a two‐state Markov process. The economy has two types of agents, one that learns about transition probabilities and another that knows them. We examine allocations, the market price of risk and the rate at which asset prices converge to values that would be computed under the assumption that all agents know the transition probabilities. Cogley and Sargent (2008) showed that market prices of risk would be high in an economy with a risk‐neutral Bayesian representative agent who learns about the parameters of a transition matrix for aggregate consumption growth starting with a pessimistic prior in 1933.1 This article studies the robustness of that finding to a perturbation that adds a small fraction of agents who know the parameters of the transition matrix. Traders participate in a Walrasian equilibrium in which they do not infer information from prices (Grossman, 1981).2,3 Under what we assume to be the true data‐generating mechanism, the survival‐of‐the‐fittest force analysed by Blume and Easley (2006) causes the more knowledgeable agents’ influence on equilibrium prices to grow over time along with their wealth. We study how quickly that dissipates the effects of the initial pessimism of the less informed agents on equilibrium prices.4 To give the survival mechanism a large scope to moderate the effects of initial pessimism, we assume complete markets that allow agents to make trades of claims to wealth that are motivated solely by the different subjective probabilities they put on future states. That gives the agents many opportunities to place bets that over time stochastically increase the share of wealth of the traders who know transition probabilities. We solve a Pareto problem to compute competitive equilibrium prices and allocations, thereby implicitly defining an initial allocation of wealth. We study how the market price of risk evolves as a function of the relative Pareto weight on the better‐informed agent. Among other things, we want to know how large the Pareto weight on the better‐informed agent has to be in order to eradicate the effects of the initial pessimism that Cogley and Sargent (2008) attributed to a representative agent. Because we specify the data‐generating mechanism and agents’ beliefs so that the truth is in the support of both agents’ beliefs, the survival analysis of Blume and Easley (2006) lets both types of agents have positive wealth in the limit. However, the agents’ ultimate shares of aggregate consumption are random variables that depend on the history of the growth rate of aggregate consumption. We calculate probability distributions of these shares for various horizons.5 1. The Model The aggregate endowment process is the same as in Cogley and Sargent (2008). The two types of agents have identical one‐period utility functions but different priors that imply different beliefs about histories of aggregate growth rates. Agent 1 uses Bayes’ law to learn about transition probabilities. Bayes’ law induces a different probability measure over histories of aggregate consumption growth rates for agent 1 than is believed by agent 2, who knows the true transition probabilities from the outset. Agents take prices as given and trade history‐contingent claims to consumption for all finite histories. 1.1. The Endowment Process, Beliefs and Trading Opportunities The consumption good arrives exogenously and is non‐storable, so all current‐period output is consumed immediately. Realisations for gross consumption growth follow a two‐state Markov process with high and low growth states, denoted and respectively. The Markov chain has a transition matrix F, where We let gt = [gt,gt−1,…,g0] denote a history of aggregate growth rates. At time t ≥ 0, agents of both types have the information set gt. The two types of agents begin with different priors in the form of joint densities over (F, g∞). The marginal distribution over F for the type 1 agent who learns is non‐trivial and includes in its support the true F that actually governs the data. For the type 2 agent, the marginal distribution over F is concentrated on the true F.6 1.2. Walrasian Versus Rational Expectations Equilibrium We study a complete markets economy with time 0 trading of a complete set of claims to consumption contingent on finite histories gt for all t ≥ 0. We study what Grossman (1981) calls a Walrasian equilibrium, in which traders take prices as given and do not infer information from prices. We put individuals in a setting in which the only information revealed by prices is subjective probabilities of future gs. We do this by assuming that agents have different priors over g∞ and common information sets, and not a common prior with different information sets.7 If we had made a different assumption about agents’ beliefs, it would be have been appropriate to study an equilibrium in which traders do extract information from observed prices, what Grossman (1981) calls a rational expectations equilibrium.8 In particular, we could have started our two types of agents with a common prior over (F, g∞, s), where s is a signal that the type 2 agent but not the type 1 agent receives at time 0. We could let the signal reveal the value of F and assume that while a type 1 consumer observes gt and equilibrium prices at t ≥ 0, a type 2 agent observes s as well as gt and equilibrium prices. Under these assumptions about priors and information, rational‐expectations equilibrium prices would immediately reveal s to the type 1 agents, and the two types of agents would have a common posterior over (g∞, F) (Milgrom and Stokey, 1982). In that case, the pessimism of the type 1 agent would completely evaporate at time 0.9 Since we are interested in continuing effects of gradual learning, we chose our Walrasian specification to keep learning alive. 1.3. Calibration We calibrate F from estimates reported by Cecchetti et al. (2000) who estimated a hidden Markov model for aggregate consumption growth, (1) where st is an indicator variable that records whether consumption growth is high or low and ɛt is an identically and independently distributed normal random variable with mean 0 and variance They estimated the model by maximum likelihood using data on annual per capita US consumption for the period 1890–1994. We reproduce their results in Table 1. Table 1 
Maximum Likelihood Estimates of the Consumption Process (Cecchetti et al., 2000) . Fhh . Fll . μh . μl . σ . Estimate 0.978 0.515 2.251 −6.785 3.127 Standard Error 0.019 0.264 0.328 1.885 0.241 . Fhh . Fll . μh . μl . σ . Estimate 0.978 0.515 2.251 −6.785 3.127 Standard Error 0.019 0.264 0.328 1.885 0.241 Open in new tab Table 1 
Maximum Likelihood Estimates of the Consumption Process (Cecchetti et al., 2000) . Fhh . Fll . μh . μl . σ . Estimate 0.978 0.515 2.251 −6.785 3.127 Standard Error 0.019 0.264 0.328 1.885 0.241 . Fhh . Fll . μh . μl . σ . Estimate 0.978 0.515 2.251 −6.785 3.127 Standard Error 0.019 0.264 0.328 1.885 0.241 Open in new tab The high‐growth state is persistent, and the economy spends most of its time there. Contractions are more severe than typical post‐WWII recessions, with a mean decline of 6.785 percent per annum. Moreover, because the low‐growth state is moderately persistent, a run of contractions can occur with non‐negligible probability, producing something like the Great Contraction. For example, conditional on a contraction having begun, the probability that it will last 3 more years is 14% and, if that were to occur, the cumulative fall in consumption would amount to 25%. We simplify the endowment process by suppressing the Gaussian innovation ɛt and assume instead that gross consumption growth follows a two‐point process, (2) We retain the point estimates of μh and μl made by Cecchetti et al. (2000) as well as their estimates of the transition probabilities Fhh and Fll. We assume that this model represents the true process for consumption growth. We also assume that both agents know and and that a type 2 agent knows the true transition matrix F. A type 1 agent 1 uses Bayes’ law to learn about F. 1.4. Preferences Over Consumption Plans A consumption plan for agent i is a sequence of functions Cit(gt), t ≥ 0, whose time t component maps a time t history gt into agent i’s time t consumption. Two infinitely‐lived consumers share the same isoelastic one‐period utility function and order consumption plans according to the expected utility functionals (3) or (4) where pri(gt) is agent i’s subjective probability over gt and Eit denotes conditional expectation with respect to pri(gt). The parameters α and β are the coefficient of relative risk aversion and subjective discount factor, respectively, and they are common across agents. In our simulations, we set α = 2 and β = 1.03−1. 1.5. The Pareto Problem For some initial distribution of wealth, a competitive equilibrium allocation solves a Pareto problem: where λ is the Pareto weight on the Bayesian consumer, gt represents a history of states through date t, and μ(gt) is the Lagrange multiplier on the aggregate resource constraint at date t, history gt. The Pareto planner distributes consumption so that the ratio of marginal utilities equals the ratio of Pareto weights, (5) With isoelastic utility, (5) can be solved to express consumption for agent 1 as a history‐dependent share of the aggregate endowment, (6) where (7) The more informed type 2 agent gets the remainder, (8) With common beliefs (i.e., pr1(gt) = pr2(gt)), φ = [λ/(1 − λ)]1/α, implying that the agents get constant shares of aggregate consumption. Diverse beliefs alter this common‐beliefs allocation by shifting resources toward agent 1 in histories that he thinks are more likely than agent 2. In our model, agent 1 is initially pessimistic, overestimating the probability of a contraction state. Hence, along a sample path, agent 1 gets more consumption relative to the common‐beliefs benchmark in the contraction state and less in the expansion state. Agent 2’s allocation is twisted in the opposite direction. Since expansions are the norm, agent 2 frequently benefits from agent 1’s pessimism. But in a contraction, the consumption of agent 2 falls by more than the aggregate endowment. Thus, the presence of a pessimistic agent alters equilibrium prices in ways that increase the consumption risk that the more informed agent chooses to bear in a competitive equilibrium. 1.6. Arrow Security Prices As usual, we can support a Pareto optimal allocation with an appropriate initial distribution of wealth, sequential trading of one‐period Arrow securities and a set of ‘natural’ limits on the quantities of Arrow securities that can be issued in each history, date pair; for example, see Ljungqvist and Sargent (2004, ch. 8). In the present context, it suffices to trade two Arrow securities each period, one that pays one unit of aggregate consumption when and zero units otherwise, and the other paying off when . Their prices are denoted Qht and Qlt, respectively. The gross return on the high‐growth state asset is 1/Qht when and 0 otherwise. Arrow securities prices are (9) and (10) 1.7. Financial Wealth Given a division of the aggregate endowment into an amount assigned to an agent of type i at time t and history gt, we can use implied Arrow‐Debreu prices to define a sequence of financial wealths that equal equilibrium quantities of one‐period Arrow securities; see Ljungqvist and Sargent (2004, pp. 224–33). For t ≥ 0, let be the time t Arrow‐Debreu price for a claim to a unit of consumption at date τ after history gτ and let be the consumption of a type i agent at date τ after history gτ. Then financial wealth at date t after history gt is where is a history gτ,τ ≥ t whose partial history up to t is gt. In principle, for a given assignment of individual endowments for i = 1,2, we can compute the financial wealths of our two types of consumers recursively but for our model it is computationally demanding and we do not do so because we are principally interested in allocations and market prices of risk, which are easier to compute. 1.8. Alternative Representations of the Unique SDF Because markets are complete, there is a unique stochastic discount factor with respect to the informed type 2 agent’s probability measure. The stochastic discount factor has the alternative representations (11) where mit+1 = β[Cit+1(gt+1)/Cit(gt)]−α denotes the intertemporal marginal rate of substitution for consumer i.10 Equality between the two representations of the common stochastic discount factor in (11) captures how agent‐specific consumption growth rates must adjust to offset differences in subjective conditional probabilities. We can use these two representations of the stochastic discount factor to motivate alternative notions of the market price of risk. 1.9. Market Prices of Risk Hansen and Jagannathan (1991) define the conditional market price of risk as the ratio of the conditional standard deviation of a stochastic discount factor to its conditional mean, (12) Here Eit(·) and σit(·) represent the conditional mean and standard deviation, respectively, evaluated with respect to consumer i’s predictive probabilities. To find unconditional prices of risk, we marginalise with respect to the growth state, using consumer i’s unconditional densities. Because the two consumers have diverse beliefs, they also form different assessments about the price of risk. Since agent 2 knows the true transition probabilities, his perceived law of motion for aggregate consumption coincides with the actual law of motion. Hence we call mpr2t the ‘rational‐expectations’ price of risk. Similarly, because the Bayesian consumer uses his subjective predictive probabilities to make forecasts, we call mpr1t the ‘subjective’ price of risk. 1.10. Bayesian Learning and Predictive Probabilities Agents observe the history of their own consumption, of aggregate consumption, and of Arrow security prices.11 As in Cogley and Sargent (2008), we assume that the type 1 Bayesian consumer adopts a beta‐binomial probability model for learning about F. A binomial likelihood is a natural representation for a two‐state endowment process, and a beta density is the conjugate prior for a binomial likelihood. We inject additional pessimism by applying the T2 risk‐sensitivity operator of Hansen and Sargent (2007b). This operator distorts a benchmark beta prior by tilting probabilities towards the low‐growth state. 1.10.1. A type 1 agent’s prior As in Cogley and Sargent (2008), for the type 1 agent, we imagine a consumer who is about to emerge from the Great Contraction in 1933 and has a conventional beta prior (13) where f(Fhh) and f(Fll) are independent beta densities, (14) The variable is a counter that records the number of transitions from state i to j up to date t, and the parameters represent prior beliefs about the frequency of transitions. In the following subsections, we describe how we elicit a pessimistic prior for the type 1 agent. 1.10.2. Using a short sample To elicit a pessimistic outlook, we calibrate f(Fhh,Fll) by fitting to a short training sample covering the period 1919–33 that oversamples contraction states. Because actual data on consumption growth are realisations of a continuous random variable, we fit a hidden Markov model to the actual data and then calibrate f(Fhh) and f(Fll) so that they have the same mean and degrees of freedom.12 The results are recorded in the middle column of Table 2. Consumption growth was sharply negative during 1930–3 and, with a short training sample, this experience would have made a Bayesian pessimistic about the onset and persistence of contractions. Thus, Fhh is lower and Fll is higher than the estimates of Cecchetti et al. (2000). Table 2 
Prior Means forFhhandFll . Beta . Worst‐Case . . Fhh . Fll . Fhh . Fll . 1919–1933 0.915 0.805 0.869 0.966 . Beta . Worst‐Case . . Fhh . Fll . Fhh . Fll . 1919–1933 0.915 0.805 0.869 0.966 Worst‐case priors are calculated for α = 2 and θ = 125. Open in new tab Table 2 
Prior Means forFhhandFll . Beta . Worst‐Case . . Fhh . Fll . Fhh . Fll . 1919–1933 0.915 0.805 0.869 0.966 . Beta . Worst‐Case . . Fhh . Fll . Fhh . Fll . 1919–1933 0.915 0.805 0.869 0.966 Worst‐case priors are calculated for α = 2 and θ = 125. Open in new tab 1.10.3. Pessimistic twisting In Cogley and Sargent (2008), we found that more pessimism is needed to attain good results for the equity premium and market price of risk. Accordingly, we multiply the benchmark beta prior by a nonnegative random variable ζ(Fhh, Fll; θ) that pessimistically distorts beliefs, (15) To obtain the function ζ(Fhh, Fll; θ), we apply the T2 risk‐sensitivity operator of Hansen and Sargent (2007b). This operator helps the consumer evaluate continuation values in a way that guards against misspecification of his prior. Application of the operator gives the indirect utility function for a problem in which the decision maker chooses a distortion to his benchmark prior f(Fhh,Fll) in order to minimise the expectation of a continuation value function plus an entropy penalty. The penalty on entropy constrains the set of alternative priors against which the decision maker wants to guard, with the size of the set decreasing in a positive robustness parameter θ. The worst‐case distortion to the prior is (16) where V(Xt) is the consumer’s value function and the state Xt consists of statistics summarising the observed history gt along with the unobserved parameters Fhh, Fll. Since we use T2 only to elicit a prior, we condition on the training sample for gt, obtaining an initial distortion ζ(Fhh, Fll; θ). Notice that ζ(Fhh, Fll; θ) → 1 as θ→ +∞. Thus, in the limit as θ → +∞ we recover the undistorted beta prior. We set θ = 125 to make fwc(Fhh, Fll) resemble one of the worst‐case priors in our earlier paper. The results are recorded in the third column of Table 2. Relative to the beta priors, the worst‐case priors underestimate Fhh and exaggerate Fll. Thus, the robust consumer initially believes that contractions occur more often and are longer when they do occur. Since long contractions have the character of Great Depressions, our robust consumer is initially wary of another crash. A Bayes factor actually favours the distorted prior over the benchmark beta prior, so the Bayesian consumer would not dismiss this as implausible. For further discussion of the worst‐case priors, see Cogley and Sargent (2008). Next, we approximate fwc(Fhh, Fll) by another product of beta densities, (17) where p(Fhh) and p(Fll) are calibrated so that pwc(Fhh, Fll) has the same mean and degrees of freedom as fwc(Fhh, Fll). We do this partly for computation reasons, as it speeds our calculations quite a lot. But there is also a substantive reason. The dependence induced by ζ(Fhh, Fll; θ) is an interesting feature in its own right and, in our earlier paper, it contributed to higher prices of risk. In that paper, α was calibrated at 0 and the worst‐case prior induced positive correlation between Fhh and Fll. Thus, after a transition from to , the mean of Fhh would increase but so would the mean of Fll. Similarly, after exiting a contraction, the mean of Fll would decline but so would the mean of Fhh. In this way, every step in the direction of optimism was accompanied by a partially offsetting step toward pessimism. This caused pessimism to evaporate more slowly and contributed to high prices of risk. With α = 2, the effect seems to be different. In this case, (15) induces negative correlation between Fhh and Fll. Thus, as Fhh rises, Fll falls and vice versa. Since inverse dependence makes pessimism evaporate more quickly, it causes the market price of risk to decline more rapidly. To counteract this effect, we endow the consumer with the independent prior (17). The two priors have the same mean and degrees of freedom but (17) implies that Fhh and Fll are updated separately.13 Figure 1 depicts the marginal priors for Fhh and Fll. Solid lines portray the benchmark beta prior and dashed and dotted lines portray the two worst‐case densities. Notice how the risk‐sensitivity adjustment reshapes the benchmark priors by shifting probability mass toward lower values of Fhh and higher values of Fll. Fig. 1. Open in new tabDownload slide Beta and Robust Priors
Notes: Solid lines depict undistorted Beta priors, dashed lines portray worst‐case priors for α = 2 and θ2 = 125, and dotted lines illustrate the independent beta approximation to the worst‐case prior. Fig. 1. Open in new tabDownload slide Beta and Robust Priors
Notes: Solid lines depict undistorted Beta priors, dashed lines portray worst‐case priors for α = 2 and θ2 = 125, and dotted lines illustrate the independent beta approximation to the worst‐case prior. 1.10.4. The posterior on Fhh and Fll Next, we derive an expression for agent 1’s posterior, . Given the history of aggregate and own consumption, the history of Arrow securities prices Qt conveys no extra information. This follows from the fact that Arrow prices are deterministic functions of the other conditioning information; see (9) and (10).14 Hence, the posterior simplifies to (18) Similarly, given knowledge of the sharing rule and history of aggregate consumption, C1t is also a deterministic function of the other conditioning information (see (6)). Therefore, the history of own consumption is also redundant, (19) Hence, Bayesian updating simplifies to learning about the transition probabilities in light of observations on aggregate consumption. The Appendix describes how this is done. Among other things, the Appendix establishes that the prior pwc is conjugate to a binomial likelihood function. Hence the posterior is also a product of beta densities, and the vector of counters nt constitutes sufficient statistics. The Bayesian consumer enters each period with a prior of the form (17). After observing aggregate consumption growth, he updates the counters, incrementing by 1 the element that corresponds to the realisations of gt+1 and gt: (20) Substituting the updated counters into (24) and normalising delivers the new posterior, which then becomes his prior for the following period. It is convenient to factor pri(gt) as (21) where pri(g1 | g0) is agent i’s prior distribution. To solve the Pareto problem and compute Arrow securities prices, we need the posterior predictive probabilities, (22) In the Appendix, we demonstrate that , the posterior mean of Fij. Given our assumptions, the posterior mean reduces to . 2. Two Benchmarks Before studying the diverse‐beliefs economy, we present results for two benchmarks, a rational‐expectations economy populated only by a fully‐informed consumer and a Bayesian economy in which the fully‐informed consumer is absent. These benchmarks correspond to λ = 0 and λ = 1, respectively. Later we compare these polar cases to outcomes for intermediate values of λ. 2.1. A Representative Agent With Full Information When λ = 0, the model reduces to a standard representative‐agent economy in which the consumer knows the transition probabilities. Tables 3 and 4 report the Arrow security prices and market prices of risk that emerge from this model. Despite the possibility of a sharp decline in consumption, market prices of risk are quite small. The unconditional price of risk is just 0.032, an order of magnitude smaller than the lower bound of Hansen and Jagannathan (1991). The price of risk is higher in contractions than in expansions – 0.092 as opposed to 0.030 – but the contraction‐state price of risk also falls well short of the Hansen and Jagannathan lower bound. Table 4 
Market Prices of Risk . Expansion . Contraction . Unconditional . MPR 0.030 0.092 0.032 . Expansion . Contraction . Unconditional . MPR 0.030 0.092 0.032 Open in new tab Table 4 
Market Prices of Risk . Expansion . Contraction . Unconditional . MPR 0.030 0.092 0.032 . Expansion . Contraction . Unconditional . MPR 0.030 0.092 0.032 Open in new tab Table 3 
Arrow Security Prices . Qht . Qlt . 0.908 0.025 0.449 0.577 . Qht . Qlt . 0.908 0.025 0.449 0.577 Open in new tab Table 3 
Arrow Security Prices . Qht . Qlt . 0.908 0.025 0.449 0.577 . Qht . Qlt . 0.908 0.025 0.449 0.577 Open in new tab 2.2. A Representative Bayesian Consumer When λ = 1, the model reduces to a representative‐agent economy in which the consumer uses Bayes’ law to learn about the transition probabilities. Figures 2 and 3 summarise Arrow prices and market prices of risk averaged across 1,000 sample paths. Fig. 3. Open in new tabDownload slide Market Prices of Risk in a Bayesian Economy
Note: Dashed and dotted lines depict prices of risk in expansions and contractions, respectively, while the solid line portrays the unconditional price of risk. Fig. 3. Open in new tabDownload slide Market Prices of Risk in a Bayesian Economy
Note: Dashed and dotted lines depict prices of risk in expansions and contractions, respectively, while the solid line portrays the unconditional price of risk. Fig. 2. Open in new tabDownload slide Arrow Security Prices
Note: Solid lines portray Bayesian prices and dashed lines depict full‐information rational‐expectations prices. Fig. 2. Open in new tabDownload slide Arrow Security Prices
Note: Solid lines portray Bayesian prices and dashed lines depict full‐information rational‐expectations prices. The consumer’s beliefs satisfy a Bayesian consistency theorem, so Arrow prices eventually converge to their λ = 0 full‐information rational‐expectations values. But this takes a long time. Along a sample path, the consumer is pessimistic about the onset of a contraction. Thus, conditional on being in an expansion, Qh is lower and Ql higher than their full‐information values (see the first row of Figure 2). The consumer is also pessimistic about the persistence of contractions. Therefore, conditional on being in a contraction, Qh is again lower and Ql higher than their limiting values (see the second row of Figure 2). An outside observer who imputes knowledge of the transition probabilities to a representative consumer would say either that the consumer is making systematic pricing errors or that he is more risk averse than α = 2. Figure 3 depicts subjective and rational‐expectations prices of risk. Because the consumer is mildly risk averse, subjective prices of risk are small, of the order of 0.03 to 0.09 (see the top panel of Figure 3). These values are in the same ballpark as the full‐information prices of risk reported above. The prices of risk needed to reconcile Arrow prices with rational expectations are substantially higher, however (see the bottom panel of Figure 3). The unconditional rational‐expectations price of risk is initially above 0.8 and declines gradually to 0.23 after 75 years (1933 + 75 =2008). This is in the region of Hansen and Jagannathan’s (1991) lower bound. Going forward in time, the model predicts a further decline to around 0.15 after 200 years. Table 5 summarises the distribution of unconditional prices of risk in year 75. The subjective price of risk is always smaller than 0.1 but the rational expectations (RE) price of risk is greater than 0.2 on roughly half of the sample paths and it exceeds 0.25 on more than a quarter of the paths. Table 5 
Cumulative Distribution of Unconditional MPR in year 75 pr(mpr>x) . x = 0.1 . 0.15 . 0.2 . 0.25 . Subjective MPR 0 0 0 0 RE MPR 1.0 1.0 0.495 0.279 pr(mpr>x) . x = 0.1 . 0.15 . 0.2 . 0.25 . Subjective MPR 0 0 0 0 RE MPR 1.0 1.0 0.495 0.279 Open in new tab Table 5 
Cumulative Distribution of Unconditional MPR in year 75 pr(mpr>x) . x = 0.1 . 0.15 . 0.2 . 0.25 . Subjective MPR 0 0 0 0 RE MPR 1.0 1.0 0.495 0.279 pr(mpr>x) . x = 0.1 . 0.15 . 0.2 . 0.25 . Subjective MPR 0 0 0 0 RE MPR 1.0 1.0 0.495 0.279 Open in new tab As in Cogley and Sargent (2008), the high rational‐expectations price of risk reflects the change of measure that reconciles Bayesian asset prices with the true transition probabilities. That change of measure introduces a highly volatile learning wedge into a rational‐expectations Euler equation, disconnecting the rational‐expectations pricing kernel from the consumer’s subjective IMRS. The learning wedge makes the rational‐expectations pricing kernel highly volatile, even though the consumer’s subjective IMRS is not. That explains why a high rational‐expectations price of risk can coexist with a mild degree of risk aversion. 3. The Diverse Beliefs Economy 3.1. How Consumption is Distributed Figure 4 illustrates the share of consumption for agent 2 averaged across 1000 sample paths. The respective values of λ are calibrated to deliver initial mean shares of 1, 5, 10 and 50%.15 Fig. 4. Open in new tabDownload slide Average Consumption Share of the Fully‐Informed Agent for Various λ Fig. 4. Open in new tabDownload slide Average Consumption Share of the Fully‐Informed Agent for Various λ On average, the well‐informed agent’s consumption share increases over time. The rate of growth is higher the lower is his initial mean share. For instance, when his average share is initially 10% or less, his share of consumption increases by a factor of 3 or 4 over the first 100 years and by a factor of 4 to 6 over 200. But when average consumption shares are initially even, agent 2’s share increases by a factor of only 1.7 over 200 years. Figure 5 depicts histograms for consumption shares in various years, with the share allocated to the better‐informed agent on the x‐axis and the proportion of sample paths on the y‐axis. As time passes, the histograms shift to the right, illustrating how the better‐informed agent’s consumption share increases with high probability. The histograms also spread out over time and acquire long lower tails. This means that there are some sample paths on which his consumption share fails to increase and a few paths where it actually declines. Thus, although the fully‐informed consumer frequently does quite well relative to the Bayesian consumer, he does not always prosper. As t increases, the histograms converge to a non‐degenerate ergodic distribution16 but that takes a long time and we did not run the simulation long enough to learn what it looks like. Fig. 5. Open in new tabDownload slide Histograms of Consumption Shares for the Better‐Informed Agent Fig. 5. Open in new tabDownload slide Histograms of Consumption Shares for the Better‐Informed Agent Figure 6 displays particular sample paths that show how various events alter the consumption shares. This Figure refers to the simulation in which the fully‐informed agent has an initial consumption share of 5%; the figures for initial shares of 1% and 10% are similar.17 Solid lines portray aggregate consumption growth, and dashed and dotted lines depict consumption shares for the Bayesian and fully‐informed consumers, respectively. The message of this Figure is that a consumer’s share increases when his cumulative forecasting record is superior to that of his counterpart. The full set of sample paths contains a variety of experiences. The Figure portrays just a few of them in order to inform intuition. Fig. 6. Open in new tabDownload slide Particular Sample Paths, Initial Mean Share = 0.05
Note: Solid lines portray aggregate consumption growth, and dashed and dotted lines depict consumption shares for the Bayesian and fully‐informed consumers, respectively. Fig. 6. Open in new tabDownload slide Particular Sample Paths, Initial Mean Share = 0.05
Note: Solid lines portray aggregate consumption growth, and dashed and dotted lines depict consumption shares for the Bayesian and fully‐informed consumers, respectively. The upper left panel illustrates a path along which no contractions occur. At first, this favours the fully‐informed consumer. The Bayesian consumer is initially pessimistic about the onset of a contraction and worries too much about contractions that do not occur. Eventually, their roles reverse. As good outcomes recur, rises and eventually surpasses Fhh. At that point, expansions are more likely under the Bayesian predictive density and his forecasting record makes a comeback relative to that of the fully‐informed agent. That shifts consumption back toward agent 1. The upper right panel depicts a sample path on which there are just a few short contractions. Because most transitions are from to converges fairly quickly to the neighbourhood of Fhh and, since there is little disagreement about this transition probability, the onset of a contraction has only a slight effect on their consumption shares. But because no long contractions occur on this sample path, there is substantial disagreement about the persistence of contractions, the Bayesian remaining much more pessimistic. A quick end to a contraction therefore favours the fully‐informed agent, improving his cumulative forecasting record relative to that of the Bayesian consumer. That shifts consumption toward the fully‐informed agent. The sample path depicted in the lower left panel has many short contractions. The occurrence of many contractions favours the Bayesian consumer. He is pessimistic about and predicts more to transitions than the fully‐informed consumer. The realisation of many such transitions therefore improves his relative forecasting record, shifting consumption in his favour at the onset of a contraction. On the other hand, the fully‐informed agent attaches a higher probability to high‐growth states and he rallies when the economy transits into an expansion. Finally, the bottom right panel illustrates a sample path with a pair of long contractions. According to the fully‐informed agent, these are rare events, so his relative forecasting record suffers when they are realised. Hence consumption shifts toward the Bayesian consumer when long contractions occur. Notice also how long the penalty persists. Because of the history dependence in the Pareto allocation, the share of the fully‐informed agent remains low for many, many years after the contraction ends. Relative to what happens in the limit, along the transition path the Bayesian consumer buys extra contraction insurance from the fully‐informed agent. That insurance pays off in the event of frequent and/or long contractions, in which case the Bayesian’s share increases at the expense of the fully‐informed agent. So during frequent and/or long contractions, Bayesian consumption falls by less than aggregate consumption and that of the fully‐informed agent falls by more. The payoff for the fully‐informed agent is a higher consumption share in expansions. In those states, his consumption increases by more than aggregate consumption. For initial consumption shares of 10% of less, the risk‐sharing arrangement dampens consumption volatility for the Bayesian agent and amplifies it for the fully‐informed agent. Figure 7 illustrates consumption for the four sample paths shown above. In each panel, the top line portrays aggregate consumption on a log scale and the bottom line depicts consumption for the fully‐informed consumer. In the aggregate, contractions are small bumps, in some cases visually hard to discern. For the fully‐informed consumer, contractions are proportionally much larger, often resulting in a very substantial decline in consumption. Fig. 7. Open in new tabDownload slide Particular Sample Paths, Initial Mean Share = 0.05
Note: In each panel, the top line portrays aggregate consumption, and the bottom line depicts consumption for the fully‐informed consumer. Fig. 7. Open in new tabDownload slide Particular Sample Paths, Initial Mean Share = 0.05
Note: In each panel, the top line portrays aggregate consumption, and the bottom line depicts consumption for the fully‐informed consumer. Table 6 reports the standard deviation of consumption growth in the aggregate and for the two agents. Averaging across all sample paths, the standard deviation of aggregate consumption growth is 1.96% per annum. When agent 2 has a small initial consumption share, Bayesian consumption is a bit smoother than the aggregate. But for the fully‐informed agent consumption growth is almost 10 times more volatile. Thus, the better‐informed agent bears a disproportionate share of aggregate consumption risk. In effect, the risk‐sharing arrangement amplifies consumption catastrophes for the fully‐informed consumer relative to the aggregate data‐generating process. This affects his perception of the market price of risk. Table 6 
Standard Deviation of Consumption Growth Initial Share . Δ ln C . Δ ln C1 . Δ ln C2 . 0.01 0.0196 0.0170 0.1785 0.05 0.0196 0.0155 0.1679 0.10 0.0196 0.0177 0.1565 0.50 0.0196 0.0477 0.0911 Initial Share . Δ ln C . Δ ln C1 . Δ ln C2 . 0.01 0.0196 0.0170 0.1785 0.05 0.0196 0.0155 0.1679 0.10 0.0196 0.0177 0.1565 0.50 0.0196 0.0477 0.0911 Open in new tab Table 6 
Standard Deviation of Consumption Growth Initial Share . Δ ln C . Δ ln C1 . Δ ln C2 . 0.01 0.0196 0.0170 0.1785 0.05 0.0196 0.0155 0.1679 0.10 0.0196 0.0177 0.1565 0.50 0.0196 0.0477 0.0911 Initial Share . Δ ln C . Δ ln C1 . Δ ln C2 . 0.01 0.0196 0.0170 0.1785 0.05 0.0196 0.0155 0.1679 0.10 0.0196 0.0177 0.1565 0.50 0.0196 0.0477 0.0911 Open in new tab Matters are slightly different when the fully‐informed trader has an initial consumption share of 0.5 (see Figure 8 and the last row of Table 6). The risk‐sharing arrangement still amplifies consumption volatility for the well‐informed consumer but it also increases consumption volatility for the Bayesian consumer. Figure 8 portrays consumption shares for this calibration along the same sample paths shown in Figure 6. Consumption covaries negatively across consumers, so there is still a lot of risk sharing. But relative to the previous calibrations, the consumption of the Bayesian consumer 1 increases a lot more in favourable states of the world and falls more in unfavourable states. This amplifies the Bayesian consumer’s perception of the price of risk. Fig. 8. Open in new tabDownload slide Particular Sample Paths, Initial Mean Share = 0.5
Note: Solid lines portray aggregate consumption growth, and dashed and dotted lines depict consumption shares for the Bayesian and fully‐informed consumers, respectively. Fig. 8. Open in new tabDownload slide Particular Sample Paths, Initial Mean Share = 0.5
Note: Solid lines portray aggregate consumption growth, and dashed and dotted lines depict consumption shares for the Bayesian and fully‐informed consumers, respectively. 3.2. Arrow Security Prices Figure 9 illustrates Arrow prices in the diverse‐beliefs economies and compares them with those in polar Bayesian (λ = 1) and RE (λ = 0) economies. As before, the Figures depict mean prices averaged across 1000 sample paths. The top and bottom row depict prices conditional on being in an expansion and contraction, respectively. Fig. 9. Open in new tabDownload slide Arrow Security Prices
Top: conditional on expansion; bottom: conditional on contraction. Fig. 9. Open in new tabDownload slide Arrow Security Prices
Top: conditional on expansion; bottom: conditional on contraction. The presence of a fully‐informed type 2 consumer moves prices toward their rational‐expectations values. But when his initial consumption share is small, his effect on prices is also small. Thus, when the initial mean share is 0.01, prices in the diverse‐beliefs economy are almost identical to those in the Bayesian economy. In this case, the two lines are visually hard to distinguish. The differences are a bit larger when his initial mean share is 0.05 or 0.10 but prices remain closer to Bayesian outcomes than to RE values. His influence is greater, however, when his initial mean consumption share is 0.5; in that case convergence to the rational‐expectations benchmark is much more rapid. Because the fully‐informed agent bears a disproportionate share of aggregate consumption risk, the price gaps shown in Figure 2 no longer present such attractive opportunities to trade. For instance, consider the Arrow security paying off in the low‐growth state. At first glance, Figure 2 might seem to suggest that the fully‐informed trader could profit by selling to the Bayesian consumer because the benchmark Bayesian price exceeds the RE price. That impression is misplaced, however, because the fully‐informed trader bears much more downside consumption risk in the diverse‐beliefs economy than in the representative‐agent, rational‐expectations economy and requires a higher selling price to compensate for the extra risk. 3.3. Market Prices of Risk Figure 10 illustrates market prices in the diverse‐beliefs economies and compares them with prices of risk in the purely Bayesian economy. The left‐hand column portrays the subjective price of risk for the Bayesian consumer and the right‐hand column depicts rational‐expectations prices of risk for the fully‐informed trader.18 Fig. 10. Open in new tabDownload slide Market Prices of Risk
Top: unconditional; middle, conditional on expansion; bottom, conditional on contraction. Fig. 10. Open in new tabDownload slide Market Prices of Risk
Top: unconditional; middle, conditional on expansion; bottom, conditional on contraction. In all but one of the calibrations, the subjective price of risk is quite small. When the well‐informed trader has a small initial consumption share, the Bayesian consumer can buy contraction insurance and therefore bears less consumption risk than in the pure Bayesian economy. Hence subjective prices of risk are lower in the mixed economy. The one exception occurs when the agents initially share consumption equally. As we have seen, in that case both agents bear more consumption risk and that elevates the Bayesian consumer’s subjective price of risk. RE prices of risk are also smaller than in the Bayesian economy but in most cases only slightly. For the fully‐informed type 2 consumer, prices of risk remain high because he is exposed to more consumption risk than in the aggregate. For the Bayesian consumer, the price of risk is high because of the learning wedge that appears after expressing his Euler equation in terms of the true probabilities. Table 7 summarises the distribution of the rational expectations market price of risk in year 75. When the fully‐informed agent has a small initial consumption share, the distribution is much like that in the Bayesian economy. The distribution shifts to the left as the fully‐informed trader becomes more important but high prices of risk emerge on a substantial fraction of sample paths even when his initial consumption share is 0.1. Hence, the introduction of a small measure of fully‐informed consumers does not reverse the results of Cogley and Sargent (2008). A large measure of fully‐informed agents is needed to overturn those results. Table 7 
Distribution of the Unconditional RE‐MPR in Year 75 Initial Share . Pr(mpr > 0.1) . Pr(mpr > 0.15) . Pr(mpr > 0.2) . Pr(mpr > 0.25) . 0 1.0 1.0 0.495 0.279 0.01 1.0 0.913 0.493 0.252 0.05 1.0 0.726 0.339 0.185 0.10 1.0 0.492 0.237 0.114 0.50 0.184 0.060 0.022 0.012 Initial Share . Pr(mpr > 0.1) . Pr(mpr > 0.15) . Pr(mpr > 0.2) . Pr(mpr > 0.25) . 0 1.0 1.0 0.495 0.279 0.01 1.0 0.913 0.493 0.252 0.05 1.0 0.726 0.339 0.185 0.10 1.0 0.492 0.237 0.114 0.50 0.184 0.060 0.022 0.012 Open in new tab Table 7 
Distribution of the Unconditional RE‐MPR in Year 75 Initial Share . Pr(mpr > 0.1) . Pr(mpr > 0.15) . Pr(mpr > 0.2) . Pr(mpr > 0.25) . 0 1.0 1.0 0.495 0.279 0.01 1.0 0.913 0.493 0.252 0.05 1.0 0.726 0.339 0.185 0.10 1.0 0.492 0.237 0.114 0.50 0.184 0.060 0.022 0.012 Initial Share . Pr(mpr > 0.1) . Pr(mpr > 0.15) . Pr(mpr > 0.2) . Pr(mpr > 0.25) . 0 1.0 1.0 0.495 0.279 0.01 1.0 0.913 0.493 0.252 0.05 1.0 0.726 0.339 0.185 0.10 1.0 0.492 0.237 0.114 0.50 0.184 0.060 0.022 0.012 Open in new tab 4. Concluding Remarks Survival arguments depend sensitively on market completeness as well as the distribution of risks and agents’ attitudes toward risk.19 Complete markets give the agents in this paper many opportunities to make trades that are motivated by the different subjective probabilities they put on future outcomes. Thus, by assuming complete markets, we have given the survival argument ample scope to eradicate the effects of initial pessimism on equilibrium prices. It would be interesting to compute how market incompleteness would change that. Footnotes 1 " Friedman and Schwartz (1963) used a related evaporating pessimism hypothesis to explain the behaviour of investors’ portfolio choices during the two decades after the Great Depression. 2 " We endow our two types of agents with different priors. For reasons discussed in subsections 1.1 and 1.2, if we had endowed the two types of agents with a common prior, our robustness exercise would be trivial: the presence of the more knowledgeable type 2 agent would cause the pessimism of the type 1 agent to evaporate completely at time 0. 3 " Kogan et al. (2006) study a setting in which most agents know the data‐generating mechanism and form forecasts accordingly but a low‐wealth small measure of irrational agents still has important influences on prices. 4 " In the representative agent economy of Cogley and Sargent (2008), Bayes’ law also dissipates pessimism. 5 " Beker and Espino (2008) study limiting portfolios and volume in a related economy. 6 " The term ‘true F’ has no special status in the theory underlying the Walrasian competitive equilibrium prices and allocations. Two distinct probability densities over infinite sequences of consumption growth are simply ingredients of the two types of agents’ preferences. We do not have to use the term ‘true F’ until we simulate equilibrium allocations and prices under a particular probability distribution. 7 " Thus, we do not adhere to the ‘Harsanyi Doctrine’ that asserts that differences in individuals’ beliefs are to be attributed entirely to differences in information. 8 " Pearlman and Sargent (2005) study the rational expectations equilibrium for the private information environment of Townsend (1983) and show that firms can extract all of other firms’ private information from prices. 9 " Sometimes differences in priors can be reformulated in terms of common priors but different information sets. Thus, we could have started our two types of agents with a common prior over (g∞, F), then given the type 1 agent the information set gt at t and the type 2 agent both gt and knowledge of particular tail events for the {gt} process in the form of limiting values of the empirical fractions of transitions from high to low growth and from low to high growth states. Knowing those tail events is tantamount to knowing F. In the text, we allow agents to exchange claims contingent only on finite histories gt for all t ≥ 0, so there is no market in which agents can bet on tail events. 10 " Cogley and Sargent (2008) featured the learning wedge captured by the likelihood ratio pr1(gt+1 | gt)/pr2(gt+1 | gt). In their economy, the representative agent is of type 1, there is no type 2 informed agent, but pr2(gt+1 | gt) represents the true data generator. Bossaerts (2002, 2004) also uses a ratio of the likelihood of a Bayesian agent to the likelihood for a data‐generating process to model prices of risk. Hansen (2007) and Hansen and Sargent (2007a) develop models of robust asset pricing that feature another probability ratio, prwc(gt+1 | gt)/prdgp(gt+1 | gt), where the denominator represents probabilities under the true data‐generating process and the numerator is a worst‐case probability model. 11 " They also know the sharing rules (6)–(8) and from this they can deduce the other type of agent’s beliefs. Although the Bayesian consumer deduces the beliefs of the fully‐informed agent, that does not mean that he recognises they are the true probabilities. The Bayesian type 1 agent quickly discovers that the type 2 agent has a dogmatic prior. If agent 1 knew that agent 2 knew the truth, the sharing rule would reveal F and agent 1 could also become fully informed. But we assume that from the perspective of agent 1, the beliefs of agent 2 are just someone else’s prior. Therefore, they do not influence the type 1 agent’s Bayesian updating. See the discussion in subsections 1.1 and 1.2. 12 " For details, see Cogley and Sargent (2008). 13 " Because the worst‐case prior depends on the utility function, the value of α affects the outcome of applying the T2 operator. When α = 0 as in Cogley and Sargent (2008), the agent cares only about mean consumption growth and not about smoothing consumption across states. When α = 2, the agent prefers a smooth consumption process. The worst‐case transition matrix for an α = 0 consumer therefore differs from the worst‐case transition matrix for an α = 2 consumer. 14 " Bayesians remember their past beliefs as well. 15 " Although this is a convenient way to calibrate λ, one should keep in mind that agent 2’s initial consumption share understates his initial share of wealth. In this economy, for both types of consumer, the time 0 financial wealths defined in subsection 1.7 are zero. Total wealth, which includes the present value of the consumer’s endowment, equals the present value of future consumption, evaluated with Arrow‐Debreu history‐contingent prices. Since the better‐informed agent’s consumption share increases over time, it follows that his initial share of wealth exceeds his initial share of consumption. Thus, for example, when λ is calibrated so that the two agents initially share consumption equally, we allocate more than half of initial aggregate wealth to the well‐informed agent. 16 " This follows from Blume and Easley (2006) and the fact that the truth lies in the support of both agents’ beliefs. 17 " Matters are slightly different when the initial shares are 0.5. 18 " In the purely Bayesian economy, the rational‐expectations price of risk involves a pricing kernel which reconciles Bayesian asset prices with the true transition probabilities. In the diverse‐beliefs economy, this coincides with the fully‐informed consumer’s price of risk. 19 " This is a message of Kogan et al. (2006). 20 " According to this notation, represents the sum of prior plus observed counters. References Beker , Pablo F. and Espino , Emilio ( 2008 ). ‘The dynamics of efficient asset trading with heterogeneous beliefs’ , mimeo, Department of Economics University of Warwick, Department of Economics Universidad Torcuato Di Tella . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Blume , Lawrence and Easley , David ( 2006 ). If you’re so smart, why aren’t you rich? Belief selection in complete and incomplete markets’ , Econometrica , vol. 74 ( 4 ), pp. 929 – 66 . Google Scholar Crossref Search ADS WorldCat Bossaerts , Peter ( 2002 ). The Paradox of Asset Pricing , Princeton, NJ: Princeton University Press . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Bossaerts , Peter ( 2004 ). ‘Filtering returns for unspecified biases in priors when testing asset pricing theory’ , Review of Economic Studies , vol. 71 , pp. 63 – 86 . Google Scholar Crossref Search ADS WorldCat Cecchetti , Stephen G. , Lam , Pok‐Sang and Mark , Nelson C. ( 2000 ). ‘Asset pricing with distorted beliefs: are equity returns too good to be true?’ , American Economic Review , vol. 90 ( 4 ), pp. 787 – 805 . Google Scholar Crossref Search ADS WorldCat Cogley , Timothy and Sargent , Thomas J. ( 2008 ). ‘The market price of risk and the equity premium: a legacy of the great depression?’ , Journal of Monetary Economics vol. 55 , pp. 454 – 78 . Google Scholar Crossref Search ADS WorldCat Friedman , M. and Schwartz , A.J. ( 1963 ). A Monetary History of the United States, 1857–1960 , Princeton, NJ : Princeton University Press. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Grossman , Sanford J. ( 1981 ). ‘An introduction to the theory of rational expectations under asymmetric information’ , Review of Economic Studies , vol. 48 ( 4 ), pp. 541 – 59 . Google Scholar Crossref Search ADS WorldCat Hansen , Lars Peter ( 2007 ). ‘Beliefs, doubts, and learning: valuing macroeconomic risk’ , American Economic Review , vol. 92 , pp. 1 – 30 . Google Scholar Crossref Search ADS WorldCat Hansen , Lars Peter and Jagannathan , Ravi ( 1991 ). ‘Implications of security market data for models of dynamic economics’ , Journal of Political Economy , vol. 99 , pp. 225 – 62 . Google Scholar Crossref Search ADS WorldCat Hansen , Lars Peter and Sargent , Thomas J. ( 2007a ). ‘Fragile beliefs and the price of model uncertainty’ mimeo, Department of Economics Chicago University and Department of Economics New York University . Hansen , Lars Peter and Sargent , Thomas J. ( 2007b ). ‘Recursive robust estimation and control without commitment’ , Journal of Economic Theory , vol. 136 , pp. 1 – 27 . Google Scholar Crossref Search ADS WorldCat Kogan , Leonid , Ross , Stephen A., Wang , Jiang and Westerfield , Mark M. ( 2006 ). ‘The price impact and survival of irrational traders’ , Journal of Finance , vol. 61 ( 1 ), pp. 195 – 228 . Google Scholar Crossref Search ADS WorldCat Ljungqvist , Lars and Sargent , Thomas J. ( 2004 ). Recursive Macroeconomic Theory , Second Edition , Cambridge MA: MIT Press . Milgrom , Paul and Stokey , Nancy ( 1982 ). ‘Information, trade and common knowledge’ , Journal of Economic Theory vol. 26 , pp. 17 – 27 . Google Scholar Crossref Search ADS WorldCat Pearlman , Joseph G. and Sargent , Thomas J. ( 2005 ). ‘Knowing the forecasts of others’ , Review of Economic Dynamics , vol. 8 ( 2 ), pp. 480 – 97 . Google Scholar Crossref Search ADS WorldCat Townsend , Robert M. ( 1983 ) ‘Forecasting the forecasts of others’ , Journal of Political Economy , vol. 91 ( 4 ), pp. 546 – 88 . Google Scholar Crossref Search ADS WorldCat Appendix Appendix: Bayesian Updating The likelihood function for a batch of data, is proportional to the product of binomial densities, (23) where is the number of transitions from state i to j observed in the sample.20 Multiplying the likelihood by the prior (17) delivers the posterior kernel, (24) where (25) Hence, the prior and likelihood form a conjugate pair. The posterior is also a product of independent beta densities, and the counters are sufficient statistics. The posterior predictive probabilities are where is the posterior mean of Fij. After integrating, one can show that . Author notes " We thank V.V. Chari, Michael Dotsey, Patrick Kehoe, Larry Jones, Aubhik Khan, Narayana Kocherlakota, Erzo Luttmer, Fabrizio Perri, Monika Piazzesi, Martin Schneider and Andrew Scott for helpful discussions and comments on earlier drafts. We also thank an anonymous referee for useful suggestions. Sargent thanks the National Science Foundation for research support. © The Author(s). Journal compilation © Royal Economic Society 2009

Huang, Kevin, X.D.;Liu,, Zheng;Zha,, Tao

doi: 10.1111/j.1468-0297.2008.02238.xpmid: N/A

Abstract This study explores the macroeconomic implications of adaptive expectations in a standard growth model. We show that the self‐confirming equilibrium under adaptive expectations is the same as the steady state rational expectations equilibrium for all admissible parameter values, but that dynamics around the steady state are substantially different between the two equilibria. The differences are driven mainly by the dampened wealth effect and the strengthened intertemporal substitution effect, not by escapes emphasised by Williams (2003). Consequently, adaptive expectations can be an important source of frictions that amplify and propagate technology shocks and seem promising for generating plausible labour market dynamics. Learning models have been used for many macroeconomic applications (Sargent, 2007).1 We focus, in this article, on yet another application in the context of a standard real business cycle model in which rational expectations are replaced by adaptive expectations. The stability of rational expectations under learning in real business cycle (RBC) models has been studied in the literature (Evans and Honkapohia, 2001; Bullard and Duffy, 2004; Carceles‐Poveda and Giannitsarou, 2007; Eusepi and Preston, 2008). In a closely related paper, Williams (2003) considers a variety of standard learning rules in a RBC model. The learning rules that he considers do not separate agents’ beliefs and their decision making. Agents are learning about the structural parameters in the reduced form of the model and the learning does not influence optimising decisions. Under this type of learning, Williams (2003) finds that learning dynamics differ very little from rational expectations dynamics. Consequently, one would have concluded that learning dynamics do not teach us anything new, as compared to the rational expectations version of the RBC model. In this article, we re‐examine this conclusion in the standard RBC model with both neutral and investment‐specific technology shocks. Following the commonly‐used learning mechanism studied by Marcet and Nicolini (2003) and Sargent et al. (2006a), we examine the implications of misspecified (i.e., under‐parameterised) learning rules by separating agents’ beliefs and their decision rules.2 Rational expectations are simply replaced by adaptive expectations, while all decision equations under rational expectations remain intact. We show that this slight departure from rational expectations has important ramifications. Specifically, we address the following questions: Is there a self‐confirming equilibrium (SCE) in our learning environment? Is it unique? Are there strong escape dynamics away from the domain of attraction of the SCE? How does learning amplify the effects of technology shocks compared to rational expectations? How does learning affect the transmission mechanisms of technology shocks, especially in the labour market? To answer these questions, we obtain closed form solutions for both the log‐linearised rational expectations model and the corresponding learning model. These analytical solutions enable us to prove the existence and uniqueness of the SCE under all admissible parameterisations in our learning model. We further prove that the SCE coincides with the steady state rational expectations equilibrium (REE), but that learning dynamics are substantially different from rational expectations dynamics. Unlike Marcet and Nicolini (2003), Williams (2003) and Sargent et al. (2006a), however, we show that learning dynamics are stationary and that the differences between learning dynamics and rational‐expectations dynamics are not driven by escape dynamics. These theoretical results enable one to draw macroeconomic implications from our learning model. The dynamic responses of output, consumption, investment and labour hours, following a neutral technology shock, are substantially larger in the adaptive expectations model than in the rational expectations model. In the rational expectations equilibrium, hours change too little and the real wage fluctuates too much compared to the data. In contrast, learning amplifies the response of hours and dampens the response of the real wage. In our adaptive expectations model, agents form forecasts of future capital stock based on the past observations. Thus, introducing learning dampens the wealth effect of the neutral technology shock and strengthens the intertemporal substitution effect. Consequently, it helps to amplify the effects of the neutral technology shock on output and investment and improve the model’s predictions on the labour market dynamics. Introducing learning also helps to amplify the effects of a biased technology shock. The responses of hours to both types of technology shocks can be negative after initial periods in the learning model, whereas the hours responses to each of the two shocks are positive in the rational expectations model. The less persistent the shocks are, the more pronounced the negative responses of hours under learning can become. Furthermore, the learning model is more likely to generate hump‐shaped responses of consumption, investment, real wage and hours, the less persistent the shocks are. To relate our work to a broader literature on learning, we also examine a sophisticated nonlinear learning rule that has a correct specification of the rational expectations solution. Consistent with the results reported by Carceles‐Poveda and Giannitsarou (2007), we find that the transmission and propagation mechanisms of technology shocks depend crucially on initial conditions, the size of the shocks and the size of the gain. We illustrate some cases where learning generates strong amplification effects of the technology shocks. In particular, we show that adaptive learning, acting as a friction, is capable of generating negative responses of hours to a neutral technology shock, as documented by some recent empirical studies e.g., Galí (1999), Basu et al. (2006) and Gambetti (2006). Overall, our results suggest that introducing adaptive expectations in the standard stochastic growth model can assign a more important role for technology shocks to generate fluctuations in key macroeconomic variables than under rational expectations. Introducing learning can be particular helpful in improving the model’s predictions in the labour market. 1. The Model In this Section, we describe the standard growth model with both neutral and biased technologies. The economy is populated by a continuum of infinitely lived and identical households. The representative household is endowed with a unit of time. The household derives utility from consumption and leisure, with the utility function (1) where Ct denotes consumption, Lt denotes labour hours, β ∈ (0,1) denotes the subjective discount factor and E0 denotes an expectation at the initial time 0. The economy is also populated by a continuum of identical, perfectly competitive firms. The representative firm has access to a constant returns to scale technology represented by the production function (2) where Yt denotes output, Kt−1 denotes capital input and Lt denotes labour input. The term Zt denotes the neutral technological change and follows the stochastic process (3) where λz is the trend component and νt is the stationary component that follows the AR(1) process (4) The persistence parameter ρ ∈ (0,1] and the shock ɛνt is a white noise process with mean zero and variance . The shock process specified in (3)–(4) implies that, if 0 < ρ < 1, then the neutral technology follows a stationary stochastic process with a deterministic trend; if ρ = 1, then the neutral technology follows a random walk process with a drift.3 The economy has an initial stock of capital denoted by K−1. Capital stock evolves over time according to the law of motion (5) where Kt denotes the period‐t capital stock, It denotes investment, Q t denotes the investment‐specific technological change (the inverse of the relative price of investment goods) and the parameter δ ∈ (0,1) denotes the capital depreciation rate. As argued in Greenwood et al. (1997), the investment‐specific technological change is an important driving force of US growth in the post‐war period. Similar to the neutral technology, we assume that the investment‐specific technology shock Q t follows the stochastic process (6) where λq is the trend component and μt is the stationary component that follows the AR(1) process (7) The persistence parameter ρ ∈ (0,1) and the innovation term ɛμt is a white‐noise process with mean zero and variance . Again, our specification of the Q t process here nests the random‐walk process as a special case with ρ = 1. The aggregate resource constraint is given by (8) 2. Equilibrium Allocation and Balanced Growth Since the model economy has perfect competition and no externality, the First Welfare Theorem applies. Thus, the equilibrium allocations are Pareto efficient and can be found by solving a social planner’s problem. The social planner maximises the representative household’s utility (1) subject to the resource constraint (8) and the capital law of motion (5). The first order conditions imply that (9) (10) On the balanced growth path, Ct, It and Yt grow at the same rate of while the capital stock Kt grows at a faster rate of . We define the following stationary variables4 Given these stationary variables, we can rewrite the equilibrium conditions (2), (5), (8), (9) and (10) as (11) (12) (13) (14) (15) Denote . It follows from the above conditions that the steady state equilibrium can be described by the following equations (16) (17) (18) (19) (20) where and are the steady state values of and . The consumption – output and investment – output ratios can derived from the above steady state conditions: (21) (22) Log‐linearising the equilibrium conditions (11), (12), (13), (14) and (15) and rearranging the terms, we obtain the following five equations describing the production function, the law of motion for capital accumulation, the resource constraint, the optimal consumption‐labour‐supply decision and the optimal investment decision: (23) (24) (25) (26) (27) where Δ is the first difference operator (e.g., Δzt = zt − zt−1), the notation denotes for X = C, I, Y, K or  ln Xt −  ln  X for X = L, ik, cy, iy and yk are steady‐state ratios defined in (17), (22), (21) and (20), and is derived as (28) Definition 1. Admissible values of the deep parameters areβ ∈ (0,1), η ≥ 0, α ∈ (0,1), δ ∈ [0,1], λz ≥ 1 andλq ≥ 1. In the literature, dynamics are often simulated for a particular set of admissible values of the deep parameters by numerically solving the rational‐expectations equilibrium system given by the above conditions. We shall show, however, that the equilibrium characterised by (23)–(27) can be solved analytically for all admissible values of the deep parameters. The crucial step is to derive a stochastic process for capital, as stated in the following proposition. Proposition 1. The equilibrium solution for capital satisfies the following second‐order stochastic difference equation: (29) where the coefficients γ1, γ2, γμ1, γν1, γμ2andγν2are reported in Appendix A. Further, as we show in the Appendix, the structural parameters (which are functions of the deep parameters) satisfy the restrictions that γ1 > 0, γ2 > 0 andγ1 + γ2 < 1. Proof. See Appendix B. Proposition 1 is the key to obtaining all of our theoretical results, as is shown in the next Section. 3. REE vs. SCE: Theoretic Results In this Section, we derive the closed‐form solutions for both the REE and the SCE. The key is to solve (29); the solution depends on how agents form expectations of the endogenous accumulation process of capital. Once this solution is obtained, it is relatively straightforward to derive the closed‐form solutions for the other variables, which are reported in Appendix A. For the REE solution, we have the following result. Proposition 2. The solution to the second‐order differential equation (29) under the rational expectations assumption is (30)where Furthermore, this solution is stationary and unique. Proof. See Appendix C. If we replace the capital‐accumulation Euler equation (27) by the closed‐form expression (30), the system of equations (23)–(26) and (30) constitutes a reduced‐form solution to the rational‐expectations model. Given the shock processes and an initial condition for capital (30) gives the dynamic solution for capital. For a comparison with the SCE solution, this dynamic solution can be expressed as (31) where for all i ≥ 0, We now assume that agents have adaptive expectations. We follow Marcet and Nicolini (2003) and Sargent et al. (2006a) to replace by such that Agents update their beliefs using the following constant‐gain learning (CGL) algorithm: (32) where 0 < g < 1 is a gain representing how fast past observations are discounted in the learning regression. The dynamics of produced by (29) under the above learning algorithm (32) follow the process (33) In self‐confirming equilibrium, beliefs are not contradicted by observations along the equilibrium path (Sargent, 1999). To find an SCE is to solve a fixed‐point problem. For our model, the solution to the SCE is to find the fixed point that solves the orthogonality condition (34) where E() is a mathematical unconditional expectation operator and itself is a function of the belief in self‐confirming equilibrium such that Proposition 3. As g → 0, the belief sequence in (32) converges weakly to the unique and stationary SCE given by for all admissible values of the deep parameters. Proof. From (33) one can see that is a function of current and past beliefs and fundamental shocks. We denote this function as κ() such that Denote We can then rewrite the CGL algorithm (32) as (35) To prove that (34) holds at and the fixed point is unique, we denote the left‐hand‐side term in (34) by Under our assumptions, it follows from Kushner and Yin (1997) that as g → 0, the beliefs in (35) converge weakly to the solution of the ordinary differential equation (ODE) One can further show that Since γ1 > 0, γ2 > 0, and γ2 + γ1 < 1, the ODE has a unique fixed point at . The ODE is stable since (γ2 + γ1−1)/(1 − γ2) < 0. As one can see from Proposition 3, the SCE is exactly the same as the rational expectations steady state. Since an SCE is a limit of adaptive (learning) dynamics, it is important to characterise these dynamics and to study whether they are significantly different from dynamics under rational expectations. We rewrite the stochastic processes (32) and (33) as (36) Given the initial belief , the initial capital stock , and the shock processes, the bivariate autoregressive process (36) determines the belief and capital dynamics jointly; then, (23)–(26) in Section 2, or (A1)–(A4) in Appendix A, determine the dynamics of investment, labour, output and consumption. Clearly this learning model is linear and consequently the impulse responses do not depend on initial conditions. In Section 5, we discuss an alternative learning rule that nests the rational‐expectations solution and show that the results do depend on initial conditions and the size of the gain. We now provide a result showing that the linear system represented by the above learning model is stationary. Proposition 4. The learning dynamics, described by (23)–(26) and (36) for g ∈ (0,1), are stationary for all admissible values of the deep parameters. Proof. Given (A1)–(A4) in Appendix A that characterise the dynamics of investment, labour, output and consumption as a function of , it suffices to show that (36) is a stationary process. The two characteristic roots of the 2 × 2 coefficient matrix of and on the right‐hand side of (36) are Since γ1 > 0, γ2 > 0 and γ1 + γ2 < 1 for all admissible values of the deep parameters, it follows that both λ1 and λ2 are real numbers and for any g ∈ (0,1), 0 < λ1 < λ2 < 1. Hence, the adaptive process for , given by (36), is stationary. Proposition 4 implies that the learning dynamics studied in this article remain in the domain of attraction of the SCE (the rational expectations steady state) and thus the probability of escapes from the SCE is very small. To assess how different the learning dynamics differ from dynamics under rational expectations, we derive the belief and capital dynamics under the CGL as (37) (38) where L is the lag operator. It follows from (37) that (39) This can be simplified to If ρ ≠ λ1 or λ2, and ρ ≠ λ1 or λ2, then it simplifies further to 40 On the other hand, we can compute the rational expectations from (31) as (41) A comparison of (40) and (41) shows that, although the SCE is the same as the steady state REE, the dynamics of the beliefs can be different from the dynamics of the expectations . These differences lead to quantitatively important differences in the dynamics of other macroeconomic variables, as we show in the next section. 4. REE vs. SCE: Transmission of Technology Shocks We now analyse the transmission mechanisms of the model under both rational and adaptive expectations. We discuss simulated results based on a few sets of parameter values but the quantitative differences between learning and rational expectations dynamics exist for a wide range of values. The model parameters include β, the subjective discount factor; α, the labour share of income; δ, the capital depreciation rate; η, the inverse Frisch elasticity of labour supply; λz and λq, the average growth rate of the neutral and biased technologies; ξ, the weight parameter in the preferences for leisure; ρ, ρ, σ, and σ, the parameters controlling the shock processes, and g, the constant gain in the learning process. 4.1. Benchmark Parameter Values Table 1 summarises the benchmark parameter values that we use for our simulations. The model that we have in mind has a quarterly frequency. We set α = 0.7, corresponding to a labour income share of 70%. We set λq = 1.008 such that the investment‐specific technology grows at an annual rate of 3.2%, as suggested by Greenwood et al. (1997). We set λz = 1.0016 such that, given our value of λq and α, real per capita GDP grows at an annual rate of 2% on the path of balanced growth.5 We set δ = 0.03, so that the annual depreciation rate of capital is 12%. We follow the business cycle literature and set β = 0.99. We use a value of ξ = 3.17 so that the steady state working hours are about 1/3 of the representative agent’s time endowment. We follow Hansen (1985) and Rogerson (1988) and assume that labour is indivisible, implying that η = 0. For the parameters in the shock processes, we set ρ = ρ = 0.95, σ = 0.01, and σ = 0.005. These standard‐deviation values are consistent with the estimates in the empirical literature (Liu et al., 2008). Finally, we set the gain g = 0.05 in the learning process. This value is in the range of empirical estimates found in Sargent et al. (2006a). We have also experimented with other gain values and find that, under our benchmark learning rule (32), the results do not change much. Table 1 
Benchmark Parameter Values Preference . β = 0.99 . η = 0 . ξ = 3.17 . Labour share α = 0.7 Capital Depreciation δ = 0.03 Neutral Technology  λz = 1.0016 ρ  = 0.95 σ  = 0.01 Biased Technology  λq = 1.008 ρ  = 0.95 σ = 0.005 Learning Gain g = 0.05 Preference . β = 0.99 . η = 0 . ξ = 3.17 . Labour share α = 0.7 Capital Depreciation δ = 0.03 Neutral Technology  λz = 1.0016 ρ  = 0.95 σ  = 0.01 Biased Technology  λq = 1.008 ρ  = 0.95 σ = 0.005 Learning Gain g = 0.05 Open in new tab Table 1 
Benchmark Parameter Values Preference . β = 0.99 . η = 0 . ξ = 3.17 . Labour share α = 0.7 Capital Depreciation δ = 0.03 Neutral Technology  λz = 1.0016 ρ  = 0.95 σ  = 0.01 Biased Technology  λq = 1.008 ρ  = 0.95 σ = 0.005 Learning Gain g = 0.05 Preference . β = 0.99 . η = 0 . ξ = 3.17 . Labour share α = 0.7 Capital Depreciation δ = 0.03 Neutral Technology  λz = 1.0016 ρ  = 0.95 σ  = 0.01 Biased Technology  λq = 1.008 ρ  = 0.95 σ = 0.005 Learning Gain g = 0.05 Open in new tab 4.2. Amplification Effects To understand the role of introducing learning in transmitting the two types of technology shocks, we examine the impulse responses of macroeconomic variables in the model to each shock. 4.2.1. Neutral technology shock Figure 1 displays the impulse responses of several key macroeconomic variables, including output, consumption, investment, the real interest rate, labour hours, the real wage, the expectation (or the belief) of the next‐period capital and the current‐period capital stock, following a positive one‐standard‐deviation shock to the neutral technology under our benchmark parameter values. The solid lines represent the responses under rational expectations and the dashed lines represent the responses under adaptive expectations. Fig. 1. Open in new tabDownload slide Benchmark Model: Impulse Responses to a One‐standard Deviation Neutral Technology Shock
Notes. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. Fig. 1. Open in new tabDownload slide Benchmark Model: Impulse Responses to a One‐standard Deviation Neutral Technology Shock
Notes. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. The responses of aggregate variables to a neutral technology shock in the rational expectations model should be familiar to a student of real business cycle studies. As the solid line in the Figure shows, output rises on impact and declines gradually. Consumption, investment, hours, the real wage and the real interest rate all co‐move with output. In the impact period, consumption responds less and investment responds more than does output. These patterns of responses are consistent with the stylised facts about business cycles. A well‐documented difficulty facing the standard RBC model with rational expectations lies in the labour market dynamics (Christiano and Eichenbaum, 1992). The RBC model typically fails to generate the observed large responses of labour hours and small responses of the real wage following a neutral technology shock. In the RBC model, a positive neutral technology shock raises the demand for labour at any given real wage so that the labour demand schedule shifts out, creating a substitution effect. Thus, holding the labour supply schedule unchanged, the substitution effect drives up both hours and the real wage. In the mean time, since the shock is persistent and therefore raises future productivity, it creates a wealth effect that raises current consumption and thus shifts the labour supply curve up. The wealth effect partially cancels out the substitution effect on hours, rendering the responses of equilibrium hours small; meanwhile, the wealth effect reinforces the substitution effect on the real wage, pushing up the equilibrium wage sharply. As shown by Hansen (1985) and Rogerson (1988), labour indivisibility flattens the labour supply curve and thus magnifies the substitution effect following the positive neutral technology shock, although the wealth effect still makes the real wage rise sharply.6 As is evident in Figure 1 and in Table 2, the model with rational expectations implies that the initial response of hours is about 67% of that of output and the magnitude of the real wage response about 33% of that of output response. Indeed, as shown in Table 2, in the rational expectations model, the cumulative responses of hours at longer forecasting horizons (from 4 quarters to 24 quarters) are less than 58% and those of the real wages are more than 42% relative to the output responses. Table 2 
Cumulative Responses of Labour Market Variables Relative to Output Following the Neutral Technology Shock: Benchmark Parameters . Rational expectations . Adaptive expectations . Forecast Horizon Hours Real wage Hours Real wage 1 quarter 0.67 0.33 1.05 0.05 4 quarters 0.58 0.42 0.71 0.36 8 quarters 0.49 0.51 0.58 0.61 16 quarters 0.35 0.65 0.53 0.83 24 quarters 0.30 0.74 0.52 0.93 . Rational expectations . Adaptive expectations . Forecast Horizon Hours Real wage Hours Real wage 1 quarter 0.67 0.33 1.05 0.05 4 quarters 0.58 0.42 0.71 0.36 8 quarters 0.49 0.51 0.58 0.61 16 quarters 0.35 0.65 0.53 0.83 24 quarters 0.30 0.74 0.52 0.93 Open in new tab Table 2 
Cumulative Responses of Labour Market Variables Relative to Output Following the Neutral Technology Shock: Benchmark Parameters . Rational expectations . Adaptive expectations . Forecast Horizon Hours Real wage Hours Real wage 1 quarter 0.67 0.33 1.05 0.05 4 quarters 0.58 0.42 0.71 0.36 8 quarters 0.49 0.51 0.58 0.61 16 quarters 0.35 0.65 0.53 0.83 24 quarters 0.30 0.74 0.52 0.93 . Rational expectations . Adaptive expectations . Forecast Horizon Hours Real wage Hours Real wage 1 quarter 0.67 0.33 1.05 0.05 4 quarters 0.58 0.42 0.71 0.36 8 quarters 0.49 0.51 0.58 0.61 16 quarters 0.35 0.65 0.53 0.83 24 quarters 0.30 0.74 0.52 0.93 Open in new tab Introducing learning helps to alleviate some of the problems for the RBC model, especially for the labour market variables. The dashed lines in Figure 1 display the impulse responses of the aggregate variables in the model with adaptive expectations following a positive neutral technology shock. As in the rational expectations model, the shock raises the demand for labour at any given wage and this substitution effect leads to a rise in both hours and the real wage. Unlike the rational expectations model, however, the wealth effect is dampened because agents form expectations about future productivity and capital based on past observations. Consequently, on impact, consumption does not rise as much and thus the labour supply curve does not shift as much as in the rational expectations model. By dampening the wealth effect of the shock, the learning mechanism leads to a greater response of equilibrium hours and a smaller response of equilibrium real wage than those in the rational expectations model. Table 2 confirms these findings: in the model with adaptive expectations, the cumulative responses of hours relative to output for all forecasting horizons (up to 24 quarters) are much larger while the cumulative responses of the real wage relative to output are, at least in the short run (up to 4 quarters), much smaller than those in the rational expectations model. To the extent that some other frictions such as habit formation can also slow down the adjustment in consumption, one might wonder whether or not habit formation can help to alleviate the labour market puzzle as does our learning mechanism. Lettau and Uhlig (2000) show that habit formation slows down the adjustments of consumption for all periods, not just for the current period. As the agent desires slow adjustments of consumption in all future periods, he does not want to work hard in the current period to accumulate capital. Thus, a positive neutral technology shock leads to a small increase in hours and a large increase in the marginal product of labour and the real wage. In this sense, introducing habit formation can actually deepen the labour market puzzle. In contrast, the model with adaptive expectations that we consider here contains a very different propagation mechanism and helps to alleviate the labour market puzzle. Introducing adaptive expectations in the model also helps to amplify the responses of other aggregate variables. As shown in Figure 1, under adaptive expectations, the sharp rise in hours following the positive productivity shock leads to a sharp rise in output. As consumption does not change much on impact, investment rises sharply. The amplified response of investment implies amplified responses of the capital stock and the beliefs of future capital stocks relative to the rational expectations model. In summary, following a neutral technology shock, introducing learning amplifies the response of hours and dampens the responses of the real wage. Furthermore, learning helps to amplify the effects of the neutral technology shock on output, investment, and capital. 4.2.2 Biased technology shock There is a large literature on the macroeconomic effects of investment‐specific technology shocks in the context of rational‐expectations. Examples include Greenwood et al. (2000), Krusell et al. (2000), Fisher (2006) and He and Liu (2008). In this Section, we examine the effects of biased technology shocks in the context of adaptive expectations. In Figure 2, we plot the impulse responses of the same set of macroeconomic variables following a positive one‐standard‐deviation shock to the biased technology. In both the rational expectations model (solid lines) and the adaptive expectations model (dashed lines), the shock leads to a rise in output, investment, hours, capital stock and the real interest rate, and a short‐run decline in consumption and the real wage. Fig. 2. Open in new tabDownload slide Benchmark Model: Impulse Responses to a One‐standard Deviation Biased Technology Shock
Note. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. Fig. 2. Open in new tabDownload slide Benchmark Model: Impulse Responses to a One‐standard Deviation Biased Technology Shock
Note. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. As the biased shock raises the efficiency of investment, current investment becomes cheaper relative to consumption. Thus, this type of shock, unlike the neutral technology shock, shifts resources from consumption to investment. Consequently, investment rises and consumption declines for several periods. The decline in consumption shifts the labour supply curve down. Since the neutral technology stays unchanged and aggregate capital stock is predetermined, the labour demand curve does not shift. Thus, the downward shift of the labour supply curve lowers the real wage and raises equilibrium hours. The rise in labour hours helps to produce more output and raise the marginal product of capital, so that the real interest rate rises as well. This mechanism operates under both rational expectations and adaptive expectations. The patterns of the impulse responses following a positive biased technology shock are broadly consistent with the empirical evidence provided by Altig et al. (2004), except that consumption and the real wage in the model do not co‐move with output whereas consumption is weakly procyclical and the real wage is acyclical in the data based on VAR studies. The lack of co‐movement in the model is not surprising since Barro and King (1984) show that the standard one‐sector growth model can generate co‐movement only in the presence of contemporaneous total factor productivity shocks (i.e., the neutral technology shocks in our model). It is possible to fix the co‐movement problem by introducing several sources of frictions in the model; see, for example, Jaimovich and Rebelo (2008). We do not introduce other frictions because we would like to isolate the role of learning, which itself acts as a friction, in propagating technology shocks. The main difference between the learning model and the rational expectations model is that, with learning in place of full rationality, agents do not perfectly foresee the increase in the future level of investment technology. They respond to the persistent shock as though it had only a temporary effect. The wealth effect is thus dampened and the intertemporal substitution effect strengthened. Consequently, in the learning model, the biased technology shock leads to a greater rise in investment and a greater decline in consumption than that in the rational expectations model. The sharp decline in consumption amplifies the decline in the real wage and the rise in hours. The amplified increase in hours in turn leads to a sharp rise in output and thus in the real interest rate. These patterns are shown in Figure 2. In summary, introducing learning can substantially amplify the responses of all the aggregate variables following a biased technology shock. Overall, relaxing the assumption of perfect rationality helps to give a larger role to both neutral and biased technology shocks in shaping business cycles. 4.3. Less Persistent Shocks Since the transmission of the shocks in the model with adaptive expectations works through the muted wealth effect, the quantitative importance of learning should depend on the persistence of the shock. To understand to what extent the propagation mechanism in the learning model depends on the persistence of the shocks, we consider the case with less persistent shocks. In particular, we set ρ = ρ = 0.7 (instead of 0.95) and compute the impulse responses following each of the two types of technology shocks. Figure 3 displays the impulse responses of the key macroeconomic variables to a positive one‐standard‐deviation shock to the neutral technology.7 The responses under rational expectations are denoted by the solid lines and those under adaptive expectations are denoted by the dashed lines. Since the shock is less persistent, the wealth effect is weaker so that, in the rational expectations model, the rise in consumption is smaller and the rise in hours is larger than that under the benchmark parameter values. With the less persistent shock and the weaker wealth effect, introducing adaptive learning dampens the response of the real wage and amplifies the responses of other aggregate variables but to a lesser extent than in the benchmark case. These results are evident by comparing Figure 3 with Figure 1. Fig. 3. Open in new tabDownload slide Benchmark Model with low Persistence of the Shock: Impulse Responses to a Neutral Technology Shock
Notes. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. Fig. 3. Open in new tabDownload slide Benchmark Model with low Persistence of the Shock: Impulse Responses to a Neutral Technology Shock
Notes. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. Moreover, with the less persistent shock, the responses of both consumption and the real wage display a clear hump shape; the responses of investment, hours and the real interest rate all display an inverted hump shape; output rises in the impact period and declines monotonically thereafter. Under adaptive expectations, the representative agent is backward looking when forming expectations. In the impact period, the wealth effect of the shock is muted; the intertemporal substitution effect induced by the rise in the real interest rate makes consumption more expensive and saving more attractive. Thus, in the short run, consumption rises by less and investment rises by more than in the rational expectations model. Over time, however, the agent learns about the wealth effect of the positive technology shock while the intertemporal substitution effect becomes weaker as the real interest rate goes back to its steady state. Thus, consumption rises further before it begins to decline back to the steady state. The rise in consumption shifts the labour supply curve up and thus lowers labour hours and raises the real wage. As consumption climbs to its peak over time, hours and investment fall to the trough and the real wage rises to the peak. Since output falls back to the steady state over time, consumption, investment, and hours return gradually to the steady state. In summary, with less persistent shocks, the wealth effect in the rational expectations model becomes weaker and accordingly the amplification effect of adaptive expectations become weaker as well. The adaptive expectations model generates pronounced hump‐shaped responses while the rational expectations model does not. 5. An Alternative Learning Rule One interesting question is whether our main findings hinge on the particular learning rule (32). There are many alternative learning mechanisms, such as least‐square learning (Evans and Honkapohja, 2001), Bayesian updating through Kalman filtering (Sargent and Williams, 2005) and signal extraction when agents are confused between shocks to the level or to the growth rate of the technology (Edge et al., 2007). We focus on one particular constant‐gain learning rule that has the same specification as the rational expectations solution (30). Specifically, we replace by such that where Agents update their beliefs αt+1|t using the following recursive algorithm: (42) (43) As g → 0, the equilibrium under this adaptive learning approaches the rational expectations equilibrium and is therefore E‐stable in the usual sense of Evans and Honkapohja (2001). Unlike the benchmark learning rule studied in Section 3, this alternative rule is updated nonlinearly and thus short‐run dynamic results can be quite different for different initial conditions. This point is discussed in Carceless‐Poveda and Giannitsarou (2007). One particular type of initial conditions studied by Carceles‐Poveda and Giannitsarou (2007) is to generate the initial data, from the equilibrium solution to the rational‐expectations model.8 The initial conditions can then be computed as With these initial conditions, one can update the beliefs recursively according to (42) and (43). We simulate the model under the benchmark parameter values summarised in Table 1 and we also examine the sensitivity of the learning equilibrium to changes in the initial conditions and the size of the gain parameter. When the gain is small and the initial data set is large, the differences between the dynamics under learning and those under rational expectations tend to be very small. Figure 4 displays an example of impulse responses to one‐standard‐deviation neutral technology shock with g = 0.001 and t0 = 10000. As the Figure shows, the learning model and the rational expectations model generate quantitatively similar responses. This result is consistent with the findings in Williams (2003) and Carceles‐Poveda and Giannitsarou (2007). In a recent paper, Eusepi and Preston (2008) show that learning can nonetheless amplify the dynamic responses if one relaxes the standard assumption that agents use only one‐period ahead forecasts to form their beliefs. Fig. 4. Open in new tabDownload slide Model With Alternative Learning Rule (g = 0.001 and t0 = 10,000): Impulse Responses to a Neutral Technology Shock
Note. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. Fig. 4. Open in new tabDownload slide Model With Alternative Learning Rule (g = 0.001 and t0 = 10,000): Impulse Responses to a Neutral Technology Shock
Note. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. We argue that even with the standard learning mechanism (42)–(43), different gain values or different initial conditions can produce qualitatively different impulse responses. In this Section we focus on cases where adaptive learning under this sophisticated rule can amplify the dynamic responses of aggregate variables to a neutral technology shock, generate negative responses of hours and produce procyclical movements of consumption and output.9 As the gain parameter increases, the sophisticated learning rule can amplify the dynamic responses to a technology shock in the same magnitude as does the simple learning mechanism studied in Section 4. Figure 5 displays such an example, where we set g = 0.05 and t0 = 10,000. As one can see, the impulse responses under our alternative learning are qualitatively similar to those under the benchmark learning rule shown in Figure 1. Fig. 5. Open in new tabDownload slide Model With Alternative Learning Rule (g = 0.05 and t0 = 10,000): Impulse Responses to a Neutral Technology Shock
Note. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. Fig. 5. Open in new tabDownload slide Model With Alternative Learning Rule (g = 0.05 and t0 = 10,000): Impulse Responses to a Neutral Technology Shock
Note. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. It is important to note that the dynamics under nonlinear learning are in general sensitive not only to changes in initial conditions and the size of the gain, as found by Carceles‐Poveda and Giannitsarou (2007) but also to changes in some of the deep parameters.10 Consider a case with a smaller sample of initial data (t0 = 100 instead of 10,000) and with a smaller Frisch elasticity of labour supply (η = 2 instead of 0). Figure 6 shows the impulse responses to a positive neutral technology shock in this case. The results reveal that the learning model is capable of generating negative responses of labour hours following a neutral technology shock even in this one‐sector growth model that abstracts from other frictions such as habit formation and investment adjustment costs considered by, for example, Francies and Ramey (2005). In response to the neutral technology shock, consumption rises more and output rises less in the learning model than in the rational‐expectations model. The sharp rise in consumption shifts the labour supply curve up so much that the real wage rises sharply and the hours fall. In the mean time, the sharp rise in consumption and the modest rise in output leads to a smaller rise in investment than that in the rational expectations model. Fig. 6. Open in new tabDownload slide Model with Alternative Learning Rule (g = 0.05 and t0 = 100) and Low Frisch elasticity (η = 2): Impulse Responses to a Neutral Technology Shock
Note. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. Fig. 6. Open in new tabDownload slide Model with Alternative Learning Rule (g = 0.05 and t0 = 100) and Low Frisch elasticity (η = 2): Impulse Responses to a Neutral Technology Shock
Note. The solid line represents the responses under rational expectations. The dashed line represents the responses under adaptive expectations. The most interesting result is that hours can decline following a positive neutral technology shock in the learning model, whereas the responses of hours are always positive under rational expectations. Recent empirical work has documented evidence in favour of negative responses of hours to a positive neutral technology shock (e.g., Galí (1999) and Basu et al. (2006)). Learning, serving as a friction, is capable of generating the responses of investment and hours similar to Francies and Ramey (2005), where investment‐adjustment costs and habit are introduced into a standard real‐business‐cycle model as alternative frictions. In summary, the exercise in this Section shows that the sophisticated learning rule has much flexibility to amplify the effects of technology shocks and produce qualitatively different transmission mechanisms than does the rational‐expectations model. Since this learning mechanism is nonlinear, not only changes in initial conditions and the size of the gain can alter the equilibrium dynamics, changes in the size of shock variance can also affect the dynamics considerably. In future work, therefore, we would like to estimate the initial conditions, the variances, and the gain parameters along with other model parameters, as proposed in Sargent et al. (2006b). 6. Conclusion We have studied a standard stochastic growth model with adaptive expectations in which beliefs are decoupled from decision rules. For the benchmark learning rule studied in Marcet and Nicolini (2003) and Sargent et al. (2006a), we have established that there exists a unique, stable SCE in our learning model and that the SCE is the same as the steady state REE. In contrast to the existing literature, however, we have shown that the learning model can generate substantially different dynamics from those implied by the rational expectations model. These differences are not driven by escape dynamics. It is known that technology shocks in the standard growth model do not generate enough fluctuations in key macroeconomic variables such as hours and output. Introducing learning in the growth model dampens the wealth effect. This muted wealth effect, coupled with the strong intertemporal substitution effect, amplifies the responses of macroeconomic variables and can make dynamic responses hump‐shaped. These results hold true with a more sophisticated learning rule under certain initial conditions. Our results suggest that the learning mechanism is flexible enough to generate some realistic features in a simple one‐sector growth model. Our findings also suggest that, to gauge the full potential of the learning mechanism in propagating the shocks in the growth model, one would need to jointly estimate the initial conditions with the gain parameter and other deep parameters. We hope our work helps to motivate future empirical studies on the importance of learning. Footnotes 1 " To give a few examples, Lucas (1986), Marcet and Sargent (1989) and Evans and Honkapohja (2001) recommend selecting rational expectations equilibria that are stable under least squares learning; Primiceri (2006), Sargent et al. (2006b) and Carboni and Ellison (2008) use learning mechanisms to explain the rise and fall of American inflation; Adam et al. (2008) show how learning helps to improve the fit of the model of asset pricing. 2 " Williams (2003) studies another form of misspecified learning in which agents do not know the true parameters of the production function. By assuming full depreciation of the capital stock, an i.i.d. technology process, and inelastic labour, he shows that learning leads to occasional, but recurrent, large deviations away from an SCE, called ‘escape dynamics.’ For other studies of escape dynamics, see Sargent (1999), Cho et al. (2002), Kasa (2004) and Adam et al. (in press). 3 " In the case with ρ = 1, we have and νt = νt−1 exp (ɛνt), or equivalently, Zt = Zt−1λz exp (ɛνt). 4 " An alternative approach to induce stationarity in the model is to detrend the variable by its deterministic trend. For instance, one can define , where Xt ∈ {Yt,Ct,It,Kt} and λx is a function of λz and λq. Our approach has an advantage in that it nests the model with stochastic trends (e.g., random walk processes) as a special case while the other approach does not. 5 " The average growth rate for output in the model is given by . 6 " If the Frisch elasticity of labour supply is small (i.e., if η is large), as the micro evidence suggests, the labour supply curve would be steep and the substitution effect would be small. Consequently, the response of hours would be smaller and the response of the real wage would be even larger than in the model with indivisible labour. 7 " To conserve space, we do not report the impulse responses following the biased technology shock here. The responses are qualitatively similar to those in the benchmark model, although the amplification effects of learning become smaller as the shock is less persistent than that in the benchmark model. 8 " With imperfectly rational agents, it seems logically incoherent to generate the initial data. Nonetheless, we follow this approach in the literature to make our work comparable. 9 " To conserve space, we do not present the impulse responses following the biased technology shock under the alternative learning rule. These results are similar to those displayed in Figure 2. 10 " Our sophisticated learning rule is similar to the one studied by Carceles‐Poveda and Giannitsarou (2007), who also examine the role of learning in a stochastic growth model. As in Carceles‐Poveda and Giannitsarou (2007), we find that the dynamics are sensitive to changes in the initial conditions and the size of the gain. Different from Carceles‐Poveda and Giannitsarou (2007), we focus on the model’s ability to generate plausible labour market dynamics, whereas Carceles‐Poveda and Giannitsarou (2007) assume inelastically supplied labour. 11 " We can also show that, provided ρ ≠ a1 and ρ ≠ a1, the solution prescribed by a = a2 above corresponds to an explosive path. References Adam , K. , Evans , G. 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( 1988 ). ‘Indivisible labor, lotteries and equilibrium’ , Journal of Monetary Economics , vol. 21 , pp. 3 – 16 . Google Scholar Crossref Search ADS WorldCat Sargent , T. J. ( 1999 ). The Conquest of American Inflation . Princeton University Press , Princeton, New Jersey. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Sargent , T. J. ( 2007 ). ‘Evolution and intelligent design’ , AEA Presidential Address , New York University. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Sargent , T. J. and Williams , N. ( 2005 ). ‘Impacts of priors on convergence and escapes from nash inflation’ , Review of Economic Dynamics , vol. 8 ( 2 ), pp. 360 – 91 . Google Scholar Crossref Search ADS WorldCat Sargent , T. J. , Williams , N. and Zha , T. ( 2006a ). ‘The conquest of South American inflation’ , NBER Working Paper No. 12606. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Sargent , T. J. , Williams , N. and Zha , T. ( 2006b ). ‘Shocks and government beliefs: the rise and fall of American inflation’ , American Economic Review , vol. 96 ( 4 ), pp. 1193 – 224 . Google Scholar Crossref Search ADS WorldCat Williams , N. ( 2003 ). ‘Adaptive learning and business cycles’ , mimeo, Princeton University . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Appendix A. Analytical Solution The coefficients in (29) in Proposition 1 are defined as: The steady state ratios such as ck and ik have been derived in Section 2. One can verify that, for all admissible values of the deep parameters, that is, for any β ∈ (0,1), η ≥ 0, α ∈ (0,1), δ ∈ [0,1], λz ≥ 1, and λq ≥ 1, all the steady‐state ratios are well‐defined and positive, and so are γ1 and γ2. The closed‐form solutions for investment, hours, output and consumption are derived as the the following system of equations under either rational or adaptive expectations: (A1) (A2) (A3) (A4) It is clear how the equilibrium can be solved. Once the solution for capital is obtained, as shown in Section 3, (A1) can be used to solve for investment, (A2) for labour, (A3) for output, and (A4) for consumption. B. Proof of Proposition 1 By successive substitutions in (23)–(27), one can derive (29). Specific steps are described below. We begin by first deriving the following two relations from (25) and (26): (A5) (A6) Substituting (A5) into (23), we get: (A7) Substituting (A7) into (24) yields (A8) Substituting (A6) and (A7) into (27) yields (A9) Rewrite (A8) as (A10) It follows that (A11) Substituting (A10) and (A11) into (A9), and rearranging, we get where Further simplifying, we get where Simplifying further, we have which gives the results in Appendix A. C. Proof of Proposition 2 Because (29) is a second‐order differential equation, there are only two solutions. We will show, next, that one solution is stationary and the other explosive. Thus, there is a unique stationary solution. The coefficient a in (30) takes on one of the following two values: We can verify that γ1 > 0 and γ2 > 0 for all admissible values of the deep parameters. We can further show that γ1 + γ2 < 1 if and only if , which holds too for all admissible values of the deep parameters. Since γ1 > 0, γ2 > 0, γ1 + γ2 < 1, we have γ1 ∈ (0,1), γ2 ∈ (0,1), and 4γ1γ2 < 1. It follows that a1 and a2 are real numbers. Knowing the above ranges for γ1 and γ2, we can in fact show that a1 ∈ (0,1) and a2 > 1. We can then verify that (ρ + a1)γ1 < 1 and (ρ + a1)γ1 < 1, which imply that γ1a1 < 1, and so the solution prescribed by a = a1 above corresponds to a (unique) stationary rational expectations equilibrium.11 Given the initial condition and the driving processes, (30) completely pins down capital, and then (A1), (A2), (A3) and (A4) determine investment, labour, output and consumption, respectively. From Proposition 2 on, whenever we mention REE, we refer to this stationary REE, where we also write a1 simply as a. Author notes " We thank the referees and the editor as well as Klaus Adam, James Bullard, Marty Eichenbaum, Martin Ellison, George Evans, Seppo Honkapohja, Selo Imrohoroglu, Bruce Preston, Tom Sargent and Paolo Surico for helpful comments. The views expressed herein are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Atlanta, the Federal Reserve Bank of San Francisco or the Federal Reserve System. © The Author(s). Journal compilation © Royal Economic Society 2009

Lockwood,, Ben;Migali,, Giuseppe

doi: 10.1111/j.1468-0297.2008.02235.xpmid: N/A

Abstract Tax competition theory predicts that the introduction of the EU Single Market in 1993 should have caused excise tax competition and thus increased strategic interaction in the setting of excise taxes among EU countries. We test this prediction using a panel data set of 12 EU countries over the period 1987–2004. We find that for excise duties on still and sparkling wine, beer and ethyl alcohol, strategic interaction significantly increased after 1993. There is weaker evidence of increased interaction in cigarette taxes, possibly because cigarettes are widely smuggled, giving rise to tax competition even before the Single Market. The Single European Act, which came into force in July 1987, initiated a vast legislative programme involving the adoption of hundreds of directives and regulations, which gradually established the single market amongst EU member states over a period up to the end of 1992. Two of the most important provisions of the single market were: first, to allow individuals to import relatively large quantities of goods purchased abroad, which had previously been subject to the importing country’s rate of tax and, second, the abolition of physical border controls, which were replaced by random spot checks. Before 1 January 1993, all imports by EU residents from other EU countries were essentially subject to destination‐based taxation i.e. taxation at the rate of excise and VAT of the country to which the good was imported.1 But, since 1 January 1993, all imports by EU residents from other EU countries were subject to origin‐based taxation. Specifically, there are no restrictions on such imports, except  (i) that tax must have been paid in the country of purchase of the good and  (ii) that goods are not for resale. Condition (ii) is enforced by generous upper limits, plus random customs checks at borders. For example, according to the UK Customs and Excise, ‘if you bring back large quantities of alcohol or tobacco, a Customs Officer is more likely to ask about the purposes for which you hold the goods. This will most likely be the case if you appear at the airport with more than: 3,200 cigarettes, 400 cigarillos, 200 cigars, 3kg of smoking tobacco, 110 litres of beer, 10 litres of spirits, 90 litres of wine, 20 litres of fortified wine i.e.: port or sherry’. The above allowance is more than enough for the annual consumption of the average two‐adult household. Moreover, imports in excess of these levels do not automatically trigger fines or prosecution: the levels are indicative only, and the onus is on Customs officials to prove smuggling. These changes in the rules create incentives both for legitimate tax‐induced cross‐border shopping and for smuggling. There is evidence that both these activities are occurring on a large scale at some borders. For example, the rates of excise duty on alcoholic drinks and tobacco products in the UK are significantly higher than those in most other EU Member States, especially France. The UK tax authority (HMRC, 2002) estimates that 2001/2: 7% of all cigarettes consumed in the UK were cross‐border shopped, and 21% illegally smuggled, implying a tax revenue loss of £3.6 billion to the UK Treasury, 7% of all wine consumed in the UK was cross‐border shopped and 2% illegally smuggled, implying a tax revenue loss of over £250 million, and 1% of all beer consumed in the UK was cross‐border shopped and 4% smuggled, mostly by ‘cross‐channel passenger smuggling’, implying a loss of also over £250 million. What is less clear is whether these changes, and the subsequent excise revenue losses in high‐tax countries, have caused tax competition between EU member states to occur or intensify. Certainly, the theory (Kanbur and Keen, 1993; Lockwood, 1993; Ohsawa, 1999; Nielsen, 2001) suggest that this should happen. As just observed, the Single Market resulted in a switch from destination‐ to origin‐based taxation of cross‐border transactions by individuals. These models predict that tax competition only occurs with origin‐based taxation. So, the models predict, unambiguously and generally, that we should observe competition in excise taxes between EU countries only after 1993.2 It is important to test this prediction, not least because of widespread concern on the part of policy makers, perhaps motivated by the theory, about the single market and tax competition. For example, it is well documented that fear of excise tax competition after the completion of the single market caused the European Commission to push for minimum excise taxes in the late 1980s; these minima were actually introduced in 1993.3 This article represents the first attempt, to our knowledge, to do this directly. Of course, strategic interaction can occur for other reasons e.g. yardstick competition, or common intellectual trends. So, the observable implication of the theory is that strategic interaction between EU countries in the setting of excise taxes should intensify after 1993. How much it intensifies depends on the scale of cross‐border shopping and potential revenue losses from high taxes: as the above discussion indicates, these might be quite large. The key idea of the article is that completion of the single market can be interpreted as a kind of ‘natural experiment’ that allows us to separate the effects of tax competition from other forms of strategic interaction. We employ a balanced panel data set of 12 EU countries over the period 1987–2004, which has excise taxes on five commodities: still wine, sparking wine, beer, products made from ethyl alcohol, i.e. spirits, and cigarettes. The excise tax data were taken from the European Commission’s Excise Duty Tables and Inventory of Taxes. Using this data set, we estimate an empirical model where the excise tax in a given country depends linearly on the weighted average of other countries’ taxes and a set of control variables. Following the literature, we assume that the weights are contiguity weights; that is, country i reacts to j’s tax only if they have a common border. This is a very plausible assumption to make, as cross‐border shopping typically occurs between immediate geographical neighbours.4 We test for structural breaks in reaction functions around 1993 in two ways. First, in order to conserve degrees of freedom, given the relatively small size of the sample, we only allow the slope of the tax reaction function to vary before and after 1993, imposing equality on all the other coefficients. We call this specification a tax‐specific structural break. Then, we allow for a completely general structural break, estimating the tax reaction functions separately on sub‐samples before and after 1993. For both specifications, we find robust evidence that for all product groups except cigarettes, the degree of strategic interaction has increased since 1993. For the baseline tax‐specific structural break model, the slope of the tax reaction function is insignificantly different from zero prior to 1993 for wine, beer or alcohol taxes, but it is always significantly positive after 1993. A 1 euro increase in a tax on one of these product groups by all other countries causes a typical country in the sample to raise its own tax by about 0.2–0.28 euro. For the general structural break model, the findings are similar. The slope of the tax reaction function is always insignificantly different from zero prior to 1993 for wine, beer or alcohol taxes, but it is always significantly positive after 1993. Moreover, we can always reject the null hypothesis of equality of coefficients in the two regressions. Thus one could go further and say that for these four products, there is evidence, consistent with the theory, that the single market, by creating incentives for cross‐border shopping, caused strategic interaction between countries in the form of tax competition. The situation for cigarette taxes, is however, rather different. As explained in more detail below, overall, there is much weaker evidence that tax competition intensified with the single market in the case of cigarettes.5 One possible explanation for this difference is that, as remarked above, the amount of illegal smuggling relative to cross‐border shopping is much larger for cigarettes than it is for the other products. So, it is possible that governments of the countries in our sample took account of how their neighbours were taxing cigarettes even before 1993 for this reason.6 In Section 4, we discuss the robustness of our findings to various changes in the empirical specification of the model. We consider the effect of dropping country controls in the general structural break model, because they seem to be imprecisely estimated in the period 1987–2002, due to the small number of observations. Our results are robust to this change. We also experiment with different weighting schemes, and measuring the taxes in national currency, rather than euros. Finally, we also investigate the impact of minimum tax rates, also introduced in 1993, on strategic interaction. Unfortunately, as explained in Section 4.3, the theory does not have any robust predictions about how a minimum tax will affect tax reaction functions. Also, because we split the sample in 1993, we can only consider minimum taxes that change in real terms after 1993. Only two such minima meet this criterion, the minimum taxes on beer and ethyl alcohol.7 An increase in both of these minima have a significantly positive effect on the amount of strategic interaction. The related literature is as follows. First, there is a small empirical literature on spatial interactions in excise taxes in the US (Nelson, 2002; Rork, 2003; Devereux et al., 2007). But in the US, there has been no ‘natural experiment’ similar to the completion of the single market in the EU in recent times. Within the US, transactions by individuals of excisable commodities that cross state borders are essentially unrestricted, meaning that the origin regime is firmly in place for these kinds of transactions.8 There are also a couple of cross‐country empirical studies of strategic interaction in commodity taxes (Egger et al. 2005; Evers et al. 2004). Egger et al. (2005) test some of the predictions of Ohsawa’s theoretical model of commodity tax competition on commodity tax data for a panel of 22 OECD countries. But, unlike our study, they use an aggregate indicator of commodity taxation taken from national accounts data, which, relative to our article, obviously has the disadvantage that it does not measure the setting of individual tax instruments by governments very precisely. The article by Evers et al. (2004), in contrast, studies strategic interaction in the setting of diesel excises in EU countries, plus Norway and Switzerland, and so is closest to our article. But, almost by definition, the treatment of imports of fuel in the tank of a vehicle must be on an origin basis9 and so completion of the single market has no predicted effect on the setting of this excise, except possibly through the introduction of a minimum EU excise; the latter effect is the focus of Evers et al. (2004). Finally, Crawford et al. (1999) study a related issue; whether the elasticity of demand for beer, wines and spirits has increased in the UK since the advent of the single market. They reject the hypothesis that elasticities have increased, which is somewhat surprising given the very large scale of cross‐border shopping for these goods in France. In any case, this does not directly contradict our findings, as tax competition could be driven by the belief on the part of governments that elasticity of the domestic tax base has increased, whether or not it has in reality. The rest of the article is structured as follows. In Section 1, we explain our econometric method and estimation procedure. Section 2 describes the data, Section 3 the results and Section 4 some robustness checks. Section 5 provides concluding comments. 1. The Econometric Model In the theoretical model first presented by Kanbur and Keen (1993) and developed by Ohsawa (1999) and Nielsen (2001) amongst others, origin‐based commodity taxation generates positively sloped tax reaction functions between a set of countries.10 That is, under the assumptions made in those papers, in country i = 1,…,n, the excise tax, τi, is an increasing, piecewise linear, function of the tax rate in the other countries, τj, j ≠ i. Moreover, under realistic assumptions,11 the response of τi to τj will be non‐zero only if i and j are contiguous, i.e. share a common border. Finally, this response will depend on the length of the border between i and j and also on the population sizes in the two countries (Ohsawa, 1999; Devereux et al., 2007). Our empirical specification is therefore the following: (1) where i = 1,…,n denotes a country, t = 1,…,T a time‐period, fi a country fixed effect, zit a k × 1 vector of relevant characteristics of country i at time t, δ a k × 1 vector of coefficients and, finally, αij are coefficients measuring how τi responds to τj. However, this cannot be estimated as it stands, as there are too many parameters αij to be estimated. The usual approach is define αij = βωij and thus to modify (1) as: (2) where the ωij are exogenously chosen weights that aggregate the tax rates in other countries into a single variable τ−i,t, which has coefficient β. The ωij are usually normalised so that ∑j≠i ωij = 1. This is a widely used procedure and there is considerable discussion of the appropriate weights in the literature, e.g., Brueckner (2003). Our key theoretical hypothesis is that β is higher when the Single Market regime is in place. In fact, if only tax competition and no other form of strategic interaction is present, we expect β = 0 before 1993. We test for this dependence in two ways. First, we allow for a change only in the reaction function slope coefficient β after 1993, assuming that all other coefficients remain unchanged. That is, we estimate (3) where Dt = 1 if t≥1993 and Dt = 0 otherwise. The theory thus predicts that γ > 0. This has the advantage of being a relatively parsimonious specification, with only β,γ and coefficients on five exogenous covariates to be estimated.12 This is important because of the relatively small size of the panel; we only have 204 observations. We call this the tax‐specific structural break specification. We test the robustness of the tax‐specific structural break specification by allowing for a more general structural break; that is, by estimating (2) separately on sub‐samples 1987–92 and 1993–2004. Let the estimates of β on the earlier and later sub‐samples be β1,β2 respectively. So, our basic hypothesis is that β2 > β1. Note also that with this specification we effectively allow the intercept of the reaction functions (2) to shift after 1993. We call this the general structural break specification. This specification is more demanding of the data, as then in the earlier period, six parameters β,δ are to be estimated from only 60 observations. The system (2) is known as a spatial autoregressive model (SAR). OLS estimation of a SAR model is inappropriate, because the right‐hand side variables τjt, j ≠ i are endogenous. We estimate this system by instrumental variables. In the case of the general structural break model, at the first stage, the endogenous variable τ−i,t is instrumented by the weighted averages of the controls i.e. , for control c = 1,..k. In the case of the tax‐specific structural break model, there are two endogenous variables, τ−i,t and Dt × τ−i,t, and these are instrumented by , and . So, our maintained hypothesis is that in country, the controls are exogenous to the setting of excise taxes on tobacco and alcohol products; given our list of controls in Table 1 below, this seems reasonable. Table 1 
Descriptive Statistics . Mean . Standard deviation . Overall . Within . Between . Tax variables Still wine* 49.222 77.858 18.094 78.899 Sparkling wine* 107.711 139.652 29.825 142.147 Beer† 2.095 2.207 0.539 2.230 Ethyl alcohol‡ 1299.449 814.965 375.130 753.811 Cigarettes spec§ 29.574 34.595 16.355 31.763 Cigarettes tot¶ 64.566 11.195 9.754 5.724 Controls Poptot 292.126 268.515 6.899 279.674 Govcons 19.864 3.295 0.991 3.274 Govright 0.436 0.497 0.461 0.191 Govleft 0.274 0.447 0.326 0.318 . Mean . Standard deviation . Overall . Within . Between . Tax variables Still wine* 49.222 77.858 18.094 78.899 Sparkling wine* 107.711 139.652 29.825 142.147 Beer† 2.095 2.207 0.539 2.230 Ethyl alcohol‡ 1299.449 814.965 375.130 753.811 Cigarettes spec§ 29.574 34.595 16.355 31.763 Cigarettes tot¶ 64.566 11.195 9.754 5.724 Controls Poptot 292.126 268.515 6.899 279.674 Govcons 19.864 3.295 0.991 3.274 Govright 0.436 0.497 0.461 0.191 Govleft 0.274 0.447 0.326 0.318 *euro per h1 of product not exceeding 12% of alcohol. †euro per h1/degree Plato, alcoholic strength by volume exceeding 0.5%. ‡euro per h1 of pure alcohol. §euro per 1000 cigarettes. ¶% retail price. Euro converted from national currency, before 01/01/1999 ECU. Open in new tab Table 1 
Descriptive Statistics . Mean . Standard deviation . Overall . Within . Between . Tax variables Still wine* 49.222 77.858 18.094 78.899 Sparkling wine* 107.711 139.652 29.825 142.147 Beer† 2.095 2.207 0.539 2.230 Ethyl alcohol‡ 1299.449 814.965 375.130 753.811 Cigarettes spec§ 29.574 34.595 16.355 31.763 Cigarettes tot¶ 64.566 11.195 9.754 5.724 Controls Poptot 292.126 268.515 6.899 279.674 Govcons 19.864 3.295 0.991 3.274 Govright 0.436 0.497 0.461 0.191 Govleft 0.274 0.447 0.326 0.318 . Mean . Standard deviation . Overall . Within . Between . Tax variables Still wine* 49.222 77.858 18.094 78.899 Sparkling wine* 107.711 139.652 29.825 142.147 Beer† 2.095 2.207 0.539 2.230 Ethyl alcohol‡ 1299.449 814.965 375.130 753.811 Cigarettes spec§ 29.574 34.595 16.355 31.763 Cigarettes tot¶ 64.566 11.195 9.754 5.724 Controls Poptot 292.126 268.515 6.899 279.674 Govcons 19.864 3.295 0.991 3.274 Govright 0.436 0.497 0.461 0.191 Govleft 0.274 0.447 0.326 0.318 *euro per h1 of product not exceeding 12% of alcohol. †euro per h1/degree Plato, alcoholic strength by volume exceeding 0.5%. ‡euro per h1 of pure alcohol. §euro per 1000 cigarettes. ¶% retail price. Euro converted from national currency, before 01/01/1999 ECU. Open in new tab Finally, we turn to the specification of the weighting matrix. Following the theoretical literature and several empirical studies, our baseline weighting matrix uses contiguity weights. These weights capture the idea that with cross‐border shopping, tax bases are typically mobile only between geographically neighbouring countries and so governments are likely to react only to what their geographical neighbours do. Specifically, we define contiguity weights as: (4) where Ni is the set of states that border state i, and ni = #Ni. This assigns equal weight to all countries on the border of country i, and weight zero to the other countries. The matrix is normalised to have rows summing to one. One problem in implementing (4) is that it is difficult to define ‘neighbours’ when a country is an island, or part of an island, or has no direct EU neighbours. These problems arise for three of the eight countries in our data‐set: UK, Ireland and Greece. A strict imposition of contiguity weights for the UK, for example, would give only Ireland as the neighbour for the UK and vice versa. This is inaccurate, because it does not account for the considerable tax‐induced cross‐border shopping between the UK and France. Our solution is to say that if i is an island, a positive contiguity weight was given to country j when j could be directly reached from country i by crossing only over water, i.e. without passing through a third country.13 In Section 4.2, we consider the robustness of our results to alternative weighting schemes. 2. Data We construct a balanced panel of data from 12 EU countries over 17 years, 1987 and 1989–2004 inclusive. We consider only the countries which were members of the EU in 1987, excluding those that joined the EU later on. Data are not available for the year 1988, so there are 204 observations. Data on excises are based on the Excise Duty Table issued by the European Commission, cross‐checked against the available issues of the Inventory of Taxes (only available for 1994, 1999, 2002). In the case of a discrepancies, which were not many, we took the data from the Inventory of Taxes as being authoritative, as these data are directly supplied by the member countries. We study taxes on five kinds of products: still wine, sparkling wine, beer, cigarettes and ethyl alcohol, the last being effectively an excise tax on spirits, such as whisky, brandy etc.14 All of these products, except for cigarettes, are only subject to a specific excise tax, i.e. levied per unit of physical quantity. Where there are several rates of tax, e.g., standard and reduced rates, we use only the standard rates. The physical units in which the goods are measured are indicated in Table 1. In the case of cigarettes, all countries also levy an ad valorem excise tax. Moreover, depending on the country, either the specific or ad valorem component of the tax can be the more important one and so we cannot safely ignore either. We do not have data separately on the retail price of cigarettes, so we are constrained by data in the Excise Duty Tables. These report both the specific tax and the total tax (specific, ad valorem and VAT) as a percentage of the retail price. We use both these tax measures. In Figures A.1–A.5 in the Appendix, we report for each of the five goods the time series plot of the tax rates in national currency, unadjusted for inflation. Some general features can be identified. First, as might be expected, countries generally adjust their taxes upwards, in response to general price inflation. Second, there are some exceptions, associated with the start of the single market in 1993. For example, both Denmark and Luxembourg cut their tax on wine (still and sparkling) by large amounts in 1992, in the case of Luxembourg to zero. Again, Denmark cut its tax on beer, and Germany and Luxembourg raised their tax on beer, both by large amounts, in 1992. When we run the regressions, we make two changes to the dependent variable. First, we adjust for inflation by dividing through by the RPI for the relevant country, with 2000 as the base year, because rational governments will be concerned with the real, rather than nominal, value of the taxes they set. Perhaps for this reason, we did not find any evidence of strategic interaction when we used nominal taxes. Second, we find that our regressions work a little better when the dependent variable is converted to euros,15 possibly because countries are comparing their own taxes to others in different national currencies and can only do so in a common currency.16 Table 1 gives some basic decomposition of the variance of both taxes and covariates between country and within‐country components. The taxes are in real terms, expressed in euros. Note that while most of the variation is between countries, there is some variation in taxes over time.17 Finally, in estimating the determinants of the taxes, we need to control for other factors. We use a parsimonious set of controls that can be found in most of the existing empirical literature on tax competition. First, we have the basic variables of GDP per capita in local currency units and total population in hundreds of thousands of inhabitants. We expect total population to increase the level of tax, as it is a robust prediction of the theory that larger countries set higher taxes in the origin regime, because they have a larger domestic tax base. (The GDP per capita variable is not reported in Table 1, as it is not comparable across countries.) We also include government final consumption expenditure as a percentage of GDP as an indicator of demand for tax revenue. All of these variables are taken from World Bank WDI. We add two political 0–1 dummy variables for the ideological orientation of governments. We used the Schmidt Index,18 included in the Comparative Political Data Set 1960–2004 (Armingeon et al., 2006), to define a dummy for right‐wing cabinets, a dummy for stand‐off between left and right cabinets, and a dummy for left‐wing cabinets. The second dummy is used as the reference category in the estimation. The descriptive statistics for the controls are also given in Table 1. 3. Results The results are given by commodity in Tables 2–4. All have the same format. Each Table gives the results for a pair of taxes. The top panel gives regression coefficients. In columns 1 and 4, the estimate of the baseline tax‐specific structural break model (3) is reported. The key coefficient of interest is the coefficient on D × τ−i, i.e. just γ in (3). In columns 2 and 3, and in columns 5 and 6, the estimate of the general structural break model is reported. For example, looking at columns 2 and 3 of Table 2, we see that these report estimates of (2) for the specific tax on still wine for each of the two sub‐periods 1987–92, and 1993–2004 are separately. Table 2 
Estimates for Wine Taxes . Still wine . Sparkling wine . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i −0.165 −0.521 0.423*** −0.044 −0.704 1.215*** (0.318) (1.458) (0.151) (0.417) (2.467) (0.323) D × τ−i 0.280** 0.206** (0.131) (0.095) Total population 0.461** 0.669 0.440* 0.961*** 1.839 −0.023 (0.228) (0.588) (0.258) (0.312) (1.362) (0.226) gdppc −0.037 −0.043 0.005 −0.137** −0.103 −0.061 (0.023) (0.174) (0.015) (0.057) (1.021) (0.048) govcons −2.066* 0.491 −0.566 −4.463* −0.504 4.509 (1.206) (2.751) (1.100) (2.467) (5.592) (3.161) govright −3.048 7.046 −1.413 −4.861 15.431 7.076 (3.320) (5.944) (3.433) (6.075) (13.587) (8.238) govleft −3.892 7.956 −2.330 −6.457 12.950 4.842 (4.128) (6.911) (4.430) (6.279) (16.250) (8.095) N 204 60 144 204 60 144 F‐test 4.010 0.515 3.124 7.136 0.917 4.319 (0.000) (0.794) (0.007) (0.000) (0.493) (0.001) Str. break Reject H0 Reject H0 Pagan‐H 80.656 7.693 72.984 78.595 6.212 39.825 (0.000) (0.989) (0.000) (0.000) (0.997) (0.003) FIV1 4.625 1.120 3.774 7.454 0.262 4.823 (0.000) (0.352) (0.012) (0.000) (0.852) (0.003) FIV2 9.017 18.508 (0.000) (0.000) Anderson 26.146 3.518 14.902 34.408 0.919 18.156 (0.000) (0.318) (0.002) (0.000) (0.821) (0.000) Hansen 6.669 0.059 0.207 11.452 0.162 0.201 (0.246) (0.971) (0.902) (0.043) (0.922) (0.904) . Still wine . Sparkling wine . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i −0.165 −0.521 0.423*** −0.044 −0.704 1.215*** (0.318) (1.458) (0.151) (0.417) (2.467) (0.323) D × τ−i 0.280** 0.206** (0.131) (0.095) Total population 0.461** 0.669 0.440* 0.961*** 1.839 −0.023 (0.228) (0.588) (0.258) (0.312) (1.362) (0.226) gdppc −0.037 −0.043 0.005 −0.137** −0.103 −0.061 (0.023) (0.174) (0.015) (0.057) (1.021) (0.048) govcons −2.066* 0.491 −0.566 −4.463* −0.504 4.509 (1.206) (2.751) (1.100) (2.467) (5.592) (3.161) govright −3.048 7.046 −1.413 −4.861 15.431 7.076 (3.320) (5.944) (3.433) (6.075) (13.587) (8.238) govleft −3.892 7.956 −2.330 −6.457 12.950 4.842 (4.128) (6.911) (4.430) (6.279) (16.250) (8.095) N 204 60 144 204 60 144 F‐test 4.010 0.515 3.124 7.136 0.917 4.319 (0.000) (0.794) (0.007) (0.000) (0.493) (0.001) Str. break Reject H0 Reject H0 Pagan‐H 80.656 7.693 72.984 78.595 6.212 39.825 (0.000) (0.989) (0.000) (0.000) (0.997) (0.003) FIV1 4.625 1.120 3.774 7.454 0.262 4.823 (0.000) (0.352) (0.012) (0.000) (0.852) (0.003) FIV2 9.017 18.508 (0.000) (0.000) Anderson 26.146 3.518 14.902 34.408 0.919 18.156 (0.000) (0.318) (0.002) (0.000) (0.821) (0.000) Hansen 6.669 0.059 0.207 11.452 0.162 0.201 (0.246) (0.971) (0.902) (0.043) (0.922) (0.904) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in paranthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(6,42) for 1987–92, F(6,126) for 1993–2004 and F(7,185) for 1987–2004. Str. break: H0 = no structural break. Open in new tab Table 2 
Estimates for Wine Taxes . Still wine . Sparkling wine . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i −0.165 −0.521 0.423*** −0.044 −0.704 1.215*** (0.318) (1.458) (0.151) (0.417) (2.467) (0.323) D × τ−i 0.280** 0.206** (0.131) (0.095) Total population 0.461** 0.669 0.440* 0.961*** 1.839 −0.023 (0.228) (0.588) (0.258) (0.312) (1.362) (0.226) gdppc −0.037 −0.043 0.005 −0.137** −0.103 −0.061 (0.023) (0.174) (0.015) (0.057) (1.021) (0.048) govcons −2.066* 0.491 −0.566 −4.463* −0.504 4.509 (1.206) (2.751) (1.100) (2.467) (5.592) (3.161) govright −3.048 7.046 −1.413 −4.861 15.431 7.076 (3.320) (5.944) (3.433) (6.075) (13.587) (8.238) govleft −3.892 7.956 −2.330 −6.457 12.950 4.842 (4.128) (6.911) (4.430) (6.279) (16.250) (8.095) N 204 60 144 204 60 144 F‐test 4.010 0.515 3.124 7.136 0.917 4.319 (0.000) (0.794) (0.007) (0.000) (0.493) (0.001) Str. break Reject H0 Reject H0 Pagan‐H 80.656 7.693 72.984 78.595 6.212 39.825 (0.000) (0.989) (0.000) (0.000) (0.997) (0.003) FIV1 4.625 1.120 3.774 7.454 0.262 4.823 (0.000) (0.352) (0.012) (0.000) (0.852) (0.003) FIV2 9.017 18.508 (0.000) (0.000) Anderson 26.146 3.518 14.902 34.408 0.919 18.156 (0.000) (0.318) (0.002) (0.000) (0.821) (0.000) Hansen 6.669 0.059 0.207 11.452 0.162 0.201 (0.246) (0.971) (0.902) (0.043) (0.922) (0.904) . Still wine . Sparkling wine . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i −0.165 −0.521 0.423*** −0.044 −0.704 1.215*** (0.318) (1.458) (0.151) (0.417) (2.467) (0.323) D × τ−i 0.280** 0.206** (0.131) (0.095) Total population 0.461** 0.669 0.440* 0.961*** 1.839 −0.023 (0.228) (0.588) (0.258) (0.312) (1.362) (0.226) gdppc −0.037 −0.043 0.005 −0.137** −0.103 −0.061 (0.023) (0.174) (0.015) (0.057) (1.021) (0.048) govcons −2.066* 0.491 −0.566 −4.463* −0.504 4.509 (1.206) (2.751) (1.100) (2.467) (5.592) (3.161) govright −3.048 7.046 −1.413 −4.861 15.431 7.076 (3.320) (5.944) (3.433) (6.075) (13.587) (8.238) govleft −3.892 7.956 −2.330 −6.457 12.950 4.842 (4.128) (6.911) (4.430) (6.279) (16.250) (8.095) N 204 60 144 204 60 144 F‐test 4.010 0.515 3.124 7.136 0.917 4.319 (0.000) (0.794) (0.007) (0.000) (0.493) (0.001) Str. break Reject H0 Reject H0 Pagan‐H 80.656 7.693 72.984 78.595 6.212 39.825 (0.000) (0.989) (0.000) (0.000) (0.997) (0.003) FIV1 4.625 1.120 3.774 7.454 0.262 4.823 (0.000) (0.352) (0.012) (0.000) (0.852) (0.003) FIV2 9.017 18.508 (0.000) (0.000) Anderson 26.146 3.518 14.902 34.408 0.919 18.156 (0.000) (0.318) (0.002) (0.000) (0.821) (0.000) Hansen 6.669 0.059 0.207 11.452 0.162 0.201 (0.246) (0.971) (0.902) (0.043) (0.922) (0.904) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in paranthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(6,42) for 1987–92, F(6,126) for 1993–2004 and F(7,185) for 1987–2004. Str. break: H0 = no structural break. Open in new tab The middle panel gives the number of observations, and two tests. The first is an F‐test for joint significance of the controls. The second is a test for the equality of coefficients across the two sub‐periods in the general structural break model.19 In the bottom panel of the Table, the following diagnostic statistics are also reported. First, Pagan and Hall’s (1983) test is a test of heteroscedasticity for instrumental variables (IV) estimation. This statistic is distributed as chi‐squared under the null of no heteroscedasticity and under the maintained hypothesis that the error of the regression is normally distributed. When we find heteroscedasticity we report the corrected standard errors using a robust variance estimator. Second, the FIV in the first stage of the estimation tests the null hypothesis that the instruments are not correlated with the endogenous variable. A rejection means that there is such a correlation. We can reject the null in all but three cases (the shorter sample period 1987–92 for wine and beer). Note that as there are two endogenous variables in the tax‐specific structural break, there are two such tests, denoted FIV1, FIV2. In the general structural break model, only FIV1 applies. Under the null hypothesis that instruments are not correlated with the endogenous variable, FIV1 and FIV2 follow an F distribution.20 Third, the Anderson canonical correlations likelihood‐ratio tests whether the equation is identified.21 The statistic provides a measure of instrument relevance, and rejection of the null indicates that the model is identified. Fourth, the Hansen‐Sargan test is a test of overidentifying restrictions. The joint null hypothesis is that the instruments are valid instruments, i.e., uncorrelated with the error term. Under the null, the test statistic is distributed as chi‐squared in the number of overidentifying restrictions. A rejection casts doubt on the validity of the instruments. Looking across all regressions in Tables 2–4, this test is passed at 5% in all but one case (the tax‐specific structural break model in the case of sparkling wine). We now discuss the results by type of taxable product, beginning with still wine. In the baseline model, we see that β, the coefficient on τ−i, is insignificantly different from zero but γ, the coefficient on D × τ−i, is significantly positive at 0.28. That is, there is evidence of strategic interaction only after 1993. Specifically, an increase in the weighted average of all other countries’ duties on wine by 1 euro increases country i’s excise by 0.28 euro. Turning to the control variables, we see first that total population is significantly positive, a pattern that is repeated across other taxes. This is interesting because it confirms a robust prediction of the theory that larger countries have higher taxes in the origin regime, because they have a larger domestic tax base (Kanbur and Keen, 1993). In the general structural break model, the key finding about increased strategic interaction is replicated. Before 1993, β1, the coefficient on τ−i, is insignificantly different from zero but, after 1993, it is significantly positive at 0.423. That is, an increase in the weighted average of all other countries’ duties on wine by 1 euro increases country i’s excise by approximately 0.42 euro. There is some instability in the coefficients on the control variables, however; these are markedly different during the period 1987–92 from both the period 1993–2004 and the single estimate for the tax‐specific structural break model; the latter two are much closer to each other. This may indicate overfitting for the regressions over the period 1987–92, where six coefficients are estimated from just 60 observations. This pattern of markedly different coefficients for the period 1987–92 appears right across the six taxes. Turning now to the tax on sparkling wine, the same general pattern emerges. In the baseline model, we see that β, the coefficient on τ−i, is insignificantly different from zero but γ, the coefficient on D × τ−i, is significantly positive at 0.206. That is, there is evidence of strategic interaction only after 1993. Specifically, an increase in the weighted average of all other countries’ duties on wine by 1 euro increases country i’s excise by approximately 0.21 euro. In the general structural break model, the key finding about increased strategic interaction is replicated. Before 1993, β1, the coefficient on τ−i, is insignificantly different from zero, but after 1993, β2 is significantly positive22 at 1.215. In Table 3, the same story is also apparent for the specific taxes on beer and ethyl alcohol. For beer, in the baseline model, we see that β, the coefficient on τ−i, is insignificantly different from zero but γ, the coefficient on D × τ−i, is significantly positive at 0.199. In the general structural break model, the key finding about increased strategic interaction is again replicated. Before 1993, β1, the coefficient on τ−i, is insignificantly different from zero but, after 1993, β2 is significantly positive at 0.309. For ethyl alcohol, in the baseline model, we see that β, the coefficient on τ−i, is insignificantly different from zero but γ, the coefficient on D × τ−i, is significantly positive at 0.261. In the general structural break model, before 1993, β1 is insignificantly different from zero but, after 1993, β2 is significantly positive at 0.649. Table 3 
Estimates for Beer and Ethyl Alcohol Taxes . Beer . Ethyl Alcohol . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i 0.130 0.215 0.309* −0.260 0.334 0.649** (0.200) (0.456) (0.175) (0.496) (0.320) (0.257) D × τ−i 0.199** 0.261** (0.084) (0.115) Total population 0.021*** 0.016 0.021** 7.162 20.414** 1.673 (0.006) (0.012) (0.009) (4.913) (9.344) (2.619) gdppc −0.003*** 0.003 −0.000 2.294** −3.546 2.300* (0.001) (0.004) (0.001) (1.008) (5.345) (1.287) govcons 0.036 0.082 0.033 15.633 48.981 0.971 (0.035) (0.053) (0.035) (18.896) (31.459) (20.409) govright 0.078 0.003 0.037 −21.713 5.584 −40.644 (0.111) (0.063) (0.108) (58.550) (55.096) (83.888) govleft 0.002 0.045 0.016 −57.364 139.213 −180.054 (0.123) (0.139) (0.139) (85.777) (105.619) (113.589) N 204 60 144 204 60 144 F‐test 6.643 2.468 1.966 16.950 3.854 10.286 (0.000) (0.039) (0.075) (0.000) (0.004) (0.000) Str. break Reject H0 Reject H0 Pagan‐H 74.158 17.019 66.545 105.660 36.206 79.249 (0.000) (0.652) (0.000) (0.000) (0.010) (0.000) FIV1 9.174 1.420 4.093 22.288 12.938 18.037 (0.000) (0.245) (0.004) (0.000) (0.000) (0.000) FIV2 7.105 99.926 (0.000) (0.000) Anderson 63.282 4.635 18.536 39.793 12.314 26.534 (0.000) (0.327) (0.001) (0.000) (0.006) (0.000) Hansen 10.320 3.673 7.129 9.717 4.251 1.342 (0.112) (0.299) (0.068) (0.205) (0.119) (0.511) . Beer . Ethyl Alcohol . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i 0.130 0.215 0.309* −0.260 0.334 0.649** (0.200) (0.456) (0.175) (0.496) (0.320) (0.257) D × τ−i 0.199** 0.261** (0.084) (0.115) Total population 0.021*** 0.016 0.021** 7.162 20.414** 1.673 (0.006) (0.012) (0.009) (4.913) (9.344) (2.619) gdppc −0.003*** 0.003 −0.000 2.294** −3.546 2.300* (0.001) (0.004) (0.001) (1.008) (5.345) (1.287) govcons 0.036 0.082 0.033 15.633 48.981 0.971 (0.035) (0.053) (0.035) (18.896) (31.459) (20.409) govright 0.078 0.003 0.037 −21.713 5.584 −40.644 (0.111) (0.063) (0.108) (58.550) (55.096) (83.888) govleft 0.002 0.045 0.016 −57.364 139.213 −180.054 (0.123) (0.139) (0.139) (85.777) (105.619) (113.589) N 204 60 144 204 60 144 F‐test 6.643 2.468 1.966 16.950 3.854 10.286 (0.000) (0.039) (0.075) (0.000) (0.004) (0.000) Str. break Reject H0 Reject H0 Pagan‐H 74.158 17.019 66.545 105.660 36.206 79.249 (0.000) (0.652) (0.000) (0.000) (0.010) (0.000) FIV1 9.174 1.420 4.093 22.288 12.938 18.037 (0.000) (0.245) (0.004) (0.000) (0.000) (0.000) FIV2 7.105 99.926 (0.000) (0.000) Anderson 63.282 4.635 18.536 39.793 12.314 26.534 (0.000) (0.327) (0.001) (0.000) (0.006) (0.000) Hansen 10.320 3.673 7.129 9.717 4.251 1.342 (0.112) (0.299) (0.068) (0.205) (0.119) (0.511) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(6,42) for 1987–92, F(6,126) for 1993–2004 and F(7,185) for 1987–2004. Str. break: H0 = no structural break. Open in new tab Table 3 
Estimates for Beer and Ethyl Alcohol Taxes . Beer . Ethyl Alcohol . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i 0.130 0.215 0.309* −0.260 0.334 0.649** (0.200) (0.456) (0.175) (0.496) (0.320) (0.257) D × τ−i 0.199** 0.261** (0.084) (0.115) Total population 0.021*** 0.016 0.021** 7.162 20.414** 1.673 (0.006) (0.012) (0.009) (4.913) (9.344) (2.619) gdppc −0.003*** 0.003 −0.000 2.294** −3.546 2.300* (0.001) (0.004) (0.001) (1.008) (5.345) (1.287) govcons 0.036 0.082 0.033 15.633 48.981 0.971 (0.035) (0.053) (0.035) (18.896) (31.459) (20.409) govright 0.078 0.003 0.037 −21.713 5.584 −40.644 (0.111) (0.063) (0.108) (58.550) (55.096) (83.888) govleft 0.002 0.045 0.016 −57.364 139.213 −180.054 (0.123) (0.139) (0.139) (85.777) (105.619) (113.589) N 204 60 144 204 60 144 F‐test 6.643 2.468 1.966 16.950 3.854 10.286 (0.000) (0.039) (0.075) (0.000) (0.004) (0.000) Str. break Reject H0 Reject H0 Pagan‐H 74.158 17.019 66.545 105.660 36.206 79.249 (0.000) (0.652) (0.000) (0.000) (0.010) (0.000) FIV1 9.174 1.420 4.093 22.288 12.938 18.037 (0.000) (0.245) (0.004) (0.000) (0.000) (0.000) FIV2 7.105 99.926 (0.000) (0.000) Anderson 63.282 4.635 18.536 39.793 12.314 26.534 (0.000) (0.327) (0.001) (0.000) (0.006) (0.000) Hansen 10.320 3.673 7.129 9.717 4.251 1.342 (0.112) (0.299) (0.068) (0.205) (0.119) (0.511) . Beer . Ethyl Alcohol . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i 0.130 0.215 0.309* −0.260 0.334 0.649** (0.200) (0.456) (0.175) (0.496) (0.320) (0.257) D × τ−i 0.199** 0.261** (0.084) (0.115) Total population 0.021*** 0.016 0.021** 7.162 20.414** 1.673 (0.006) (0.012) (0.009) (4.913) (9.344) (2.619) gdppc −0.003*** 0.003 −0.000 2.294** −3.546 2.300* (0.001) (0.004) (0.001) (1.008) (5.345) (1.287) govcons 0.036 0.082 0.033 15.633 48.981 0.971 (0.035) (0.053) (0.035) (18.896) (31.459) (20.409) govright 0.078 0.003 0.037 −21.713 5.584 −40.644 (0.111) (0.063) (0.108) (58.550) (55.096) (83.888) govleft 0.002 0.045 0.016 −57.364 139.213 −180.054 (0.123) (0.139) (0.139) (85.777) (105.619) (113.589) N 204 60 144 204 60 144 F‐test 6.643 2.468 1.966 16.950 3.854 10.286 (0.000) (0.039) (0.075) (0.000) (0.004) (0.000) Str. break Reject H0 Reject H0 Pagan‐H 74.158 17.019 66.545 105.660 36.206 79.249 (0.000) (0.652) (0.000) (0.000) (0.010) (0.000) FIV1 9.174 1.420 4.093 22.288 12.938 18.037 (0.000) (0.245) (0.004) (0.000) (0.000) (0.000) FIV2 7.105 99.926 (0.000) (0.000) Anderson 63.282 4.635 18.536 39.793 12.314 26.534 (0.000) (0.327) (0.001) (0.000) (0.006) (0.000) Hansen 10.320 3.673 7.129 9.717 4.251 1.342 (0.112) (0.299) (0.068) (0.205) (0.119) (0.511) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(6,42) for 1987–92, F(6,126) for 1993–2004 and F(7,185) for 1987–2004. Str. break: H0 = no structural break. Open in new tab However, in Table 4, the story comes though less clearly for taxes on cigarettes. First, unlike for the other four products, there is evidence of strategic interaction prior to 1993. Specifically, for both model specifications and for both the specific component of the tax and the total tax, there is evidence of significant strategic interaction prior to 1993. Second, for the baseline model with a tax‐specific structural break, there is evidence of increased strategic interaction (i.e. a positive γ) only for the total tax, whereas in the other specification, the reverse is true. One possible explanation for this discrepancy is that, as discussed in the introduction, the problem of illegal smuggling is much more serious for cigarettes and other tobacco products than it is for the other products. Table 4 
Estimates for Cigarettes Taxes . Cigarettes specific . Cigarettes total . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i 1.070*** 0.497*** 1.320*** 0.761*** 1.070*** 1.007*** (0.251) (0.182) (0.277) (0.128) (0.091) (0.058) D × τ−i −0.045 0.074** (0.156) (0.031) Total population 0.187 0.560*** −0.280 −0.019 −0.072 −0.028 (0.169) (0.126) (0.320) (0.039) (0.180) (0.054) gdppc −0.045** −0.035 −0.079** −0.005 −0.044* −0.004 (0.020) (0.033) (0.039) (0.004) (0.025) (0.007) govcons 1.932* 0.726* 3.624** −0.256 −0.242 −0.815* (1.020) (0.428) (1.593) (0.287) (0.675) (0.481) govright 1.973 −0.146 5.389 0.674 1.462 0.066 (2.722) (0.998) (4.079) (0.923) (2.209) (1.097) govleft 0.613 1.293 6.941 −0.755 1.075 −2.003 (3.319) (1.298) (4.569) (1.211) (2.860) (1.256) N 204 60 144 204 60 144 F‐test 14.113 7.974 8.797 67.248 30.853 50.435 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Str. break Reject H0 Reject H0 Pagan‐H 91.089 21.111 55.899 71.354 18.804 48.517 (0.000) (0.391) (0.000) (0.000) (0.535) (0.000) FIV1 5.911 11.525 2.817 89.266 33.204 17.360 (0.000) (0.000) (0.028) (0.000) (0.000) (0.000) FIV2 8.220 292.137 (0.000) (0.000) Anderson 40.331 13.785 13.338 34.398 19.995 38.892 (0.000) (0.008) (0.010) (0.000) (0.001) (0.000) Hansen 13.684 0.378 4.511 6.384 5.928 2.637 (0.057) (0.945) (0.211) (0.172) (0.115) (0.451) . Cigarettes specific . Cigarettes total . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i 1.070*** 0.497*** 1.320*** 0.761*** 1.070*** 1.007*** (0.251) (0.182) (0.277) (0.128) (0.091) (0.058) D × τ−i −0.045 0.074** (0.156) (0.031) Total population 0.187 0.560*** −0.280 −0.019 −0.072 −0.028 (0.169) (0.126) (0.320) (0.039) (0.180) (0.054) gdppc −0.045** −0.035 −0.079** −0.005 −0.044* −0.004 (0.020) (0.033) (0.039) (0.004) (0.025) (0.007) govcons 1.932* 0.726* 3.624** −0.256 −0.242 −0.815* (1.020) (0.428) (1.593) (0.287) (0.675) (0.481) govright 1.973 −0.146 5.389 0.674 1.462 0.066 (2.722) (0.998) (4.079) (0.923) (2.209) (1.097) govleft 0.613 1.293 6.941 −0.755 1.075 −2.003 (3.319) (1.298) (4.569) (1.211) (2.860) (1.256) N 204 60 144 204 60 144 F‐test 14.113 7.974 8.797 67.248 30.853 50.435 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Str. break Reject H0 Reject H0 Pagan‐H 91.089 21.111 55.899 71.354 18.804 48.517 (0.000) (0.391) (0.000) (0.000) (0.535) (0.000) FIV1 5.911 11.525 2.817 89.266 33.204 17.360 (0.000) (0.000) (0.028) (0.000) (0.000) (0.000) FIV2 8.220 292.137 (0.000) (0.000) Anderson 40.331 13.785 13.338 34.398 19.995 38.892 (0.000) (0.008) (0.010) (0.000) (0.001) (0.000) Hansen 13.684 0.378 4.511 6.384 5.928 2.637 (0.057) (0.945) (0.211) (0.172) (0.115) (0.451) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(6,42) for 1987–92, F(6,126) for 1993–2004 and F(7,185) for 1987–2004. Str. break: H0 = no structural break. Open in new tab Table 4 
Estimates for Cigarettes Taxes . Cigarettes specific . Cigarettes total . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i 1.070*** 0.497*** 1.320*** 0.761*** 1.070*** 1.007*** (0.251) (0.182) (0.277) (0.128) (0.091) (0.058) D × τ−i −0.045 0.074** (0.156) (0.031) Total population 0.187 0.560*** −0.280 −0.019 −0.072 −0.028 (0.169) (0.126) (0.320) (0.039) (0.180) (0.054) gdppc −0.045** −0.035 −0.079** −0.005 −0.044* −0.004 (0.020) (0.033) (0.039) (0.004) (0.025) (0.007) govcons 1.932* 0.726* 3.624** −0.256 −0.242 −0.815* (1.020) (0.428) (1.593) (0.287) (0.675) (0.481) govright 1.973 −0.146 5.389 0.674 1.462 0.066 (2.722) (0.998) (4.079) (0.923) (2.209) (1.097) govleft 0.613 1.293 6.941 −0.755 1.075 −2.003 (3.319) (1.298) (4.569) (1.211) (2.860) (1.256) N 204 60 144 204 60 144 F‐test 14.113 7.974 8.797 67.248 30.853 50.435 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Str. break Reject H0 Reject H0 Pagan‐H 91.089 21.111 55.899 71.354 18.804 48.517 (0.000) (0.391) (0.000) (0.000) (0.535) (0.000) FIV1 5.911 11.525 2.817 89.266 33.204 17.360 (0.000) (0.000) (0.028) (0.000) (0.000) (0.000) FIV2 8.220 292.137 (0.000) (0.000) Anderson 40.331 13.785 13.338 34.398 19.995 38.892 (0.000) (0.008) (0.010) (0.000) (0.001) (0.000) Hansen 13.684 0.378 4.511 6.384 5.928 2.637 (0.057) (0.945) (0.211) (0.172) (0.115) (0.451) . Cigarettes specific . Cigarettes total . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . τ−i 1.070*** 0.497*** 1.320*** 0.761*** 1.070*** 1.007*** (0.251) (0.182) (0.277) (0.128) (0.091) (0.058) D × τ−i −0.045 0.074** (0.156) (0.031) Total population 0.187 0.560*** −0.280 −0.019 −0.072 −0.028 (0.169) (0.126) (0.320) (0.039) (0.180) (0.054) gdppc −0.045** −0.035 −0.079** −0.005 −0.044* −0.004 (0.020) (0.033) (0.039) (0.004) (0.025) (0.007) govcons 1.932* 0.726* 3.624** −0.256 −0.242 −0.815* (1.020) (0.428) (1.593) (0.287) (0.675) (0.481) govright 1.973 −0.146 5.389 0.674 1.462 0.066 (2.722) (0.998) (4.079) (0.923) (2.209) (1.097) govleft 0.613 1.293 6.941 −0.755 1.075 −2.003 (3.319) (1.298) (4.569) (1.211) (2.860) (1.256) N 204 60 144 204 60 144 F‐test 14.113 7.974 8.797 67.248 30.853 50.435 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Str. break Reject H0 Reject H0 Pagan‐H 91.089 21.111 55.899 71.354 18.804 48.517 (0.000) (0.391) (0.000) (0.000) (0.535) (0.000) FIV1 5.911 11.525 2.817 89.266 33.204 17.360 (0.000) (0.000) (0.028) (0.000) (0.000) (0.000) FIV2 8.220 292.137 (0.000) (0.000) Anderson 40.331 13.785 13.338 34.398 19.995 38.892 (0.000) (0.008) (0.010) (0.000) (0.001) (0.000) Hansen 13.684 0.378 4.511 6.384 5.928 2.637 (0.057) (0.945) (0.211) (0.172) (0.115) (0.451) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(6,42) for 1987–92, F(6,126) for 1993–2004 and F(7,185) for 1987–2004. Str. break: H0 = no structural break. Open in new tab 4. Robustness Checks 4.1. No Country Characteristics In the general structural break model, there is a potential problem of overfitting: six parameters are estimated on just 60 observations. This manifests itself in two ways. First, the coefficients on the control variables vary noticeably across the two sub‐periods. Moreover, the controls are jointly insignificant in the case of still and sparkling wine in the first sub‐period. As a robustness check, therefore, we estimate the general structural break model without controls i.e. just with country fixed effects. The results are reported in Table 5. Table 5 
All Taxes – No Country Controls . Still Wine . Sparkling Wine . 1987–92 . 1993–2004 . 1987–92 . 1993–2004 . τ−i −0.661 0.684*** −0.142 1.009*** (1.235) (0.216) (0.936) (0.204) Anderson 8.970 18.136 8.115 35.276 (0.030) (0.000) (0.044) (0.000) Hansen 1.661 0.022 3.391 0.041 (0.436) (0.989) (0.184) (0.980) Str. break Reject H0 Reject H0 Beer Ethyl Alcohol τ−i 0.725*** 0.715*** 0.241 1.194*** (0.237) (0.243) (0.563) (0.253) Anderson 19.234 32.952 20.993 38.250 (0.001) (0.000) (0.000) (0.000) Hansen 3.490 5.936 4.389 2.349 (0.322) (0.115) (0.111) (0.309) Str. break Reject H0 Reject H0 Cigarettes specific Cigarettes total τ−i 0.556*** 1.056*** 1.071*** 0.986*** (0.118) (0.160) (0.082) (0.062) Anderson 14.329 36.945 19.514 38.301 (0.006) (0.000) (0.001) (0.000) Hansen 2.154 1.991 4.868 2.147 (0.541) (0.574) (0.182) (0.542) Str. break Reject H0 Reject H0 . Still Wine . Sparkling Wine . 1987–92 . 1993–2004 . 1987–92 . 1993–2004 . τ−i −0.661 0.684*** −0.142 1.009*** (1.235) (0.216) (0.936) (0.204) Anderson 8.970 18.136 8.115 35.276 (0.030) (0.000) (0.044) (0.000) Hansen 1.661 0.022 3.391 0.041 (0.436) (0.989) (0.184) (0.980) Str. break Reject H0 Reject H0 Beer Ethyl Alcohol τ−i 0.725*** 0.715*** 0.241 1.194*** (0.237) (0.243) (0.563) (0.253) Anderson 19.234 32.952 20.993 38.250 (0.001) (0.000) (0.000) (0.000) Hansen 3.490 5.936 4.389 2.349 (0.322) (0.115) (0.111) (0.309) Str. break Reject H0 Reject H0 Cigarettes specific Cigarettes total τ−i 0.556*** 1.056*** 1.071*** 0.986*** (0.118) (0.160) (0.082) (0.062) Anderson 14.329 36.945 19.514 38.301 (0.006) (0.000) (0.001) (0.000) Hansen 2.154 1.991 4.868 2.147 (0.541) (0.574) (0.182) (0.542) Str. break Reject H0 Reject H0 Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(1,47) for 1987–92, F(1,131) for 1993–2004 and F(2,190) for 1987–2004. Str. break: H0 = no structural break. Open in new tab Table 5 
All Taxes – No Country Controls . Still Wine . Sparkling Wine . 1987–92 . 1993–2004 . 1987–92 . 1993–2004 . τ−i −0.661 0.684*** −0.142 1.009*** (1.235) (0.216) (0.936) (0.204) Anderson 8.970 18.136 8.115 35.276 (0.030) (0.000) (0.044) (0.000) Hansen 1.661 0.022 3.391 0.041 (0.436) (0.989) (0.184) (0.980) Str. break Reject H0 Reject H0 Beer Ethyl Alcohol τ−i 0.725*** 0.715*** 0.241 1.194*** (0.237) (0.243) (0.563) (0.253) Anderson 19.234 32.952 20.993 38.250 (0.001) (0.000) (0.000) (0.000) Hansen 3.490 5.936 4.389 2.349 (0.322) (0.115) (0.111) (0.309) Str. break Reject H0 Reject H0 Cigarettes specific Cigarettes total τ−i 0.556*** 1.056*** 1.071*** 0.986*** (0.118) (0.160) (0.082) (0.062) Anderson 14.329 36.945 19.514 38.301 (0.006) (0.000) (0.001) (0.000) Hansen 2.154 1.991 4.868 2.147 (0.541) (0.574) (0.182) (0.542) Str. break Reject H0 Reject H0 . Still Wine . Sparkling Wine . 1987–92 . 1993–2004 . 1987–92 . 1993–2004 . τ−i −0.661 0.684*** −0.142 1.009*** (1.235) (0.216) (0.936) (0.204) Anderson 8.970 18.136 8.115 35.276 (0.030) (0.000) (0.044) (0.000) Hansen 1.661 0.022 3.391 0.041 (0.436) (0.989) (0.184) (0.980) Str. break Reject H0 Reject H0 Beer Ethyl Alcohol τ−i 0.725*** 0.715*** 0.241 1.194*** (0.237) (0.243) (0.563) (0.253) Anderson 19.234 32.952 20.993 38.250 (0.001) (0.000) (0.000) (0.000) Hansen 3.490 5.936 4.389 2.349 (0.322) (0.115) (0.111) (0.309) Str. break Reject H0 Reject H0 Cigarettes specific Cigarettes total τ−i 0.556*** 1.056*** 1.071*** 0.986*** (0.118) (0.160) (0.082) (0.062) Anderson 14.329 36.945 19.514 38.301 (0.006) (0.000) (0.001) (0.000) Hansen 2.154 1.991 4.868 2.147 (0.541) (0.574) (0.182) (0.542) Str. break Reject H0 Reject H0 Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(1,47) for 1987–92, F(1,131) for 1993–2004 and F(2,190) for 1987–2004. Str. break: H0 = no structural break. Open in new tab This Table shows that our main results on strategic interaction are generally robust to the omission of the controls. That is, same pattern of coefficients on τ−i emerges, with one exception. This is that there is now evidence of strategic interaction in the beer excise prior to 1993, with the reaction function slope actually being larger prior to 1993 than afterwards. However, in the case of beer, the controls are jointly significant prior to 1993, and so omission of the controls may lead to bias, and thus perhaps not too much weight should be placed on this. 4.2. Alternative Weighting Schemes So far, we have weighted other countries’ taxes using contiguity weights. Given the nature of commodity tax competition, these seem to be clearly the appropriate weights. However, we conduct several robustness checks to see if they indeed do work better than other weighting schemes. In Table 6, only the reaction function slope coefficients are reported, although controls and fixed effects are included in all regressions. Table 6 
Estimates With Other Weighting Schemes . Wdis1 . Wdis2 . Wrand . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . Still wine  τ−i −0.036 1.088 1.705*** 0.013 1.256 1.655*** −0.194 −0.099 −0.176   (0.476) (1.088) (0.537) (0.560) (1.211) (0.509) (0.172) (0.224) (0.137)  D × τ−i 0.256*** 0.195** 0.068   (0.083) (0.098) (0.051) Sparkling Wine  τ−i 0.384 1.248 1.565*** −0.072 −0.349 1.452*** −0.030 0.053 −0.019   (0.412) (0.823) (0.437) (0.411) (1.625) (0.337) (0.198) (0.304) (0.169)  D × τ−i 0.115* 0.153** 0.053   (0.069) (0.070) 0.059) Beer  τ−i 1.433*** 1.617*** 1.661*** 1.253*** 1.415*** 1.465*** 0.109 0.743** −0.062   (0.251) (0.559) (0.457) (0.287) (0.524) (0.391) (0.132) (0.302) (0.119)  D × τ−i 0.009 0.003 0.050   (0.058) (0.064) (0.042) Ethyl Alcohol  τ−i 0.249 0.969 1.144*** 0.516** 1.170 1.197*** −118.027 468.042*** 25.795   (0.268) (0.626) (0.290) (0.246) (0.745) (0.285) (72.521) (170.743) (72.316)  D × τ−i 0.142** 0.092 105.536***   (0.069) (0.075) (27.121) Cigarettes specific  τ−i 0.009 0.902*** 1.958*** 1.312*** 0.679** 1.718*** 1.692*** 0.423** 0.366***   (0.389) (0.312) (0.354) (0.277) (0.308) (0.288) (0.560) (0.184) (0.102)  D × τ−i 0.361* −0.040 −0.285   (0.190) (0.132) (0.183) Cigarettes total  τ−i 1.379*** 0.885*** 1.726*** 0.643*** 1.036*** 1.537*** 0.083 −0.027 −0.022   (0.197) (0.184) (0.211) (0.226) (0.196) (0.188) (0.108) (0.192) (0.044)  D × τ−i −0.036 0.126** 0.045   (0.034) (0.055) (0.028) . Wdis1 . Wdis2 . Wrand . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . Still wine  τ−i −0.036 1.088 1.705*** 0.013 1.256 1.655*** −0.194 −0.099 −0.176   (0.476) (1.088) (0.537) (0.560) (1.211) (0.509) (0.172) (0.224) (0.137)  D × τ−i 0.256*** 0.195** 0.068   (0.083) (0.098) (0.051) Sparkling Wine  τ−i 0.384 1.248 1.565*** −0.072 −0.349 1.452*** −0.030 0.053 −0.019   (0.412) (0.823) (0.437) (0.411) (1.625) (0.337) (0.198) (0.304) (0.169)  D × τ−i 0.115* 0.153** 0.053   (0.069) (0.070) 0.059) Beer  τ−i 1.433*** 1.617*** 1.661*** 1.253*** 1.415*** 1.465*** 0.109 0.743** −0.062   (0.251) (0.559) (0.457) (0.287) (0.524) (0.391) (0.132) (0.302) (0.119)  D × τ−i 0.009 0.003 0.050   (0.058) (0.064) (0.042) Ethyl Alcohol  τ−i 0.249 0.969 1.144*** 0.516** 1.170 1.197*** −118.027 468.042*** 25.795   (0.268) (0.626) (0.290) (0.246) (0.745) (0.285) (72.521) (170.743) (72.316)  D × τ−i 0.142** 0.092 105.536***   (0.069) (0.075) (27.121) Cigarettes specific  τ−i 0.009 0.902*** 1.958*** 1.312*** 0.679** 1.718*** 1.692*** 0.423** 0.366***   (0.389) (0.312) (0.354) (0.277) (0.308) (0.288) (0.560) (0.184) (0.102)  D × τ−i 0.361* −0.040 −0.285   (0.190) (0.132) (0.183) Cigarettes total  τ−i 1.379*** 0.885*** 1.726*** 0.643*** 1.036*** 1.537*** 0.083 −0.027 −0.022   (0.197) (0.184) (0.211) (0.226) (0.196) (0.188) (0.108) (0.192) (0.044)  D × τ−i −0.036 0.126** 0.045   (0.034) (0.055) (0.028) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(6,42) for 1987–92, F(6,126) for 1993–2004 and F(7,185) for 1987–2004. Str. break: H0 = no structural break. Open in new tab Table 6 
Estimates With Other Weighting Schemes . Wdis1 . Wdis2 . Wrand . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . Still wine  τ−i −0.036 1.088 1.705*** 0.013 1.256 1.655*** −0.194 −0.099 −0.176   (0.476) (1.088) (0.537) (0.560) (1.211) (0.509) (0.172) (0.224) (0.137)  D × τ−i 0.256*** 0.195** 0.068   (0.083) (0.098) (0.051) Sparkling Wine  τ−i 0.384 1.248 1.565*** −0.072 −0.349 1.452*** −0.030 0.053 −0.019   (0.412) (0.823) (0.437) (0.411) (1.625) (0.337) (0.198) (0.304) (0.169)  D × τ−i 0.115* 0.153** 0.053   (0.069) (0.070) 0.059) Beer  τ−i 1.433*** 1.617*** 1.661*** 1.253*** 1.415*** 1.465*** 0.109 0.743** −0.062   (0.251) (0.559) (0.457) (0.287) (0.524) (0.391) (0.132) (0.302) (0.119)  D × τ−i 0.009 0.003 0.050   (0.058) (0.064) (0.042) Ethyl Alcohol  τ−i 0.249 0.969 1.144*** 0.516** 1.170 1.197*** −118.027 468.042*** 25.795   (0.268) (0.626) (0.290) (0.246) (0.745) (0.285) (72.521) (170.743) (72.316)  D × τ−i 0.142** 0.092 105.536***   (0.069) (0.075) (27.121) Cigarettes specific  τ−i 0.009 0.902*** 1.958*** 1.312*** 0.679** 1.718*** 1.692*** 0.423** 0.366***   (0.389) (0.312) (0.354) (0.277) (0.308) (0.288) (0.560) (0.184) (0.102)  D × τ−i 0.361* −0.040 −0.285   (0.190) (0.132) (0.183) Cigarettes total  τ−i 1.379*** 0.885*** 1.726*** 0.643*** 1.036*** 1.537*** 0.083 −0.027 −0.022   (0.197) (0.184) (0.211) (0.226) (0.196) (0.188) (0.108) (0.192) (0.044)  D × τ−i −0.036 0.126** 0.045   (0.034) (0.055) (0.028) . Wdis1 . Wdis2 . Wrand . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . . 1987–92 . 1993–2004 . Still wine  τ−i −0.036 1.088 1.705*** 0.013 1.256 1.655*** −0.194 −0.099 −0.176   (0.476) (1.088) (0.537) (0.560) (1.211) (0.509) (0.172) (0.224) (0.137)  D × τ−i 0.256*** 0.195** 0.068   (0.083) (0.098) (0.051) Sparkling Wine  τ−i 0.384 1.248 1.565*** −0.072 −0.349 1.452*** −0.030 0.053 −0.019   (0.412) (0.823) (0.437) (0.411) (1.625) (0.337) (0.198) (0.304) (0.169)  D × τ−i 0.115* 0.153** 0.053   (0.069) (0.070) 0.059) Beer  τ−i 1.433*** 1.617*** 1.661*** 1.253*** 1.415*** 1.465*** 0.109 0.743** −0.062   (0.251) (0.559) (0.457) (0.287) (0.524) (0.391) (0.132) (0.302) (0.119)  D × τ−i 0.009 0.003 0.050   (0.058) (0.064) (0.042) Ethyl Alcohol  τ−i 0.249 0.969 1.144*** 0.516** 1.170 1.197*** −118.027 468.042*** 25.795   (0.268) (0.626) (0.290) (0.246) (0.745) (0.285) (72.521) (170.743) (72.316)  D × τ−i 0.142** 0.092 105.536***   (0.069) (0.075) (27.121) Cigarettes specific  τ−i 0.009 0.902*** 1.958*** 1.312*** 0.679** 1.718*** 1.692*** 0.423** 0.366***   (0.389) (0.312) (0.354) (0.277) (0.308) (0.288) (0.560) (0.184) (0.102)  D × τ−i 0.361* −0.040 −0.285   (0.190) (0.132) (0.183) Cigarettes total  τ−i 1.379*** 0.885*** 1.726*** 0.643*** 1.036*** 1.537*** 0.083 −0.027 −0.022   (0.197) (0.184) (0.211) (0.226) (0.196) (0.188) (0.108) (0.192) (0.044)  D × τ−i −0.036 0.126** 0.045   (0.034) (0.055) (0.028) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(6,42) for 1987–92, F(6,126) for 1993–2004 and F(7,185) for 1987–2004. Str. break: H0 = no structural break. Open in new tab What do we expect to find with other weights? Suppose that the data are really being generated by a process of tax competition between geographical neighbours after 1993 only. Then, we expect other weights to show weaker evidence of strategic interaction and this evidence should be poorer, the more different the other weights are from contiguity weights. This is broadly what we do find. First, we look at modified contiguity weights, or triangulation weights, generated by Delauney triangulation.23 This works as follows. Each country is identified by a point in the plane (i.e. 2) given by the longitude and latitude coordinates of the capital. These points are then joined in such a way that all of the space is subdivided in triangles. Now if a country i shares an edge with country j, then the two countries are contiguous and in the weight matrix ωij = 1, otherwise ωij = 0. There are two different versions of this weight matrix, the first being symmetric and the second being row‐normalised. These weights have the advantage that they deal systematically, rather than in an ad hoc way, with countries that are islands or separated by sea from other countries, of which there are quite a few in our sample. As the triangulation weights are positively, although not perfectly, correlated with our baseline contiguity weights, we would expect the regressions with triangulation weights to still show evidence of strategic interaction after 1993 but less clearly than with contiguity weights.24 This is more or less what we see in Table 6. Looking first at the tax‐specific structural break model, i.e. comparing columns 1 and 4 of Table 6 to the relevant columns of Tables 2–4 we see that this is what happens.25 Finally, we compare contiguity weights to ‘placebo’ weights which are chosen in some random way without regard to any economic considerations. Following Case et al. (1992), we construct a weighting matrix based on a ‘nonsense’ procedure; ωij > 0 only if the name of country j comes after country i in the alphabet.26 If we continue to find evidence of strategic interaction with these placebo weights after 1993, that might indicate some general positive correlation between all excise taxes generated by omitted common shocks, which would cast doubt on our claim that we have found evidence of tax competition. Happily, we see from Table 6 that placebo weights do not show any evidence of positive strategic interaction after 1993, with the exception of specific excises on cigarettes. Looking across commodities and across the two sub‐samples, there does not seem to be any pattern in the reaction function slope coefficients at all; most of them are insignificant. 4.3. Minimum Tax Rates So far in the analysis, we have ignored any possible effects of minimum tax rates. Evers et al. (2004), based on the theoretical literature, argue that such rates, if they affect the Nash equilibrium at all, will generally cause rates to rise. For example, in Nielsen’s (2001) model, it is easily verified in the two‐country case that if the minimum tax is binding on the lower‐tax country, it will raise the tax not only in that country but also in the other, high‐tax country, as the latter country is moved along its upward‐sloping tax reaction function. So, we should expect, other things equal, the minimum tax to increase the intercepts of the reaction functions. It is less clear how the minimum tax will affect the amount of strategic interaction. Here, we simply follow Evers et al. (2004) by interacting the minimum tax with the weighted average of other countries’ taxes. So, given that minimum taxes did not come in force until 1993, we estimate, over the period 1993–2004, an augmented version of (2) i.e. (5) where mt is the minimum tax at time t and τ−i,t = ∑j≠iωijτjt. We expect θ > 0 and possibly γ ≠ 0. But there are some complications. First, for wine (still and sparkling) the minimum tax rate is zero, so (5) cannot be estimated for these products. Second, for cigarettes, the minimum tax rate (measured as a percentage of the retail price) has been unchanged since 1993, at 57%. So, as the minimum tax rate mt is not time‐varying in this case, θ, γ cannot be identified from regression (5) just over the period 1993–2004. For beer the minimum tax rate has been unchanged since 1993, and it is equal to 0.7448 euro per hl/degree Plato or 1.87 euro per hl/degree of alcohol of finished product. So, in real terms, mt is declining and this allows us to estimate (5) in this case. The first column of Table 7 reports the estimation of (5) for beer, using a contiguity weight matrix, and instrumenting both τ−i,t and mt × τ−i,t by weighted averages of the control variables in countries j ≠ i. The only tax‐related variable that is significant is mt × τ−i,t with a positive coefficient. Table 7 
The Effects of the Minimum Tax . Beer . Ethyl Alcohol . τ−i −0.264 −0.501 (0.293) (0.475) m × τ−i 0.958** 0.4218 (0.386) (0.309) m −1.029 0.119 (0.641) (0.581) Total population 0.021*** 7.444* (0.006) (4.392) gdppc −0.002*** 2.352** (0.001) (1.037) govcons 0.147** 39.091 (0.073) (48.322) govright 0.108 −3.205 (0.142) (85.722) govleft 0.090 −50.616 (0.156) (92.148) N 204 204 F‐test 7.88 20.16 (0.000) (0.000) . Beer . Ethyl Alcohol . τ−i −0.264 −0.501 (0.293) (0.475) m × τ−i 0.958** 0.4218 (0.386) (0.309) m −1.029 0.119 (0.641) (0.581) Total population 0.021*** 7.444* (0.006) (4.392) gdppc −0.002*** 2.352** (0.001) (1.037) govcons 0.147** 39.091 (0.073) (48.322) govright 0.108 −3.205 (0.142) (85.722) govleft 0.090 −50.616 (0.156) (92.148) N 204 204 F‐test 7.88 20.16 (0.000) (0.000) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(8, 184). Open in new tab Table 7 
The Effects of the Minimum Tax . Beer . Ethyl Alcohol . τ−i −0.264 −0.501 (0.293) (0.475) m × τ−i 0.958** 0.4218 (0.386) (0.309) m −1.029 0.119 (0.641) (0.581) Total population 0.021*** 7.444* (0.006) (4.392) gdppc −0.002*** 2.352** (0.001) (1.037) govcons 0.147** 39.091 (0.073) (48.322) govright 0.108 −3.205 (0.142) (85.722) govleft 0.090 −50.616 (0.156) (92.148) N 204 204 F‐test 7.88 20.16 (0.000) (0.000) . Beer . Ethyl Alcohol . τ−i −0.264 −0.501 (0.293) (0.475) m × τ−i 0.958** 0.4218 (0.386) (0.309) m −1.029 0.119 (0.641) (0.581) Total population 0.021*** 7.444* (0.006) (4.392) gdppc −0.002*** 2.352** (0.001) (1.037) govcons 0.147** 39.091 (0.073) (48.322) govright 0.108 −3.205 (0.142) (85.722) govleft 0.090 −50.616 (0.156) (92.148) N 204 204 F‐test 7.88 20.16 (0.000) (0.000) Significance levels: * 10%, ** 5%, *** 1%. Robust standard errors shown in parenthesis under the coefficient estimates. F‐test for joint significance of controls is distributed as: F(8, 184). Open in new tab For ethyl alcohol, the picture is similar to beer; the minimum tax rate has been unchanged since 1993 at 500 euro per hl of pure alcohol, is thus declining in real terms, again allowing us to estimate (5). In this case, no tax variables are significant. Given that there are only 204 observations available, perhaps it is asking too much of the data to estimate β, θ and γ precisely. 5. Conclusions In this work we analysed the effects of the tax competition after the introduction of the Single Market in EU in 1993. Using a panel data set of 12 EU countries over a period of 17 years from 1987 to 2004 and a spatial econometrics approach, we tested for the presence of strategic interaction among neighbouring countries in the setting of five excise taxes. Our work differs most other empirical studies in the same area, as we use actual tax rates as dependent variables and not some derived tax ratio. Our main finding is a structural break after 1993, indicating that the introduction of the Single Market has modified tax setting among the EU countries. Specifically, for taxes on still and sparkling wine, beer and ethyl alcohol, we can reject the null hypothesis that the slope of the tax reaction function was the same before and after 1993. For these taxes, the reaction function slope is always significantly positive post‐1993, and never before 1993. This is consistent with the hypothesis that the Single Market created competition between countries in these taxes where there was none before, by making tax bases internationally mobile. In the case of cigarettes, the findings are somewhat different; the reaction function slope is significantly positive before 1993 but, if the total tax is used, this slope does appear to increase after 1993. This can be explained by the fact that significant smuggling in cigarettes creates incentives for tax competition even if legal transactions are subject to destination‐based taxes. Footnotes 1 " A minor qualification is that small quantities of excisable products could be bought at duty‐free shops in airports, on boats, etc., without any tax payable. But, the amounts involved are quite small. 2 " A possible counter‐argument concerns diversion fraud i.e. diversion of goods in bonded warehouses destined for export to the domestic market, where they are illegally sold without payment of excise taxes. This activity has become easier since the advent of the single market. Diversion fraud can only be limited by cutting tax rates and so the incentives to cut rates, independently of what other countries do, may have increased since 1993. This is a force that might actually weaken tax competition since 1993 (we are indebted to a referee for this point). 3 " ‘The prospect of tax‐cutting has thus become a principal concern in discussions of indirect tax policy … Approximation is one obvious response … the original approximation proposals were replaced by a more pragmatic approach (of) a minimum standard rate of VAT of 15 per cent … (and) minimum excise rates.’ (Keen, 1993, p. 26). 4 " The robustness of the results with respect to other weights are tested in Section 4.2. 5 " Specifically, for both model specifications, and for both the specific component of the tax and the total tax, there is evidence of significant strategic interaction prior to 1993. 6 " Smuggling creates incentives for tax competition even if legal transactions are subject to destination‐based taxes, because smugglers have incentives to transport goods illegally to where taxes, and thus prices, are high. 7 " The minimum tax on wine (still or sparkling) is zero, and on cigarettes, the minimum is expressed as a percentage of the retail price, which has not changed since its introduction. 8 " The borderline of legality in the case of cigarettes is provided by the Contraband Cigarette Act of 1978, which prohibits single shipments, sale or purchase of more than 60,000 cigarettes not bearing the tax stamp of the state in which they are found. 9 " That is, even with border controls, customs officials have no way of knowing where the fuel in the tank of a vehicle has been bought. 10 " Piecewise linear reaction functions are generated by the assumption that the population is uniformly distributed within each country. If the density of the population is the same within each country, then the reaction functions are just linear. 11 " That is, that prices are such that consumers do not wish to drive though a third country to buy in a low‐tax country. 12 " We estimate (3) using the within transformation (Wooldridge, 2002), so the time demeaning of (3) removes the country‐specific effect fi. 13 " For example, the UK has only Ireland as a land neighbour but we assume also that Belgium, France and Netherlands are neighbours, as they can be directly reached crossing the Channel. For Ireland, due to its distance from continental Europe, we assume the UK as the only neighbour. Greece does not have any EU land neighbour and so Italy is its only neighbour by this criterion. 14 " In the case of beer, there were two kinds of physical unit used in the Excise Duty Tables: degree Plato and degree of alcohol by volume. According to Directive 92/84/EEC it has been accepted that a tax of 0.748 euro Plato is equal to a tax of 1.87 euro alcohol by volume so we applied this conversion factor. 15 " Before 1999, we converted national currencies to ECU using the exchange rates provided in the Excise Duty Tables. 16 " We tried the same regressions using the tax variables in real national currency. The results are broadly similar and are not reported here to save space. The results are in Table 9 of Lockwood and Migali (2008). 17 " Due to the way that Stata calculates the decomposition, the two components add up to more than the total variance. 18 " This is an index created by Schmidt (1996), which gives different weights according to the cabinet composition. Schmidt‐Index: (1) hegemony of right‐wing parties (govleft = 0), (2) dominance of right‐wing (and centre) parties (govleft < 33.3), (3) stand‐off between left and right (33.3 < govleft < 66.6), (4) dominance of social‐democratic and other left parties (govleft > 66.6), (5) hegemony of social‐democratic and other left parties (govleft = 100). 19 " The test statistic is , where RSS, RSS1, RSS2 are the residual sums of squares of the regressions on the full sub‐sample and the first and second sub‐samples respectively. Under the null hypothesis of equality of all coefficients, this has a distribution F(K,NT − 2K). 20 " The degree of freedom of these tests depend on the set of instruments used and, in our estimation, we do not always use the full set but the combination that passes the identification tests. In general, the F test is distributed as F(L,N − K) where L = number of instruments, N = sample size (reduced by the number of fixed effects, 12 in our case), K = number of regressors including the instruments. 21 " The null hypothesis of the test is that the matrix of reduced form coefficients has rank = K − 1, where K = number of regressors, i.e, that the equation is underidentified. Under the null of underidentification, the statistic is distributed as chi‐squared with degrees of freedom = (L − K + 1), where L = number of instruments (included + excluded). 22 " It is worth noting that the usual models of excise tax competition under the origin principle generate tax reaction functions with a slope of less than one, so this coefficient is not fully consistent with the theory. 23 " Kelley Pace has written the code (FDELW2.m) to convert Delauney algorithm results into a contiguity matrix. The code is included in his Spatial Statistics toolbox 2.0 for Matlab, which can be downloaded from http://www.spatial‐statistics.com. 24 " For example, in our baseline weighting scheme, Greece only has Italy as a neighbour but, in the triangulation scheme, it also has Spain, Portugal, Germany and Denmark. 25 " Specifically, for the first triangulation weights, the main changes are as follows. Strategic interaction in sparkling wine excises is now only significant at 10% after 1993. There is now evidence of strategic interaction in beer excises before 1993 which does not intensify after 1993. There is now no evidence of strategic interaction in specific cigarette excises before 1993 but some evidence (a positive coefficient significant at 10%) of interaction after 1993. Competition in the total tax on cigarettes does not seem to intensify after 1993. A similar comparison can be made for the second triangulation weight. 26 " The weights are also row‐normalised in this case. 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Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Appendix Appendix Figures A.1 [ Still Wine – Specific Excise in National Currency ] A.2 [ Sparkling Wine – Specific Excise in National Currency ] A.3 [ Beer – Specific Excise in National Currency ] A.4 [ Ethyl Alcohol – Specific Excise in National Currency ] A.5 [ Cigarettes – Specific Excise in National Currency ] A.6 [ Cigarettes – Total Tax‐% Retail Price ] Author notes " We thank Paul Elhorst, Paulo Parente, two anonymous referees, the editor, the seminar participants at the 2008 RES conference in Warwick, at the 2007 summer school on Tax Competition at Institut d’Economia de Barcelona, for helpful comments and discussions and we are grateful to the Office of Taxation and Customs of the European Commission for useful advice. © The Author(s). Journal compilation © Royal Economic Society 2009

Clark, Andrew, E.;Kristensen,, Nicolai;Westergård‐Nielsen,, Niels

doi: 10.1111/j.1468-0297.2008.02236.xpmid: N/A

Abstract We use matched employer–employee panel data to show that individual job satisfaction is higher when other workers in the same establishment are better‐paid. This runs counter to substantial existing evidence of income comparisons in subjective well‐being. We argue that the difference hinges on the nature of the reference group. Here we use co‐workers. Their earnings not only induce jealousy but also provide a signal about the worker’s own future earnings. In our data, this positive future earnings signal outweighs any negative status effect. This phenomenon is stronger for men and in the private sector but weaker for those nearer retirement. A significant amount of work in the burgeoning literature on subjective well‐being has focused on the role of relative income in determining satisfaction or happiness. Some labour‐market examples are Capelli and Sherer (1988), Pfeffer and Langton (1993), Clark and Oswald (1996), Law and Wong (1998), Bygren (2004), Ferrer‐i‐Carbonell (2005) and Brown et al. (2008), using survey data, and Shafir et al. (1997) in experimental work.1 This work has generally concluded that relative income is important in determining individual satisfaction. One implication is that the simple neoclassical utility model, where utility depends only on the individual’s own income or consumption, should probably be extended to incorporate relative income or consumption terms. In parallel, the literature on establishment wage policies has highlighted the potential importance of wage compression. One prominent example is the fair wage‐effort hypothesis formulated by Akerlof and Yellen (1990), which largely corresponds to Adams’ (1963) theory of equity, in which effort depends on the relationship between fair and actual wages. In this theory, higher wages for some groups of workers – perhaps because they are in short supply – will raise wages for all of the workers in the establishment through the demand for pay equity. The link between worker well‐being and the establishment wage distribution is important for human resource managers, whose choice of pay policy will take into account the impact of worker dissatisfaction on profits and worker turnover; for empirical evidence, see Patterson et al. (2004). More broadly, income comparisons may have important consequences for the functioning of the entire labour market, explaining women’s labour force participation (Neumark and Postlewaite, 1998), unionisation (Farber and Saks, 1980), money illusion (Shafir et al., 1997), hysteresis in unemployment (Summers, 1988; Bewley, 1998), and wage rigidity (Levine, 1993; Campbell and Kamlani, 1997). The above literature appeals to the general area of preference interactions, as termed by Manski (2000), where what others do, or what happens to them, directly affects my own utility. While evidence of such income interactions has been steadily accumulating for a number of years, a smaller number of recent papers have uncovered empirical results of the opposite sign, with some measure of individual well‐being being positively correlated with reference group income or earnings: the more others earn, the happier I am. This finding has been interpreted as demonstrating Hirschman’s tunnel effect (Hirschman and Rothschild, 1973): while others’ good fortune might make me jealous, it may also provide information about my own future prospects. Manski (2000) calls these phenomena expectations interactions, where what happens to others allows me to update my information set. The associated empirical work refers to information effects or signals. In this article we provide some of the first evidence that information effects may be stronger than comparison effects (i.e. that signal outweighs status) in the context of developed Western economies. Individuals may therefore be better off as others earn more and, consequently, may not object to some degree of income or earnings inequality. We emphasise that the key parameter on which the balance between status and signal rests is the strength of the correlation between current reference group income and my own future earnings. At the peer group (those who share the same characteristics) or geographical level, this correlation is arguably small. In the context of Luttmer (2005), it is not because my neighbour receives a wage raise that my own future income prospects may necessarily look any brighter. The signal effect is arguably far greater within the same establishment. In this article we thus appeal to employer–employee panel data and model individual job satisfaction as a function of the earnings of all other workers within the same establishment. This unusually rich data set results from the matching of survey panel data (over the period 1994‐2001) to administrative longitudinal records. We show that workers are indeed more satisfied when their co‐workers are better‐paid. The ‘Hirschmanian establishment’ or signal interpretation is that others’ earnings provide sufficient information about my own future prospects to outweigh any jealousy I might feel towards my colleagues. We find that this Hirschman effect is weaker for those nearer retirement but there is some evidence that it is stronger for men than for women, and in the private sector. We check that current average establishment earnings do indeed predict individual future earnings, as a signal story would predict. These results are broadly supportive of Tournament theory (Lazear and Rosen, 1981), where (some of) my colleagues’ current earnings reflect my opportunities in the establishment’s internal labour market. This article is organised as follows. Section 1 presents a simple model of status and signal effects from others’ earnings. Section 2 then describes the data that we use and Section 3 presents the main empirical results. Last, Section 4 concludes. 1. Status or Signal? There has been substantial interest across most of social science in the notion of status or comparisons to others. The very broad idea here is of negative externalities emanating from the consumption or income of others within the reference group: the more others earn, the lower is my utility, ceteris paribus. Empirically, the majority of work in this area has appealed to either measures of individual behaviour (such as labour supply or consumption), or measures of subjective well‐being. In this latter case, a variable such as life satisfaction is shown to be positively correlated with own income but negatively correlated with reference group income.2 The negative correlation is consistent with the presence of income comparison terms in the utility function. Personnel Economics has arguably not paid much attention to such income comparison effects. However, it has underlined the incentive role played by the earnings that certain others within the same establishment may receive. In particular, in the tournament model (Lazear and Rosen, 1981), employees within a given establishment are seen as contestants for promotion. Relative worker performance determines the winner, who receives a fixed prize set in advance. The level of individual effort then increases with the earnings difference between winning and losing the tournament. High earnings at the top of the establishment’s hierarchy are incentives for workers at lower job levels. These two literatures confront each other when we consider individuals within the same establishment. In this case, one viable reference group is co‐workers. As such, co‐workers’ earnings may have two opposing effects on individual utility. The first is a comparison or status effect, whereby co‐workers’ higher earnings make me feel relatively deprived, and the second is a signal effect, where higher co‐worker earnings provide me with information about my own future prospects. To illustrate this tension, we develop a simple model encompassing both status and signal effects. Imagine a simple linear utility function for individual i at time t: (1) Here wit denotes the individual’s own earnings and denotes the level of reference group earnings, which in our model is within‐establishment average earnings. We imagine that α > 0 and a standard comparison story would have β < 0; the latter reflects the importance of others’ earnings in the individual utility function. For expositional purposes, assume that there are two time periods, 1 and 2. There is a probability p that, if you stay in the same job, you will earn reference group (establishment average) earnings next year, increased by θ%, say. Otherwise you will earn w2. In addition, there is a chance δ of the match finishing. If it does, your outside earnings are next period, with ‘outside’ reference group earnings of . Individuals are assumed to maximise the present discounted value of expected utility. Setting the discount rate to zero, without loss of generality, we have: So that It is assumed that individuals take their future into account, so that their satisfaction response today includes information on how they expect their job to be in the future3 (otherwise the information element plays no role by construction). A standard regression in the field of income comparisons models job/life satisfaction at time t as a function of both wi1 and . The δ(·) term, the third above, represents the outside options (in terms of both earnings and reference group earnings) should the match come to an end. This can be considered to be picked up by demographic variables, or by the individual effect in panel analyses. Most empirical estimation does not control for the levels of future earnings and reference group earnings (wi2 and that pertain when the individual does not accede to the current reference group earnings (although we can argue that wi2 will be closely correlated with wi1). The key implication of this model is that the coefficient on in the estimation of will not only represent the comparison part of the utility function, but also the information that establishment average earnings (or whatever the measure of reference group earnings is) provides about the worker’s future prospects. In our model, instead of estimating β, we in fact obtain an estimate of (2) This estimated coefficient, , will be positive, setting θ equal to zero for simplicity, if Proposition 1. The signal effect is more likely to dominate the status effect, so that others’ earnings are positively correlated with my own well‐being, as: (i) the probability of acceding to the reference group (p) is higher; (ii) the jealousy parameter (β) is lower; (iii) the match destruction rate (δ) is lower; and (iv) the marginal utility of own income (α) is higher. The empirical literature on income comparisons has taken the estimated value of β in (1) as an indicator of the strength of status effects. However, the simple model above highlights that this interpretation fails when there is also a signal component; in this case there is no clean test of comparisons as the estimated coefficient on w* picks up two opposing phenomena. In general, any estimated value of will be consistent with the presence of income comparisons in the utility function. From (2), the strength of the comparison term can only be estimated in three distinct cases: (i) α = 0, so that a priori only others’ income matters in the utility function, with no role for one’s own income. This prior is obviously unattractive. (ii) p = 0, so that there is no chance of acceding to the reference group job. It might be argued that a geographical definition of a reference group in Western countries, as in Luttmer (2005) or Blanchflower and Oswald (2004), goes some way to meeting this condition – I am perhaps relatively unlikely to end up with my neighbour’s job. This would likely be a worse assumption in the case of Knight and Song (2006), where the reference group (others in the same rural Chinese village) is more homogeneous. (iii) δ = 1. All matches are destroyed, so that there is no chance of staying in the same job. This is unlikely in field data but can easily be engineered in experimental tests of comparison income, such as McBride (2007). Our empirical work uses matched employer–employee data and considers a reference group of other workers within the same establishment. We therefore expect a non‐zero information effect from others’ earnings, especially for those who have a greater chance of moving up the establishment earnings ladder and for those who expect to stay in the establishment longer. This kind of data provides a good setting in which to test for the relative strength of status and signal effects. 2. Empirical Approach and Data 2.1. The Data This article is based on data of unusual richness. Eight waves of survey data from the Danish sample of the European Community Household Panel (ECHP)4 have been merged with administrative records. The ECHP survey data, which constitute a panel spanning 1994–2001, cover about 7,000 individuals in the first few years. Due to sample attrition this falls to about 5,000 individuals by 2001. Here we only consider employees, aged 18–64, producing an effective sample of about 16,000 observations on around 4,000 individuals over the eight‐year period. Our dependent variable results from an overall job satisfaction question as follows: How satisfied are you with your work or other main activity? Respondents answer the satisfaction question using an ordered scale from 1 (not at all satisfied) to 6 (fully satisfied). Figure 1 shows the distribution of job satisfaction in this sample. As is usual, there is bunching towards the right‐hand side of the satisfaction scale. Fig. 1. Open in new tabDownload slide Distribution of Job Satisfaction. Danish ECHP Sample, 1994–2001
Note: The question reads: How satisfied are you with your work or other main activity? The responses are on an ordered scale from 1 (not at all satisfied) to 6 (fully satisfied). Fig. 1. Open in new tabDownload slide Distribution of Job Satisfaction. Danish ECHP Sample, 1994–2001
Note: The question reads: How satisfied are you with your work or other main activity? The responses are on an ordered scale from 1 (not at all satisfied) to 6 (fully satisfied). The Danish component of the ECHP was sampled randomly from the central administrative database, the Central Personal Register (CPR). The CPR contains an entry for each individual in Denmark; each individual has a unique CPR number. This CPR number can then be matched to the administrative IDA5 database, maintained by Statistics Denmark, which contains labour‐market information on all individuals aged 15 to 74 (demographic characteristics, education, labour market experience, tenure and earnings) and employees in all workplaces in Denmark over the period 1980–2001. This database includes, amongst many other things, identifiers for both the firm and the establishment where the individual works and the earnings of each individual. In our work we consider other workers in the same establishment as the reference group. We pay particular attention to ensuring that the job that the individual held when interviewed in the ECHP is the same as that in the administrative register data. The earnings in the register data refer to the annual earnings of the job that the individual held at the end of the November of each year, as reported by firms to the tax authorities. The firms’ declarations of each worker’s earnings are cross‐checked against the worker’s own tax filings. Our matching of the two databases therefore allows us to use administrative information on both individual earnings and the earnings of all of the individual’s colleagues at their place of work. Our use of administrative data helps to minimise the common problems associated with measurement error regarding earnings.6 We now have information on survey respondents’ job satisfaction (from the ECHP), their own earnings and the entire establishment earnings distribution (the latter two from register data). To flesh out the idea of an earnings distribution, we limit the sample to establishments where the respondent has a minimum of 5 colleagues.7 Our key regressions will model individual job satisfaction as a function of both own earnings and a measure of others’ earnings within the same establishment, as well as a set of standard demographic control variables.8 2.2. Econometric Specification We are interested here in the determinants of overall job satisfaction and, in particular, the role of the individual’s position in the establishment’s wage distribution. Job satisfaction is an ordered variable, reported on a scale from 1 to 6. In comparison to previous work that has considered the role of the establishment’s wage structure, our use of panel data means that we are able to control for unobserved individual characteristics. Lykken and Tellegen (1996) estimate that between 50% and 80% of the variation in individuals’ reported well‐being results from genes and upbringing, underlining the importance of controlling for individual‐specific fixed effects. However, controlling for an individual effect in this particular case is problematic. A first issue is that establishment’s average earnings may change only little over time (and relatively few individuals change establishments), producing little variation in reference group wages. A second issue is that job satisfaction is measured on an ordinal, rather than a cardinal, scale. A common approach to fixed‐effect ordinal estimation requires a dichotomous dependent variable, which loses a great deal of information. However, random‐effects estimation is likely to be inconsistent, as own wage is very likely endogenous in a model with job satisfaction as the dependent variable. In this article we take two different approaches to introducing individual effects into our baseline model. We assume a latent unobserved continuous measure of reported job satisfaction, JS*, which is assumed to be a function of individual covariates such as age, education and other background characteristics, Xit and earnings‐related terms, ITit (which will also be discussed below). The empirical model is then: (3) The error term consists of γi and ɛit, where γi is the individual‐specific time‐invariant component and ɛit is the individual and time‐varying disturbance term. Our first approach is to use a Mundlak correction term. This preserves the ordinal nature of the dependent variable, without any need for dichotomising, and also dispenses with the orthogonality requirements of random‐effect estimation. Here we parameterise the individual effect as , where denotes the mean wage of individual i over all the waves in which she is observed. This term is included as an application of Mundlak’s (1978) method, where the individual effect is decomposed into a random effect (γ0i) that is uncorrelated with the right‐hand side variables and the mean values of some of the (time‐varying) regressors that are allowed to be correlated with the individual random effects. Here we use the individual‐specific mean values of earnings. The second approach is, following Ferrer‐i‐Carbonell and Frijters (2004), to consider satisfaction as a cardinal variable and apply linear techniques, producing ‘within’ regressions. This is also the approach adopted by Luttmer (2005). 3. Results In this Section we first present the main results and then a number of extensions and robustness tests. Finally, we discuss the results and their implications. 3.1. Baseline Results Table 2 presents the results from our baseline specification, including the individuals’ own earnings, wit, and establishment average earnings, , in the earnings‐related terms, ITit, in (3) above. Table 2 
Baseline Specification. Job Satisfaction, Own and Establishment Earnings . Random Effects Ordered Probit . Random Effects Ordered Probit . Fixed Effects Linear Regression (‘Within’) . Ln(Own earnings) 0.068** 0.052* 0.032 (0.024) (0.026) (0.020) Ln(Average own earnings) (=The Mundlak term) — 0.079+ — — (0.047) — Ln(Average establishment earnings) 0.109* 0.100* 0.080+ (0.046) (0.046) (0.043) Age −0.053** −0.058** Age Dummies (3) (0.011) (0.011) Age‐squared/100 0.076** 0.081** (0.013) (0.013) Health problem −0.079** −0.079** −0.024 (0.030) (0.030) (0.023) Female −0.045 −0.032 — (0.039) (0.040) — Managers 0.091* 0.083+ 0.025 (0.045) (0.045) (0.035) White collar 0.028 0.024 −0.014 (0.040) (0.040) (0.032) Single −0.044 −0.041 0.036 (0.034) (0.034) (0.034) Hours work/week −0.001 −0.001 −0.003 (0.002) (0.002) (0.002) Subordinates 0.061* 0.057* 0.005 (0.029) (0.029) (0.024) Establishment size 5–19 0.162** 0.165** 0.091* (0.039) (0.039) (0.039) Establishment size 20–49 0.086* 0.089* 0.067+ (0.038) (0.038) (0.035) Establishment size 50–99 0.105** 0.107** 0.094** (0.038) (0.038) (0.033) Education dummies (5) Yes Yes Yes Industry dummies (6) Yes Yes Yes Regional dummies (13) Yes Yes Yes Year dummies (7) Yes Yes Yes No. of Observations 16,031 16,031 12,059 . Random Effects Ordered Probit . Random Effects Ordered Probit . Fixed Effects Linear Regression (‘Within’) . Ln(Own earnings) 0.068** 0.052* 0.032 (0.024) (0.026) (0.020) Ln(Average own earnings) (=The Mundlak term) — 0.079+ — — (0.047) — Ln(Average establishment earnings) 0.109* 0.100* 0.080+ (0.046) (0.046) (0.043) Age −0.053** −0.058** Age Dummies (3) (0.011) (0.011) Age‐squared/100 0.076** 0.081** (0.013) (0.013) Health problem −0.079** −0.079** −0.024 (0.030) (0.030) (0.023) Female −0.045 −0.032 — (0.039) (0.040) — Managers 0.091* 0.083+ 0.025 (0.045) (0.045) (0.035) White collar 0.028 0.024 −0.014 (0.040) (0.040) (0.032) Single −0.044 −0.041 0.036 (0.034) (0.034) (0.034) Hours work/week −0.001 −0.001 −0.003 (0.002) (0.002) (0.002) Subordinates 0.061* 0.057* 0.005 (0.029) (0.029) (0.024) Establishment size 5–19 0.162** 0.165** 0.091* (0.039) (0.039) (0.039) Establishment size 20–49 0.086* 0.089* 0.067+ (0.038) (0.038) (0.035) Establishment size 50–99 0.105** 0.107** 0.094** (0.038) (0.038) (0.033) Education dummies (5) Yes Yes Yes Industry dummies (6) Yes Yes Yes Regional dummies (13) Yes Yes Yes Year dummies (7) Yes Yes Yes No. of Observations 16,031 16,031 12,059 Notes. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Column 3 includes a constant, and columns 1 and 2 five estimated cut‐points. Open in new tab Table 2 
Baseline Specification. Job Satisfaction, Own and Establishment Earnings . Random Effects Ordered Probit . Random Effects Ordered Probit . Fixed Effects Linear Regression (‘Within’) . Ln(Own earnings) 0.068** 0.052* 0.032 (0.024) (0.026) (0.020) Ln(Average own earnings) (=The Mundlak term) — 0.079+ — — (0.047) — Ln(Average establishment earnings) 0.109* 0.100* 0.080+ (0.046) (0.046) (0.043) Age −0.053** −0.058** Age Dummies (3) (0.011) (0.011) Age‐squared/100 0.076** 0.081** (0.013) (0.013) Health problem −0.079** −0.079** −0.024 (0.030) (0.030) (0.023) Female −0.045 −0.032 — (0.039) (0.040) — Managers 0.091* 0.083+ 0.025 (0.045) (0.045) (0.035) White collar 0.028 0.024 −0.014 (0.040) (0.040) (0.032) Single −0.044 −0.041 0.036 (0.034) (0.034) (0.034) Hours work/week −0.001 −0.001 −0.003 (0.002) (0.002) (0.002) Subordinates 0.061* 0.057* 0.005 (0.029) (0.029) (0.024) Establishment size 5–19 0.162** 0.165** 0.091* (0.039) (0.039) (0.039) Establishment size 20–49 0.086* 0.089* 0.067+ (0.038) (0.038) (0.035) Establishment size 50–99 0.105** 0.107** 0.094** (0.038) (0.038) (0.033) Education dummies (5) Yes Yes Yes Industry dummies (6) Yes Yes Yes Regional dummies (13) Yes Yes Yes Year dummies (7) Yes Yes Yes No. of Observations 16,031 16,031 12,059 . Random Effects Ordered Probit . Random Effects Ordered Probit . Fixed Effects Linear Regression (‘Within’) . Ln(Own earnings) 0.068** 0.052* 0.032 (0.024) (0.026) (0.020) Ln(Average own earnings) (=The Mundlak term) — 0.079+ — — (0.047) — Ln(Average establishment earnings) 0.109* 0.100* 0.080+ (0.046) (0.046) (0.043) Age −0.053** −0.058** Age Dummies (3) (0.011) (0.011) Age‐squared/100 0.076** 0.081** (0.013) (0.013) Health problem −0.079** −0.079** −0.024 (0.030) (0.030) (0.023) Female −0.045 −0.032 — (0.039) (0.040) — Managers 0.091* 0.083+ 0.025 (0.045) (0.045) (0.035) White collar 0.028 0.024 −0.014 (0.040) (0.040) (0.032) Single −0.044 −0.041 0.036 (0.034) (0.034) (0.034) Hours work/week −0.001 −0.001 −0.003 (0.002) (0.002) (0.002) Subordinates 0.061* 0.057* 0.005 (0.029) (0.029) (0.024) Establishment size 5–19 0.162** 0.165** 0.091* (0.039) (0.039) (0.039) Establishment size 20–49 0.086* 0.089* 0.067+ (0.038) (0.038) (0.035) Establishment size 50–99 0.105** 0.107** 0.094** (0.038) (0.038) (0.033) Education dummies (5) Yes Yes Yes Industry dummies (6) Yes Yes Yes Regional dummies (13) Yes Yes Yes Year dummies (7) Yes Yes Yes No. of Observations 16,031 16,031 12,059 Notes. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Column 3 includes a constant, and columns 1 and 2 five estimated cut‐points. Open in new tab There are three columns in Table 2, all of which control for individual effects. The first two columns refer to random‐effect ordered probit estimation. Column 1 includes both own and establishment earnings, while column 2 introduces the Mundlak term described above. The estimated coefficient on own earnings is positive and significant in both of these columns (at the 1% level in column 1 and at the 5% level in column 2). The estimated coefficient on the Mundlak term is positive in column 2 and significant at the 10% level. The positive effect of the Mundlak term explains why the coefficient on own earnings falls somewhat in both size and significance between columns 1 and 2. The broad positive relationship between own earnings and job satisfaction, conditional on the other right‐hand side variables, is unsurprising and is consistent with most results in the literature. More unusually, the estimated coefficient on establishment average earnings is positive and significant at the 5% level in both columns 1 and 2, and is little affected by the Mundlak correction. Column 3 takes a different tack, estimating within regressions. Here own earnings attracts a positive coefficient, which is only borderline significant (p‐value = 0.12), but again the average establishment earnings attract a positive and significant coefficient (p‐value =  0.06).9 The fact that establishment average earnings have a positive effect on satisfaction within the same individual argues against a selection story, whereby intrinsically‐satisfied workers choose to work in establishments where average earnings are higher. Not only do we not find the standard negative comparison effect in our empirical results but the estimated coefficient is also significant in the opposite direction. In terms of the model in Section 1, this is consistent with the signal effect dominating the status effect, yielding a net positive estimated coefficient (, as in Hirschman’s tunnel effect. The implications of this finding are discussed in Section 3.4 below. The results for the other control variables are standard. In the random effects specifications the quadratic age terms suggest a U‐shape between job satisfaction and age, minimising in the mid‐thirties (Clark et al., 1996). The quadratic specification is inappropriate with a fixed effect and in column 3 we introduce a set of three age dummies (coefficients not shown). We also find a strong effect of health, at least in columns 1 and 2 (although we cannot say anything about causality), and that employees in relatively small establishments (fewer than 100 employees) report statistically significant higher job satisfaction levels than do employees in establishments with 100 employees or more. To evaluate the size of the establishment earnings effect on job satisfaction, we calculate a marginal effect for a representative individual.10 This person has a predicted probability of reporting the highest satisfaction level of 30.3%; doubling average establishment earnings increases this figure to 32.8%. This relatively modest‐looking marginal impact is typical in subjective data, where the dependent variable is often tightly distributed (see Figure 1). 3.2. Robustness Checks Table 2 showed that establishment average earnings are positively correlated with individual job satisfaction in panel estimation. The interpretation we have advanced is that others’ good fortune today reflects my potential good fortune tomorrow: others’ earnings are a signal. This sub‐section reports a number of robustness checks to validate this reading of the empirical results. A first obvious test, based on the panel nature of the data, is to check that others’ earnings today do indeed predict the individual’s own future earnings. We thus run a set of regressions explaining own earnings growth k waves in the future as a function of both own and average establishment earnings today, plus a set of standard demographic controls: (4) If own future earnings depend on current average establishment earnings, then we expect the estimated value of α2 to be positive. Table 3 shows the results, for values of k ranging from one to five (i.e. predicting one to five years into the future). The estimated value of α2 is indeed positive and very significant, and changes only little according to the time frame over which prediction is carried out. The estimation in Table 3 refers only to those who stay in the same establishment between t and t + k (although estimating on the whole sample, whether they move or not, yields similar parameter estimates). Table 3 
Own Future Earnings Growth and Current Average Establishment Earnings . k = 1 . k = 2 . k = 3 . k = 4 . k = 5 . Ln(Own earnings) (=α1) −0.836** −0.880** −0.856** −0.834** −0.806** (0.007) (0.009) (0.011) (0.014) (0.019) Ln(Average establishment earnings) (=α2) 0.130** 0.169** 0.157** 0.155** 0.177** (0.012) (0.016) (0.018) (0.022) (0.029) Observations 10,019 6,703 4,490 2,961 1,835 . k = 1 . k = 2 . k = 3 . k = 4 . k = 5 . Ln(Own earnings) (=α1) −0.836** −0.880** −0.856** −0.834** −0.806** (0.007) (0.009) (0.011) (0.014) (0.019) Ln(Average establishment earnings) (=α2) 0.130** 0.169** 0.157** 0.155** 0.177** (0.012) (0.016) (0.018) (0.022) (0.029) Observations 10,019 6,703 4,490 2,961 1,835 Notes. The equation estimated is . The other control variables in X are as in column 1 of Table 2. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Estimated only on those who stay in the same establishment between t and t + k. Open in new tab Table 3 
Own Future Earnings Growth and Current Average Establishment Earnings . k = 1 . k = 2 . k = 3 . k = 4 . k = 5 . Ln(Own earnings) (=α1) −0.836** −0.880** −0.856** −0.834** −0.806** (0.007) (0.009) (0.011) (0.014) (0.019) Ln(Average establishment earnings) (=α2) 0.130** 0.169** 0.157** 0.155** 0.177** (0.012) (0.016) (0.018) (0.022) (0.029) Observations 10,019 6,703 4,490 2,961 1,835 . k = 1 . k = 2 . k = 3 . k = 4 . k = 5 . Ln(Own earnings) (=α1) −0.836** −0.880** −0.856** −0.834** −0.806** (0.007) (0.009) (0.011) (0.014) (0.019) Ln(Average establishment earnings) (=α2) 0.130** 0.169** 0.157** 0.155** 0.177** (0.012) (0.016) (0.018) (0.022) (0.029) Observations 10,019 6,703 4,490 2,961 1,835 Notes. The equation estimated is . The other control variables in X are as in column 1 of Table 2. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Estimated only on those who stay in the same establishment between t and t + k. Open in new tab A further issue is that of establishment size: are the results driven by only very small or very large establishments? To check, Table 4 reproduces our baseline results for the whole sample from column 2 of Table 2 and then shows analogous estimates first excluding large establishments (100+ employees) and then excluding small establishments (< =20 employees). The results show that, while the estimated coefficient on average establishment earnings is positive under both restrictions, it is only significantly so for larger establishments. This might be thought of as consistent with the greater presence of internal labour markets in larger establishments. Table 4 
Job Satisfaction, Own and Establishment Earnings: The Role of Establishment Size . Random Effects Ordered Probit . All . Establishment < 100 . Establishment > 20 . Ln(Own earnings) 0.052* 0.090** 0.032 (0.026) (0.030) (0.032) Ln(Average establishment earnings) 0.100* 0.058 0.137* (0.046) (0.052) (0.060) Observations 16,031 11,803 12,603 . Random Effects Ordered Probit . All . Establishment < 100 . Establishment > 20 . Ln(Own earnings) 0.052* 0.090** 0.032 (0.026) (0.030) (0.032) Ln(Average establishment earnings) 0.100* 0.058 0.137* (0.046) (0.052) (0.060) Observations 16,031 11,803 12,603 Notes. Other control variables as in column 2 of Table 2. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Open in new tab Table 4 
Job Satisfaction, Own and Establishment Earnings: The Role of Establishment Size . Random Effects Ordered Probit . All . Establishment < 100 . Establishment > 20 . Ln(Own earnings) 0.052* 0.090** 0.032 (0.026) (0.030) (0.032) Ln(Average establishment earnings) 0.100* 0.058 0.137* (0.046) (0.052) (0.060) Observations 16,031 11,803 12,603 . Random Effects Ordered Probit . All . Establishment < 100 . Establishment > 20 . Ln(Own earnings) 0.052* 0.090** 0.032 (0.026) (0.030) (0.032) Ln(Average establishment earnings) 0.100* 0.058 0.137* (0.046) (0.052) (0.060) Observations 16,031 11,803 12,603 Notes. Other control variables as in column 2 of Table 2. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Open in new tab An additional testable implication of the signal reading is that establishment earnings matter more for those who have more years left in which to enjoy higher earnings. As a test, we add an interaction between establishment average earnings and a dummy for ‘older workers’. We defined the latter as workers aged over 51. The estimated coefficient on this interaction (results available on request) is negative and significant at the 1% level: establishment average earnings provide a smaller satisfaction boost for workers who are nearer retirement. The main effect of average establishment earnings remains positive and significant at the 5% level. 3.3. Specifications of Reference Earnings In this Section, we ask whether we can identify certain groups for whom the signal effect of others’ earnings is stronger and also whether other specifications of reference earnings produce similar results. We first consider whether the linear‐in‐means specification of reference earnings is the most appropriate. In the context of tournaments, arguably only the earnings of those above you in the hierarchy matter; to investigate, we replace average establishment earnings in the baseline specification by the 75th percentile of earnings. To help pinpoint this figure, we only consider establishments where there are at least ten employees (although the same qualitative results hold for the whole sample). The results in the first column of Table 5 show that, again, workers are more satisfied in high‐earnings firms. The coefficient on the 75th percentile of establishment earnings is positive and significant, and is larger in size than that on mean establishment earnings in Table 2. Table 5 
Comparisons to the 75th Percentile . Random Effects Ordered Probit . All . Below Median . Above Median but below 75th percentile . Above 75th percentile . Ln(Own earnings) 0.033 0.011 −0.168 0.212 (0.028) (0.034) (0.210) (0.156) Ln(75th percentile establishment earnings) 0.156** 0.214* 0.565* −0.012 (0.053) (0.090) (0.223) (0.125) Observations 14,941 5,877 4,381 4,683 . Random Effects Ordered Probit . All . Below Median . Above Median but below 75th percentile . Above 75th percentile . Ln(Own earnings) 0.033 0.011 −0.168 0.212 (0.028) (0.034) (0.210) (0.156) Ln(75th percentile establishment earnings) 0.156** 0.214* 0.565* −0.012 (0.053) (0.090) (0.223) (0.125) Observations 14,941 5,877 4,381 4,683 Notes. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Other control variables as in column 2 of Table 2. Sample restricted to establishments with 10 or more employees. Open in new tab Table 5 
Comparisons to the 75th Percentile . Random Effects Ordered Probit . All . Below Median . Above Median but below 75th percentile . Above 75th percentile . Ln(Own earnings) 0.033 0.011 −0.168 0.212 (0.028) (0.034) (0.210) (0.156) Ln(75th percentile establishment earnings) 0.156** 0.214* 0.565* −0.012 (0.053) (0.090) (0.223) (0.125) Observations 14,941 5,877 4,381 4,683 . Random Effects Ordered Probit . All . Below Median . Above Median but below 75th percentile . Above 75th percentile . Ln(Own earnings) 0.033 0.011 −0.168 0.212 (0.028) (0.034) (0.210) (0.156) Ln(75th percentile establishment earnings) 0.156** 0.214* 0.565* −0.012 (0.053) (0.090) (0.223) (0.125) Observations 14,941 5,877 4,381 4,683 Notes. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Other control variables as in column 2 of Table 2. Sample restricted to establishments with 10 or more employees. Open in new tab We might also suspect, in line with tournament theory, that the signal applies more strongly to those who earn less than the 75th percentile earnings and that the size of this signal will increase the closer the individual is to the 75th percentile (from below). The last three columns of Table 5 explore this possibility, by running separate estimations according to whether the individual is in the bottom half of the earnings distribution, the third quartile (i.e. the 50th to the 75th percentile) or the top quartile. The results are consistent with the prior: the effect of 75th percentile earnings is positive and significant for those in the first three quartiles, especially for those in the third quartile (i.e. those who are closest to the establishment earnings measure).11 By way of contrast, 75th percentile earnings is very insignificant for those in the top quartile of the establishment wage distribution.12 It is worth emphasising that this correlation holds, controlling for the individual’s own earnings, so that the establishment earnings is not acting as a proxy for own earnings in these regressions. A second specification issue refers to the sample used to calculate establishment average earnings. One topic of discussion in the income comparisons literature has been to whom individuals actually compare. Within the establishment, it is perhaps likely that workers compare their earnings more to those of others who are doing the same kind of job. With this in mind, Table 6 shows the results of estimations with two establishment earnings terms. The first is the 75th percentile establishment earnings, as in Table 5: we expect this to reflect the signal component of others’ earnings. The second is mean earnings by occupation, split up into three categories (Managers and equivalent, Middle‐ranking positions and Lower‐level jobs).13 We calculate 75th percentile establishment earnings at the establishment level (and not by occupation within the establishment) as the whole ethos of tournaments is that the winners climb up the establishment hierarchy. Table 6 
Comparisons to the 75th Percentile and Mean Occupational Earnings . All . Male . Female . Private sector . Public sector . Ln(own earnings) 0.046 0.035 0.067 0.047 0.081+ (0.029) (0.040) (0.041) (0.037) (0.048) Ln(75th percentile establishment earnings) 0.236** 0.367** 0.123 0.268** 0.084 (0.065) (0.097) (0.089) (0.079) (0.133) Ln(avg. earnings by establishment & occupation) −0.123* −0.254** −0.012 −0.187** −0.048 (0.055) (0.080) (0.077) (0.070) (0.093) Observations 14,941 7,968 6,973 8,445 6,496 . All . Male . Female . Private sector . Public sector . Ln(own earnings) 0.046 0.035 0.067 0.047 0.081+ (0.029) (0.040) (0.041) (0.037) (0.048) Ln(75th percentile establishment earnings) 0.236** 0.367** 0.123 0.268** 0.084 (0.065) (0.097) (0.089) (0.079) (0.133) Ln(avg. earnings by establishment & occupation) −0.123* −0.254** −0.012 −0.187** −0.048 (0.055) (0.080) (0.077) (0.070) (0.093) Observations 14,941 7,968 6,973 8,445 6,496 Notes. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Other control variables as in column 2 of Table 2. Sample restricted to establishments with 10 or more employees. Open in new tab Table 6 
Comparisons to the 75th Percentile and Mean Occupational Earnings . All . Male . Female . Private sector . Public sector . Ln(own earnings) 0.046 0.035 0.067 0.047 0.081+ (0.029) (0.040) (0.041) (0.037) (0.048) Ln(75th percentile establishment earnings) 0.236** 0.367** 0.123 0.268** 0.084 (0.065) (0.097) (0.089) (0.079) (0.133) Ln(avg. earnings by establishment & occupation) −0.123* −0.254** −0.012 −0.187** −0.048 (0.055) (0.080) (0.077) (0.070) (0.093) Observations 14,941 7,968 6,973 8,445 6,496 . All . Male . Female . Private sector . Public sector . Ln(own earnings) 0.046 0.035 0.067 0.047 0.081+ (0.029) (0.040) (0.041) (0.037) (0.048) Ln(75th percentile establishment earnings) 0.236** 0.367** 0.123 0.268** 0.084 (0.065) (0.097) (0.089) (0.079) (0.133) Ln(avg. earnings by establishment & occupation) −0.123* −0.254** −0.012 −0.187** −0.048 (0.055) (0.080) (0.077) (0.070) (0.093) Observations 14,941 7,968 6,973 8,445 6,496 Notes. Standard errors in parentheses; + significant at 10%; * significant at 5%; ** significant at 1%. Other control variables as in column 2 of Table 2. Sample restricted to establishments with 10 or more employees. Open in new tab The results in the first column of Table 6 show the estimation results over the whole sample. These reveal a positive effect from the 75th percentile establishment earnings, as before, but a negative significant effect from mean earnings by occupation (within the establishment). The first of these may be interpreted as a signal effect but the second as reflecting earnings comparisons to similar others, as emphasised in much of the existing empirical literature. We are aware, however, that these estimations put considerable structure on a dependent variable that does not exhibit that much variation. The first column of Table 6 is thus consistent with the presence of both signal and status effects from others’ earnings. The remaining columns of this Table show that these effects are not homogeneous across different labour market groups. Columns 2 and 3 of Table 6 indicate that the signal effects from establishment earnings are stronger for men than for women, and that the putative status earnings effect is very significant and negative for men but totally insignificant for women. The latter result might be thought of as a large‐sample survey data counterpart to the well‐known findings in the experimental literature that men react more strongly in competitive environments, i.e. that they are more status‐sensitive (Gneezy et al., 2003; Niederle and Vesterlund, 2007). Finally, columns 4 and 5 of Table 6 show that the signal vs. status distinction in others’ earnings is sharper in the private than in the public sector. This is perhaps unsurprising, as earnings in the Danish public sector are determined by centralised collective bargaining, with relatively little scope for individual public‐sector establishments to set up tournaments. 3.4. Discussion and Implications The results presented above are largely consistent with a ‘Hirschmanian’ role for others’ earnings within the establishment, in the sense that the signal effect from others’ earnings may dominate any jealousy or status effect. As tournament theory would imply, this signal effect is insignificant for those who earn more than the indicator of establishment earnings that we employ. 3.4.1. Alternative explanations Before considering the implications of the signal effect of co‐workers’ wages, it is as well to consider other plausible explanations of our previous results. One first natural reaction to survey data on earnings is that it is measured with some error. If this is the case, then co‐workers’ wages may be proxying for the individual’s own wage (and will thus attract a positive coefficient). However, as noted in Section 2.1, the earnings measures used (both own and others) are derived from firms’ checked tax declarations (in the administrative IDA database), rather than self‐reported by respondents and are thus presumably measured with much less error. Second, there may well be heterogeneity in the amount of rents that firms give their workers, perhaps due to the degree of competition. Any rents that are paid will consist of earnings (which we measure) and perks (which we do not). In this case, conditional on own earnings, co‐workers’ earnings will be correlated with the firm provision of perks, which has a direct effect on job satisfaction. Although we cannot measure perks directly, we can appeal to the asymmetric effect of co‐workers’ earnings in Table 5, where only the satisfaction of those earning less than the measure of establishment earnings was related to establishment earnings. The perks explanation will then only hold if any such non‐monetary rewards are specifically not targeted towards higher‐paid workers (which may seem unlikely). Last, we might imagine a sorting story based on differences in worker ‘disposition’– some workers are intrinsically positive and satisfied, and are not particularly sensitive to status, while other workers are less happy and do care about where they stand in the earnings distribution. Consequently, ‘happy’ workers may prefer firms where others’ earnings are high (they do not mind this, as they are not status‐sensitive) while the unhappy choose firms where average earnings are low (because they want to rank high in the earnings distribution). Here we have an omitted variable, disposition, which is correlated with the earnings of co‐workers. While it is difficult to test for this selection of workers directly, the fixed‐effects estimation in Table 2 should rule out this interpretation if we believe that disposition varies only little over time. We might equally ask, from Table 5, why any such sorting would then seem to be far stronger in the third quartile of the establishment earnings distribution than in the fourth quartile. 3.4.2. Implications The finding of a positive well‐being effect from others’ wages differs from those in the majority of the published literature. We think that the key distinction lies in the composition of the reference group. As previously noted, the fact that the Joneses living next door earn more than I do, as in Luttmer (2005), may reveal only little information about my future pay prospects: the entire effect of the Joneses’ pay thus passes by a comparison or status effect, reducing relative income and satisfaction. Things may well be very different when work colleagues serve as the comparison group. In this case high reference earnings serve as a signal regarding one’s own future pay cheque. The published work that has found a positive well‐being effect from others’ income, Senik (2004, 2008) and Kingdon and Knight (2007), can also be interpreted in terms of signal effects. Senik (2004) uses Russian RLMS data to establish a positive correlation between life satisfaction and (geographical) reference group income, especially for younger workers. In general, Senik (2008) makes the point that most evidence of comparison or jealousy effects comes from stable Western countries. In Senik’s work, the reference group consists of other people who are similar to you. In a very unstable labour market, what happens to similar others today may well be thought of as providing a signal about your own future labour market outcomes. Kingdon and Knight (2007) use South African data to show that the average income of others in the local residential area is positively correlated with household utility (while average income by district or province is negatively correlated with well‐being). Again, this can be interpreted as showing that individuals are more likely to end up with their close neighbour’s job than with their more distant neighbour’s job. This article has uncovered this kind of signal effect using a natural reference group (colleagues within the same establishment) in an OECD country. Denmark has one of the most equal income distributions in the world, as well as very high income and wage mobility by international standards (OECD, 1997). These two facts together with our results suggest that: (i) even in a stable economic environment there can be substantial income mobility and, in this context, it is not surprising that signal effects exist even in the affluent Danish economy; and (ii) there are likely to be limits to income re‐distribution. The theoretical and empirical work on ‘Prospects of upward mobility’ (POUM: see Alesina and La Ferrara (2005) and Bénabou and Ok (2001)) has underlined that the demand for redistribution depends not only on where individuals are now but also where they might reasonably expect to find themselves in the future. In the same way, individuals’ evaluations of their current job are likely to reflect both their current and their expected future rewards from working. In this article, we have argued that the latter, which is analogous to the rewards from POUM in this case, might be picked up by colleagues’ current earnings, especially those who figure above the individual in the establishment earnings distribution. In this case, increasing the earnings of the well‐paid may potentially increase everyone’s job satisfaction: that of the well‐paid because their own pay has gone up and that of the low‐paid due to higher establishment earnings. This kind of phenomenon may be behind some earlier findings in economics and psychology, underlining a positive relationship between income inequality and measures of subjective well‐being; see Clark (2003) and the references therein. 4. Conclusion A common theme in the subjective well‐being literature has been comparisons to others, whereby low income relative to a reference group reduces well‐being. We argue that this correlation is conditional on reference group wage being uninformative about the individual’s own future income prospects. In much of the existing literature, this condition is satisfied (it is not necessarily because my neighbours or my cohort receive a pay rise that my own future prospects look brighter). Here we analyse a data set where this condition probably does not hold, using earnings information on all other workers within the same establishment. We do so by matching Danish ECHP data to administrative records. The results are unambiguous. Job satisfaction is positively correlated with own earnings but it is also positively correlated with the average earnings of all other workers within the same establishment. Although we have not presented any direct tests of tournament theory, our results are nonetheless consistent with this model. When my colleagues earn higher wages, I learn about my future opportunities within the establishment. In line with the Tournament model this effect is more pronounced for men (who are more likely to be promoted), in the private sector (where wage‐setting is more individualised), and for those who earn less than the establishment wage measure. Our results corroborate the findings of one of the few empirical studies of Tournament theory, Eriksson (1999), who finds support for this theory using Danish data. Taking these results at face value, workers may not always oppose earnings inequality – at least not within the establishment. Higher earnings for better‐paid workers may improve everyone’s job satisfaction. There are however likely limits beyond which this result will no longer hold. Future research should attempt to identify more accurately the relationship between worker well‐being, on the one hand, and both own and others’ wages on the other, while explicitly recognising that my own current relative wage misfortune may contain the promise of a brighter future. Table 1 
Means and Standard Deviations of Key Variables Variable . Mean . Std. Dev. . Real earnings/1000 (1995 DKK) 227.49 109.10 Age 40.29 10.66 Female 0.46 0.50 Occupation  Managers 0.19 0.39  White collar 0.17 0.38  Blue collar 0.43 0.50 Health problem 0.20 0.40 Single 0.23 0.42 Hours of work per week 37.28 6.99 Subordinates (yes = 1) 0.31 0.46 Establishment size  5–19 0.21 0.41  20–49 0.19 0.39  50–99 0.18 0.38  100 or more 0.26 0.44 Education  Primary/Secondary 0.21 0.40  High School 0.07 0.25  Vocational 0.39 0.49  College‐short 0.06 0.23  College‐long 0.20 0.40  University 0.08 0.26 Job Satisfaction 4.96 0.95 Variable . Mean . Std. Dev. . Real earnings/1000 (1995 DKK) 227.49 109.10 Age 40.29 10.66 Female 0.46 0.50 Occupation  Managers 0.19 0.39  White collar 0.17 0.38  Blue collar 0.43 0.50 Health problem 0.20 0.40 Single 0.23 0.42 Hours of work per week 37.28 6.99 Subordinates (yes = 1) 0.31 0.46 Establishment size  5–19 0.21 0.41  20–49 0.19 0.39  50–99 0.18 0.38  100 or more 0.26 0.44 Education  Primary/Secondary 0.21 0.40  High School 0.07 0.25  Vocational 0.39 0.49  College‐short 0.06 0.23  College‐long 0.20 0.40  University 0.08 0.26 Job Satisfaction 4.96 0.95 Note. The PPP exchange rate between the Danish Kroner (DKK) and the US dollar was 8.66 in 1994. Open in new tab Table 1 
Means and Standard Deviations of Key Variables Variable . Mean . Std. Dev. . Real earnings/1000 (1995 DKK) 227.49 109.10 Age 40.29 10.66 Female 0.46 0.50 Occupation  Managers 0.19 0.39  White collar 0.17 0.38  Blue collar 0.43 0.50 Health problem 0.20 0.40 Single 0.23 0.42 Hours of work per week 37.28 6.99 Subordinates (yes = 1) 0.31 0.46 Establishment size  5–19 0.21 0.41  20–49 0.19 0.39  50–99 0.18 0.38  100 or more 0.26 0.44 Education  Primary/Secondary 0.21 0.40  High School 0.07 0.25  Vocational 0.39 0.49  College‐short 0.06 0.23  College‐long 0.20 0.40  University 0.08 0.26 Job Satisfaction 4.96 0.95 Variable . Mean . Std. Dev. . Real earnings/1000 (1995 DKK) 227.49 109.10 Age 40.29 10.66 Female 0.46 0.50 Occupation  Managers 0.19 0.39  White collar 0.17 0.38  Blue collar 0.43 0.50 Health problem 0.20 0.40 Single 0.23 0.42 Hours of work per week 37.28 6.99 Subordinates (yes = 1) 0.31 0.46 Establishment size  5–19 0.21 0.41  20–49 0.19 0.39  50–99 0.18 0.38  100 or more 0.26 0.44 Education  Primary/Secondary 0.21 0.40  High School 0.07 0.25  Vocational 0.39 0.49  College‐short 0.06 0.23  College‐long 0.20 0.40  University 0.08 0.26 Job Satisfaction 4.96 0.95 Note. The PPP exchange rate between the Danish Kroner (DKK) and the US dollar was 8.66 in 1994. Open in new tab Footnotes 1 " See Clark et al. (2008) for a recent survey. 2 " Where the reference group might be the individual’s peer group, others in the same household, their spouse/partner, friends, neighbours, work colleagues, or the individual herself in the past. 3 " This interpretation is explicitly tested in the context of worker quitting by Lévy‐Garboua et al. (2007). A second piece of supporting evidence is that promotion opportunities attract a positive estimated coefficient in job satisfaction regressions. 4 " See http://epp.eurostat.cec.eu.int for details of the ECHP data. 5 " Integreret Database for Arbejdsmarkedsstatistik (Integrated Database for Labour Market Statistics). 6 " See Kristensen and Westergaard‐Nielsen (2007) for a comparison of key individual variables, including earnings, between the ECHP and register data. 7 " Using thresholds of 4 and 6 colleagues makes little difference to the results. As one of the robustness tests in Section 4 will show, the results also hold when excluding establishments with 20 or fewer employees. 8 " The means and standard deviations of the key variables are presented in Table 1. 9 " A Hausman test on the linear specification shows that, overall, fixed‐effects is preferred to random‐effects estimation. However, the estimated coefficient on establishment average earnings is almost identical in the two specifications. 10 " A 40‐year‐old single female Manager in the Manufacturing sector with a professional qualification, working a 37‐hour week with average earnings, both own and establishment, in a small establishment and with a health problem. 11 " The point estimate on own earnings is generally positive but is negative, although insignificant, for the third quartile in this specification. The effect of establishment earnings is very strong for this last group. This may seem implausible. 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( 1988 ). ‘Relative wages, efficiency wages, and Keynesian un‐employment’, American Economic Review, Papers and Proceedings , vol. 78 ( 2 ) (May), pp. 383 – 8 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Author notes " We are very grateful to the Editor and two anonymous referees for particularly constructive suggestions. We also thank Tor Eriksson, Ada Ferrer‐i‐Carbonell, Carol Graham, Takao Kato, Andrew Oswald and seminar participants at Amsterdam, the DTI Conference ’New Perspectives on Job Satisfaction and Subjective Well‐Being at Work’ (London), the 8th ISQOLS Conference (San Diego), the 24th JMA (Fribourg), Lyon 2, Rennes I, the Royal Economic Society Conference (Warwick), the Tinbergen Institute Workshop ’Economics of the Workplace’ at Rotterdam (especially our discussant Mirjam van Praag) and the 2006 SOLE meetings (Cambridge, MA) for useful comments. © The Author(s). Journal compilation © Royal Economic Society 2009

Kassenboehmer, Sonja, C.;Haisken‐DeNew, John, P.

doi: 10.1111/j.1468-0297.2008.02246.xpmid: N/A

Abstract This article examines the impact of unemployment for men and women on life satisfaction for Germany 1991–2006 using the German Socio‐Economic Panel. We find that for women in east and west Germany, company closures in the year of entry into unemployment produce strongly negative effects on life satisfaction over and above an overall effect of unemployment, providing prima facie evidence of reduced outside work options, large investments in firm‐specific human capital or a family constraint. The large compensating variation in terms of income indicates enormous non‐pecuniary negative effects for women of exogenous entry unemployment due to company closures. In recent years, economists have become increasingly interested in the factors influencing happiness (Frey and Stutzer, 2002; Frijters et al., 2004a, b). This line of research builds on the findings of psychologists who study decision making using people’s own valuations of their life satisfaction levels. The responses are usually collated on an ordinal scale, ranging, for example, from 0 (very unhappy) to 10 (very happy). Behind this self‐assessed well‐being lies a cognitive process that takes circumstances, aspirations, comparisons with others, one’s own baseline of happiness, past experiences and dispositional outlook into consideration (Frey and Stutzer, 2002; Blanchflower and Oswald, 2004). The determinants of life satisfaction are usually investigated in a microeconomic life satisfaction model with life satisfaction as the dependent variable, explained by various socio‐demographic and socio‐economic variables. The high level of empirical support provided for the concept of happiness by psychology has helped to promote the notion of measurable utility. The potential for new insights of this research has been demonstrated by a large empirical literature; for an overview see Clark et al. (2006). Economists have been keenly interested in determining the effect of labour market status (especially unemployment) on life satisfaction. The previous literature such as Winkelmann and Winkelmann (1998) has sought to quantify the non‐pecuniary costs of unemployment due to reduced well‐being. The article is particularly innovative in that subjective information is used to identify model outcomes in an otherwise completely objective model. The article concludes that the non‐pecuniary effect of unemployment is much larger than the effect from the associated loss of income. This is primarily due to loss of social contact, reduced self‐esteem and identity in society (Winkelmann and Winkelmann, 1998). The higher the pressure of the social norm for an individual to work, the higher the psychological pressure to regain employment (Akerlof, 1980; Stutzer and Lalive, 2004). Because of the large detrimental effect of unemployment on life satisfaction, the literature concludes that unemployment is largely involuntary. Existing studies, however, face a number of limitations. The negative effect of unemployment found in the literature, even with panel data, might simply reflect the fact that workers become dissatisfied with their jobs and therefore decide to become voluntarily unemployed; see Mortensen and Pissarides (1999a, b) for an overview of search models. Hence, not distinguishing between exogenous or endogenous unemployment – as was not explicitly examined in Winkelmann and Winkelmann (1998) – limits the causal interpretability of measured association between unemployment and life satisfaction. Also, many of the studies, especially conducted by psychologists, use cross‐section data and as such are subject to the usual limitations with this data. Further, the ordinal scale on which answers to life satisfaction questions are collated is often interpreted in a cardinal manner. Until recently it was unclear whether the results differ when assuming ordinality or cardinality across persons and how the results differ when using panel data as opposed to mere cross‐sections. It is also uncertain how these results differ from those of Ferrer‐i‐Carbonell and Frijters (2004) who developed a new estimator which even relaxes the ordinal comparability assumption. Furthermore, datasets used are often small and based on narrow sub‐populations. The effect of unemployment is typically only investigated for men and not for women or other samples. This study contributes to the existing literature in that it addresses these issues directly by closely examining exogenous entry into unemployment in order to identify causal effects. Additionally, it compares different estimation techniques. An approximation to the advanced fixed‐effects conditional logit technique of Ferrer‐i‐Carbonell and Frijters (2004) is implemented in this study to control for time‐invariant person‐specific heterogeneity and this is shown to make a significant difference to the estimation results. Different subsamples are compared: men and women in west and east Germany. In this context, we implement the most recent data for the period 1991–2006. The basis for the present analysis is data from the German Socio‐Economic Panel (SOEP),1 which allow explicit identification of different reasons for entry into unemployment since 1991. 1. Background Information While traditional economic theories suggest that the utility loss from unemployment is accompanied by the experienced loss of income and increase in leisure, the latter suggests that there are also non‐pecuniary costs associated with unemployment, as in Carroll (2007). This is also picked up by a large section of empirical literature that investigates the impact of unemployment on psychological well‐being. Researchers, such as Jensen and Smith (1990), investigating the impact of unemployment on adverse individual outcomes such as decreased marital stability, increased mortality, suicide risk and crime rates, found in general that unemployment has negative psychological effects because it leads to a substantial increase in these factors (Winkelmann and Winkelmann, 1998). Many researchers have tried to quantify these non‐pecuniary costs and some of them, such as Bjoerklund and Erikson (1998) and Korpi (1997), related the costs directly to decreased mental well‐being. They related the negative effect of unemployment to certain health symptoms such as sleeplessness, stomach pain and depression. Many studies have also used the General Health Questionnaire (GHQ) which is implemented in the British Household Panel Study (BHPS) and asks for certain health symptoms. Clark and Oswald (1994) used the first wave of the BHPS to regress a mental distress score, calculated from the answers to the GHQ, on unemployment and other factors. Here, unemployment was also found to have a significant negative effect on mental states, even when controlling for income (Winkelmann and Winkelmann, 1998). Further psychological findings provide some explanation for why positive aspects associated with unemployment seem to be surpassed by negative effects.2Goldsmith et al. (1996) for example, found that unemployment lowers self‐esteem, by measuring well‐being through responses that reflect the individual’s level of control (Winkelmann and Winkelmann, 1998), using the National Longitudinal Survey of Youth (NLSY). Akerlof (1980) developed a model that includes a reputation component in the utility function.3 If an individual is unemployed, then this individual breaks a social custom, which may result in a loss of reputation and hence in a lower utility‐level, in other words, a decline in life satisfaction results. This theoretical conclusion is difficult to prove because there is typically no direct measure of the intensity of a social norm. However, using Swiss voters’ referendum information on reducing unemployment benefits, Stutzer and Lalive (2004) identify these social norms directly and find that the stronger the social norm to work, the shorter the duration of unemployment. While the many studies mentioned above are largely theoretical, qualitative, cross‐sectional quantitative or longitudinal with only a few observations and not controlling for other variables, the presence of life satisfaction data in many of today’s large‐scale longitudinal datasets suggests an alternative way of measuring the psychological cost of unemployment. The psychological effect of unemployment is not directly measured by certain health symptoms or a mental distress score but, rather, indirectly, by multivariate regression analysis with individual life satisfaction as the dependent variable. This method allows controlling for income and other factors and thereby isolates the non‐pecuniary costs of unemployment. The advantage of longitudinal designs is that they permit stronger inferences about the causal effect of unemployment on life satisfaction. Gerlach and Stephan (1996) were among the first economists who explicitly investigated the effect of unemployment on life satisfaction for men and women. While they used OLS and OLS fixed‐effects estimation method and thus implicitly assumed that the ordinal scale of the life satisfaction questions can be cardinally interpreted, Winkelmann and Winkelmann (1998) recoded life satisfaction into a binary variable coded as 1 if life satisfaction is above the overall mean of reported life satisfaction, otherwise 0. This method allowed them to maintain the ordinality of the life satisfaction scale and at the same time to be able to account for fixed effects by implementing Chamberlain’s conditional logit estimation (Chamberlain, 1980). Because the latter approach is accompanied by a huge data loss due to the incapability of this estimator using individuals who do not have changes in the dependent variable, Ferrer‐i‐Carbonell and Frijters (2004) developed an estimator that assigns each person an individual‐specific threshold according to which life satisfaction is recoded into a 1/0 dichotomy. All studies found a detrimental effect of unemployment on life satisfaction for males. Those studies that also examined females, also found negative effects for this subgroup. The effects for females are, in general, smaller than the effects for males, which is explained by the stronger traditional attachment of men to the labour market; for analysis based on the SOEP see, for example, Gerlach and Stephan (1996, 2001), Clark et al. (2001), Frijters et al. (2004a, b). We show, basing our analysis on more advanced estimation techniques in combination with more precise data and a detailed look into the reasons for job termination for men and women, that this result can be overturned completely, providing prima facie evidence of a reduced outside work option, large investments in firm specific human capital or a family constraint for women. Because of the stable negative coefficient for unemployment for all estimation techniques, researchers such as Winkelmann and Winkelmann (1998) conclude that unemployment is involuntary. Although the literature suggests that unemployment causes decreased life satisfaction levels, reverse causation, namely that low life satisfaction leads to unemployment, is also possible. First, it is for example possible that inherently dissatisfied people are more likely to get fired. In a cross‐section analysis, a negative effect of unemployment would then lead to incorrect results. Second, unemployment might be endogenous, hence chosen by the individual. In that case, a negative effect of unemployment on life satisfaction might just reflect that a worker becomes dissatisfied with his job and therefore becomes unemployed voluntarily. The first problem has been addressed amongst others by panel studies. These showed that individuals report a drop in life satisfaction only once they are unemployed and are hence not intrinsically dissatisfied.4 However, taking the second possibility into account, namely that unemployment is endogenous and that dissatisfaction with the job may lead to voluntary unemployment, a negative regression coefficient for unemployment might still not reflect a causal impact of unemployment on life satisfaction. Winkelmann and Winkelmann (1998) investigated this possibility to some extent, in a descriptive manner, in that they calculated the change in satisfaction for transition from employment to unemployment for the involuntary unemployed and the older unemployed, assuming that unemployment is more exogenous for the older unemployed since the younger have not established careers yet. They found that both groups report significant reductions in life satisfaction. In addition, they could not ‘reject the hypothesis that the detrimental effect of unemployment is the same independently of age or reason for termination’. (p. 8) Hence, they conclude that unemployment can be treated as exogenous. However, in their regression analysis they did not distinguish between voluntary and involuntary unemployment. In this analysis, we explicitly include the reason for job termination and entry into unemployment in a multivariate regression analysis, controlling for unobserved individual heterogeneity and show highly differential effects. 2. Data The SOEP is a representative longitudinal study of private households in Germany. Starting in 1984, the same private households were followed each year. In 1990, after unification, the panel was extended to the former German Democratic Republic (GDR). Apart from the samples for east and west Germany, the SOEP consists of five other subsamples, such as the Immigrant Sample which was integrated in 1994; see Haisken‐DeNew and Frick (2005) for more technical information on the SOEP. The data include information on objective and subjective aspects. Objective aspects comprise information on occupational and family biography and household composition. Subjective aspects comprise questions on personality traits, health and personal satisfaction.5 In this study, people aged 21 to 64 who reside in Germany are included in the analysis, covering the years 1991 to 2006. The total sample consists of 74,642 valid person‐year observations (19,828 people). The effect of unemployment on life satisfaction is investigated for several sub‐samples. People are included in the west German sample, if they were living in west Germany in 1989. There are 25,802 person‐year observations for men in west Germany, 11,264 in east Germany, 25,611 for females in west Germany and 11,965 in east Germany. We specifically examine the respondent‐given reasons for entering into unemployment: voluntarily quitting, being fired, or company closing. Table 1 provides descriptive statistics of the variables used in the analysis. Table 1 
Descriptive Statistics (N = 74,642) Variable . Mean . SD . Min . Max . Female 0.5034 0.5000 0 1 West Germany 0.6888 0.4630 0 1 Satisfaction With Life Today 6.9058 1.7248 0 10 Unemployed 0.0742 0.2621 0 1 Out of Labour Force (OLF) 0.1779 0.3824 0 1 Entry Unemployment: Voluntary 0.0157 0.1243 0 1 Entry Unemployment: Fired 0.0153 0.1228 0 1 Entry Unemployment: Company Closed 0.0043 0.0654 0 1 Entry OLF 0.0197 0.1390 0 1 Entry Employment 0.0276 0.1637 0 1 State Unemployment Rate 12.1784 4.6600 4.4 21.72 Married 0.7303 0.4438 0 1 Shock: Separated 0.0145 0.1195 0 1 Shock: Divorced 0.0050 0.0704 0 1 Shock: Spouse Died 0.0022 0.0467 0 1 Shock: Child born 0.0393 0.1943 0 1 No Medical Handicap 0.6859 0.4641 0 1 Work Disability 0.0421 0.2008 0 1 Nights Stayed in Hospital 1.2859 7.0377 0 330 Age 41.8405 12.0505 21 64 Age Squared/10 189.5841 103.5849 44.1 409.6 Log Net Real Household Income 7.6491 0.4775 4.394 10.2 Years of Education 11.6810 2.5271 7 18 Number of Children: 1 0.2154 0.4111 0 1 Number of Children: 2 0.1636 0.3699 0 1 Number of Children: 3+ 0.0564 0.2307 0 1 Variable . Mean . SD . Min . Max . Female 0.5034 0.5000 0 1 West Germany 0.6888 0.4630 0 1 Satisfaction With Life Today 6.9058 1.7248 0 10 Unemployed 0.0742 0.2621 0 1 Out of Labour Force (OLF) 0.1779 0.3824 0 1 Entry Unemployment: Voluntary 0.0157 0.1243 0 1 Entry Unemployment: Fired 0.0153 0.1228 0 1 Entry Unemployment: Company Closed 0.0043 0.0654 0 1 Entry OLF 0.0197 0.1390 0 1 Entry Employment 0.0276 0.1637 0 1 State Unemployment Rate 12.1784 4.6600 4.4 21.72 Married 0.7303 0.4438 0 1 Shock: Separated 0.0145 0.1195 0 1 Shock: Divorced 0.0050 0.0704 0 1 Shock: Spouse Died 0.0022 0.0467 0 1 Shock: Child born 0.0393 0.1943 0 1 No Medical Handicap 0.6859 0.4641 0 1 Work Disability 0.0421 0.2008 0 1 Nights Stayed in Hospital 1.2859 7.0377 0 330 Age 41.8405 12.0505 21 64 Age Squared/10 189.5841 103.5849 44.1 409.6 Log Net Real Household Income 7.6491 0.4775 4.394 10.2 Years of Education 11.6810 2.5271 7 18 Number of Children: 1 0.2154 0.4111 0 1 Number of Children: 2 0.1636 0.3699 0 1 Number of Children: 3+ 0.0564 0.2307 0 1 Open in new tab Table 1 
Descriptive Statistics (N = 74,642) Variable . Mean . SD . Min . Max . Female 0.5034 0.5000 0 1 West Germany 0.6888 0.4630 0 1 Satisfaction With Life Today 6.9058 1.7248 0 10 Unemployed 0.0742 0.2621 0 1 Out of Labour Force (OLF) 0.1779 0.3824 0 1 Entry Unemployment: Voluntary 0.0157 0.1243 0 1 Entry Unemployment: Fired 0.0153 0.1228 0 1 Entry Unemployment: Company Closed 0.0043 0.0654 0 1 Entry OLF 0.0197 0.1390 0 1 Entry Employment 0.0276 0.1637 0 1 State Unemployment Rate 12.1784 4.6600 4.4 21.72 Married 0.7303 0.4438 0 1 Shock: Separated 0.0145 0.1195 0 1 Shock: Divorced 0.0050 0.0704 0 1 Shock: Spouse Died 0.0022 0.0467 0 1 Shock: Child born 0.0393 0.1943 0 1 No Medical Handicap 0.6859 0.4641 0 1 Work Disability 0.0421 0.2008 0 1 Nights Stayed in Hospital 1.2859 7.0377 0 330 Age 41.8405 12.0505 21 64 Age Squared/10 189.5841 103.5849 44.1 409.6 Log Net Real Household Income 7.6491 0.4775 4.394 10.2 Years of Education 11.6810 2.5271 7 18 Number of Children: 1 0.2154 0.4111 0 1 Number of Children: 2 0.1636 0.3699 0 1 Number of Children: 3+ 0.0564 0.2307 0 1 Variable . Mean . SD . Min . Max . Female 0.5034 0.5000 0 1 West Germany 0.6888 0.4630 0 1 Satisfaction With Life Today 6.9058 1.7248 0 10 Unemployed 0.0742 0.2621 0 1 Out of Labour Force (OLF) 0.1779 0.3824 0 1 Entry Unemployment: Voluntary 0.0157 0.1243 0 1 Entry Unemployment: Fired 0.0153 0.1228 0 1 Entry Unemployment: Company Closed 0.0043 0.0654 0 1 Entry OLF 0.0197 0.1390 0 1 Entry Employment 0.0276 0.1637 0 1 State Unemployment Rate 12.1784 4.6600 4.4 21.72 Married 0.7303 0.4438 0 1 Shock: Separated 0.0145 0.1195 0 1 Shock: Divorced 0.0050 0.0704 0 1 Shock: Spouse Died 0.0022 0.0467 0 1 Shock: Child born 0.0393 0.1943 0 1 No Medical Handicap 0.6859 0.4641 0 1 Work Disability 0.0421 0.2008 0 1 Nights Stayed in Hospital 1.2859 7.0377 0 330 Age 41.8405 12.0505 21 64 Age Squared/10 189.5841 103.5849 44.1 409.6 Log Net Real Household Income 7.6491 0.4775 4.394 10.2 Years of Education 11.6810 2.5271 7 18 Number of Children: 1 0.2154 0.4111 0 1 Number of Children: 2 0.1636 0.3699 0 1 Number of Children: 3+ 0.0564 0.2307 0 1 Open in new tab The SOEP does not obtain a comprehensive job diary at all time periods of all jobs held by a respondent. Detailed information is obtained concerning the current main job at the time of the survey and then, approximately one year later, an update of the current situation is made. It could be that the time between having lost a job and being interviewed varies among respondents over the year. The particular month within the last survey period that a respondent actually lost a job is subject to substantially more recall bias than whether or not a job was lost and, as such, we just focus on having lost the job and not on the exact timing of the particular month in the last year. We therefore interpret the entry unemployment coefficients as average first year effects observed from one survey period to the next (typically one year). 3. Econometric Framework The previous economic research has concluded that unemployment is involuntary because of the strong negative effect of unemployment on life satisfaction, found by regression results. This effect was found to be strong even when controlling for income. The resulting coefficient is then interpreted as psychological distress due to potential social exclusion or loss of work identity for example. This study investigates the effect of unemployment in general and entry unemployment on life satisfaction in more detail. The first improvement of this study will be to isolate the effect of voluntary and involuntary entry into unemployment clearly. The SOEP allows this distinction to be made because it contains a question concerning self‐reported reasons for entry job termination. Since 1985, the SOEP has included a question on the reason for terminating of a job. People are asked to select all the responses that apply in their case, such as ‘quit for personal reasons’, ‘transferred by firm’, ‘transferred on own account’, ‘reaching retirement age’, ‘wanting to look for another job’, ‘personal reasons’, ‘time‐limited work contract’, ‘quit on one’s own’, ‘giving up working’, ‘fired by employer’ and ‘other reasons’. In 1991, the possible answers were extended to ‘company closing’ and ‘on leave on sabbatical’. With this question, it is possible to distinguish the involuntarily unemployed from the voluntarily unemployed. In this study someone is defined as becoming involuntarily unemployed if he is fired by the employer or if the company closed within the last 12 months. If someone reports ‘wanting to look for another job’, ‘personal reasons’, ‘time‐limited work contract’, ‘quit on one’s own’, ‘giving up working’ and ‘other reasons’ in combination with entry into unemployment he is assumed to become voluntarily unemployed. It might be questionable if someone who is fired is really involuntarily unemployed: certain people might be more likely to get fired because of personality, others might set out to get fired rather than quitting, in order to receive compensation. Therefore, getting fired and company closure are both included in the regression as separate variables. The sample is directly divided into different subsamples. As argued, there could possibly be heterogeneity in people’s reaction to unemployment, for example due to different commitments to work. Women, for example, might be less hurt by unemployment than men because the social norm’s pressure to work might be higher for men due to their role in society as the primary providers. In contrast, they might be less flexible due to family constraints in dealing with an unemployment shock. For example, there might also be regional differences between east and west Germany because of their different historical backgrounds in labour market characteristics and involvement with employment. Women in east Germany might be expected to be more hurt by unemployment than their western counterparts because eastern females have historically been more attached to employment in the GDR. The dataset will be divided into four different groups: west males, east males, west females and east females. Regression analysis is conducted on the different subsamples, so that the influences of several socio‐demographic variables on life satisfaction are investigated. Because researchers in the literature have used different methodologies, these will be compared to determine their influences on the results. OLS and logit regression are undertaken in each case in a pooled and fixed‐effect framework. For the fixed‐effects logit model, a conditional maximum likelihood estimator is used in order to obtain consistent estimates because the standard maximum likelihood model gives inconsistent results. As such, the dependent variable is collapsed into binary format. As a threshold value for the classification into the binary format, average life satisfaction is used, which is approximately 7.0. Therefore, if the reported satisfaction score on an 11‐point scale is above 7, the life satisfaction variable is coded as 1, otherwise as 0. The drawback of the model is that the effect on satisfaction is only identified by individuals that change labour force states and satisfaction status. This huge data loss can be solved by the Frijters and Ferrer‐i‐Carbonell (2004) estimator and its approximation,6 which applies individual specific thresholds to collapse the data into binary format. Because their method of finding the individual‐specific thresholds is computationally very intensive, this study uses a simpler approach to determining these thresholds, namely the individual’s mean life satisfaction values over time. Hence, a binary variable (yit) is generated that relates to (reported) life satisfaction () as follows: (1) This variable becomes one if life satisfaction is above the individual specific threshold, otherwise zero. On this binary variable, Chamberlain’s (1980) conditional logit estimator can be applied that estimates coefficients conditional on the number of ones in the dependent variable. Combining the joint probability functions of each particular sequence (each set of T observations) of yit = sit ones and zeros leads for a sample of n person‐observations to the following Log‐Likelihood function which can be maximised by standard programmes (Chamberlain, 1980): (2) where xit represents a vector of explanatory variables, yit the dependent binary life satisfaction variable and d = (d1,…,dT) indicates the alternative set Bi varying across the observations. It consists of combinations of si ones and T − si zeros with . Because the coefficients are estimated conditional on the number of ones, the heterogeneity term can be removed. As observations without variation in the satisfaction variable do not contribute to the likelihood function. In addition, covariates that do not vary over time cannot be distinguished from αi (the individual specific fixed effect) and drop out as well. 4. Empirical Results In a working paper version not shown here (Kassenboehmer and Haisken‐DeNew, 2008), we replicate Winkelmann and Winkelmann (1998) in detail and compare the results of six different estimation methods: (a) pooled ordinary least squares, (b) linear fixed effects, (c) pooled logit based on fixed life satisfactions thresholds of value 7, (d) same as (c) but with conditional logit, (e) pooled logit based on individual averages, and (f ) same as (e) but using the conditional logit estimator. We provide results in this analysis using these different estimation methods to illustrate the value added of using non‐linear models and controlling for unobserved individual heterogeneity in the form of person fixed effects. Quite often many significant effects in the linear and non‐linear pooled regressions are rendered insignificant in the fixed‐effects/conditional logit regressions. To test the robustness of the Winkelmann and Winkelmann (1998) models, we expand their explanatory variables (listed in Tables 2 to 4 as ‘Standard Controls’) to include measures of family change, such as shock variables for separation, divorce, death of spouse, children being born. Additionally, years of education, number of children in the household (separate dummies for one, two and three or more children) and more health indicators such as work disability and medical handicap are used. We identify three types of entry unemployment: voluntary, being fired and company closing. In addition, we control directly for state‐specific unemployment rates in heterogeneous regional labour markets, even within the broad categories of east and west. Table 1 provides a complete list of the variables used in the analysis. We delve further into the mechanisms of the effects of entry unemployment on life satisfaction by examining 4 groups separately in Tables 2 and 3: west males, west females, east males and east females.7 This follows Gerlach and Stephan (2001), who have used a similar group structure. However they focus on linear models exclusively and use neither shock variables for family status nor reason for entry unemployment. For almost all estimation methods in our study, the overall effects of being unemployed are large, significant and negative. East males and females also experience significant negative effects from being out of the labour force, which could be attributed to the east German traditional attachment to labour force participation by both men and women. Table 3 
Effects of Unemployment on Life Satisfaction for Females by Region . Continuous . Fixed Thresholds . Individual Thresholds . OLS . OLS‐FE . Logit . C Logit . Logit . C Logit . West females Unemployed −0.490** −0.230** −0.431** −0.205 −0.267** −0.383** (0.075) (0.116) (0.095) (0.165) (0.084) (0.141) Out of Labour Force (OLF) −0.002 −0.027 0.040 0.053 −0.020 −0.045 (0.026) (0.049) (0.034) (0.080) (0.033) (0.073) Entry Unemployment: Voluntary −0.120 −0.074 −0.262 −0.255 0.093 0.007 (0.131) (0.166) (0.169) (0.243) (0.148) (0.215) Entry Unemployment: Fired −0.082 −0.187 −0.200 −0.332 −0.305* −0.372* (0.163) (0.173) (0.202) (0.264) (0.183) (0.226) Entry Unemployment: Company Closed −0.719** −1.023** −0.568 −1.242** −0.630* −1.769** (0.305) (0.259) (0.374) (0.530) (0.331) (0.527) Entry OLF −0.009 −0.061 0.027 −0.099 −0.006 −0.020 (0.064) (0.076) (0.084) (0.128) (0.081) (0.113) Entry Employment −0.229** 0.039 −0.211* 0.110 0.189* 0.071 (0.091) (0.099) (0.109) (0.151) (0.105) (0.137) Log Net Real Household Income 0.522** 0.265** 0.553** 0.386** 0.051* 0.295** (0.024) (0.048) (0.031) (0.069) (0.029) (0.064) State Unemployment Rate −0.010** −0.020** −0.013** −0.026** −0.005 −0.026** (0.003) (0.005) (0.004) (0.008) (0.004) (0.008) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2/Pseudo R2 0.135 0.041 0.065 0.030 0.011 0.028 N 25611 25611 25611 15090 25611 19679 East females Unemployed −0.669** −0.531** −0.418** −0.351** −0.307** −0.742** (0.065) (0.090) (0.091) (0.157) (0.074) (0.123) Out of Labour Force (OLF) −0.325** −0.237** −0.226** −0.277 −0.010 −0.276* (0.056) (0.102) (0.082) (0.174) (0.072) (0.146) Entry Unemployment: Voluntary −0.050 0.116 −0.091 −0.057 0.134 0.286* (0.120) (0.120) (0.163) (0.234) (0.127) (0.162) Entry Unemployment: Fired −0.389** −0.307** −0.191 −0.268 −0.466** −0.342* (0.135) (0.139) (0.182) (0.250) (0.140) (0.177) Entry Unemployment: Company Closed −0.777** −0.510** −0.947** −0.984** −0.942** −0.893** (0.182) (0.197) (0.330) (0.469) (0.227) (0.283) Entry OLF 0.102 0.074 0.044 0.201 −0.082 0.314 (0.145) (0.184) (0.204) (0.283) (0.176) (0.229) Entry Employment −0.282** −0.007 −0.134 0.135 0.218** −0.021 (0.072) (0.082) (0.098) (0.145) (0.088) (0.111) Log Net Real Household Income 0.709** 0.427** 0.728** 0.503** 0.242** 0.665** (0.040) (0.073) (0.057) (0.119) (0.049) (0.104) State Unemployment Rate 0.000 −0.008 −0.006 −0.008 0.007 −0.014 (0.004) (0.008) (0.006) (0.015) (0.006) (0.012) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2/Pseudo R2 0.151 0.052 0.059 0.028 0.015 0.042 N 11,965 11,965 11,965 6,540 11,965 9,973 . Continuous . Fixed Thresholds . Individual Thresholds . OLS . OLS‐FE . Logit . C Logit . Logit . C Logit . West females Unemployed −0.490** −0.230** −0.431** −0.205 −0.267** −0.383** (0.075) (0.116) (0.095) (0.165) (0.084) (0.141) Out of Labour Force (OLF) −0.002 −0.027 0.040 0.053 −0.020 −0.045 (0.026) (0.049) (0.034) (0.080) (0.033) (0.073) Entry Unemployment: Voluntary −0.120 −0.074 −0.262 −0.255 0.093 0.007 (0.131) (0.166) (0.169) (0.243) (0.148) (0.215) Entry Unemployment: Fired −0.082 −0.187 −0.200 −0.332 −0.305* −0.372* (0.163) (0.173) (0.202) (0.264) (0.183) (0.226) Entry Unemployment: Company Closed −0.719** −1.023** −0.568 −1.242** −0.630* −1.769** (0.305) (0.259) (0.374) (0.530) (0.331) (0.527) Entry OLF −0.009 −0.061 0.027 −0.099 −0.006 −0.020 (0.064) (0.076) (0.084) (0.128) (0.081) (0.113) Entry Employment −0.229** 0.039 −0.211* 0.110 0.189* 0.071 (0.091) (0.099) (0.109) (0.151) (0.105) (0.137) Log Net Real Household Income 0.522** 0.265** 0.553** 0.386** 0.051* 0.295** (0.024) (0.048) (0.031) (0.069) (0.029) (0.064) State Unemployment Rate −0.010** −0.020** −0.013** −0.026** −0.005 −0.026** (0.003) (0.005) (0.004) (0.008) (0.004) (0.008) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2/Pseudo R2 0.135 0.041 0.065 0.030 0.011 0.028 N 25611 25611 25611 15090 25611 19679 East females Unemployed −0.669** −0.531** −0.418** −0.351** −0.307** −0.742** (0.065) (0.090) (0.091) (0.157) (0.074) (0.123) Out of Labour Force (OLF) −0.325** −0.237** −0.226** −0.277 −0.010 −0.276* (0.056) (0.102) (0.082) (0.174) (0.072) (0.146) Entry Unemployment: Voluntary −0.050 0.116 −0.091 −0.057 0.134 0.286* (0.120) (0.120) (0.163) (0.234) (0.127) (0.162) Entry Unemployment: Fired −0.389** −0.307** −0.191 −0.268 −0.466** −0.342* (0.135) (0.139) (0.182) (0.250) (0.140) (0.177) Entry Unemployment: Company Closed −0.777** −0.510** −0.947** −0.984** −0.942** −0.893** (0.182) (0.197) (0.330) (0.469) (0.227) (0.283) Entry OLF 0.102 0.074 0.044 0.201 −0.082 0.314 (0.145) (0.184) (0.204) (0.283) (0.176) (0.229) Entry Employment −0.282** −0.007 −0.134 0.135 0.218** −0.021 (0.072) (0.082) (0.098) (0.145) (0.088) (0.111) Log Net Real Household Income 0.709** 0.427** 0.728** 0.503** 0.242** 0.665** (0.040) (0.073) (0.057) (0.119) (0.049) (0.104) State Unemployment Rate 0.000 −0.008 −0.006 −0.008 0.007 −0.014 (0.004) (0.008) (0.006) (0.015) (0.006) (0.012) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2/Pseudo R2 0.151 0.052 0.059 0.028 0.015 0.042 N 11,965 11,965 11,965 6,540 11,965 9,973 Open in new tab Table 3 
Effects of Unemployment on Life Satisfaction for Females by Region . Continuous . Fixed Thresholds . Individual Thresholds . OLS . OLS‐FE . Logit . C Logit . Logit . C Logit . West females Unemployed −0.490** −0.230** −0.431** −0.205 −0.267** −0.383** (0.075) (0.116) (0.095) (0.165) (0.084) (0.141) Out of Labour Force (OLF) −0.002 −0.027 0.040 0.053 −0.020 −0.045 (0.026) (0.049) (0.034) (0.080) (0.033) (0.073) Entry Unemployment: Voluntary −0.120 −0.074 −0.262 −0.255 0.093 0.007 (0.131) (0.166) (0.169) (0.243) (0.148) (0.215) Entry Unemployment: Fired −0.082 −0.187 −0.200 −0.332 −0.305* −0.372* (0.163) (0.173) (0.202) (0.264) (0.183) (0.226) Entry Unemployment: Company Closed −0.719** −1.023** −0.568 −1.242** −0.630* −1.769** (0.305) (0.259) (0.374) (0.530) (0.331) (0.527) Entry OLF −0.009 −0.061 0.027 −0.099 −0.006 −0.020 (0.064) (0.076) (0.084) (0.128) (0.081) (0.113) Entry Employment −0.229** 0.039 −0.211* 0.110 0.189* 0.071 (0.091) (0.099) (0.109) (0.151) (0.105) (0.137) Log Net Real Household Income 0.522** 0.265** 0.553** 0.386** 0.051* 0.295** (0.024) (0.048) (0.031) (0.069) (0.029) (0.064) State Unemployment Rate −0.010** −0.020** −0.013** −0.026** −0.005 −0.026** (0.003) (0.005) (0.004) (0.008) (0.004) (0.008) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2/Pseudo R2 0.135 0.041 0.065 0.030 0.011 0.028 N 25611 25611 25611 15090 25611 19679 East females Unemployed −0.669** −0.531** −0.418** −0.351** −0.307** −0.742** (0.065) (0.090) (0.091) (0.157) (0.074) (0.123) Out of Labour Force (OLF) −0.325** −0.237** −0.226** −0.277 −0.010 −0.276* (0.056) (0.102) (0.082) (0.174) (0.072) (0.146) Entry Unemployment: Voluntary −0.050 0.116 −0.091 −0.057 0.134 0.286* (0.120) (0.120) (0.163) (0.234) (0.127) (0.162) Entry Unemployment: Fired −0.389** −0.307** −0.191 −0.268 −0.466** −0.342* (0.135) (0.139) (0.182) (0.250) (0.140) (0.177) Entry Unemployment: Company Closed −0.777** −0.510** −0.947** −0.984** −0.942** −0.893** (0.182) (0.197) (0.330) (0.469) (0.227) (0.283) Entry OLF 0.102 0.074 0.044 0.201 −0.082 0.314 (0.145) (0.184) (0.204) (0.283) (0.176) (0.229) Entry Employment −0.282** −0.007 −0.134 0.135 0.218** −0.021 (0.072) (0.082) (0.098) (0.145) (0.088) (0.111) Log Net Real Household Income 0.709** 0.427** 0.728** 0.503** 0.242** 0.665** (0.040) (0.073) (0.057) (0.119) (0.049) (0.104) State Unemployment Rate 0.000 −0.008 −0.006 −0.008 0.007 −0.014 (0.004) (0.008) (0.006) (0.015) (0.006) (0.012) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2/Pseudo R2 0.151 0.052 0.059 0.028 0.015 0.042 N 11,965 11,965 11,965 6,540 11,965 9,973 . Continuous . Fixed Thresholds . Individual Thresholds . OLS . OLS‐FE . Logit . C Logit . Logit . C Logit . West females Unemployed −0.490** −0.230** −0.431** −0.205 −0.267** −0.383** (0.075) (0.116) (0.095) (0.165) (0.084) (0.141) Out of Labour Force (OLF) −0.002 −0.027 0.040 0.053 −0.020 −0.045 (0.026) (0.049) (0.034) (0.080) (0.033) (0.073) Entry Unemployment: Voluntary −0.120 −0.074 −0.262 −0.255 0.093 0.007 (0.131) (0.166) (0.169) (0.243) (0.148) (0.215) Entry Unemployment: Fired −0.082 −0.187 −0.200 −0.332 −0.305* −0.372* (0.163) (0.173) (0.202) (0.264) (0.183) (0.226) Entry Unemployment: Company Closed −0.719** −1.023** −0.568 −1.242** −0.630* −1.769** (0.305) (0.259) (0.374) (0.530) (0.331) (0.527) Entry OLF −0.009 −0.061 0.027 −0.099 −0.006 −0.020 (0.064) (0.076) (0.084) (0.128) (0.081) (0.113) Entry Employment −0.229** 0.039 −0.211* 0.110 0.189* 0.071 (0.091) (0.099) (0.109) (0.151) (0.105) (0.137) Log Net Real Household Income 0.522** 0.265** 0.553** 0.386** 0.051* 0.295** (0.024) (0.048) (0.031) (0.069) (0.029) (0.064) State Unemployment Rate −0.010** −0.020** −0.013** −0.026** −0.005 −0.026** (0.003) (0.005) (0.004) (0.008) (0.004) (0.008) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2/Pseudo R2 0.135 0.041 0.065 0.030 0.011 0.028 N 25611 25611 25611 15090 25611 19679 East females Unemployed −0.669** −0.531** −0.418** −0.351** −0.307** −0.742** (0.065) (0.090) (0.091) (0.157) (0.074) (0.123) Out of Labour Force (OLF) −0.325** −0.237** −0.226** −0.277 −0.010 −0.276* (0.056) (0.102) (0.082) (0.174) (0.072) (0.146) Entry Unemployment: Voluntary −0.050 0.116 −0.091 −0.057 0.134 0.286* (0.120) (0.120) (0.163) (0.234) (0.127) (0.162) Entry Unemployment: Fired −0.389** −0.307** −0.191 −0.268 −0.466** −0.342* (0.135) (0.139) (0.182) (0.250) (0.140) (0.177) Entry Unemployment: Company Closed −0.777** −0.510** −0.947** −0.984** −0.942** −0.893** (0.182) (0.197) (0.330) (0.469) (0.227) (0.283) Entry OLF 0.102 0.074 0.044 0.201 −0.082 0.314 (0.145) (0.184) (0.204) (0.283) (0.176) (0.229) Entry Employment −0.282** −0.007 −0.134 0.135 0.218** −0.021 (0.072) (0.082) (0.098) (0.145) (0.088) (0.111) Log Net Real Household Income 0.709** 0.427** 0.728** 0.503** 0.242** 0.665** (0.040) (0.073) (0.057) (0.119) (0.049) (0.104) State Unemployment Rate 0.000 −0.008 −0.006 −0.008 0.007 −0.014 (0.004) (0.008) (0.006) (0.015) (0.006) (0.012) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2/Pseudo R2 0.151 0.052 0.059 0.028 0.015 0.042 N 11,965 11,965 11,965 6,540 11,965 9,973 Open in new tab Table 2 
Effects of Unemployment on Life Satisfaction for Males by Region . Continuous . Fixed Thresholds . Individual Thresholds . OLS . OLS‐FE . Logit . C Logit . Logit . C Logit . West males Unemployed −1.086** −0.724** −0.940** −0.771** −0.378** −0.901** (0.067) (0.108) (0.089) (0.163) (0.076) (0.140) Out of Labour Force (OLF) −0.374** −0.166** −0.195** −0.124 0.071 −0.171 (0.051) (0.084) (0.060) (0.140) (0.057) (0.124) Entry Unemployment: Voluntary 0.278** 0.107 0.226 0.101 −0.069 0.134 (0.136) (0.158) (0.167) (0.242) (0.148) (0.199) Entry Unemployment: Fired −0.034 −0.127 0.033 0.064 −0.228 0.123 (0.141) (0.161) (0.169) (0.241) (0.144) (0.192) Entry Unemployment: Company Closed −0.089 −0.136 0.204 0.291 −0.567** −0.386 (0.259) (0.280) (0.291) (0.432) (0.282) (0.349) Entry OLF 0.071 −0.012 0.085 0.068 −0.185* 0.031 (0.096) (0.103) (0.109) (0.187) (0.105) (0.150) Entry Employment −0.301** 0.082 −0.356** 0.119 0.245** 0.072 (0.074) (0.087) (0.093) (0.135) (0.089) (0.114) Log Net Real Household Income 0.462** 0.235** 0.534** 0.415** 0.099** 0.386** (0.024) (0.043) (0.032) (0.076) (0.030) (0.066) State Unemployment Rate −0.015** −0.028** −0.018** −0.050** −0.015** −0.052** (0.003) (0.005) (0.004) (0.009) (0.004) (0.008) Standard Controls Yes Yes Yes Yes Yes Yes Adj−R2 / Pseudo R2 0.147 0.053 0.062 0.036 0.013 0.035 N 25,802 25,802 25,802 14,577 25,802 19,788 East males Unemployed −0.857** −0.702** −0.619** −0.893** −0.412** −0.839** (0.093) (0.117) (0.136) (0.231) (0.099) (0.152) Out of Labour Force (OLF) −0.274** −0.293** −0.008 −0.056 −0.031 −0.428** (0.073) (0.135) (0.100) (0.233) (0.088) (0.177) Entry Unemployment: Voluntary −0.173 −0.025 −0.365* −0.117 −0.196 −0.060 (0.139) (0.138) (0.221) (0.319) (0.151) (0.187) Entry Unemployment: Fired 0.042 0.062 −0.135 0.191 −0.175 0.016 (0.130) (0.138) (0.191) (0.286) (0.140) (0.173) Entry Unemployment: Company Closed −0.434* −0.176 −0.196 0.358 −0.539** −0.269 (0.235) (0.234) (0.318) (0.433) (0.238) (0.284) Entry OLF −0.082 0.046 −0.230 −0.094 −0.223 0.182 (0.160) (0.179) (0.214) (0.311) (0.178) (0.222) Entry Employment −0.328** −0.058 −0.369** −0.165 0.116 −0.172 (0.079) (0.083) (0.111) (0.159) (0.093) (0.122) Log Net Real Household Income 0.595** 0.493** 0.635** 0.654** 0.206** 0.787** (0.040) (0.075) (0.057) (0.128) (0.050) (0.108) State Unemployment Rate 0.005 −0.009 −0.007 −0.035** 0.029** −0.009 (0.005) (0.008) (0.007) (0.015) (0.006) (0.013) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2 / Pseudo R2 0.142 0.058 0.058 0.038 0.016 0.043 N 11,264 11,264 11,264 5,955 11,264 9,333 . Continuous . Fixed Thresholds . Individual Thresholds . OLS . OLS‐FE . Logit . C Logit . Logit . C Logit . West males Unemployed −1.086** −0.724** −0.940** −0.771** −0.378** −0.901** (0.067) (0.108) (0.089) (0.163) (0.076) (0.140) Out of Labour Force (OLF) −0.374** −0.166** −0.195** −0.124 0.071 −0.171 (0.051) (0.084) (0.060) (0.140) (0.057) (0.124) Entry Unemployment: Voluntary 0.278** 0.107 0.226 0.101 −0.069 0.134 (0.136) (0.158) (0.167) (0.242) (0.148) (0.199) Entry Unemployment: Fired −0.034 −0.127 0.033 0.064 −0.228 0.123 (0.141) (0.161) (0.169) (0.241) (0.144) (0.192) Entry Unemployment: Company Closed −0.089 −0.136 0.204 0.291 −0.567** −0.386 (0.259) (0.280) (0.291) (0.432) (0.282) (0.349) Entry OLF 0.071 −0.012 0.085 0.068 −0.185* 0.031 (0.096) (0.103) (0.109) (0.187) (0.105) (0.150) Entry Employment −0.301** 0.082 −0.356** 0.119 0.245** 0.072 (0.074) (0.087) (0.093) (0.135) (0.089) (0.114) Log Net Real Household Income 0.462** 0.235** 0.534** 0.415** 0.099** 0.386** (0.024) (0.043) (0.032) (0.076) (0.030) (0.066) State Unemployment Rate −0.015** −0.028** −0.018** −0.050** −0.015** −0.052** (0.003) (0.005) (0.004) (0.009) (0.004) (0.008) Standard Controls Yes Yes Yes Yes Yes Yes Adj−R2 / Pseudo R2 0.147 0.053 0.062 0.036 0.013 0.035 N 25,802 25,802 25,802 14,577 25,802 19,788 East males Unemployed −0.857** −0.702** −0.619** −0.893** −0.412** −0.839** (0.093) (0.117) (0.136) (0.231) (0.099) (0.152) Out of Labour Force (OLF) −0.274** −0.293** −0.008 −0.056 −0.031 −0.428** (0.073) (0.135) (0.100) (0.233) (0.088) (0.177) Entry Unemployment: Voluntary −0.173 −0.025 −0.365* −0.117 −0.196 −0.060 (0.139) (0.138) (0.221) (0.319) (0.151) (0.187) Entry Unemployment: Fired 0.042 0.062 −0.135 0.191 −0.175 0.016 (0.130) (0.138) (0.191) (0.286) (0.140) (0.173) Entry Unemployment: Company Closed −0.434* −0.176 −0.196 0.358 −0.539** −0.269 (0.235) (0.234) (0.318) (0.433) (0.238) (0.284) Entry OLF −0.082 0.046 −0.230 −0.094 −0.223 0.182 (0.160) (0.179) (0.214) (0.311) (0.178) (0.222) Entry Employment −0.328** −0.058 −0.369** −0.165 0.116 −0.172 (0.079) (0.083) (0.111) (0.159) (0.093) (0.122) Log Net Real Household Income 0.595** 0.493** 0.635** 0.654** 0.206** 0.787** (0.040) (0.075) (0.057) (0.128) (0.050) (0.108) State Unemployment Rate 0.005 −0.009 −0.007 −0.035** 0.029** −0.009 (0.005) (0.008) (0.007) (0.015) (0.006) (0.013) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2 / Pseudo R2 0.142 0.058 0.058 0.038 0.016 0.043 N 11,264 11,264 11,264 5,955 11,264 9,333 Open in new tab Table 2 
Effects of Unemployment on Life Satisfaction for Males by Region . Continuous . Fixed Thresholds . Individual Thresholds . OLS . OLS‐FE . Logit . C Logit . Logit . C Logit . West males Unemployed −1.086** −0.724** −0.940** −0.771** −0.378** −0.901** (0.067) (0.108) (0.089) (0.163) (0.076) (0.140) Out of Labour Force (OLF) −0.374** −0.166** −0.195** −0.124 0.071 −0.171 (0.051) (0.084) (0.060) (0.140) (0.057) (0.124) Entry Unemployment: Voluntary 0.278** 0.107 0.226 0.101 −0.069 0.134 (0.136) (0.158) (0.167) (0.242) (0.148) (0.199) Entry Unemployment: Fired −0.034 −0.127 0.033 0.064 −0.228 0.123 (0.141) (0.161) (0.169) (0.241) (0.144) (0.192) Entry Unemployment: Company Closed −0.089 −0.136 0.204 0.291 −0.567** −0.386 (0.259) (0.280) (0.291) (0.432) (0.282) (0.349) Entry OLF 0.071 −0.012 0.085 0.068 −0.185* 0.031 (0.096) (0.103) (0.109) (0.187) (0.105) (0.150) Entry Employment −0.301** 0.082 −0.356** 0.119 0.245** 0.072 (0.074) (0.087) (0.093) (0.135) (0.089) (0.114) Log Net Real Household Income 0.462** 0.235** 0.534** 0.415** 0.099** 0.386** (0.024) (0.043) (0.032) (0.076) (0.030) (0.066) State Unemployment Rate −0.015** −0.028** −0.018** −0.050** −0.015** −0.052** (0.003) (0.005) (0.004) (0.009) (0.004) (0.008) Standard Controls Yes Yes Yes Yes Yes Yes Adj−R2 / Pseudo R2 0.147 0.053 0.062 0.036 0.013 0.035 N 25,802 25,802 25,802 14,577 25,802 19,788 East males Unemployed −0.857** −0.702** −0.619** −0.893** −0.412** −0.839** (0.093) (0.117) (0.136) (0.231) (0.099) (0.152) Out of Labour Force (OLF) −0.274** −0.293** −0.008 −0.056 −0.031 −0.428** (0.073) (0.135) (0.100) (0.233) (0.088) (0.177) Entry Unemployment: Voluntary −0.173 −0.025 −0.365* −0.117 −0.196 −0.060 (0.139) (0.138) (0.221) (0.319) (0.151) (0.187) Entry Unemployment: Fired 0.042 0.062 −0.135 0.191 −0.175 0.016 (0.130) (0.138) (0.191) (0.286) (0.140) (0.173) Entry Unemployment: Company Closed −0.434* −0.176 −0.196 0.358 −0.539** −0.269 (0.235) (0.234) (0.318) (0.433) (0.238) (0.284) Entry OLF −0.082 0.046 −0.230 −0.094 −0.223 0.182 (0.160) (0.179) (0.214) (0.311) (0.178) (0.222) Entry Employment −0.328** −0.058 −0.369** −0.165 0.116 −0.172 (0.079) (0.083) (0.111) (0.159) (0.093) (0.122) Log Net Real Household Income 0.595** 0.493** 0.635** 0.654** 0.206** 0.787** (0.040) (0.075) (0.057) (0.128) (0.050) (0.108) State Unemployment Rate 0.005 −0.009 −0.007 −0.035** 0.029** −0.009 (0.005) (0.008) (0.007) (0.015) (0.006) (0.013) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2 / Pseudo R2 0.142 0.058 0.058 0.038 0.016 0.043 N 11,264 11,264 11,264 5,955 11,264 9,333 . Continuous . Fixed Thresholds . Individual Thresholds . OLS . OLS‐FE . Logit . C Logit . Logit . C Logit . West males Unemployed −1.086** −0.724** −0.940** −0.771** −0.378** −0.901** (0.067) (0.108) (0.089) (0.163) (0.076) (0.140) Out of Labour Force (OLF) −0.374** −0.166** −0.195** −0.124 0.071 −0.171 (0.051) (0.084) (0.060) (0.140) (0.057) (0.124) Entry Unemployment: Voluntary 0.278** 0.107 0.226 0.101 −0.069 0.134 (0.136) (0.158) (0.167) (0.242) (0.148) (0.199) Entry Unemployment: Fired −0.034 −0.127 0.033 0.064 −0.228 0.123 (0.141) (0.161) (0.169) (0.241) (0.144) (0.192) Entry Unemployment: Company Closed −0.089 −0.136 0.204 0.291 −0.567** −0.386 (0.259) (0.280) (0.291) (0.432) (0.282) (0.349) Entry OLF 0.071 −0.012 0.085 0.068 −0.185* 0.031 (0.096) (0.103) (0.109) (0.187) (0.105) (0.150) Entry Employment −0.301** 0.082 −0.356** 0.119 0.245** 0.072 (0.074) (0.087) (0.093) (0.135) (0.089) (0.114) Log Net Real Household Income 0.462** 0.235** 0.534** 0.415** 0.099** 0.386** (0.024) (0.043) (0.032) (0.076) (0.030) (0.066) State Unemployment Rate −0.015** −0.028** −0.018** −0.050** −0.015** −0.052** (0.003) (0.005) (0.004) (0.009) (0.004) (0.008) Standard Controls Yes Yes Yes Yes Yes Yes Adj−R2 / Pseudo R2 0.147 0.053 0.062 0.036 0.013 0.035 N 25,802 25,802 25,802 14,577 25,802 19,788 East males Unemployed −0.857** −0.702** −0.619** −0.893** −0.412** −0.839** (0.093) (0.117) (0.136) (0.231) (0.099) (0.152) Out of Labour Force (OLF) −0.274** −0.293** −0.008 −0.056 −0.031 −0.428** (0.073) (0.135) (0.100) (0.233) (0.088) (0.177) Entry Unemployment: Voluntary −0.173 −0.025 −0.365* −0.117 −0.196 −0.060 (0.139) (0.138) (0.221) (0.319) (0.151) (0.187) Entry Unemployment: Fired 0.042 0.062 −0.135 0.191 −0.175 0.016 (0.130) (0.138) (0.191) (0.286) (0.140) (0.173) Entry Unemployment: Company Closed −0.434* −0.176 −0.196 0.358 −0.539** −0.269 (0.235) (0.234) (0.318) (0.433) (0.238) (0.284) Entry OLF −0.082 0.046 −0.230 −0.094 −0.223 0.182 (0.160) (0.179) (0.214) (0.311) (0.178) (0.222) Entry Employment −0.328** −0.058 −0.369** −0.165 0.116 −0.172 (0.079) (0.083) (0.111) (0.159) (0.093) (0.122) Log Net Real Household Income 0.595** 0.493** 0.635** 0.654** 0.206** 0.787** (0.040) (0.075) (0.057) (0.128) (0.050) (0.108) State Unemployment Rate 0.005 −0.009 −0.007 −0.035** 0.029** −0.009 (0.005) (0.008) (0.007) (0.015) (0.006) (0.013) Standard Controls Yes Yes Yes Yes Yes Yes Adj‐R2 / Pseudo R2 0.142 0.058 0.058 0.038 0.016 0.043 N 11,264 11,264 11,264 5,955 11,264 9,333 Open in new tab For males in Table 2, for all of the estimation methods controlling for fixed effects, there are no significant entry year effects for unemployment due to voluntary quits, being fired and company closing. Only the main effect of being unemployed is significant and negative. This result holds in both east and west. East men are also negatively affected by being out of the labour force, as the individual threshold method shows in column 5. Here the fixed threshold method in column 6 gives an insignificant coefficient. We find a very different pattern for the effects of entry into unemployment when examining women in both east and west. In Table 3, women in both regions are greatly affected by company closing, doubling or even tripling their negative overall unemployment coefficient. While the company closing effect is stable and negative whether examining pooled or fixed effects, linear or non‐linear models, the fixed threshold method (column 4) has an insignificant general unemployment coefficient, whereas the individual threshold method gives a clearly significant coefficient (column 6). East women are also strongly negatively affected by being fired, which is stable even after controlling for fixed effects. Again this is likely to be due to the traditionally strong labour market attachment experienced by east women. In the first year of entering into unemployment due to company closing, using the linear fixed effects coefficients, women in the west and east would have to be compensated 4.7 log points of household income [(0.230 + 1.023)/0.265] and 2.4 [(0.510 + 0.531)/0.427] log points respectively. These are dramatic non‐pecuniary costs to unemployment in the first year after entry. The state‐specific unemployment rate, as shown in Table 2 and Table 3, is almost always significantly negative and fairly large for the west (males and females) and almost always quite small and insignificant for the east (males and females). For west females, going from average west levels of state unemployment (around 10%) to average east levels (around 16%) is about half the size of the negative effect (OLS‐FE) of being unemployed oneself (6 × −0.02 = −0.12 which is about half of −0.230). For west males, this would be 6 × −0.028 = −0.168 or about one quarter of the negative effect of being unemployed oneself at −0.724. There appears to be a high sensitivity to regional unemployment in the west and a sort of saturation indifference in the east. We attribute this especially negative effect for entry unemployment due to company closure (−1.769 for west, −0.893 for east) for women in Table 3 to reduced flexibility in participating in the labour market. It is likely that women in marriages supply labour conditional on the labour supply of their partners. If this were the case, then a company closure could be an indicator of reduced re‐employment prospects for the woman, i.e. being a woman, she might be less likely to be able to leave a company that is likely to default, because she is supplying her labour dependent on her partner. A man might be likely as a bread winner to leave a potentially dying company and move elsewhere, whereas a (married) woman might not have this flexibility to the same extent as a man. To investigate this hypothesis further, we expand on this especially negative entry unemployment effect for women and separate the sample of women into two further subgroups, those married and those not married for each region. We expect to find much stronger negative effects of entry unemployment for those married as they are less likely to be flexible, whereas women who are not married should be more flexible in finding another job and/or relocating and thus be less affected by entry unemployment. Indeed in Table 4, focusing only on the results from the preferred conditional logit model with individual specific effects and thresholds, we find significantly negative effects for married women in the west and the east for entry unemployment due to company closing, whereas these effects are insignificant for non‐married women. We interpret this as evidence for reduced flexibility for females on entering unemployment due to family considerations. For east married women we also find significant negative effects for being fired as the reason for entry unemployment, indicating additional inflexibility. Table 4 
Effects of Unemployment on Life Satisfaction for Females by Marriage . Not Married . Married . West . East . West . East . Unemployed −0.866** −0.737** −0.220 −0.717** (0.321) (0.254) (0.163) (0.146) Out of Labour Force (OLF) −0.447** −0.314 0.015 −0.323* (0.202) (0.347) (0.081) (0.166) Entry Unemployment: Voluntary 0.388 0.300 −0.069 0.297 (0.361) (0.305) (0.287) (0.193) Entry Unemployment: Fired −0.571 −0.293 −0.302 −0.363* (0.488) (0.365) (0.258) (0.205) Entry Unemployment: Company Closed 0.968 −0.866 −2.859** −0.901** (1.068) (0.678) (0.746) (0.311) Entry OLF 0.338 0.483 −0.101 0.244 (0.277) (0.458) (0.126) (0.273) Entry Employment −0.184 −0.082 0.157 0.017 (0.210) (0.234) (0.192) (0.130) State Unemployment Rate −0.046** −0.023 −0.022** −0.009 (0.017) (0.025) (0.009) (0.014) Standard Controls Yes Yes Yes Yes Pseudo‐R2 0.031 0.04 0.032 0.045 N 4,309 2,261 14,563 7,432 . Not Married . Married . West . East . West . East . Unemployed −0.866** −0.737** −0.220 −0.717** (0.321) (0.254) (0.163) (0.146) Out of Labour Force (OLF) −0.447** −0.314 0.015 −0.323* (0.202) (0.347) (0.081) (0.166) Entry Unemployment: Voluntary 0.388 0.300 −0.069 0.297 (0.361) (0.305) (0.287) (0.193) Entry Unemployment: Fired −0.571 −0.293 −0.302 −0.363* (0.488) (0.365) (0.258) (0.205) Entry Unemployment: Company Closed 0.968 −0.866 −2.859** −0.901** (1.068) (0.678) (0.746) (0.311) Entry OLF 0.338 0.483 −0.101 0.244 (0.277) (0.458) (0.126) (0.273) Entry Employment −0.184 −0.082 0.157 0.017 (0.210) (0.234) (0.192) (0.130) State Unemployment Rate −0.046** −0.023 −0.022** −0.009 (0.017) (0.025) (0.009) (0.014) Standard Controls Yes Yes Yes Yes Pseudo‐R2 0.031 0.04 0.032 0.045 N 4,309 2,261 14,563 7,432 Note. All models fixed effects conditional binary logit and individual thresholds. Open in new tab Table 4 
Effects of Unemployment on Life Satisfaction for Females by Marriage . Not Married . Married . West . East . West . East . Unemployed −0.866** −0.737** −0.220 −0.717** (0.321) (0.254) (0.163) (0.146) Out of Labour Force (OLF) −0.447** −0.314 0.015 −0.323* (0.202) (0.347) (0.081) (0.166) Entry Unemployment: Voluntary 0.388 0.300 −0.069 0.297 (0.361) (0.305) (0.287) (0.193) Entry Unemployment: Fired −0.571 −0.293 −0.302 −0.363* (0.488) (0.365) (0.258) (0.205) Entry Unemployment: Company Closed 0.968 −0.866 −2.859** −0.901** (1.068) (0.678) (0.746) (0.311) Entry OLF 0.338 0.483 −0.101 0.244 (0.277) (0.458) (0.126) (0.273) Entry Employment −0.184 −0.082 0.157 0.017 (0.210) (0.234) (0.192) (0.130) State Unemployment Rate −0.046** −0.023 −0.022** −0.009 (0.017) (0.025) (0.009) (0.014) Standard Controls Yes Yes Yes Yes Pseudo‐R2 0.031 0.04 0.032 0.045 N 4,309 2,261 14,563 7,432 . Not Married . Married . West . East . West . East . Unemployed −0.866** −0.737** −0.220 −0.717** (0.321) (0.254) (0.163) (0.146) Out of Labour Force (OLF) −0.447** −0.314 0.015 −0.323* (0.202) (0.347) (0.081) (0.166) Entry Unemployment: Voluntary 0.388 0.300 −0.069 0.297 (0.361) (0.305) (0.287) (0.193) Entry Unemployment: Fired −0.571 −0.293 −0.302 −0.363* (0.488) (0.365) (0.258) (0.205) Entry Unemployment: Company Closed 0.968 −0.866 −2.859** −0.901** (1.068) (0.678) (0.746) (0.311) Entry OLF 0.338 0.483 −0.101 0.244 (0.277) (0.458) (0.126) (0.273) Entry Employment −0.184 −0.082 0.157 0.017 (0.210) (0.234) (0.192) (0.130) State Unemployment Rate −0.046** −0.023 −0.022** −0.009 (0.017) (0.025) (0.009) (0.014) Standard Controls Yes Yes Yes Yes Pseudo‐R2 0.031 0.04 0.032 0.045 N 4,309 2,261 14,563 7,432 Note. All models fixed effects conditional binary logit and individual thresholds. Open in new tab There are some methodological and technical issues worth mentioning here. As was shown in the analysis, the results between the fixed and individual threshold methods can differ substantially. The reason for this is that using the Ferrer‐i‐Carbonell and Frijters (2004) estimator allows us to use observations originally not incorporated into the fixed threshold model. These observations, were either previously always above the fixed threshold of 7, or always below. By allowing individual‐specific thresholds, we gain substantially more observations. For the east, the overwhelming majority of these newly won observations contained satisfaction levels consistently under the fixed threshold of 7, thereby under‐representing the observations of low satisfaction using the fixed threshold method. In a similar manner but to a lesser extent, the west contained substantially more people consistently below the fixed threshold of 7 than were consistently above. Not incorporating these observations would explicitly exclude many in the east, as the average life satisfaction in the east is substantially lower (6.4 as compared to 7.0 in the west on the scale of 0 to 10). While a plant closing can be considered largely exogenous to the individual worker, it is likely that the closing itself is not in all cases a complete surprise event and, as such, there may be some gradual leaving process prior to closing. Pfann (2006) examines the dynamics behind downsizing prior to plant closings in manufacturing. He finds that during the downsizing process prior to closure, the firm displaces workers with low firing costs, low expected future productivity growth and low layoff option values. He uses personnel records from a Dutch aircraft building company that went bankrupt in 1996 and shows that workers with high chances of high future productivity are most likely to be retained. However, this can be difficult to implement in general. In German corporate law (§111 and §112 BetrVG), the future employment prospects of the employees to be laid off must be considered explicitly in the lay‐off process. As such, those remaining to the bitter end, often have much to lose upon plant closure. Thus the first waves of layoffs due to closings typically affect those who are easiest to fire (low severance payments or low tenure). The last waves of layoffs must have had some strong reason to stay with the firm (i.e. inflexibility, no outside option) even though the workers might have known of the potential economic plight of the firm. As shown here empirically, this effect might be even stronger for women who are perhaps less flexible in changing their employers due to family considerations. This would be consistent with those workers who stay on to the bitter end, because they have large amounts of firm‐specific human capital, and then suffer a dramatic depreciation of that capital. Taken to the very extreme, if all plant closings had a very long closing process lasting months if not years with only the very least flexible and the most to lose remaining to the bitter end, then a coefficient for plant closings would represent an upper bound in the absolute size of the negative effect on life satisfaction, rather than an average effect for all employees. 5. Conclusion This article examines the impact of unemployment on life satisfaction for Germany 1991–2006, using a sample of men and women from the German Socio‐Economic Panel (SOEP). It expands on previous ground‐breaking research from Winkelmann Winkelmann (1995, 1998) and Gerlach and Stephan (1996) and explicitly identifies exogenous unemployment entries with additional information on the reasons for unemployment: voluntary, being fired and company closing. Further, the article implements an approximation to the Ferrer‐i‐Carbonell and Frijters (2004) estimator, allowing conditional fixed effects estimation with individual‐specific thresholds, thereby maximising the number of usable observations. This technical innovation leads to significantly negative effects of being in unemployment on life satisfaction for west women, whereas results obtained with a common life satisfaction threshold would otherwise be found to be insignificant (compare in Table 3−0.205 in column 4 with −0.383** in column 6). The coefficient of entry unemployment due to company closing is strongly negative for west women, amounting to about 4.6 (−1.769/−0.383) times the coefficient of being unemployed in general as shown in column 6. For east women, the additional shock effect due to company closing is about the same size as being unemployed in general. For the four subgroups, the negative and significant psychological effects of unemployment in general remain fairly constant over the entire period and similar in magnitude. For men, with few exceptions (depending on the estimation method), the reason for entry into (voluntary or involuntary) unemployment has no additional effect in the year of entry into unemployment. For women, company closures in the year of entry into unemployment are strongly negative, providing prima facie evidence of a reduced outside work option, large investments in firm‐specific human capital, or a family constraint. As married women experience substantially larger negative effects due to company closure than do non‐married women for both east and west Germany, we interpret this as a family constraint. Indeed the strong negative effects for women are almost entirely driven by married women, with the shock effect for west women being more than 12 times larger than the effect of unemployment in general. Exogenous entry into unemployment produces dramatic negative non‐pecuniary psychological costs to women in the order of several log points of income, increasing in severity by the degree of inflexibility due to family constraints. Footnotes 1 " The data used in this article were extracted using the Add‐On package PanelWhiz v2.0 (September 2007) for Stata. PanelWhiz was written by Haisken‐DeNew. The following authors supplied PanelWhiz SOEP Plugins used to ensure longitudinal consistency, Haisken‐DeNew (29), Markus Hahn and Haisken‐DeNew (18). The PanelWhiz generated DO file to retrieve the SOEP data used here and any Panelwhiz Plugins are available upon request. Any data or computational errors in this article are our own. Haisken‐DeNew and Hahn (2006) describes PanelWhiz in detail. 2 " Overviews of the psychological findings on unemployment are given by Argyle (1999), Feather (1990), Fryer and Payne (1986), Murphy and Athanasou (1999) and Clark (2006). 3 " See Carroll (2007) for more information. 4 " In regression analysis, intrinsic differences in satisfaction can be accounted for. 5 " See http://www.diw.de/soep for more information. 6 " We thank Ada Ferrer‐i‐Carbonell heartily for this tip. 7 " Residency in Germany is determined by place of residence in 1989. References Akerlof , G. A . ( 1980 ). ‘A theory of social custom, of which unemployment may be one consequence’ , Quarterly Journal of Economics , vol. 94 ( 4 ), pp. 749 – 75 . Google Scholar Crossref Search ADS WorldCat Argyle , M. ( 1999 ). ‘Causes and correlates of happiness’, in ( D. Kahneman, E. Diener and N. Schwarz eds.), Well Being: The Foundations of Hedonic Psychology , pp. 353 – 73 . New York: Russel Sage Foundation . 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Google Scholar Crossref Search ADS WorldCat Author notes " The authors thank Thomas K. Bauer, Jan Brenner, Andrew Clark, Anette Fasang, Martin Kroh, Simon Luechinger, Steve Machin, Anna Raute, Christoph M. Schmidt, Michael A. Shields, Rainer Winkelmann, Nicolas Ziebarth and two anonymous referees for very helpful comments. © The Author(s). Journal compilation © Royal Economic Society 2009

Gregory‐Smith,, Ian;Thompson,, Steve;Wright, Peter, W.

doi: 10.1111/j.1468-0297.2008.02243.xpmid: N/A

Abstract We apply duration analysis to model the tenure and mode of exit of CEOs from FTSE 350 companies from 1996–2005, a decade in which corporate governance reforms have sought to increase the accountability of the CEO to shareholders and their representatives on the board. We find a greater likelihood of dismissal in the latter part of the period. However, we also find that the likelihood of forced departure sharply decreases from the fifth year of a CEO’s tenure. We find evidence that this is because CEOs who survive beyond year four are able to entrench themselves in their position. In a UK public company, whilst the board sets the company’s aims and the broad strategies for achieving them, the chief executive officer (CEO) is responsible for the day‐to‐day running of the company. Concern has been raised, however, about the ability of the board to control the actions of the CEO adequately, with the result being that the CEO may depart from the efficient pursuit of shareholder value maximisation (Jensen and Meckling, 1976; Fama, 1980; Shleifer and Vishny, 1997). One instrument used to align the interests of the shareholders and the CEO is the CEO’s remuneration package. The level of remuneration is often twice as high for the CEO as that of the second highest paid director (MM & K Ltd, 2007) and typically contains large performance‐related elements. A second instrument is the ability of the board of directors to sack the CEO (Fama and Jensen, 1983; Zajac, 1990; Lin 1996). Indeed, Fama (1980) argues that damage to managerial reputation, with the implied threat to future earnings, is the main constraint on CEO behaviour. The strength of this incentive will be influenced by the extent to which boards are able to monitor the actions of the CEO and, as with remuneration, it is typical that the board will proxy the CEO’s ability by a measure of firm performance. Poorly performing CEOs should lose their jobs. There is a perception in the business press that the typical length of service for CEOs within large UK companies has decreased in recent times1 and, moreover, CEOs are experiencing shorter tenures due to a greater likelihood of being fired.2 This increased risk of dismissal in the UK is in turn attributed to the ongoing reform of corporate governance arrangements that began with the Cadbury (1992) Report and continued in the review of board effectiveness by Higgs (2003), whose recommendations were included in the revised version of the Combined Code (2003).3 It has also been suggested that an increase in shareholder activism and voting levels, as called for by the Hampel (1998) and Myners (2001, 2004) Reports, have contributed to a more demanding governance regime. It is argued that institutions have increasingly coordinated their behaviour to provide a more effective constraint on CEO actions (Leech, 2003). Indeed, the ability of shareholders in the UK to dismiss the board at a company meeting is envied by activists in the US (Monks and Minow, 2004). Despite this, there is an increasing body of literature that has raised concerns about whether boards are willing or able to remove under‐performing CEOs, even if these can be identified (Lipton and Lorsch, 1992; Jensen, 1993). Although boards are traditionally constituted as guardians of shareholder interests, they are likely to fail in this task if they have inadequate incentives to avoid the rational attempts by the CEO to capture or negate their influence. Indeed, boards have been accused of providing inefficient contracts, that are heavily weighted in favour of the CEO, because of the undue influence the latter has in the pay‐setting process (Bebchuk and Fried, 2003; 2004). Similarly, if the board gets ‘captured’ by the CEO the latter will become entrenched and difficult, if not impossible, to dismiss. The extent to which policy measures are able to impact on the relative power of the CEO and shareholders is also disputed in the literature (Weisbach, 2007). If CEOs have the capacity to capture the remuneration and dismissals processes, it follows that efforts to reduce their power relative to the board might also be captured and rendered ineffective.4 A less ambiguous impact of the reform process in relation to CEO tenure has been the reduction in contract length and of the notice period in a CEO’s service contract. Prior to the Cadbury (1992) and Greenbury (1995) Reports, contracts with 3‐ or even 5‐year rolling notice periods were not uncommon. Moreover, contract termination provisions were typically opaque and often resulted in compensation payments that included forgone annual bonus opportunities, enhanced pension provision and an acceleration in the vesting of share options (Trade and Industry Select Committee, 2003). After Greenbury, contracts were reduced and termination provisions curtailed to the point that, under the revised Combined Code (2003), service contracts should provide for no more than 12 months’ salary.5 In addition, disclosure was made more transparent and formalised in the Directors’ Remuneration Report Regulations (Department of Trade and Industry, 2002). There is empirical evidence that poor performance increases CEO turnover in US corporations from, inter alia, Coughlan and Schmidt (1985), Dalton and Kesner (1985), Friedman and Singh (1989), Parrino (1997), Audas et al. (1999) and Brickley (2003). The composition of the board of directors, both in terms of its size and insider‐outsider ratio, has also been shown to impact the probability of CEO turnover (Weisbach, 1988; Boeker and Goodstein, 1993; Yermack, 1996). An interesting finding in this literature is that CEO replacement decisions may have similar determinants across different corporate governance regimes. Kaplan (1994) and Kaplan and Minton (1994) found that CEOs in Japan and Germany, countries whose governance systems are traditionally characterised as involving long job tenure, were subject to similar influences to their Anglo‐American counterparts. Whilst such studies are instructive, there are good reasons to suspect that they are not telling the whole story. For example, it has been suggested that CEOs may use their control of information and board appointments to entrench themselves during their tenure, ensuring the board of directors becomes increasingly favourably disposed towards them (Hermalin and Weishbach 2003). If this is true, then it is likely that the impact of performance on the probability of CEO exit will vary over time. An alternative hypothesis, which would also lead to a time‐varying impact of performance relates to imperfect monitoring: if the output of a CEO cannot be observed directly and must be inferred from the firm’s results, then there will be some lag before a CEO is judged to be under‐performing. It is only after this period that a badly performing CEO will be removed from their position. Finally, as outlined above, it is widely conjectured that substantial changes to the governance environment in which CEOs have been operating will have affected exit probabilities. In this article we seek to examine these issues using a dataset that is unique in terms of its detail. It allows us to model the duration of CEO tenure and to ascertain the varying likelihood of CEO exit by using a competing risks framework. This permits us to test between a number of the competing hypotheses outlined above by deriving the determinants of competing exit states for appointed CEOs. Section 1 gives an overview of the data, including a graphical inspection of the hazard rates before a more formal semi‐parametric analysis is presented in Section 2. Section 3 of the article concludes. 1. Data The primary information used in this study is supplied by Manifest Information Services Ltd, corporate governance consultants, who maintain a comprehensive governance and compensation database for all UK companies that have featured in the FTSE 350 Index during any financial year between January 1996 and December 2005. A major advantage of Manifest’s data is that the name of the CEO, together with their appointment and departure date are identified.6 The period chosen covers a full economic cycle, with market growth until 2001, subsequent decline and recovery. Moreover, the period under analysis is particularly interesting given the steady flow of corporate governance reforms designed to improve the transparency and accountability of boards. Investment trusts that contained no executive directors are excluded from the sample, although self‐managed investment trusts are retained. Manifest’s data was further supplemented with other control variables from Thomson Datastream. Summary statistics are provided in Table 1 below. Table 1 
Sample Description . 1996–2000 . 2001–5 . 1996–2005 . No. of companies 505 508 590 No. of CEOs 676 759 1179 No. of CEO exits 333 579 912 No. of interim appointments 23 84 107 % of CEOs exiting (excluding interim) 47% 73% 75% Total Observations 2,120 2,413 4,533 Survival times, years  1st quartile 2.53 2.18 2.33  Median 5.41 4.00 4.34  3rd quartile 10.01 6.51 7.24 Age  1st quartile 46 45 46  Median 51 50 51  3rd quartile 55 55 55 Total Shareholder Return  1st quartile −9.40% −18.00% −13.48%  Median 11.74% 8.35% 10.12%  3rd quartile 33.40% 26.30% 29.60% %Insiders on board (median)  Company assessment 0.510 0.500 0.500 Sales (median) (2006, £) 563 m 573 m 570 m Board Size (median) 8 8 8 . 1996–2000 . 2001–5 . 1996–2005 . No. of companies 505 508 590 No. of CEOs 676 759 1179 No. of CEO exits 333 579 912 No. of interim appointments 23 84 107 % of CEOs exiting (excluding interim) 47% 73% 75% Total Observations 2,120 2,413 4,533 Survival times, years  1st quartile 2.53 2.18 2.33  Median 5.41 4.00 4.34  3rd quartile 10.01 6.51 7.24 Age  1st quartile 46 45 46  Median 51 50 51  3rd quartile 55 55 55 Total Shareholder Return  1st quartile −9.40% −18.00% −13.48%  Median 11.74% 8.35% 10.12%  3rd quartile 33.40% 26.30% 29.60% %Insiders on board (median)  Company assessment 0.510 0.500 0.500 Sales (median) (2006, £) 563 m 573 m 570 m Board Size (median) 8 8 8 Open in new tab Table 1 
Sample Description . 1996–2000 . 2001–5 . 1996–2005 . No. of companies 505 508 590 No. of CEOs 676 759 1179 No. of CEO exits 333 579 912 No. of interim appointments 23 84 107 % of CEOs exiting (excluding interim) 47% 73% 75% Total Observations 2,120 2,413 4,533 Survival times, years  1st quartile 2.53 2.18 2.33  Median 5.41 4.00 4.34  3rd quartile 10.01 6.51 7.24 Age  1st quartile 46 45 46  Median 51 50 51  3rd quartile 55 55 55 Total Shareholder Return  1st quartile −9.40% −18.00% −13.48%  Median 11.74% 8.35% 10.12%  3rd quartile 33.40% 26.30% 29.60% %Insiders on board (median)  Company assessment 0.510 0.500 0.500 Sales (median) (2006, £) 563 m 573 m 570 m Board Size (median) 8 8 8 . 1996–2000 . 2001–5 . 1996–2005 . No. of companies 505 508 590 No. of CEOs 676 759 1179 No. of CEO exits 333 579 912 No. of interim appointments 23 84 107 % of CEOs exiting (excluding interim) 47% 73% 75% Total Observations 2,120 2,413 4,533 Survival times, years  1st quartile 2.53 2.18 2.33  Median 5.41 4.00 4.34  3rd quartile 10.01 6.51 7.24 Age  1st quartile 46 45 46  Median 51 50 51  3rd quartile 55 55 55 Total Shareholder Return  1st quartile −9.40% −18.00% −13.48%  Median 11.74% 8.35% 10.12%  3rd quartile 33.40% 26.30% 29.60% %Insiders on board (median)  Company assessment 0.510 0.500 0.500 Sales (median) (2006, £) 563 m 573 m 570 m Board Size (median) 8 8 8 Open in new tab Over our sample period we observe 1,179 CEOs working for 590 companies. Of these, 912 end with the termination of the CEO’s contract. The median survival time for a CEO is about 4 years. Note that, in line with popular perception, the proportion of CEOs experiencing an exit event is significantly higher in the second period, with the median survival time being approximately 1 years shorter in the second half of the sample. This increase is shown year on year in Figure 1. This decline in average CEO tenure coincides with a decline in market performance, as measured by total shareholder return.7 Fig. 1. Open in new tabDownload slide CEO Exits Over Time
Notes. Figure excludes interim appointments and internal position changes. Fig. 1. Open in new tabDownload slide CEO Exits Over Time
Notes. Figure excludes interim appointments and internal position changes. The Table also reflects the institutional changes over the period, with the percentage of insiders8 falling steadily during the period (Figure 2) and the percentage of non‐executive directors rising.9 Fig. 2. Open in new tabDownload slide Mean Board Composition Fig. 2. Open in new tabDownload slide Mean Board Composition There are a number of ways in which CEOs can leave their position, only one of which is dismissal. We conducted an electronic search of financial news archives and regulatory news service announcements in order to identify the circumstances under which the CEO left his/her position and so exited the sample. Information confirming their departure was found in every case and, in all but 65, some explanation of their leaving was offered. This allowed us to split the exit events into 9 types, details of which are given in Table 2. Table 2 
CEO Turnover by Mode of Exit . 1996–2000 . 2001–5 . 1996–2005 . Number . % . Number . % . Number . % . Dismissed 3 0.90 7 1.21 10 1.10 Ousted 41 12.31 84 14.51 125 13.71 Internal Change 28 8.41 28 4.84 56 6.14 Interim Appointment 23 6.91 84 14.51 107 11.73 Retirement 90 27.03 162 27.98 252 27.63 Retired to Part Time 30 9.01 54 9.33 84 9.21 Change of Control 74 22.22 89 15.37 163 17.87 Head‐hunted 23 6.91 27 4.66 50 5.48 Unclassified 21 6.31 44 7.60 65 7.13 Total exits 333 100 579 100 912 100 . 1996–2000 . 2001–5 . 1996–2005 . Number . % . Number . % . Number . % . Dismissed 3 0.90 7 1.21 10 1.10 Ousted 41 12.31 84 14.51 125 13.71 Internal Change 28 8.41 28 4.84 56 6.14 Interim Appointment 23 6.91 84 14.51 107 11.73 Retirement 90 27.03 162 27.98 252 27.63 Retired to Part Time 30 9.01 54 9.33 84 9.21 Change of Control 74 22.22 89 15.37 163 17.87 Head‐hunted 23 6.91 27 4.66 50 5.48 Unclassified 21 6.31 44 7.60 65 7.13 Total exits 333 100 579 100 912 100 Open in new tab Table 2 
CEO Turnover by Mode of Exit . 1996–2000 . 2001–5 . 1996–2005 . Number . % . Number . % . Number . % . Dismissed 3 0.90 7 1.21 10 1.10 Ousted 41 12.31 84 14.51 125 13.71 Internal Change 28 8.41 28 4.84 56 6.14 Interim Appointment 23 6.91 84 14.51 107 11.73 Retirement 90 27.03 162 27.98 252 27.63 Retired to Part Time 30 9.01 54 9.33 84 9.21 Change of Control 74 22.22 89 15.37 163 17.87 Head‐hunted 23 6.91 27 4.66 50 5.48 Unclassified 21 6.31 44 7.60 65 7.13 Total exits 333 100 579 100 912 100 . 1996–2000 . 2001–5 . 1996–2005 . Number . % . Number . % . Number . % . Dismissed 3 0.90 7 1.21 10 1.10 Ousted 41 12.31 84 14.51 125 13.71 Internal Change 28 8.41 28 4.84 56 6.14 Interim Appointment 23 6.91 84 14.51 107 11.73 Retirement 90 27.03 162 27.98 252 27.63 Retired to Part Time 30 9.01 54 9.33 84 9.21 Change of Control 74 22.22 89 15.37 163 17.87 Head‐hunted 23 6.91 27 4.66 50 5.48 Unclassified 21 6.31 44 7.60 65 7.13 Total exits 333 100 579 100 912 100 Open in new tab Note that CEOs are rarely officially ‘dismissed’, with only 10 CEOs suffering this fate in the 10 years of the sample. In many cases it is suspected that face‐saving descriptions are used, either to avoid further damage to the ousted executive’s reputation or to facilitate the conclusion of negotiations over compensation. Therefore, care was required when classifying executive departures by exit state. However, where clear evidence was found to show that the CEO had been forced out of their position, the CEO was considered to have been ‘ousted’. A common occurrence during the sample period was that the roles of Chairman and Chief Executive were split, consistent with the post‐Cadbury recommendation for best practice. We code these cases separately as ‘internal change’ since they do not appear to constitute a forced CEO exit. We also code separately those CEO exits arising from restructuring or change of control.10‘Interim’ appointments to the CEO’s position generally arise as a consequence of the sudden departure of the previous CEO, when someone, most often the Chairman, steps in to fill the role of Chief Executive on a caretaker basis. As these appointments are temporary by definition we exclude them from our analysis. In a small number of cases no clear reason was given for the departure of the CEO and we could find no clear evidence of either an ousting or an immediate appointment to another company. We put these into an ‘unclassified’ departure category. The absence of any press rumours of dismissal suggests these cases were not among the more egregious examples of CEO behaviour but it is suspected this category includes departures from a number of causes, including changes of career, moves to private equity companies etc. Table 3 breaks down CEO tenure by exit event. The survival times are lowest for interim appointments, as might be expected, followed by those who are headhunted, who also tend to be relatively young. Those who are dismissed and ousted have the next shortest tenure. Those whose positions end with retirement generally have the longest tenures and are oldest at exit. This illustrates the importance of carefully distinguishing exit states in any empirical analysis. Table 3 
Tenure by Exit Event . Survival times . Age at exit . Lower . . Upper . . . quartile . Median . quartile . Median . Mean . Dismissed 2.0 2.4 5.0 52.5 49.06 Ousted 1.9 3.0 4.5 50 50.51 Interim appointment 0.3 0.5 0.8 53 51.05 Retirement 2.5 4.8 7.5 56 54.75 Retired to part‐time 2.5 3.6 6.0 56 54.14 Change of control 1.4 2.3 4.4 50 49.25 Headhunted 1.7 2.9 5.1 49 47.96 Unclassified 1.9 3.6 6.3 54 52.13 . Survival times . Age at exit . Lower . . Upper . . . quartile . Median . quartile . Median . Mean . Dismissed 2.0 2.4 5.0 52.5 49.06 Ousted 1.9 3.0 4.5 50 50.51 Interim appointment 0.3 0.5 0.8 53 51.05 Retirement 2.5 4.8 7.5 56 54.75 Retired to part‐time 2.5 3.6 6.0 56 54.14 Change of control 1.4 2.3 4.4 50 49.25 Headhunted 1.7 2.9 5.1 49 47.96 Unclassified 1.9 3.6 6.3 54 52.13 Note. Survival times allow for left truncation and right censoring. Open in new tab Table 3 
Tenure by Exit Event . Survival times . Age at exit . Lower . . Upper . . . quartile . Median . quartile . Median . Mean . Dismissed 2.0 2.4 5.0 52.5 49.06 Ousted 1.9 3.0 4.5 50 50.51 Interim appointment 0.3 0.5 0.8 53 51.05 Retirement 2.5 4.8 7.5 56 54.75 Retired to part‐time 2.5 3.6 6.0 56 54.14 Change of control 1.4 2.3 4.4 50 49.25 Headhunted 1.7 2.9 5.1 49 47.96 Unclassified 1.9 3.6 6.3 54 52.13 . Survival times . Age at exit . Lower . . Upper . . . quartile . Median . quartile . Median . Mean . Dismissed 2.0 2.4 5.0 52.5 49.06 Ousted 1.9 3.0 4.5 50 50.51 Interim appointment 0.3 0.5 0.8 53 51.05 Retirement 2.5 4.8 7.5 56 54.75 Retired to part‐time 2.5 3.6 6.0 56 54.14 Change of control 1.4 2.3 4.4 50 49.25 Headhunted 1.7 2.9 5.1 49 47.96 Unclassified 1.9 3.6 6.3 54 52.13 Note. Survival times allow for left truncation and right censoring. Open in new tab This Table illustrates that existing research on executive tenure is likely to suffer from two inter‐related difficulties: first, CEOs resign for a variety of reasons some of which (e.g. being headhunted) may be associated with success, some (e.g. dismissal) with failure and others (e.g. retirement) may have ambiguous performance associations. This clearly requires any analysis to allow for different determinants for the alternative exit states. Datasets which do not distinguish between these competing events have distinct disadvantages to those, such as ours, that can. We now consider how best to model the duration of CEO tenure. 2. Duration Analysis In modelling the duration of CEO tenure, we adopt the Cox (1972) proportional hazard model. A hazard‐based analysis is useful as our data contains both left truncation (as some CEOs began their tenure prior to the sample start date) and right censoring (as some CEOs have not completed their tenure by the end of the sample) both of which can be readily handled in this framework. 2.1. Non‐parametric Analysis Prior to estimation, we briefly present a graphical analysis of the hazard rate by exit type. To do so, we combine the possible exit types into three groups: Forced exits (dismissals and ousted), retirements (including remaining as Chairman) and other exits (headhunted, change of control and unclassified).11 Figure 3 demonstrates the different likelihood of exit to the competing exit states over the tenure of a CEO. At the start of a CEO’s employment, the least likely reason for exit is retirement, though this probability steadily increases as time passes. The risk of being forced out rises steadily in the early years, peaks in the fifth year and declines thereafter – eventually becoming the least likely exit state. Hence, once the CEO has completed 6 years, the most likely form of departure is retirement. Fig. 3. Open in new tabDownload slide Cause Specific Hazards Fig. 3. Open in new tabDownload slide Cause Specific Hazards Since one might expect different influences to impact on the hazard rates for forced exit and retirement, Figure 4 examines the impact of firm performance. We would expect poor firm performance to have a stronger influence on the hazard of forced departure than the hazard of retirement. For simplicity, we identify four performance quartiles determined by the annual total shareholder return (TSR) ranking within the FTSE 350. Fig. 4. Open in new tabDownload slide Breakdown by Firm Performance Fig. 4. Open in new tabDownload slide Breakdown by Firm Performance Figure 4 shows that TSR has an impact on the hazard of forced exit with the divergence between the bottom and top quartile performers increasing until year 4 and remaining higher until year 12. With respect to retirements, the lower quartile performers also have a marginally higher risk of exit up to year 10 or 11, which could reflect CEOs with disappointing performance retiring early. To investigate the possibility that CEOs may be less likely to be ousted from ‘captured’ boards, Figure 5 compares the hazard rates of those CEOs who have an insider dominated board with those that have independent boards. As can be seen, the hazard for forced exits is consistently lower if a board is dominated by insiders. This is suggestive of an entrenchment effect. Although the effect is less obvious, the probability of early retirement is also less in dominated boards, also suggesting entrenchment. Moreover, since the difference in the hazard between the dominated boards and the independent boards is greatest between years 9 and 12, this is consistent with the notion that it may take a number of years for a CEO to capture their board. Fig. 5. Open in new tabDownload slide Breakdown by Board Type Fig. 5. Open in new tabDownload slide Breakdown by Board Type 2.2. Semi‐parametric Analysis 2.2.1. All exit states Whilst the graphical analysis is indicative, many additional factors could be impacting on the probability of CEO exit. We therefore proceed with an econometric analysis. In standard parametric survival analysis one needs to assume an explicit form for the underlying hazard rate, which imposes restrictions on the range of allowable behaviour. By contrast, the Cox (1972) proportional hazard model is a semi‐parametric method which allows the estimation of the impact of a covariate without restricting the shape of the baseline hazard. This is convenient for our purposes since we have few priors concerning the form of the underlying baseline hazard. Under the Cox model, the hazard rate that the j’th CEO faces is multiplicatively proportional to the baseline hazard, λ0(t), that all CEOs face, modified by covariates xj (Cleves et al., 2002)12 (1) Table 4 shows the results from running a basic Cox proportional hazards model with all exit states constituting a single failure event.13 The t‐statistics indicate whether the co‐variate has a statistically significant impact, as normal. However, for ease of interpretation, hazard ratios are reported and thus a coefficient indicates the probability of exit compared to the baseline. A number greater than one indicates the hazard is increased, a number less than one indicates that it is decreased. Table 4 
Hazard to Any Exit . a . b . Total shareholder return  Lower quartile‐Median 0.764*** (−2.83) 0.530 (−1.13)  Median‐Upper quartile 0.612*** (−4.59) 0.432 (−1.37)  Upper quartile 0.458*** (−7.20) 0.367* (−1.85) Ln Sales 1.092*** (2.99) 1.094*** (2.96) Age 1.005*** (4.06) 1.005*** (4.08) Board Size 0.918*** (−4.47) 0.905*** (−3.04) %Insiders on Board 0.322*** (−3.44) 0.323*** (−3.18) %Board Appointed by CEO 0.257*** (−6.64) 0.248*** (−5.08) Ave NED Tenure 0.909*** (−4.87) 0.894*** (−3.44) Block equity‐CEO equity 1.013*** (4.20) 1.013*** (4.08) Total shareholder return interactions Board Size  Lower quartile‐Median 1.028 (0.66)  Median‐Upper quartile 1.010 (0.23)  Upper quartile 1.024 (0.50) %Insiders on Board  Lower quartile‐Median 1.073 (0.12)  Median‐Upper quartile 1.076 (0.11)  Upper quartile 0.968 (−0.05) %Board appointed by CEO  Lower quartile‐Median 0.936 (−0.18)  Median‐Upper quartile 1.145 (0.32)  Upper quartile 1.081 (0.17) Ave non‐executive tenure  Lower quartile‐Median 1.029 (0.62)  Median‐Upper quartile 1.031 (0.59)  Upper quartile 1.000 (0.00) N 3,364 3,364 No. CEOs 871 871 No. Failures 607 607 Wald (χ2) 252.096(19) 256.561(31) . a . b . Total shareholder return  Lower quartile‐Median 0.764*** (−2.83) 0.530 (−1.13)  Median‐Upper quartile 0.612*** (−4.59) 0.432 (−1.37)  Upper quartile 0.458*** (−7.20) 0.367* (−1.85) Ln Sales 1.092*** (2.99) 1.094*** (2.96) Age 1.005*** (4.06) 1.005*** (4.08) Board Size 0.918*** (−4.47) 0.905*** (−3.04) %Insiders on Board 0.322*** (−3.44) 0.323*** (−3.18) %Board Appointed by CEO 0.257*** (−6.64) 0.248*** (−5.08) Ave NED Tenure 0.909*** (−4.87) 0.894*** (−3.44) Block equity‐CEO equity 1.013*** (4.20) 1.013*** (4.08) Total shareholder return interactions Board Size  Lower quartile‐Median 1.028 (0.66)  Median‐Upper quartile 1.010 (0.23)  Upper quartile 1.024 (0.50) %Insiders on Board  Lower quartile‐Median 1.073 (0.12)  Median‐Upper quartile 1.076 (0.11)  Upper quartile 0.968 (−0.05) %Board appointed by CEO  Lower quartile‐Median 0.936 (−0.18)  Median‐Upper quartile 1.145 (0.32)  Upper quartile 1.081 (0.17) Ave non‐executive tenure  Lower quartile‐Median 1.029 (0.62)  Median‐Upper quartile 1.031 (0.59)  Upper quartile 1.000 (0.00) N 3,364 3,364 No. CEOs 871 871 No. Failures 607 607 Wald (χ2) 252.096(19) 256.561(31) Robust t‐statistics, clustered on CEO, are reported in the parentheses. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Year dummies included. Open in new tab Table 4 
Hazard to Any Exit . a . b . Total shareholder return  Lower quartile‐Median 0.764*** (−2.83) 0.530 (−1.13)  Median‐Upper quartile 0.612*** (−4.59) 0.432 (−1.37)  Upper quartile 0.458*** (−7.20) 0.367* (−1.85) Ln Sales 1.092*** (2.99) 1.094*** (2.96) Age 1.005*** (4.06) 1.005*** (4.08) Board Size 0.918*** (−4.47) 0.905*** (−3.04) %Insiders on Board 0.322*** (−3.44) 0.323*** (−3.18) %Board Appointed by CEO 0.257*** (−6.64) 0.248*** (−5.08) Ave NED Tenure 0.909*** (−4.87) 0.894*** (−3.44) Block equity‐CEO equity 1.013*** (4.20) 1.013*** (4.08) Total shareholder return interactions Board Size  Lower quartile‐Median 1.028 (0.66)  Median‐Upper quartile 1.010 (0.23)  Upper quartile 1.024 (0.50) %Insiders on Board  Lower quartile‐Median 1.073 (0.12)  Median‐Upper quartile 1.076 (0.11)  Upper quartile 0.968 (−0.05) %Board appointed by CEO  Lower quartile‐Median 0.936 (−0.18)  Median‐Upper quartile 1.145 (0.32)  Upper quartile 1.081 (0.17) Ave non‐executive tenure  Lower quartile‐Median 1.029 (0.62)  Median‐Upper quartile 1.031 (0.59)  Upper quartile 1.000 (0.00) N 3,364 3,364 No. CEOs 871 871 No. Failures 607 607 Wald (χ2) 252.096(19) 256.561(31) . a . b . Total shareholder return  Lower quartile‐Median 0.764*** (−2.83) 0.530 (−1.13)  Median‐Upper quartile 0.612*** (−4.59) 0.432 (−1.37)  Upper quartile 0.458*** (−7.20) 0.367* (−1.85) Ln Sales 1.092*** (2.99) 1.094*** (2.96) Age 1.005*** (4.06) 1.005*** (4.08) Board Size 0.918*** (−4.47) 0.905*** (−3.04) %Insiders on Board 0.322*** (−3.44) 0.323*** (−3.18) %Board Appointed by CEO 0.257*** (−6.64) 0.248*** (−5.08) Ave NED Tenure 0.909*** (−4.87) 0.894*** (−3.44) Block equity‐CEO equity 1.013*** (4.20) 1.013*** (4.08) Total shareholder return interactions Board Size  Lower quartile‐Median 1.028 (0.66)  Median‐Upper quartile 1.010 (0.23)  Upper quartile 1.024 (0.50) %Insiders on Board  Lower quartile‐Median 1.073 (0.12)  Median‐Upper quartile 1.076 (0.11)  Upper quartile 0.968 (−0.05) %Board appointed by CEO  Lower quartile‐Median 0.936 (−0.18)  Median‐Upper quartile 1.145 (0.32)  Upper quartile 1.081 (0.17) Ave non‐executive tenure  Lower quartile‐Median 1.029 (0.62)  Median‐Upper quartile 1.031 (0.59)  Upper quartile 1.000 (0.00) N 3,364 3,364 No. CEOs 871 871 No. Failures 607 607 Wald (χ2) 252.096(19) 256.561(31) Robust t‐statistics, clustered on CEO, are reported in the parentheses. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Year dummies included. Open in new tab The null hypothesis of this article is that poorly performing CEOs should be dismissed. In our regressions, the total shareholder return variables identify annual performance quartiles compared to the lower quartile performers in the FTSE 350 Index. Even with all exit states bundled together, the impact of a low performance ranking is clear. The probability of exit for low to median performers is 76% that of the worst performers, whilst those in the upper quartile have a hazard that is only 46% of the lowest quartile. The theoretical caveat to our null hypothesis is that the threat of dismissal is mitigated if the CEOs are able to entrench him/herself and capture the board. Table 4 shows that the insider variables are also important. Increasing the proportion of independent directors on the board by 20 percentage points, whilst holding the total number of directors the same, would result in an increase in the hazard rate of approximately 14%. In addition, CEOs with larger boards face lower hazard rates, with the results indicating that losing 4 directors from the board would increase the hazard rate by 33%. Age also has a positive impact on the probability of exit.14 A 65‐year‐old CEO has double the hazard rate of a 55‐year‐old. Boards which comprise a greater proportion of directors appointed during the tenure of the current CEO result in lower hazard rates.15 The average length of service of the non‐executive directors decreases the hazard, suggesting that a non‐executive director does not become more rigorous at monitoring with experience but rather the CEO carries more influence the longer the director serves in office. The ownership structure of the firm may also be important in determining CEO turnover. To examine this, we include the difference between the equity holdings of the largest blockholder and those of the CEO. The results indicate that the higher the relative holdings of the blockholder, the more likely the CEO is to be forced from their position.16 It is possible that the governance of the company modifies the effect that performance has on the likelihood of CEO exit. To investigate this, we interact board size, % insiders, % board appointed by the CEO and average non‐executive tenure with the total shareholder return variables. The results are show in column b of Table 4. None of these interactions are statistically significant and so the structural measures of entrenchment described above appear not to diminish the impact of performance on the likelihood of exit. 2.2.2. Competing risk estimates By grouping all exit types together, the model presented in Table 4 implicitly assumes the same underlying hazard rate across all failure types. However, as we have seen, there are good reasons to suspect that the baseline hazard is likely to vary depending on the event from which the CEO is at risk. For example, under an entrenchment hypothesis, one would expect the hazard of dismissal to reduce over the course of the CEO’s tenure but the hazard of retirement will increase. One strategy, as used by Geddes and Vinod (1997), is to exclude observations that experience the competing event and just analyse the event of primary interest, in this case dismissal. However, a more efficient and informative approach is to directly compare alternative exit states in a common framework. We therefore adopt a competing risks methodology (Prentice et al., 1978; Kalbfleisch and Prentice, 1980). The risks are competing in the sense that the exit states are mutually exclusive (i.e. upon retirement the CEO can no longer be dismissed) and thus each event censors each other event. We distinguish between three competing exit types: forced departures; retirements; and other exits. We follow the method of Lunn and McNeil (1995) and stratify by risk type, since we do not wish to restrict the baseline hazards of the different risk types to share a constant ratio. This is achieved by duplicating the data so that there are three entries per observation, one for each risk type. The duplicated entries show the other risk types and are always censored. If the original observation is right censored, then three entries exist, one for each failure type, all of which are censored. A Cox regression, stratified by failure type, is then performed with the covariates interacted with each risk type. By this method we can identify how the covariates impact upon each competing risk. Examining the competing risk estimates, a clear distinction can be observed in Table 5 with respect to the influence of covariates upon CEO turnover. Firm performance is critical in the hazard of a forced exit, with CEOs of firms in the top quartile having a hazard rate only 20% of that of the bottom quartile. In contrast, performance has a positive impact on exits to other states, presumably as high performers move on to other jobs. Table 5 
Hazard to Competing Risks . Forced Departure . Retirement . Other . Forced Departure . Retirement . Other . Total shareholder return  Lower quartile‐Median 0.402*** 2.220** 2.072** 0.246 2.685 4.762 (−3.70) (2.69) (2.34) (−0.90) (0.56) (0.83)  Median–Upper quartile 0.360*** 1.829* 2.034** 0.074* 8.066 10.477 (−4.17) (1.93) (2.21) (−1.70) (1.10) (1.20)  Upper quartile 0.196*** 3.317*** 2.325** 0.103 10.907 2.599 (−5.15) (3.28) (2.18) (−1.19) (1.13) (0.43) Ln Sales 1.194** 0.933 0.883 1.209** 0.922 0.869 (2.53) (−0.80) (−1.42) (2.60) (−0.91) (−1.55) Age 0.999 1.008*** 0.998 0.999 1.008*** 0.998 (−0.41) (2.84) (−0.58) (−0.41) (2.78) (−0.52) Board Size 0.936 0.966 1.003 0.910 0.999 0.987 (−1.42) (−0.60) (0.05) (−1.42) (−0.01) (−0.13) %Insiders on Board 0.205** 2.252 1.707 0.182** 2.137 2.423 (−2.08) (0.88) (0.54) (−2.16) (0.76) (0.85) %Board Appointed by CEO 0.196*** 2.260* 0.957 0.147*** 2.946 1.964 (−4.26) (1.72) (−0.10) (−3.77) (1.55) (0.97) Ave NED Tenure 0.806*** 1.160** 1.150** 0.814** 1.155 1.120 (−3.57) (2.24) (2.00) (−2.38) (1.35) (1.09) Block equity‐CEO equity 1.017** 0.994 0.997 1.017** 0.993 0.996 (2.38) (−0.72) (−0.36) (2.48) (−0.82) (−0.41) Total shareholder return interactions Board Size  Lower quartile‐Median 0.997 1.045 1.034 (−0.03) (0.37) (0.26)  Median–Upper quartile 1.121 0.829 0.949 (1.29) (−1.49) (−0.42)  Upper quartile 1.023 0.957 1.093 (0.16) (−0.28) (0.53) %Insiders on Board  Lower quartile‐Median 1.643 1.026 0.284 (0.30) (0.01) (−0.59)  Median–Upper quartile 1.130 1.218 0.662 (0.08) (0.10) (−0.21)  Upper quartile 2.096 0.462 0.391 (0.36) (−0.34) (−0.37) %Board appointed by CEO  Lower quartile‐Median 3.278 0.189 0.141* (1.29) (−1.46) (−1.69)  Median–Upper quartile 0.774 2.572 0.788 (−0.29) (0.81) (−0.20)  Upper quartile 2.982 0.316 0.138 (0.78) (−0.72) (−1.19) Ave non‐executive tenure  Lower quartile‐Median 0.878 1.128 1.221 (−0.77) (0.64) (1.05)  Median–Upper quartile 1.152 0.877 0.846 (1.09) (−0.85) (−0.97)  Upper quartile 0.835 1.115 1.262 (−1.20) (0.63) (1.22) No. CEOs 871 871 No. Failures 607 607 Wald (χ2) 375.810(59) 410.609(95) Equality of coefficients across risks (χ2) 78.97(20)*** 104.96(44)*** . Forced Departure . Retirement . Other . Forced Departure . Retirement . Other . Total shareholder return  Lower quartile‐Median 0.402*** 2.220** 2.072** 0.246 2.685 4.762 (−3.70) (2.69) (2.34) (−0.90) (0.56) (0.83)  Median–Upper quartile 0.360*** 1.829* 2.034** 0.074* 8.066 10.477 (−4.17) (1.93) (2.21) (−1.70) (1.10) (1.20)  Upper quartile 0.196*** 3.317*** 2.325** 0.103 10.907 2.599 (−5.15) (3.28) (2.18) (−1.19) (1.13) (0.43) Ln Sales 1.194** 0.933 0.883 1.209** 0.922 0.869 (2.53) (−0.80) (−1.42) (2.60) (−0.91) (−1.55) Age 0.999 1.008*** 0.998 0.999 1.008*** 0.998 (−0.41) (2.84) (−0.58) (−0.41) (2.78) (−0.52) Board Size 0.936 0.966 1.003 0.910 0.999 0.987 (−1.42) (−0.60) (0.05) (−1.42) (−0.01) (−0.13) %Insiders on Board 0.205** 2.252 1.707 0.182** 2.137 2.423 (−2.08) (0.88) (0.54) (−2.16) (0.76) (0.85) %Board Appointed by CEO 0.196*** 2.260* 0.957 0.147*** 2.946 1.964 (−4.26) (1.72) (−0.10) (−3.77) (1.55) (0.97) Ave NED Tenure 0.806*** 1.160** 1.150** 0.814** 1.155 1.120 (−3.57) (2.24) (2.00) (−2.38) (1.35) (1.09) Block equity‐CEO equity 1.017** 0.994 0.997 1.017** 0.993 0.996 (2.38) (−0.72) (−0.36) (2.48) (−0.82) (−0.41) Total shareholder return interactions Board Size  Lower quartile‐Median 0.997 1.045 1.034 (−0.03) (0.37) (0.26)  Median–Upper quartile 1.121 0.829 0.949 (1.29) (−1.49) (−0.42)  Upper quartile 1.023 0.957 1.093 (0.16) (−0.28) (0.53) %Insiders on Board  Lower quartile‐Median 1.643 1.026 0.284 (0.30) (0.01) (−0.59)  Median–Upper quartile 1.130 1.218 0.662 (0.08) (0.10) (−0.21)  Upper quartile 2.096 0.462 0.391 (0.36) (−0.34) (−0.37) %Board appointed by CEO  Lower quartile‐Median 3.278 0.189 0.141* (1.29) (−1.46) (−1.69)  Median–Upper quartile 0.774 2.572 0.788 (−0.29) (0.81) (−0.20)  Upper quartile 2.982 0.316 0.138 (0.78) (−0.72) (−1.19) Ave non‐executive tenure  Lower quartile‐Median 0.878 1.128 1.221 (−0.77) (0.64) (1.05)  Median–Upper quartile 1.152 0.877 0.846 (1.09) (−0.85) (−0.97)  Upper quartile 0.835 1.115 1.262 (−1.20) (0.63) (1.22) No. CEOs 871 871 No. Failures 607 607 Wald (χ2) 375.810(59) 410.609(95) Equality of coefficients across risks (χ2) 78.97(20)*** 104.96(44)*** Robust (clustered around CEO) t‐statistics reported in the parentheses. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Year dummies included. Open in new tab Table 5 
Hazard to Competing Risks . Forced Departure . Retirement . Other . Forced Departure . Retirement . Other . Total shareholder return  Lower quartile‐Median 0.402*** 2.220** 2.072** 0.246 2.685 4.762 (−3.70) (2.69) (2.34) (−0.90) (0.56) (0.83)  Median–Upper quartile 0.360*** 1.829* 2.034** 0.074* 8.066 10.477 (−4.17) (1.93) (2.21) (−1.70) (1.10) (1.20)  Upper quartile 0.196*** 3.317*** 2.325** 0.103 10.907 2.599 (−5.15) (3.28) (2.18) (−1.19) (1.13) (0.43) Ln Sales 1.194** 0.933 0.883 1.209** 0.922 0.869 (2.53) (−0.80) (−1.42) (2.60) (−0.91) (−1.55) Age 0.999 1.008*** 0.998 0.999 1.008*** 0.998 (−0.41) (2.84) (−0.58) (−0.41) (2.78) (−0.52) Board Size 0.936 0.966 1.003 0.910 0.999 0.987 (−1.42) (−0.60) (0.05) (−1.42) (−0.01) (−0.13) %Insiders on Board 0.205** 2.252 1.707 0.182** 2.137 2.423 (−2.08) (0.88) (0.54) (−2.16) (0.76) (0.85) %Board Appointed by CEO 0.196*** 2.260* 0.957 0.147*** 2.946 1.964 (−4.26) (1.72) (−0.10) (−3.77) (1.55) (0.97) Ave NED Tenure 0.806*** 1.160** 1.150** 0.814** 1.155 1.120 (−3.57) (2.24) (2.00) (−2.38) (1.35) (1.09) Block equity‐CEO equity 1.017** 0.994 0.997 1.017** 0.993 0.996 (2.38) (−0.72) (−0.36) (2.48) (−0.82) (−0.41) Total shareholder return interactions Board Size  Lower quartile‐Median 0.997 1.045 1.034 (−0.03) (0.37) (0.26)  Median–Upper quartile 1.121 0.829 0.949 (1.29) (−1.49) (−0.42)  Upper quartile 1.023 0.957 1.093 (0.16) (−0.28) (0.53) %Insiders on Board  Lower quartile‐Median 1.643 1.026 0.284 (0.30) (0.01) (−0.59)  Median–Upper quartile 1.130 1.218 0.662 (0.08) (0.10) (−0.21)  Upper quartile 2.096 0.462 0.391 (0.36) (−0.34) (−0.37) %Board appointed by CEO  Lower quartile‐Median 3.278 0.189 0.141* (1.29) (−1.46) (−1.69)  Median–Upper quartile 0.774 2.572 0.788 (−0.29) (0.81) (−0.20)  Upper quartile 2.982 0.316 0.138 (0.78) (−0.72) (−1.19) Ave non‐executive tenure  Lower quartile‐Median 0.878 1.128 1.221 (−0.77) (0.64) (1.05)  Median–Upper quartile 1.152 0.877 0.846 (1.09) (−0.85) (−0.97)  Upper quartile 0.835 1.115 1.262 (−1.20) (0.63) (1.22) No. CEOs 871 871 No. Failures 607 607 Wald (χ2) 375.810(59) 410.609(95) Equality of coefficients across risks (χ2) 78.97(20)*** 104.96(44)*** . Forced Departure . Retirement . Other . Forced Departure . Retirement . Other . Total shareholder return  Lower quartile‐Median 0.402*** 2.220** 2.072** 0.246 2.685 4.762 (−3.70) (2.69) (2.34) (−0.90) (0.56) (0.83)  Median–Upper quartile 0.360*** 1.829* 2.034** 0.074* 8.066 10.477 (−4.17) (1.93) (2.21) (−1.70) (1.10) (1.20)  Upper quartile 0.196*** 3.317*** 2.325** 0.103 10.907 2.599 (−5.15) (3.28) (2.18) (−1.19) (1.13) (0.43) Ln Sales 1.194** 0.933 0.883 1.209** 0.922 0.869 (2.53) (−0.80) (−1.42) (2.60) (−0.91) (−1.55) Age 0.999 1.008*** 0.998 0.999 1.008*** 0.998 (−0.41) (2.84) (−0.58) (−0.41) (2.78) (−0.52) Board Size 0.936 0.966 1.003 0.910 0.999 0.987 (−1.42) (−0.60) (0.05) (−1.42) (−0.01) (−0.13) %Insiders on Board 0.205** 2.252 1.707 0.182** 2.137 2.423 (−2.08) (0.88) (0.54) (−2.16) (0.76) (0.85) %Board Appointed by CEO 0.196*** 2.260* 0.957 0.147*** 2.946 1.964 (−4.26) (1.72) (−0.10) (−3.77) (1.55) (0.97) Ave NED Tenure 0.806*** 1.160** 1.150** 0.814** 1.155 1.120 (−3.57) (2.24) (2.00) (−2.38) (1.35) (1.09) Block equity‐CEO equity 1.017** 0.994 0.997 1.017** 0.993 0.996 (2.38) (−0.72) (−0.36) (2.48) (−0.82) (−0.41) Total shareholder return interactions Board Size  Lower quartile‐Median 0.997 1.045 1.034 (−0.03) (0.37) (0.26)  Median–Upper quartile 1.121 0.829 0.949 (1.29) (−1.49) (−0.42)  Upper quartile 1.023 0.957 1.093 (0.16) (−0.28) (0.53) %Insiders on Board  Lower quartile‐Median 1.643 1.026 0.284 (0.30) (0.01) (−0.59)  Median–Upper quartile 1.130 1.218 0.662 (0.08) (0.10) (−0.21)  Upper quartile 2.096 0.462 0.391 (0.36) (−0.34) (−0.37) %Board appointed by CEO  Lower quartile‐Median 3.278 0.189 0.141* (1.29) (−1.46) (−1.69)  Median–Upper quartile 0.774 2.572 0.788 (−0.29) (0.81) (−0.20)  Upper quartile 2.982 0.316 0.138 (0.78) (−0.72) (−1.19) Ave non‐executive tenure  Lower quartile‐Median 0.878 1.128 1.221 (−0.77) (0.64) (1.05)  Median–Upper quartile 1.152 0.877 0.846 (1.09) (−0.85) (−0.97)  Upper quartile 0.835 1.115 1.262 (−1.20) (0.63) (1.22) No. CEOs 871 871 No. Failures 607 607 Wald (χ2) 375.810(59) 410.609(95) Equality of coefficients across risks (χ2) 78.97(20)*** 104.96(44)*** Robust (clustered around CEO) t‐statistics reported in the parentheses. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Year dummies included. Open in new tab Table 5 shows that CEOs with a larger proportion of the board appointed during their tenure are at significantly lower risk of dismissal. Ceteris paribus, increasing the proportion of the board who have been appointed during the tenure of the CEO by 50 percentage points reduces the risk of dismissal by 40%. Boards comprising longer serving non‐executive directors also reduce the risk of dismissal for the CEO. As with the single risk estimates, we also interact the performance with the governance variables but again these effects are largely insignificant. Therefore, we are unable to conclude that the impact of poor performance upon dismissals is reduced in weakly governed firms. To summarise, we have provided evidence that poorly performing CEOs are at a greater risk of dismissal. We have also shown that governance matters: CEOs with larger boards, with more directors appointed during their tenure, with established non‐executive directors and with a greater proportion of insiders have lower hazard rates of dismissal. Yet, we fail to find evidence of an interaction between performance and governance. 2.3. Performance Revelation vs Entrenchment In the non‐parametric analysis in Section 2.1. we showed that the hazard of forced exit varied over a CEO’s tenure, increasing until year 4 and declining thereafter. This is a pattern that we might expect to see under entrenchment. The hazard rate will decrease if the CEO captures the board, which might take the CEO a number of years. Now, even if shareholders desire to remove the CEO, they will have lower rates of success due to the increasingly entrenched position of the CEO. However, Figure 3 also describes what we might expect to see with performance revelation. As information regarding the CEO’s ability increases as a result of observing additional years of firm performance under their tenure, shareholders may become more willing to stick with the CEO, even if current performance is relatively poor. However, if the declining hazard is due to information revelation, we would additionally expect the impact of cumulative good past performance to make the CEO more secure. To this end, we additionally add the cumulative change in TSR ranking to our regressions.17 We then allow the impact of the performance and insider variables to vary, by splitting our sample at 5 years of tenure.18Table 6 presents the results of this exercise. Table 6 
Performance Revelation Versus Entrenchment . Tenure < 5 . Tenure≥5 . . Forced Departure . Retirement . Other . Forced Departure . Retirement . Other . Total shareholder return Lower quartile‐Median 0.406*** 2.393** 1.464 0.320** 2.868* 2.867* (−3.06) (1.98) (0.96) (−2.12) (1.83) (1.72) Median‐Upper Quartile 0.359*** 1.432 1.565 0.231** 3.511* 2.536 (−3.17) (0.69) (1.02) (−2.40) (1.90) (1.28) Upper Quartile 0.148*** 3.269* 2.037 0.186** 3.979* 1.731 (−3.59) (1.64) (1.09) (−2.40) (1.82) (0.64) Change TSR Ranking 0.943 1.340 1.973 3.055* 0.285* 0.607 (−0.15) (0.51) (1.36) (1.60) (−1.68) (−0.60) Ln Sales 1.194** 0.905 0.894 1.217** 0.928 0.865 (2.43) (−1.08) (−1.24) (2.05) (−0.72) (−1.41) Age 1.001 1.014*** 0.990 0.998 1.008* 1.001 (0.35) (3.07) (−1.40) (−0.47) (1.67) (0.11) Board Size 0.913 0.963 0.970 0.974 0.932 1.023 (−1.57) (−0.44) (−0.39) (−0.43) (−0.99) (0.31) % Insiders on Board 0.345 3.723 8.220 0.045** 6.341 0.644 (−1.18) (0.93) (1.68) (−2.43) (1.34) (−0.30) % Board Appointed by CEO 0.298** 0.271 0.227** 0.297** 1.311 3.297 (−2.07) (−1.42) (−1.99) (−2.09) (0.38) (1.48) Ave NED Tenure 0.825** 1.086 1.132 0.862** 1.067 1.055 (−2.34) (0.70) (1.28) (−2.15) (0.88) (0.62) Block equity−CEO equity 1.020** 0.987 0.992 0.993* 1.021 1.016 (2.42) (−1.00) (−0.65) (−0.58) (1.64) (1.05) Wald χ2 544.947(95) Equality of coefficients 101.84(30)  tenure < 5 & tenure >5 (χ2) . Tenure < 5 . Tenure≥5 . . Forced Departure . Retirement . Other . Forced Departure . Retirement . Other . Total shareholder return Lower quartile‐Median 0.406*** 2.393** 1.464 0.320** 2.868* 2.867* (−3.06) (1.98) (0.96) (−2.12) (1.83) (1.72) Median‐Upper Quartile 0.359*** 1.432 1.565 0.231** 3.511* 2.536 (−3.17) (0.69) (1.02) (−2.40) (1.90) (1.28) Upper Quartile 0.148*** 3.269* 2.037 0.186** 3.979* 1.731 (−3.59) (1.64) (1.09) (−2.40) (1.82) (0.64) Change TSR Ranking 0.943 1.340 1.973 3.055* 0.285* 0.607 (−0.15) (0.51) (1.36) (1.60) (−1.68) (−0.60) Ln Sales 1.194** 0.905 0.894 1.217** 0.928 0.865 (2.43) (−1.08) (−1.24) (2.05) (−0.72) (−1.41) Age 1.001 1.014*** 0.990 0.998 1.008* 1.001 (0.35) (3.07) (−1.40) (−0.47) (1.67) (0.11) Board Size 0.913 0.963 0.970 0.974 0.932 1.023 (−1.57) (−0.44) (−0.39) (−0.43) (−0.99) (0.31) % Insiders on Board 0.345 3.723 8.220 0.045** 6.341 0.644 (−1.18) (0.93) (1.68) (−2.43) (1.34) (−0.30) % Board Appointed by CEO 0.298** 0.271 0.227** 0.297** 1.311 3.297 (−2.07) (−1.42) (−1.99) (−2.09) (0.38) (1.48) Ave NED Tenure 0.825** 1.086 1.132 0.862** 1.067 1.055 (−2.34) (0.70) (1.28) (−2.15) (0.88) (0.62) Block equity−CEO equity 1.020** 0.987 0.992 0.993* 1.021 1.016 (2.42) (−1.00) (−0.65) (−0.58) (1.64) (1.05) Wald χ2 544.947(95) Equality of coefficients 101.84(30)  tenure < 5 & tenure >5 (χ2) Robust (clustered around CEO) t‐statistics reported in the parentheses. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Year dummies included. Open in new tab Table 6 
Performance Revelation Versus Entrenchment . Tenure < 5 . Tenure≥5 . . Forced Departure . Retirement . Other . Forced Departure . Retirement . Other . Total shareholder return Lower quartile‐Median 0.406*** 2.393** 1.464 0.320** 2.868* 2.867* (−3.06) (1.98) (0.96) (−2.12) (1.83) (1.72) Median‐Upper Quartile 0.359*** 1.432 1.565 0.231** 3.511* 2.536 (−3.17) (0.69) (1.02) (−2.40) (1.90) (1.28) Upper Quartile 0.148*** 3.269* 2.037 0.186** 3.979* 1.731 (−3.59) (1.64) (1.09) (−2.40) (1.82) (0.64) Change TSR Ranking 0.943 1.340 1.973 3.055* 0.285* 0.607 (−0.15) (0.51) (1.36) (1.60) (−1.68) (−0.60) Ln Sales 1.194** 0.905 0.894 1.217** 0.928 0.865 (2.43) (−1.08) (−1.24) (2.05) (−0.72) (−1.41) Age 1.001 1.014*** 0.990 0.998 1.008* 1.001 (0.35) (3.07) (−1.40) (−0.47) (1.67) (0.11) Board Size 0.913 0.963 0.970 0.974 0.932 1.023 (−1.57) (−0.44) (−0.39) (−0.43) (−0.99) (0.31) % Insiders on Board 0.345 3.723 8.220 0.045** 6.341 0.644 (−1.18) (0.93) (1.68) (−2.43) (1.34) (−0.30) % Board Appointed by CEO 0.298** 0.271 0.227** 0.297** 1.311 3.297 (−2.07) (−1.42) (−1.99) (−2.09) (0.38) (1.48) Ave NED Tenure 0.825** 1.086 1.132 0.862** 1.067 1.055 (−2.34) (0.70) (1.28) (−2.15) (0.88) (0.62) Block equity−CEO equity 1.020** 0.987 0.992 0.993* 1.021 1.016 (2.42) (−1.00) (−0.65) (−0.58) (1.64) (1.05) Wald χ2 544.947(95) Equality of coefficients 101.84(30)  tenure < 5 & tenure >5 (χ2) . Tenure < 5 . Tenure≥5 . . Forced Departure . Retirement . Other . Forced Departure . Retirement . Other . Total shareholder return Lower quartile‐Median 0.406*** 2.393** 1.464 0.320** 2.868* 2.867* (−3.06) (1.98) (0.96) (−2.12) (1.83) (1.72) Median‐Upper Quartile 0.359*** 1.432 1.565 0.231** 3.511* 2.536 (−3.17) (0.69) (1.02) (−2.40) (1.90) (1.28) Upper Quartile 0.148*** 3.269* 2.037 0.186** 3.979* 1.731 (−3.59) (1.64) (1.09) (−2.40) (1.82) (0.64) Change TSR Ranking 0.943 1.340 1.973 3.055* 0.285* 0.607 (−0.15) (0.51) (1.36) (1.60) (−1.68) (−0.60) Ln Sales 1.194** 0.905 0.894 1.217** 0.928 0.865 (2.43) (−1.08) (−1.24) (2.05) (−0.72) (−1.41) Age 1.001 1.014*** 0.990 0.998 1.008* 1.001 (0.35) (3.07) (−1.40) (−0.47) (1.67) (0.11) Board Size 0.913 0.963 0.970 0.974 0.932 1.023 (−1.57) (−0.44) (−0.39) (−0.43) (−0.99) (0.31) % Insiders on Board 0.345 3.723 8.220 0.045** 6.341 0.644 (−1.18) (0.93) (1.68) (−2.43) (1.34) (−0.30) % Board Appointed by CEO 0.298** 0.271 0.227** 0.297** 1.311 3.297 (−2.07) (−1.42) (−1.99) (−2.09) (0.38) (1.48) Ave NED Tenure 0.825** 1.086 1.132 0.862** 1.067 1.055 (−2.34) (0.70) (1.28) (−2.15) (0.88) (0.62) Block equity−CEO equity 1.020** 0.987 0.992 0.993* 1.021 1.016 (2.42) (−1.00) (−0.65) (−0.58) (1.64) (1.05) Wald χ2 544.947(95) Equality of coefficients 101.84(30)  tenure < 5 & tenure >5 (χ2) Robust (clustered around CEO) t‐statistics reported in the parentheses. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Year dummies included. Open in new tab Current performance, measured by total shareholder return, does indeed appear to become less important after 5 years, as predicted by both the entrenchment and performance revelation hypotheses. Our reported estimates also show that the impact of insiders on the hazard of forced departures increases after the CEO has been in office for 5 or more years. This is consistent with the entrenchment hypothesis. No evidence is found for information revelation however – the coefficient on the change in TSR ranking moves in the opposite direction to that expected. This suggests that shareholders continue to regard recent, rather than good past, performance as the key indicator of CEO competence. 2.4. Governance Environment As indicated in the Introduction, the period of investigation was one of an ongoing programme of corporate governance reforms (Cadbury, 1992; Greenbury, 1995, Combined Code, 1999, 2003; Higgs, 2003) which might be expected to have impacted upon executive tenure: first, as noted above, these changes had the consequence of progressively reducing the contract length for UK senior executive from three years or more, in the early 1990s to 12 months or less by 2003 (Combined Code, 2003). This would have had a corresponding impact on the compensation requirements in the event of severance and hence be expected to reduce the costs of CEO dismissal. Second, the reforms from Cadbury onwards have consistently sought to strengthen the role and independence of non‐executive directors (Solomon, 2007). If successful, this would be expected to increase the accountability of CEOs and increase the risk of dismissal for poorer performers among their number. Finally, if less obviously, there is a widespread perception that shareholder activism has increased over the period (Davies et al., 2008). In part, this has been encouraged by corporate governance reforms which have increased direct shareholder voice – on such issues as calling shareholder meetings, replacing directors, approving remuneration committee reports etc. (Davies et al., 2008, p.4) – and thereby encouraged participation at shareholder AGMs. This is reinforced by the increased role of shareholder pressure groups and governance consultancies, such as Manifest, in providing alternative sources of information to shareholders. However, above all it reflects the view that the growth of institutional shareholdings challenges the received wisdom of the diffuse control of large public companies (Pensions Investment Research Consultants, 2003). Indeed work such as Leech (2001, 2003) suggests that effective voting control in many large UK companies could rest in the hands of a few fund managers if they coordinate their voting. Furthermore, the large absolute size of these holdings reduces their liquidity and thereby provides an incentive for intervention (Leech, 2003). Following the Myners’ Reports (2001, 2004) institutional shareholders’ organisations have acknowledged the role of fund managers in corporate governance (Davies et al., 2008, p.2). Since changes in the governance environment have occurred progressively, but incrementally, over the period, we test for their impact by splitting our data at 2000 and labelling the sub‐periods thereby created as ‘pre‐reform’ and ‘post‐reform’, respectively. The results of this exercise are given in Table 7. We find supportive evidence of an increase in the importance of firm performance post‐reform. In particular, the hazard of forced departure for the bottom quartile performers doubles between the two sub‐periods, with a corresponding fall in the other exit states. There is some suggestive decline in the hazard for the top performing companies, although these changes are not significant. Table 7 
Impact of Governance Reforms . Pre‐Reform . Post‐Reform . Forced departure . Retirement . Other . Forced departure . Retirement . Other . Total shareholder return  Lower quartile‐Median 0.260*** 3.103** 3.220** 0.526** 1.735 1.605 (−2.78) (1.97) (2.09) (−2.19) (1.57) (1.20)  Median‐Upper Quartile 0.389** 1.583 1.676 0.367*** 1.772 2.251** (−2.26) (0.86) (0.99) (−3.22) (1.47) (1.94)  Upper Quartile 0.220*** 2.913* 1.081 0.181*** 3.423** 3.454** (−3.19) (1.89) (0.12) (−3.94) (2.54) (2.45) Ln Sales 1.274* 0.822 0.954 1.183* 0.959 0.812* (1.82) (−1.23) (−0.29) (1.95) (−0.39) (−1.89) Age 1.006** 1.002 0.993* 0.988** 1.019*** 1.007 (2.01) (0.69) (−1.80) (−2.11) (3.22) (1.11) Board Size 0.976 0.970 0.976 0.899* 0.984 1.029 (−0.35) (−0.36) (−0.29) (−1.76) (−0.22) (0.37) % Insiders on Board 0.096* 4.792 0.958 0.280 1.533 3.505 (−1.83) (1.02) (−0.03) (−1.29) (0.36) (0.94) % Board Appointed by CEO 0.349** 2.769 0.574 0.114*** 2.787* 1.480 (−2.05) (1.23) (−0.85) (−4.13) (1.65) (0.61) Ave NED Tenure 0.833** 1.139 1.121 0.769*** 1.209** 1.165 (−2.25) (1.43) (1.21) (−3.14) (2.10) (1.50) Block equity‐CEO equity 1.019 0.977 0.990 1.018** 1.020 1.007 (1.08) (−1.11) (−0.47) (2.31) (0.86) (0.29) Wald χ2 488.997(89) Equality of coefficients: 56.41(30) Pre and Post‐reform (χ2) . Pre‐Reform . Post‐Reform . Forced departure . Retirement . Other . Forced departure . Retirement . Other . Total shareholder return  Lower quartile‐Median 0.260*** 3.103** 3.220** 0.526** 1.735 1.605 (−2.78) (1.97) (2.09) (−2.19) (1.57) (1.20)  Median‐Upper Quartile 0.389** 1.583 1.676 0.367*** 1.772 2.251** (−2.26) (0.86) (0.99) (−3.22) (1.47) (1.94)  Upper Quartile 0.220*** 2.913* 1.081 0.181*** 3.423** 3.454** (−3.19) (1.89) (0.12) (−3.94) (2.54) (2.45) Ln Sales 1.274* 0.822 0.954 1.183* 0.959 0.812* (1.82) (−1.23) (−0.29) (1.95) (−0.39) (−1.89) Age 1.006** 1.002 0.993* 0.988** 1.019*** 1.007 (2.01) (0.69) (−1.80) (−2.11) (3.22) (1.11) Board Size 0.976 0.970 0.976 0.899* 0.984 1.029 (−0.35) (−0.36) (−0.29) (−1.76) (−0.22) (0.37) % Insiders on Board 0.096* 4.792 0.958 0.280 1.533 3.505 (−1.83) (1.02) (−0.03) (−1.29) (0.36) (0.94) % Board Appointed by CEO 0.349** 2.769 0.574 0.114*** 2.787* 1.480 (−2.05) (1.23) (−0.85) (−4.13) (1.65) (0.61) Ave NED Tenure 0.833** 1.139 1.121 0.769*** 1.209** 1.165 (−2.25) (1.43) (1.21) (−3.14) (2.10) (1.50) Block equity‐CEO equity 1.019 0.977 0.990 1.018** 1.020 1.007 (1.08) (−1.11) (−0.47) (2.31) (0.86) (0.29) Wald χ2 488.997(89) Equality of coefficients: 56.41(30) Pre and Post‐reform (χ2) Robust (clustered around CEO) t‐statistics reported in the parentheses. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Year dummies included. Open in new tab Table 7 
Impact of Governance Reforms . Pre‐Reform . Post‐Reform . Forced departure . Retirement . Other . Forced departure . Retirement . Other . Total shareholder return  Lower quartile‐Median 0.260*** 3.103** 3.220** 0.526** 1.735 1.605 (−2.78) (1.97) (2.09) (−2.19) (1.57) (1.20)  Median‐Upper Quartile 0.389** 1.583 1.676 0.367*** 1.772 2.251** (−2.26) (0.86) (0.99) (−3.22) (1.47) (1.94)  Upper Quartile 0.220*** 2.913* 1.081 0.181*** 3.423** 3.454** (−3.19) (1.89) (0.12) (−3.94) (2.54) (2.45) Ln Sales 1.274* 0.822 0.954 1.183* 0.959 0.812* (1.82) (−1.23) (−0.29) (1.95) (−0.39) (−1.89) Age 1.006** 1.002 0.993* 0.988** 1.019*** 1.007 (2.01) (0.69) (−1.80) (−2.11) (3.22) (1.11) Board Size 0.976 0.970 0.976 0.899* 0.984 1.029 (−0.35) (−0.36) (−0.29) (−1.76) (−0.22) (0.37) % Insiders on Board 0.096* 4.792 0.958 0.280 1.533 3.505 (−1.83) (1.02) (−0.03) (−1.29) (0.36) (0.94) % Board Appointed by CEO 0.349** 2.769 0.574 0.114*** 2.787* 1.480 (−2.05) (1.23) (−0.85) (−4.13) (1.65) (0.61) Ave NED Tenure 0.833** 1.139 1.121 0.769*** 1.209** 1.165 (−2.25) (1.43) (1.21) (−3.14) (2.10) (1.50) Block equity‐CEO equity 1.019 0.977 0.990 1.018** 1.020 1.007 (1.08) (−1.11) (−0.47) (2.31) (0.86) (0.29) Wald χ2 488.997(89) Equality of coefficients: 56.41(30) Pre and Post‐reform (χ2) . Pre‐Reform . Post‐Reform . Forced departure . Retirement . Other . Forced departure . Retirement . Other . Total shareholder return  Lower quartile‐Median 0.260*** 3.103** 3.220** 0.526** 1.735 1.605 (−2.78) (1.97) (2.09) (−2.19) (1.57) (1.20)  Median‐Upper Quartile 0.389** 1.583 1.676 0.367*** 1.772 2.251** (−2.26) (0.86) (0.99) (−3.22) (1.47) (1.94)  Upper Quartile 0.220*** 2.913* 1.081 0.181*** 3.423** 3.454** (−3.19) (1.89) (0.12) (−3.94) (2.54) (2.45) Ln Sales 1.274* 0.822 0.954 1.183* 0.959 0.812* (1.82) (−1.23) (−0.29) (1.95) (−0.39) (−1.89) Age 1.006** 1.002 0.993* 0.988** 1.019*** 1.007 (2.01) (0.69) (−1.80) (−2.11) (3.22) (1.11) Board Size 0.976 0.970 0.976 0.899* 0.984 1.029 (−0.35) (−0.36) (−0.29) (−1.76) (−0.22) (0.37) % Insiders on Board 0.096* 4.792 0.958 0.280 1.533 3.505 (−1.83) (1.02) (−0.03) (−1.29) (0.36) (0.94) % Board Appointed by CEO 0.349** 2.769 0.574 0.114*** 2.787* 1.480 (−2.05) (1.23) (−0.85) (−4.13) (1.65) (0.61) Ave NED Tenure 0.833** 1.139 1.121 0.769*** 1.209** 1.165 (−2.25) (1.43) (1.21) (−3.14) (2.10) (1.50) Block equity‐CEO equity 1.019 0.977 0.990 1.018** 1.020 1.007 (1.08) (−1.11) (−0.47) (2.31) (0.86) (0.29) Wald χ2 488.997(89) Equality of coefficients: 56.41(30) Pre and Post‐reform (χ2) Robust (clustered around CEO) t‐statistics reported in the parentheses. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Year dummies included. Open in new tab The results for our governance variables suggest a rather limited impact of the reform process. Although the impact of insiders is weaker in the post‐reform period, the entrenching effect of board members appointed by the CEO appears to have increased. However, again, neither of these differences are statistically significant. In sum, our estimates cast doubt on the success of the reforms in weakening the ability of CEOs to entrench themselves in their position. 3. Conclusions We have presented evidence that the threat of CEO dismissal responds to performance as measured by total shareholder return. We have also shown that the threat of dismissal falls with certain structural measures of entrenchment such as the proportion of insiders on the board or number of directors appointed during the CEO’s tenure. However, we were unable to find a strong interaction between governance conditions and the impact of performance in determining the threat of dismissal. Our investigation has also exposed distinct differences between the hazard rates of competing risk types and in the variation of these hazard rates over time. Whilst the risk of retirement increases steadily throughout the CEO’s tenure, the risk of an exit under pressure from the board and/or shareholders only increases to year four, after which time a forced exit becomes decreasingly likely. Broadly speaking, such a result can be interpreted in two ways. Either boards are placing increased trust in the competence of CEOs who have survived until year four and therefore are more forgiving in light of subsequent poor performance or, alternatively, and less optimistically, CEOs who survive beyond year four are more capable of entrenching themselves in the position, perhaps by filling the board with compliant directors who are less rigorous in their duty as monitors of the CEO’s activity. Thus, the CEO is better able to resist punishment for poor company performance in the later years of their tenure. Our results, favour the latter explanation, as the composition of the board appears to be increasingly important as a predictor variable in the determination of the hazard rate in the later years of a CEO’s tenure. We also find a greater frequency of dismissals in the post‐2000 period. This is perhaps reflective of increased churning following the stock market downturn in 2001 but our reported estimates also provide some support for the view that corporate governance reforms have made it harder for CEOs to resist the consequences of poor share performance. The post‐2000 period is characterised by a higher ratio of outsider directors on the board and the progressive reduction in average contract length has made CEO service contracts cheaper to terminate. These changes, reflecting a succession of revisions to the Combined Code, are suggestive of a positive role for policy in increasing the incidence of performance related departures in UK business. However, the corporate governance reforms appear to have been ineffective in reducing the ability of CEOs to entrench themselves during their tenure. The threat of removal after year four continues to recede at least as fast as it did before the implementation of most of the reforms. Footnotes 1 " See, for instance, ‘The art of the sweetly timed exit’, Financial Times, 19th Aug 2004. 2 " As opposed to alternative modes of exit such as voluntary retirements. 3 " Companies listed on the London Stock Exchange are expected to comply with, or explain their non‐compliance with, the Combined Code (2003). 4 " For example, the Combined Code relies on the boards themselves to determine the independence of their non‐executive directors. If the board is already captured, then it could classify directors as independent to satisfy the provision in the Combined Code, even if such an assessment might be considered dubious. 5 " Note that, at the median, 12 months’ salary is worth approximately double in real terms in 2005 compared to 1995 (Gregory‐Smith, 2007). Nevertheless, this still means a substantial reduction in the total cost of removing a CEO has occurred over this period. 6 " To avoid survivorship bias as far as possible, companies that drop out of the index prior to 2006 are included in our sample unless the company is no longer publicly quoted. 7 " Total shareholder return reflects both the capital gain from the movement in the share price and income from dividends. 8 " The percentage of insiders is defined as the proportion of the board that consists of executive directors and affiliated non‐executive directors. 9 " Some concern has been raised in the literature regarding the reliability of company own assessments (Lin et al., 2003; Young, 2000). To examine whether our results are sensitive to this issue, we re‐estimated the model using Manifest’s assessment of independence, which differs only marginally from that suggested by Lin et al. (2003). The measured impact of insiders is reduced in significance but the results for the other covariates are not qualitatively different from the results given in the article. These results are available from the authors on request. 10 " Indeed, in some cases the CEO continues as CEO of the new company. 11 " Interim appointments are not regarded as an exit type. 12 " The Cox model only concerns itself with the ordering of failure times, not the distribution of failure times. The baseline hazard λ0 is therefore left unestimated. 13 " The model is estimated in STATA using the stcox command. 14 " Age is entered as a squared term beginning at age 50. 15 " In the UK, directors are appointed by the Nomination Committee, a subcommittee of the board, typically led by the chairman or a non‐executive director. However, the CEO or other executive directors may also sit on this committee. 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Dismissed The CEO is officially removed from their position either by shareholders or the Board. Interim Appointment The CEO resigns having been appointed only on a temporary basis following a sudden departure. Internal Position Change A positional change but the CEO effectively continues as CEO. Retired to Part Time Position The CEO retires to become a non‐executive director or Chairman of the same company. Unclassified The CEO exits the Company and there is no evidence to suggest they had resigned under pressure. Event . Definition . Retirement Retirement (including early retirement, illness or death). Headhunted CEO gave notice to immediately pursue a position at another company. Change of Control The CEO exits the sample due to their Company being acquired, wound up or taken private. Ousted The CEO leaves under pressure from the Board or shareholders. Dismissed The CEO is officially removed from their position either by shareholders or the Board. Interim Appointment The CEO resigns having been appointed only on a temporary basis following a sudden departure. Internal Position Change A positional change but the CEO effectively continues as CEO. Retired to Part Time Position The CEO retires to become a non‐executive director or Chairman of the same company. Unclassified The CEO exits the Company and there is no evidence to suggest they had resigned under pressure. Open in new tab Definition of Exit Events Event . Definition . Retirement Retirement (including early retirement, illness or death). Headhunted CEO gave notice to immediately pursue a position at another company. Change of Control The CEO exits the sample due to their Company being acquired, wound up or taken private. Ousted The CEO leaves under pressure from the Board or shareholders. Dismissed The CEO is officially removed from their position either by shareholders or the Board. Interim Appointment The CEO resigns having been appointed only on a temporary basis following a sudden departure. Internal Position Change A positional change but the CEO effectively continues as CEO. Retired to Part Time Position The CEO retires to become a non‐executive director or Chairman of the same company. Unclassified The CEO exits the Company and there is no evidence to suggest they had resigned under pressure. Event . Definition . Retirement Retirement (including early retirement, illness or death). Headhunted CEO gave notice to immediately pursue a position at another company. Change of Control The CEO exits the sample due to their Company being acquired, wound up or taken private. Ousted The CEO leaves under pressure from the Board or shareholders. Dismissed The CEO is officially removed from their position either by shareholders or the Board. Interim Appointment The CEO resigns having been appointed only on a temporary basis following a sudden departure. Internal Position Change A positional change but the CEO effectively continues as CEO. Retired to Part Time Position The CEO retires to become a non‐executive director or Chairman of the same company. Unclassified The CEO exits the Company and there is no evidence to suggest they had resigned under pressure. Open in new tab Author notes " We thank Sarah Wilson and Guy Callaghan of Manifest Information Services Ltd as well as participants at the RES Conference 2008, the Center for Financial Studies Summer School and David Yermack for useful comments. © The Author(s). Journal compilation © Royal Economic Society 2009

Luechinger,, Simon

doi: 10.1111/j.1468-0297.2008.02241.xpmid: N/A

Abstract I use the life satisfaction approach to value air quality, combining individual‐level panel and high‐resolution SO2 data. To avoid simultaneity problems, I construct a novel instrument exploiting the natural experiment created by the mandated scrubber installation at power plants, with wind directions dividing counties into treatment and control groups. I find a negative effect of pollution on well‐being that is larger for instrumental variable than conventional estimates, robust to controls for local unemployment, particulate pollution, reunification effects and rural/urban trends, and larger for environmentalists and predicted risk groups. To calculate total willingness‐to‐pay, the estimates are supplemented by hedonic housing regressions. As soon as I escaped from the oppressive atmosphere of the city, and from the stink of the smoky chimneys, which, being stirred, pour forth, along with a cloud of ashes, all the poisonous fumes they’ve accumulated in their interiors, I perceived at once change in my feelings. Seneca, epistle CIV The introductory quote by Seneca shows that urban air pollution was already a menace in first century Rome. Yet it was the twentieth century that witnessed both the worst air quality and massive improvements. Air pollution could be literally seen and felt, causing the first manmade climate change (a drop in temperature caused by sulphur particles bouncing back sunlight), occasionally forcing motorists to turn headlights on or leave their cars because of impaired visibility, damaging historic buildings and, most importantly, increasing morbidity and mortality. In response, many countries enacted air quality regulations such as the Clean Air Act in the US. Characterised by some scholars as the most significant laws aimed at advancing environmental quality, safety and health (Portney, 1990), these regulations brought about considerable improvements in air quality. However, not in all countries and not for all pollutants does the situation look bright. This raises the questions of how important air quality is for the affected population and, consequently, about benefits of air quality regulations. Traditionally, the benefits of clean air have been assessed with the hedonic method; see Smith and Huang (1995) for a meta‐analysis. The hedonic method can be applied if the public good is weakly complementary to private goods such as housing. Information on public good demand is then embedded in the prices of the private goods. But the hedonic method is afflicted by two well‐known problems: first, if migration is costly, the benefits of clean air are only incompletely capitalised in house prices. Second, individuals’ behaviour in private markets is governed by perceived rather than objective risk. To the extent that they are ignorant about pollution levels and effects, these effects are not reflected in private markets. Moreover, both reasons for incomplete capitalisation can be simultaneously present. Research suggests that hedonic estimates indeed substantially underestimate the benefits of clean air (Bayer et al., 2009; Smith and Huang, 1995); for a discussion see Section 3. I use the life satisfaction approach to assess the costs of air pollution for the exposed population. The approach builds on the recent development of happiness research in economics; for surveys see Clark et al. (2008); Di Tella and MacCulloch (2006); Frey and Stutzer (2002) and Layard (2006). With the life satisfaction approach, self‐reported life satisfaction is regressed on the public good of interest, income and other covariates. Using the coefficients for the public good and income, it is possible to calculate utility constant trade‐off ratios between the public good and income. The life satisfaction approach captures the residual effect of air pollution for which people are not already compensated in the housing market. Air pollution affects individuals’ life satisfaction directly and indirectly through reduced costs of housing. Since the indirect effect is a countervailing, compensating effect, the willingness‐to‐pay (WTP) estimates from the life satisfaction approach have to be combined with WTP estimates from the hedonic method to recover the full WTP for clean air (van Praag and Baarsma, 2005); see also Appendix A.1. If all effects of air pollution are correctly perceived and the equilibrium condition holds, air pollution should not be systematically related to life satisfaction. Thus, the life satisfaction approach also allows to directly test the fundamental assumptions of the hedonic method. The approach has been used to value (the residual effects of) climate (Becchetti et al., 2007; Frijters and van Praag, 1998; Rehdanz and Maddison, 2005), urban air pollution (Welsch, 2002, 2006) and sulphur emissions (Di Tella and MacCulloch, 2007), airport noise nuisance (van Praag and Baarsma, 2005), urban regeneration schemes (Dolan and Metcalfe, 2008), terrorism (Frey et al., 2009) and flood hazards (Luechinger and Raschky, 2009). On a conceptual level, the life satisfaction approach is compared to the standard non‐market valuation techniques in Frey et al. (2009), Kahneman and Sugden (2005), Dolan and Peasgood (2006) and Dolan and Metcalfe (2008). This article has two major objectives. First, I estimate the effect of SO2 concentration on life satisfaction and housing rents using high‐resolution pollution data and a large panel survey for Germany, a country with a large variation in pollution, both across space and over time. In my sample, mean SO2 concentration fell from 43 μg/m3 in the years 1985/6 to 5 μg/m3 in the years 2002/3. Second, using the results of the life satisfaction and hedonic housing regressions, I calculate the total WTP for improvements in air quality as the sum of the estimates based on the two different methods. A comparison of the estimates based on the two methods also reveals what part of the total effect is capitalised in private markets. Estimating the effect of SO2 concentration on life satisfaction and rents is associated with potentially serious simultaneity problems (Bayer et al., 2009; Chay and Greenstone, 2005). While technical progress and air quality regulations are important reasons for improvements in air quality, local economic downturns and declining industrial production are other likely candidates. These simultaneous developments have a countervailing effect on life satisfaction and rents. To avoid this potential source of bias, I use the estimated improvement in air quality caused by the mandated installation of scrubbers at power plants as a novel instrument for air pollution. The instrument is a difference‐in‐difference term with the retrofitting of power plants as treatment and with prevailing wind direction dividing locations into treatment and control groups. The most important finding is that SO2 concentration negatively affects life satisfaction. This indicates that the effects of SO2 are incompletely capitalised in private markets. The magnitude of the effect of SO2 is larger for the instrumental variable estimates than the conventional estimates. This suggests that improved air quality is indeed accompanied by factors with a countervailing effect on life satisfaction. The effect of SO2 concentration is robust to controls for local unemployment, particulate pollution, reunification effects and rural/urban trends. Further, the effect is larger for individuals that are concerned about the environment and that are predicted to suffer adverse health consequences from pollution exposure. The effect of pollution on life satisfaction translates into considerable implicit WTP. The marginal WTP (MWTP) for a reduction of SO2 concentration is in the range between €183 and €313 annually. In my hedonic housing regressions as well, I find a negative effect of SO2 concentration on rents. The MWTP estimates are between €6 and €34 annually. Total MWTP estimates range from €217 to €319 annually. Thus the estimates based on the life satisfaction approach are larger than the estimates based on the hedonic method and only a small proportion of the overall effects of air pollution seems to be capitalised in the housing market. In contrast to previous papers on the relationship between life satisfaction and pollution, the current setting allows me to deal with critical empirical challenges. While the earlier papers provide suggestive evidence, the estimates are afflicted with serious problems associated with the structure of the data (cross‐section) and/or the unit of analysis (country level). Differences in air pollution reflect either different natural or economic conditions or different policy choices. A failure to control for the differences in conditions may bias the estimates in either direction. The notion of choice implies that a failure to include all dimensions of the relevant trade‐off biases the estimates downwards. Improvements in air quality often come at costs, which are difficult to hold constant; if these costs cannot be controlled for, only the net benefit of clean air can be recovered. Of course, the problem of omitted variables is particularly severe in cross‐section analyses (Welsch, 2002). In repeated cross‐sections, time invariant factors can be captured by country fixed effects (Di Tella and MacCulloch, 2007; Welsch, 2006). However, the change in pollution itself indicates that either the conditions or policies have changed as well. These problems can be avoided by focusing on one country. From the point of view of individual regions, the installation of scrubbers at large power plants (the single most important reason for the improvement in air quality) amounts to a natural experiment. Although statutory provisions are the result of a choice at the national level, they disproportionately benefit downwind regions compared to upwind regions.1 Another important problem of the earlier papers is that there is a huge variation in the air quality within countries. Country level data, i.e. data on country‐wide mean concentrations, cannot capture this huge within‐country variation and are a very imprecise measure of individuals’ exposure to air pollution. In addition, the pollution variable in Di Tella and MacCulloch (2007) is SO2 emissions. However, at the country level, emissions and pollution concentration are only weakly correlated. All these problems can be interpreted as measurement errors that bias the pollution coefficient towards zero. By focusing on one country and by using high‐resolution pollution data, I minimise these measurement errors. Further, by using panel data at the individual level, I can control for individual heterogeneity. The remainder of the article is organised as follows. In section 1, I introduce the pollution data and my strategy for instrumenting SO2 concentration. Section 2 presents the panel data and the empirical strategy, the life satisfaction regressions along with various robustness tests as well as my hedonic housing regressions. In section 3, I monetise the effect of air pollution and compare the results based on the two different methods. Section 4 concludes. 1. Pollution: Data, Evolution and Instrument I concentrate on SO2 pollution for three reasons. First, for a long time, SO2 was one of the major pollutants and the primary focus of many regulations. Second, the main emitters of SO2 are large stationary sources. Taken together, these characteristics give rise to a large variation in SO2 concentrations across regions and over time. Third, SO2 contributes to the formation of acid rain, impairs visibility and, most importantly, causes adverse health effects. Consequences of SO2 exposure found in laboratory studies are bronchoconstriction, decrements in respiratory functions, mucus secretion, alterations in pulmonary defences and airway inflammation with consequent coughing, wheezing, shortness of breath and chest tightness. According to epidemiological studies, high SO2 concentrations result in increased morbidity and premature mortality due to cardiovascular and respiratory diseases (Schwartz and Dockery, 1992; Smith et al., 1994). The German federal environmental agency (Umweltbundesamt; hereafter UBA for short) provides data on the annual mean SO2 concentration measured at the monitors belonging to the monitoring networks of the 16 state environmental agencies and the UBA for the years 1985 to 2003. I have SO2 data from 553 monitors or, in individual years, between 196 monitors in 1985 and 416 monitors in 1994. In order to estimate the SO2 concentration at all other locations, I interpolate the monitor readings on a grid with cell size of 1 km2 covering the whole area of Germany. I estimate the value of cell i of the grid as the weighted average over the readings at the 9 nearest monitors j using the inverse cubed distance as weights (method of inverse distance weighting): (1) The parameters have been suggested by the UBA but interpolated values are similar for slightly different parameters. In order to match the pollution data with the survey data, I aggregate the interpolated values on the level of German counties (Kreise and kreisfreie Städte) and estimate annual mean SO2 concentrations.2 The mean SO2 concentration per county for the years 1985, 1990, 1995 and 2000 is depicted in Figure 1. Fig. 1. Open in new tabDownload slide SO2 Concentration in German Counties; 1985, 1990, 1995 and 2000
Notes:≤ 20 μg/m3, 20–40 μg/m3, 40–60 μg/m3, 60–80 μg/m3, 80–100 μg/m3, 100–125 μg/m3, 125–150 μg/m3 and  > 150 μg/m3; cities: D Dortmund in the Ruhr area, K Kassel in Northern Hesse, L Leipzig and B Berlin.
Sources. UBA, own estimates. Fig. 1. Open in new tabDownload slide SO2 Concentration in German Counties; 1985, 1990, 1995 and 2000
Notes:≤ 20 μg/m3, 20–40 μg/m3, 40–60 μg/m3, 60–80 μg/m3, 80–100 μg/m3, 100–125 μg/m3, 125–150 μg/m3 and  > 150 μg/m3; cities: D Dortmund in the Ruhr area, K Kassel in Northern Hesse, L Leipzig and B Berlin.
Sources. UBA, own estimates. The pattern and evolution of SO2 pollution reveals two striking features. First, in the mid‐1980s, pollution was highly concentrated at three hotspots: the Ruhr area in the west, Northern Hesse in the centre and the area around Leipzig in the east, by then all important industrial centres and coal mining areas. Second, air quality improved dramatically between 1985 and 1990 in the FRG and after 1990 in the former GDR. In large part, these improvements reflect the effect of air quality regulations. As a result of an amendment to the large combustion plant ordinance (Grossfeuerungsanlagenverordnung) enacted in 1983, fossil fuel fired power plants had to be retrofitted with flue gas desulphurisation, switch to low sulphur fuel or were subjected to early closure. Time limits were in the range between three and nine years from 1986 on. It is important to note that time limits were statutorily fixed and depended on the capacity of a power plant and its actual emissions but that they were not in the discretion of the operating companies or regulatory bodies. With the unification treaty signed in 1990, power plants in the former GDR were subjected to the same regulations. However, the pattern and evolution of SO2 pollution also points at the potential simultaneity of local economic activity and pollution. The Ruhrgebiet has undergone structural change since 1980. New jobs in the service sector have compensated only partially for job losses in the industrial sector. Similarly, the area around Leipzig is still recovering from the collapse of industrial production after unification. Failure to control for this simultaneity would bias the pollution coefficients in the life satisfaction and hedonic rent regression towards zero or may even lead to perverse results. To address this potential source of bias, I develop a novel instrument that exploits the mandated retrofitting of power plants, coupled with information on the geography of power plants and wind directions. I use the changes in SO2 concentration caused by the large combustion plant ordinance and consequent retrofitting of power plants as an instrument for SO2 pollution. My instrument in later stages of the analysis is the difference‐in‐difference term with desulphurisation at power plants as the treatment and with counties assigned to control and treatment groups according to prevailing wind directions at power plants. In a standard difference‐in‐difference setting, this term would simply be the interaction of a dummy variable with value one if power plant j has installed a scrubber at time t, 1(scrubber)jt, and a dummy variable and with value one if county c lies downwind of power plant j, 1(downwind)cj. Hence, I could explain the SO2 concentration in county c at time t, Pct, as follows: (2) where χc and τt are county and time specific effects respectively. I depart from this idealised setting in three respects. First, treatment and control group status is a matter of degree rather than one of kind. Although everywhere there is a predominant wind direction distinguishing counties into windward and leeward counties, wind directions can change. Therefore, the treatment group variable, f(Rcj), is the frequency with which county c lies downwind of power plant j and the difference‐in‐difference term becomes 1(scrubber)jtf(Rcj). Second, since I consider all power plants j and all counties c simultaneously, the treatment variable is a weighted sum of desulphurisation at all power plants. The weights are the uncleaned, pre‐desulphurisation, emissions of the plants, Ej, and a distance decay function, g(Dcj). The new difference‐in‐difference term thus is . The distance decay is modelled as an exponential curve with an implied characteristic decay distance of 480 km, g(Dcj) = exp(−2.1E − 6·Dcj), as suggested by field studies (Schwartz, 1989; Summers and Fricke, 1989). The decrease in concentration with distance captures both removal of material by deposition and dilution or dispersion caused by lateral or vertical mixing of air. Third, some power plants shut down, others are newly built. Therefore, it is necessary to control for changes in the power plant population by introducing an additional term in 2 for the weighted sum of uncleaned emissions, , where 1(active)jt is a dummy variable indicating whether power plant j is active at time t. Taking all three departures into account, my difference‐in‐difference setting thus becomes: 3 In (3), the second term on the right‐hand side denotes the weighted sum of uncleaned SO2 emissions, the third term denotes the weighted sum of retained SO2 emissions. In later stages of the analysis, the weighted sum of retained SO2 emissions – conditional on the weighted sum of uncleaned SO2 emissions, county and time specific effects as well as on all the control variables introduced in Section 2– is my instrument for air pollution. The identifying assumption is that there is no systematic difference in the effect of retrofitting of power plants on reported life satisfaction and rents between upwind and downwind counties except through the effect on pollution. I would also get to the specification in (3), if I started with the simple pollution model in (4) and then rearranged terms: (4) Equation (4) shows that I can estimate the average separation efficiency of scrubbers, α2, by dividing the coefficient for the weighted sum of retained SO2 emissions by the coefficient for the weighted sum of uncleaned SO2 emissions. As can be seen from (3), I require information on the pre‐desulphurisation SO2 emissions of the power plants, information on when plants installed scrubbers, wind directions at the plants as well as direction and distance vectors between counties and plants. I have information on the launching year, year of desulphurisation, the year the unit was shut down, capacity, fuel and fuel efficiency for 303 fossil fuel fired generating units, i.e. all units active between 1985 and 2003 with an electricity capacity of 100 MW and more. The data are from the UBA, information published by the operating companies and the technical literature, a survey mailed to operating companies and statutory provisions (details in Appendix A.2.). I georeference power plants using a route planner. The locations of the power plants are depicted in Figure 2(a). Annual SO2 emissions can be estimated using emission factors published in the literature and the plants’ characteristics. Frequencies of wind directions in 12 30‐degree sectors measured at 43 wind stations describe the wind situation at the power plants. I use the closest wind station for each plant, drawn from a sample of wind stations that was originally larger. The stations are shown in Figure 2(b). The predominant wind direction is west‐southwest. In order to relate the data at the plant level with the pollution data at the county level, I calculate the Euclidean distance and direction between every power plant and every county. Fig. 2. Open in new tabDownload slide Locations of Fossil Fuel Fired Power Plants and Wind Stations
Sources. UBA, information published by operating companies, technical literature, route planner and Traup and Kruse (1996). Fig. 2. Open in new tabDownload slide Locations of Fossil Fuel Fired Power Plants and Wind Stations
Sources. UBA, information published by operating companies, technical literature, route planner and Traup and Kruse (1996). Table 1 presents the results of the regression in (3). As expected, the sum of uncleaned SO2 emissions at power plants increases and the sum of retained emission decreases, measured air pollution. I estimate a separation efficiency of 69% using the coefficients for the uncleaned and the retained emissions. I can compare the estimated separation efficiency with actual separation efficiencies. Statutory provisions in Germany require a separation efficiency of 60% at the smallest units and more efficient scrubbers at larger units; separation efficiency at the largest power plants lies typically in the range of 90% to 99%. Hence, the estimated separation is close to, but marginally below, actual separation efficiencies. Table 1 
Effect of Power Plant Emissions and Flue Gas Desulphurisation on SO2 Concentration Dependent variable . SO2(μg/m3) concentration . Coef. . t‐value . Emissions from power plants  Weighted sum of uncleaned SO2 emissions 1.4E‐5** 17.64  Weighted sum of retained SO2 emissions −9.9E‐6** −36.46 County specific effects Yes Year specific effects Yes Number of observations 8,455 Prob > F 0.000 R2 0.672 ΔR2 due to inclusion of emission terms 0.065 Dependent variable . SO2(μg/m3) concentration . Coef. . t‐value . Emissions from power plants  Weighted sum of uncleaned SO2 emissions 1.4E‐5** 17.64  Weighted sum of retained SO2 emissions −9.9E‐6** −36.46 County specific effects Yes Year specific effects Yes Number of observations 8,455 Prob > F 0.000 R2 0.672 ΔR2 due to inclusion of emission terms 0.065 . Coef. . St. Err. . Estimated separation efficiency −0.686** 0.042 . Coef. . St. Err. . Estimated separation efficiency −0.686** 0.042 Notes. OLS estimates; **denotes significance at the 99% level. The standard error for the effect of flue gas desulphurisation is estimated using the delta method. Open in new tab Table 1 
Effect of Power Plant Emissions and Flue Gas Desulphurisation on SO2 Concentration Dependent variable . SO2(μg/m3) concentration . Coef. . t‐value . Emissions from power plants  Weighted sum of uncleaned SO2 emissions 1.4E‐5** 17.64  Weighted sum of retained SO2 emissions −9.9E‐6** −36.46 County specific effects Yes Year specific effects Yes Number of observations 8,455 Prob > F 0.000 R2 0.672 ΔR2 due to inclusion of emission terms 0.065 Dependent variable . SO2(μg/m3) concentration . Coef. . t‐value . Emissions from power plants  Weighted sum of uncleaned SO2 emissions 1.4E‐5** 17.64  Weighted sum of retained SO2 emissions −9.9E‐6** −36.46 County specific effects Yes Year specific effects Yes Number of observations 8,455 Prob > F 0.000 R2 0.672 ΔR2 due to inclusion of emission terms 0.065 . Coef. . St. Err. . Estimated separation efficiency −0.686** 0.042 . Coef. . St. Err. . Estimated separation efficiency −0.686** 0.042 Notes. OLS estimates; **denotes significance at the 99% level. The standard error for the effect of flue gas desulphurisation is estimated using the delta method. Open in new tab The reason for instrumenting SO2 concentration is its potential correlation with local economic activity. In order to assess the importance of this issue and to provide support for my instrumenting strategy, Table 2 presents the results from ‘pseudo first stage’ regressions, i.e. from regressions of important economic outcome variables on SO2 concentration and on my instrument as well as on the full set of control variables introduced in Section 2. The economic outcomes on the left‐hand side are the natural log of a respondent’s household labour income, household pre‐government income (including asset flows, private retirement income and private transfers) and the respondent’s unemployment status. Table 2 
Partial Correlations Between Economic Outcomes and SO2 and Predicted Δ SO2 Dependent variable . Unemployed . ln(labour income) . ln(pre govt. income) . Coef. . t‐value . Coef. . t‐value . Coef. . t‐value . SO2(μg/m3) −4.9E‐20(*) −1.74 0.002* 2.12 0.001 1.57 Control variables Yes (see Table 4) Yes (see Table 4) Yes (see Table 4) Predicted ΔSO2 2.2E‐20 0.53 −2.8E‐4 −0.39 −0.001 −0.82 Control variables Yes (see Table 4) Yes (see Table 4) Yes (see Table 4) Dependent variable . Unemployed . ln(labour income) . ln(pre govt. income) . Coef. . t‐value . Coef. . t‐value . Coef. . t‐value . SO2(μg/m3) −4.9E‐20(*) −1.74 0.002* 2.12 0.001 1.57 Control variables Yes (see Table 4) Yes (see Table 4) Yes (see Table 4) Predicted ΔSO2 2.2E‐20 0.53 −2.8E‐4 −0.39 −0.001 −0.82 Control variables Yes (see Table 4) Yes (see Table 4) Yes (see Table 4) Notes. Coefficients and t‐values are from ‘pseudo first stage’ regressions analogous to the ones in Table 4. OLS estimates. *denotes significance at the 95% level, and (*) at the 90% level. Open in new tab Table 2 
Partial Correlations Between Economic Outcomes and SO2 and Predicted Δ SO2 Dependent variable . Unemployed . ln(labour income) . ln(pre govt. income) . Coef. . t‐value . Coef. . t‐value . Coef. . t‐value . SO2(μg/m3) −4.9E‐20(*) −1.74 0.002* 2.12 0.001 1.57 Control variables Yes (see Table 4) Yes (see Table 4) Yes (see Table 4) Predicted ΔSO2 2.2E‐20 0.53 −2.8E‐4 −0.39 −0.001 −0.82 Control variables Yes (see Table 4) Yes (see Table 4) Yes (see Table 4) Dependent variable . Unemployed . ln(labour income) . ln(pre govt. income) . Coef. . t‐value . Coef. . t‐value . Coef. . t‐value . SO2(μg/m3) −4.9E‐20(*) −1.74 0.002* 2.12 0.001 1.57 Control variables Yes (see Table 4) Yes (see Table 4) Yes (see Table 4) Predicted ΔSO2 2.2E‐20 0.53 −2.8E‐4 −0.39 −0.001 −0.82 Control variables Yes (see Table 4) Yes (see Table 4) Yes (see Table 4) Notes. Coefficients and t‐values are from ‘pseudo first stage’ regressions analogous to the ones in Table 4. OLS estimates. *denotes significance at the 95% level, and (*) at the 90% level. Open in new tab Table 4 
Basic Results: Effect of SO2 Pollution on Life Satisfaction Dependent variable . I . II . Life satisfaction . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.005** −5.86 −0.008* −2.46 HH income  ln(post govt. income) 0.548** 8.36 0.548** 8.36  HH size1/2 −0.445** −9.67 −0.448** −9.73 Personal characteristics  Age below 21 Reference group Reference group  Age 21–30 −0.076** −3.03 −0.073** −2.91  Age 31–40 −0.051 −1.57 −0.050 −1.53  Age 41–50 −0.055 −1.38 −0.053 −1.32  Age 51–60 5.E‐4 0.01 0.002 0.04  Age 61–70 0.233** 4.18 0.234** 4.19  Age above 70 0.146* 2.23 0.146* 2.24  Not disabled Reference group Reference group  Disabled −0.232** −10.62 −0.233** −10.68  Single, no partner Reference group Reference group  Single, with partner 0.212** 7.20 0.210** 7.13  Married 0.255** 8.46 0.255** 8.44  Separated, no partner −0.218** −3.60 −0.220** −3.64  Separated, with partner 0.120 1.24 0.120 1.24  Divorced, no partner 0.012 0.26 0.011 0.22  Divorced, with partner 0.339** 6.41 0.340** 6.43  Widowed, no partner −0.260** −5.01 −0.261** −5.03  Widowed, with partner 0.299** 3.08 0.297** 3.05  Spouse in home country −0.066 −0.65 −0.069 −0.68  No children in HH Reference group Reference group  Children in HH 0.126** 7.19 0.127** 7.22  German citizen Reference group Reference group  EU citizen −0.211* −2.11 −0.212* −2.12  Non‐EU foreigner −0.085 −1.46 −0.084 −1.42  Not working Reference group Reference group  Retired 0.097** 3.95 0.097** 3.92  In education 0.229** 6.87 0.228** 6.86  Maternity leave 0.142** 4.08 0.144** 4.13  Military, community service −0.004 −0.07 −0.004 −0.08  Unemployed −0.418** −16.73 −0.418** −16.72  Sometimes working 0.005 0.12 0.007 0.16  Full‐time employment 0.140** 4.79 0.142** 4.84  Part‐time employment 0.003 0.10 0.003 0.13  Vocational training 0.070 1.05 0.073 1.08  Other employment −0.042 −1.07 −0.041 −1.05  Blue collar worker Reference group Reference group  Trainee 0.147* 2.44 0.146* 2.43  Public service employee −0.054 −1.33 −0.052 −1.28  White collar worker 0.012 0.76 0.012 0.77  Managerial position 0.078** 3.12 0.080** 3.17  Temporary employment −0.028 −1.29 −0.028 −1.31  Permanent employment 0.042** 3.31 0.043** 3.38  Job tenure −0.004** −5.26 −0.004** −5.33  Actual working hours 1.E‐4* 2.26 9.E‐5* 2.20  First interview 0.172** 9.89 0.179** 9.62  Second interview 0.045** 2.83 0.055** 2.88  Third and later interviews Reference group Reference group City, district size  Less than 2,000 Reference group Reference group  Less than 20,000 0.016 0.48 0.016 0.47  Less than 100,000 0.047 1.12 0.047 1.12  Less than 500,000 −0.004 −0.07 −0.004 −0.05  Over 500,000 0.026 0.34 0.027 0.36 Predicted uncleaned emissions  Predicted uncleaned emissions −0.004* −2.49 State specific time trends Yes Yes Year specific effects Yes Yes Individual specific effects Yes Yes Prob > F 0.000 0.000 R2 within 0.029 0.029 R2 between 0.025 0.050 R2 overall 0.029 0.044 Dependent variable . I . II . Life satisfaction . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.005** −5.86 −0.008* −2.46 HH income  ln(post govt. income) 0.548** 8.36 0.548** 8.36  HH size1/2 −0.445** −9.67 −0.448** −9.73 Personal characteristics  Age below 21 Reference group Reference group  Age 21–30 −0.076** −3.03 −0.073** −2.91  Age 31–40 −0.051 −1.57 −0.050 −1.53  Age 41–50 −0.055 −1.38 −0.053 −1.32  Age 51–60 5.E‐4 0.01 0.002 0.04  Age 61–70 0.233** 4.18 0.234** 4.19  Age above 70 0.146* 2.23 0.146* 2.24  Not disabled Reference group Reference group  Disabled −0.232** −10.62 −0.233** −10.68  Single, no partner Reference group Reference group  Single, with partner 0.212** 7.20 0.210** 7.13  Married 0.255** 8.46 0.255** 8.44  Separated, no partner −0.218** −3.60 −0.220** −3.64  Separated, with partner 0.120 1.24 0.120 1.24  Divorced, no partner 0.012 0.26 0.011 0.22  Divorced, with partner 0.339** 6.41 0.340** 6.43  Widowed, no partner −0.260** −5.01 −0.261** −5.03  Widowed, with partner 0.299** 3.08 0.297** 3.05  Spouse in home country −0.066 −0.65 −0.069 −0.68  No children in HH Reference group Reference group  Children in HH 0.126** 7.19 0.127** 7.22  German citizen Reference group Reference group  EU citizen −0.211* −2.11 −0.212* −2.12  Non‐EU foreigner −0.085 −1.46 −0.084 −1.42  Not working Reference group Reference group  Retired 0.097** 3.95 0.097** 3.92  In education 0.229** 6.87 0.228** 6.86  Maternity leave 0.142** 4.08 0.144** 4.13  Military, community service −0.004 −0.07 −0.004 −0.08  Unemployed −0.418** −16.73 −0.418** −16.72  Sometimes working 0.005 0.12 0.007 0.16  Full‐time employment 0.140** 4.79 0.142** 4.84  Part‐time employment 0.003 0.10 0.003 0.13  Vocational training 0.070 1.05 0.073 1.08  Other employment −0.042 −1.07 −0.041 −1.05  Blue collar worker Reference group Reference group  Trainee 0.147* 2.44 0.146* 2.43  Public service employee −0.054 −1.33 −0.052 −1.28  White collar worker 0.012 0.76 0.012 0.77  Managerial position 0.078** 3.12 0.080** 3.17  Temporary employment −0.028 −1.29 −0.028 −1.31  Permanent employment 0.042** 3.31 0.043** 3.38  Job tenure −0.004** −5.26 −0.004** −5.33  Actual working hours 1.E‐4* 2.26 9.E‐5* 2.20  First interview 0.172** 9.89 0.179** 9.62  Second interview 0.045** 2.83 0.055** 2.88  Third and later interviews Reference group Reference group City, district size  Less than 2,000 Reference group Reference group  Less than 20,000 0.016 0.48 0.016 0.47  Less than 100,000 0.047 1.12 0.047 1.12  Less than 500,000 −0.004 −0.07 −0.004 −0.05  Over 500,000 0.026 0.34 0.027 0.36 Predicted uncleaned emissions  Predicted uncleaned emissions −0.004* −2.49 State specific time trends Yes Yes Year specific effects Yes Yes Individual specific effects Yes Yes Prob > F 0.000 0.000 R2 within 0.029 0.029 R2 between 0.025 0.050 R2 overall 0.029 0.044 . Coef. . t‐value . Coef. . t‐value . (b) First stage regressions Dependent variable SO2(μg/m3) Excluded instruments  Predicted ΔSO2 −0.291** −16.87  Predicted income 0.019 1.44  Tenure income earner −0.011* −2.38 Predicted uncleaned emissions  Predicted uncleaned emissions 0.080(*) 1.68 Included instruments Yes Dependent variable ln(post govt. income) Excluded instruments  Predicted ΔSO2 2.E‐4 1.07  Predicted income 0.023** 34.09 0.023** 34.06  Tenure income earner 0.005** 24.99 0.005** 25.09 Included instruments Yes Yes Number of observations 186,628 186,628 Number of individuals 29,246 29,246 Avg. no. of obs. per individual 6.4 6.4 Number of clusters 7,118 7,118 Shea’s partial R2 for SO2 0.061 Bound et al. partial R2 0.061 F‐statistics of excluded instruments 99.54 Shea’s partial R2 for ln(post govt. income) 0.028 0.028 Bound et al. partial R2 0.028 0.028 F‐statistics of excluded instruments 1074.69 718.01 Anderson LR statistic (p‐value) 0.000 0.000 Hansen’s J statistic (p‐value) 0.195 0.214 . Coef. . t‐value . Coef. . t‐value . (b) First stage regressions Dependent variable SO2(μg/m3) Excluded instruments  Predicted ΔSO2 −0.291** −16.87  Predicted income 0.019 1.44  Tenure income earner −0.011* −2.38 Predicted uncleaned emissions  Predicted uncleaned emissions 0.080(*) 1.68 Included instruments Yes Dependent variable ln(post govt. income) Excluded instruments  Predicted ΔSO2 2.E‐4 1.07  Predicted income 0.023** 34.09 0.023** 34.06  Tenure income earner 0.005** 24.99 0.005** 25.09 Included instruments Yes Yes Number of observations 186,628 186,628 Number of individuals 29,246 29,246 Avg. no. of obs. per individual 6.4 6.4 Number of clusters 7,118 7,118 Shea’s partial R2 for SO2 0.061 Bound et al. partial R2 0.061 F‐statistics of excluded instruments 99.54 Shea’s partial R2 for ln(post govt. income) 0.028 0.028 Bound et al. partial R2 0.028 0.028 F‐statistics of excluded instruments 1074.69 718.01 Anderson LR statistic (p‐value) 0.000 0.000 Hansen’s J statistic (p‐value) 0.195 0.214 Notes. IV estimates with individual fixed effects; SO2 concentration is instrumented with the effect of flue gas desulphurisation at power plants estimated; household income is instrumented with the sum of predicted incomes of the household members and job tenure of household of the primary/secondary wage earner in specifications. Standard errors are adjusted for clustering on county and year level. **denotes significance at the 99% level, *at the 95% level, and (*) at the 90% level. Open in new tab Table 4 
Basic Results: Effect of SO2 Pollution on Life Satisfaction Dependent variable . I . II . Life satisfaction . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.005** −5.86 −0.008* −2.46 HH income  ln(post govt. income) 0.548** 8.36 0.548** 8.36  HH size1/2 −0.445** −9.67 −0.448** −9.73 Personal characteristics  Age below 21 Reference group Reference group  Age 21–30 −0.076** −3.03 −0.073** −2.91  Age 31–40 −0.051 −1.57 −0.050 −1.53  Age 41–50 −0.055 −1.38 −0.053 −1.32  Age 51–60 5.E‐4 0.01 0.002 0.04  Age 61–70 0.233** 4.18 0.234** 4.19  Age above 70 0.146* 2.23 0.146* 2.24  Not disabled Reference group Reference group  Disabled −0.232** −10.62 −0.233** −10.68  Single, no partner Reference group Reference group  Single, with partner 0.212** 7.20 0.210** 7.13  Married 0.255** 8.46 0.255** 8.44  Separated, no partner −0.218** −3.60 −0.220** −3.64  Separated, with partner 0.120 1.24 0.120 1.24  Divorced, no partner 0.012 0.26 0.011 0.22  Divorced, with partner 0.339** 6.41 0.340** 6.43  Widowed, no partner −0.260** −5.01 −0.261** −5.03  Widowed, with partner 0.299** 3.08 0.297** 3.05  Spouse in home country −0.066 −0.65 −0.069 −0.68  No children in HH Reference group Reference group  Children in HH 0.126** 7.19 0.127** 7.22  German citizen Reference group Reference group  EU citizen −0.211* −2.11 −0.212* −2.12  Non‐EU foreigner −0.085 −1.46 −0.084 −1.42  Not working Reference group Reference group  Retired 0.097** 3.95 0.097** 3.92  In education 0.229** 6.87 0.228** 6.86  Maternity leave 0.142** 4.08 0.144** 4.13  Military, community service −0.004 −0.07 −0.004 −0.08  Unemployed −0.418** −16.73 −0.418** −16.72  Sometimes working 0.005 0.12 0.007 0.16  Full‐time employment 0.140** 4.79 0.142** 4.84  Part‐time employment 0.003 0.10 0.003 0.13  Vocational training 0.070 1.05 0.073 1.08  Other employment −0.042 −1.07 −0.041 −1.05  Blue collar worker Reference group Reference group  Trainee 0.147* 2.44 0.146* 2.43  Public service employee −0.054 −1.33 −0.052 −1.28  White collar worker 0.012 0.76 0.012 0.77  Managerial position 0.078** 3.12 0.080** 3.17  Temporary employment −0.028 −1.29 −0.028 −1.31  Permanent employment 0.042** 3.31 0.043** 3.38  Job tenure −0.004** −5.26 −0.004** −5.33  Actual working hours 1.E‐4* 2.26 9.E‐5* 2.20  First interview 0.172** 9.89 0.179** 9.62  Second interview 0.045** 2.83 0.055** 2.88  Third and later interviews Reference group Reference group City, district size  Less than 2,000 Reference group Reference group  Less than 20,000 0.016 0.48 0.016 0.47  Less than 100,000 0.047 1.12 0.047 1.12  Less than 500,000 −0.004 −0.07 −0.004 −0.05  Over 500,000 0.026 0.34 0.027 0.36 Predicted uncleaned emissions  Predicted uncleaned emissions −0.004* −2.49 State specific time trends Yes Yes Year specific effects Yes Yes Individual specific effects Yes Yes Prob > F 0.000 0.000 R2 within 0.029 0.029 R2 between 0.025 0.050 R2 overall 0.029 0.044 Dependent variable . I . II . Life satisfaction . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.005** −5.86 −0.008* −2.46 HH income  ln(post govt. income) 0.548** 8.36 0.548** 8.36  HH size1/2 −0.445** −9.67 −0.448** −9.73 Personal characteristics  Age below 21 Reference group Reference group  Age 21–30 −0.076** −3.03 −0.073** −2.91  Age 31–40 −0.051 −1.57 −0.050 −1.53  Age 41–50 −0.055 −1.38 −0.053 −1.32  Age 51–60 5.E‐4 0.01 0.002 0.04  Age 61–70 0.233** 4.18 0.234** 4.19  Age above 70 0.146* 2.23 0.146* 2.24  Not disabled Reference group Reference group  Disabled −0.232** −10.62 −0.233** −10.68  Single, no partner Reference group Reference group  Single, with partner 0.212** 7.20 0.210** 7.13  Married 0.255** 8.46 0.255** 8.44  Separated, no partner −0.218** −3.60 −0.220** −3.64  Separated, with partner 0.120 1.24 0.120 1.24  Divorced, no partner 0.012 0.26 0.011 0.22  Divorced, with partner 0.339** 6.41 0.340** 6.43  Widowed, no partner −0.260** −5.01 −0.261** −5.03  Widowed, with partner 0.299** 3.08 0.297** 3.05  Spouse in home country −0.066 −0.65 −0.069 −0.68  No children in HH Reference group Reference group  Children in HH 0.126** 7.19 0.127** 7.22  German citizen Reference group Reference group  EU citizen −0.211* −2.11 −0.212* −2.12  Non‐EU foreigner −0.085 −1.46 −0.084 −1.42  Not working Reference group Reference group  Retired 0.097** 3.95 0.097** 3.92  In education 0.229** 6.87 0.228** 6.86  Maternity leave 0.142** 4.08 0.144** 4.13  Military, community service −0.004 −0.07 −0.004 −0.08  Unemployed −0.418** −16.73 −0.418** −16.72  Sometimes working 0.005 0.12 0.007 0.16  Full‐time employment 0.140** 4.79 0.142** 4.84  Part‐time employment 0.003 0.10 0.003 0.13  Vocational training 0.070 1.05 0.073 1.08  Other employment −0.042 −1.07 −0.041 −1.05  Blue collar worker Reference group Reference group  Trainee 0.147* 2.44 0.146* 2.43  Public service employee −0.054 −1.33 −0.052 −1.28  White collar worker 0.012 0.76 0.012 0.77  Managerial position 0.078** 3.12 0.080** 3.17  Temporary employment −0.028 −1.29 −0.028 −1.31  Permanent employment 0.042** 3.31 0.043** 3.38  Job tenure −0.004** −5.26 −0.004** −5.33  Actual working hours 1.E‐4* 2.26 9.E‐5* 2.20  First interview 0.172** 9.89 0.179** 9.62  Second interview 0.045** 2.83 0.055** 2.88  Third and later interviews Reference group Reference group City, district size  Less than 2,000 Reference group Reference group  Less than 20,000 0.016 0.48 0.016 0.47  Less than 100,000 0.047 1.12 0.047 1.12  Less than 500,000 −0.004 −0.07 −0.004 −0.05  Over 500,000 0.026 0.34 0.027 0.36 Predicted uncleaned emissions  Predicted uncleaned emissions −0.004* −2.49 State specific time trends Yes Yes Year specific effects Yes Yes Individual specific effects Yes Yes Prob > F 0.000 0.000 R2 within 0.029 0.029 R2 between 0.025 0.050 R2 overall 0.029 0.044 . Coef. . t‐value . Coef. . t‐value . (b) First stage regressions Dependent variable SO2(μg/m3) Excluded instruments  Predicted ΔSO2 −0.291** −16.87  Predicted income 0.019 1.44  Tenure income earner −0.011* −2.38 Predicted uncleaned emissions  Predicted uncleaned emissions 0.080(*) 1.68 Included instruments Yes Dependent variable ln(post govt. income) Excluded instruments  Predicted ΔSO2 2.E‐4 1.07  Predicted income 0.023** 34.09 0.023** 34.06  Tenure income earner 0.005** 24.99 0.005** 25.09 Included instruments Yes Yes Number of observations 186,628 186,628 Number of individuals 29,246 29,246 Avg. no. of obs. per individual 6.4 6.4 Number of clusters 7,118 7,118 Shea’s partial R2 for SO2 0.061 Bound et al. partial R2 0.061 F‐statistics of excluded instruments 99.54 Shea’s partial R2 for ln(post govt. income) 0.028 0.028 Bound et al. partial R2 0.028 0.028 F‐statistics of excluded instruments 1074.69 718.01 Anderson LR statistic (p‐value) 0.000 0.000 Hansen’s J statistic (p‐value) 0.195 0.214 . Coef. . t‐value . Coef. . t‐value . (b) First stage regressions Dependent variable SO2(μg/m3) Excluded instruments  Predicted ΔSO2 −0.291** −16.87  Predicted income 0.019 1.44  Tenure income earner −0.011* −2.38 Predicted uncleaned emissions  Predicted uncleaned emissions 0.080(*) 1.68 Included instruments Yes Dependent variable ln(post govt. income) Excluded instruments  Predicted ΔSO2 2.E‐4 1.07  Predicted income 0.023** 34.09 0.023** 34.06  Tenure income earner 0.005** 24.99 0.005** 25.09 Included instruments Yes Yes Number of observations 186,628 186,628 Number of individuals 29,246 29,246 Avg. no. of obs. per individual 6.4 6.4 Number of clusters 7,118 7,118 Shea’s partial R2 for SO2 0.061 Bound et al. partial R2 0.061 F‐statistics of excluded instruments 99.54 Shea’s partial R2 for ln(post govt. income) 0.028 0.028 Bound et al. partial R2 0.028 0.028 F‐statistics of excluded instruments 1074.69 718.01 Anderson LR statistic (p‐value) 0.000 0.000 Hansen’s J statistic (p‐value) 0.195 0.214 Notes. IV estimates with individual fixed effects; SO2 concentration is instrumented with the effect of flue gas desulphurisation at power plants estimated; household income is instrumented with the sum of predicted incomes of the household members and job tenure of household of the primary/secondary wage earner in specifications. Standard errors are adjusted for clustering on county and year level. **denotes significance at the 99% level, *at the 95% level, and (*) at the 90% level. Open in new tab Although the ultimate source of concern is a correlation between air pollution and unobserved economic outcomes, Table 2 confirms the conjecture that pollution and local economic activity are correlated and supports my instrumenting approach: while SO2 concentration is correlated with unemployment and labour income, my instrument is not. Pre‐government income is neither correlated with SO2 concentration nor with the instrument. The actual first stage regressions in Section 2 show that the instrument is also uncorrelated with post‐government income. 2. Effects of Pollution on Life Satisfaction and Rental Prices 2.1. Data In order to examine the impact of air pollution on life satisfaction and housing rents, I use the German Socio‐Economic Panel (GSOEP) containing information on individual life satisfaction and rents. The baseline life satisfaction regressions are based on a panel for the period 1985–2003 consisting of 29,246 individuals who remain in the panel for 6.4 years on average. By combining household identifiers and the date the household moved to the current dwelling, I can construct unique dwelling identifiers and thus a panel at the dwelling level. Since the information is gathered at the level of households and not at the level of dwellings, the same dwelling can have different dwelling numbers if it is occupied by different GSOEP‐households. However, it is important for the identification of pollution effects that it is not possible for two different dwellings to have the same dwelling identifier. The hedonic housing regressions are based on a panel for the period 1985–2003 consisting of 17,294 housing units with an average length in the panel of 3.7 years. I relate the survey data to the pollution data at the county level. County mergers in East Germany reduced the number of counties from 543 in 1993 to 439 in 2001. As my polygon data describe the boundaries of the 445 existing counties in 1996, I assign the same SO2 concentration to several counties in earlier years and calculate area‐weighted averages for later years. 2.2. Effects on Life Satisfaction 2.2.1. Empirical strategy and explanatory variables The main variables are individual life satisfaction, SO2 concentration and income. Summary statistics for these variables are provided in Table 3(a). The GSOEP elicits individual life satisfaction with the following question: ‘How satisfied are you at present with your life, all things considered?’. Responses run from 0 (completely dissatisfied) to 10 (completely satisfied). Table 3 
Summary Statistics of Main Variables and Functional Form of SO2 Variable . Mean . Median . Std. Dev. . (a) Summary statistics Individual panel (186,628 observations)  Life satisfaction 7.07 7.00 1.75  SO2(μg/m3) 16.68 9.71 17.67  ln(post govt. income) 10.20 10.25 0.59 Housing panel (64,672 observations)  ln(rent) 5.75 5.83 0.65  SO2(μg/m3) 17.70 9.55 19.85 . Mean . Median . Std. Dev. . (a) Summary statistics Individual panel (186,628 observations)  Life satisfaction 7.07 7.00 1.75  SO2(μg/m3) 16.68 9.71 17.67  ln(post govt. income) 10.20 10.25 0.59 Housing panel (64,672 observations)  ln(rent) 5.75 5.83 0.65  SO2(μg/m3) 17.70 9.55 19.85 . M.E. at mean . LR statistics . P > χ2 . (b) Functional form of SO2 variable Functional form  CRRA function with ρ = −0.2 −0.004 2.17 0.140  2nd order polynomial −0.005 0.58 0.446  Linear −0.005 – – . M.E. at mean . LR statistics . P > χ2 . (b) Functional form of SO2 variable Functional form  CRRA function with ρ = −0.2 −0.004 2.17 0.140  2nd order polynomial −0.005 0.58 0.446  Linear −0.005 – – Notes.‘M.E. at mean’ is the marginal effect of SO2 on life satisfaction at its sample mean of 16.68 μg/m3. The likelihood ratio (LR) statistics is asymptotically distributed as χ2 with one degree of freedom. Open in new tab Table 3 
Summary Statistics of Main Variables and Functional Form of SO2 Variable . Mean . Median . Std. Dev. . (a) Summary statistics Individual panel (186,628 observations)  Life satisfaction 7.07 7.00 1.75  SO2(μg/m3) 16.68 9.71 17.67  ln(post govt. income) 10.20 10.25 0.59 Housing panel (64,672 observations)  ln(rent) 5.75 5.83 0.65  SO2(μg/m3) 17.70 9.55 19.85 . Mean . Median . Std. Dev. . (a) Summary statistics Individual panel (186,628 observations)  Life satisfaction 7.07 7.00 1.75  SO2(μg/m3) 16.68 9.71 17.67  ln(post govt. income) 10.20 10.25 0.59 Housing panel (64,672 observations)  ln(rent) 5.75 5.83 0.65  SO2(μg/m3) 17.70 9.55 19.85 . M.E. at mean . LR statistics . P > χ2 . (b) Functional form of SO2 variable Functional form  CRRA function with ρ = −0.2 −0.004 2.17 0.140  2nd order polynomial −0.005 0.58 0.446  Linear −0.005 – – . M.E. at mean . LR statistics . P > χ2 . (b) Functional form of SO2 variable Functional form  CRRA function with ρ = −0.2 −0.004 2.17 0.140  2nd order polynomial −0.005 0.58 0.446  Linear −0.005 – – Notes.‘M.E. at mean’ is the marginal effect of SO2 on life satisfaction at its sample mean of 16.68 μg/m3. The likelihood ratio (LR) statistics is asymptotically distributed as χ2 with one degree of freedom. Open in new tab Since I have no a priori reason to adopt a specific functional form for the pollution variable, I follow an approach proposed by Layard et al. (2008) for finding the correct functional form of the income variable. The functional form is determined by using a grid search over a range of parameter values of the following constant relative risk aversion (CRRA) function: (5) This flexible form embeds convex, linear and concave functions. I compute the log likelihood for different values of the coefficient of risk aversion over the range from −2.0 to 2.0 in steps of 0.1. The log likelihood is maximised at ρ = −0.2. Thus, the functional form is slightly convex but remarkably close to linear. A log likelihood ratio test cannot reject the null of a linear relationship (see Table 3(b)). Similarly, a log likelihood ratio test does not reject the model with only a linear term in favour of a model with an additional quadratic term. Therefore, I will model pollution linearly but also report how benefit estimates change if a CRRA function with ρ = −0.2 is used instead. The other important explanatory variable is post‐government household income. Its coefficient is later used for monetisation. The variable is the sum of total household income from labour earnings (including bonuses etc.), asset flows, private retirement income, public and private transfers and social security pensions minus total household taxes. Except estimates of tax burden, which are based on tax calculation routines, all other components are actually received incomes as declared in the survey of the subsequent year. Thus, income information for households exiting the panel in the following year is not available. Further, the information is missing for East Germany in the year 1990. Estimating the effect of income on life satisfaction is afflicted by serious endogeneity and omitted variables problems. Happy people earn more and time‐varying factors may lead to both greater satisfaction and higher income (Clark et al., 2008; Gardner and Oswald, 2007). A related problem is that costs of income generation such as working hours, stress, health risks, etc. are inherently difficult to control for. Omission of such factors induces downward biased estimates. To address these problems, I instrument income with a predictor of household income and with job tenure of the main income earner or, if the respondent is the main income earner, the secondary income earner. My predictor of household income is similar in spirit to the one used by Luttmer (2005). I predict labour earnings for around 5,000 industry occupation cells by regressing log labour earnings on a full set of industry and occupation dummies, for each year, and for West and East Germany, separately.3 The exponential of the fitted values of these regressions are the predicted earnings for individuals in each industry×occupation in a particular region and year. Summing over all household members, I get a prediction of household income. Therefore, increases in predicted household income reflect industry and/or occupation wide factors but not exceptional personal efforts by one of the household members. By purging the estimates of biases related to unobserved costs of income generation, the instrument addresses one of the most pressing endogeneity problems. However, the instrument is not perfect: occupational choice is endogenous to individual preferences (though individual specific fixed effects go some way to address this problem) and predicted income may also be interpreted as comparison income. Lacking better instruments, I follow ‘best practice’, acknowledge this issue and discuss the implications for the benefit estimates (see Section 3). Based on existing results regarding the functional form of income (Layard et al., 2008), I include household income in its natural logarithm; I control for the square root of household size in order to capture the effect of household size on equivalence income. Following the previous literature, I include commonly used observable time‐varying predictors of life satisfaction (Ferrer‐i‐Carbonell, 2005; Frijters et al., 2004). These are age, disability status, marital and partnership status, labour force status, occupational position, type of employment contract and city or district size. I add own job tenure and average weekly working hours to this list because my instruments for household income might only be valid conditional on these two variables. For example, in bargaining collective work agreements, unions may accept industry‐wide income reductions in return for a shorter work week thereby reducing both income and effort cost. Dummies for individuals participating in the survey for the first and second time, respectively, serve as a proxy for interviewing experience and panel learning effects (D’Ambrosio and Frick, 2004). In order to control for the secular upward trend in life satisfaction in post‐reunification years in East Germany documented by Frijters et al. (2004), I include state‐specific time trends along with a full set of state and year fixed effects. My sample only includes individuals that stay put in their county, i.e. I exclude all individuals moving across county boundaries. Therefore, all county specific effects are absorbed by the individual specific fixed effects. A fixed effect model is appropriate as fixed personality traits are important predictors of life satisfaction and correlated with various variables of interest. Failure to control for this source of heterogeneity with individual specific fixed effects would lead to biased estimates of the corresponding coefficients (Ferrer‐i‐Carbonell and Frijters, 2004). Another source of individual heterogeneity relates to differences in preferences for air quality. If individuals are differently affected by air pollution, a sorting equilibrium may occur with the least sensitive individuals living in the most polluted areas. I would then observe the largest changes in air pollution for the least sensitive individuals. While taste sorting is theoretically plausible and almost certainly affects my WTP estimates, my setting does not allow me to address this issue empirically. Empirical evidence on taste sorting in the context of hedonic property studies for the US suggests that heterogeneity at aggregate levels such as counties and the resulting bias in WTP estimates is small (Chay and Greenstone, 2005). Following from the previous discussion, the equation to be estimated in the second stage is (6) where LSicst is the life satisfaction of respondent i living in county c in state s at time t, Pcst pollution at county level, micst respondent’s household income, Zicst a vector of personal characteristics, trendst state specific time trends, τt year effects, ιi individual (and thereby also county) fixed effects, and ɛicst an error term. Robust standard errors are adjusted for clustering on county and year level. Life satisfaction scores are reported on an ordinal scale. However, assuming ordinality or cardinality of life satisfaction scores makes usually little difference (Ferrer‐i‐Carbonell and Frijters, 2004). This is also the case here. For ease of interpretation, I report the full results based on a cardinal interpretation but I also present benefit estimates based on Probit adjusted OLS (Ferrer‐i‐Carbonell and van Praag, 2004). With this method, a linear model is estimated for a transformed dependent variable, namely the expectation of a double truncated standard normal variate where the truncation points are derived from the marginal distribution of the satisfaction variable. 2.2.2. Basic results Table 4 reports the basic life satisfaction regressions in full with the results for all control variables. The effects of the control variables contain no surprises and correspond to results documented in the literature. The variables of interest are SO2 concentration and household income. Both have the expected sign and are statistically significant. I will discuss the size of the effect extensively in the next Section in which I monetise the effect. The raw coefficients are difficult to interpret and cannot be readily compared to previous estimates, except with respect to sign and significance. Welsch (2002) finds essentially no effect of SO2 concentration on happiness in a cross‐section of 54 countries, both in terms of size and significance. Di Tella and MacCulloch (2007) find a negative and statistically significant effect of SO2 emissions in a repeated cross‐section of 12 countries and 23 years but there is no general method to convert emissions into pollution levels. Finally, Welsch (2006) only considers other pollutants. The size of the conventional estimate of SO2 on life satisfaction (column I of Table 4) is only 58% of the size of the instrumental variable estimate (column II). This finding is consistent with the conjecture that improvements in air quality are accompanied by negative developments. However, given the (generically) large standard errors of instrumental variable estimates, the difference between the instrumental variable estimates and the conventional estimate is not significant in a statistical sense. Income has a positive effect on life satisfaction that is highly statistically significant. The estimated effect of log household income on life satisfaction more than triples if income is instrumented compared to the conventional estimates.4 This change is of similar magnitude as the one reported by Luttmer (2005) and suggests that the OLS estimates are indeed biased. Turning to the first stage regressions, the instruments have the expected effect on the endogenous variables they are intended for: the estimated effect of flue gas desulphurisation negatively affects SO2 concentration. Predicted household income and job tenure of the main or secondary income earner both have a positive impact on household income. My pollution instrument has no effect on income, which is reassuring that the instrument is orthogonal to local economic activity. For unknown reasons, job tenure is weakly negatively associated with SO2 concentration. It is important to sound a note of caution regarding statistical significance in the income first stage regressions: predicted household income is an estimated regressor and, thus, t‐statistics are inflated. However, under general conditions, the parameters in the first stage regressions are consistently estimated and the second stage regressions not afflicted (Murphy and Topel, 1985). In all cases, the statistical tests suggest that the instruments are relevant. Shea’s partial R2s are nearly identical to standard R2s, Anderson canonical correlations likelihood‐ratio tests reject the null of underidentification and F‐tests indicate joint significance of the excluded instruments. Further, none of the Hansen’s J‐statistics rejects the null that the instruments are satisfying the orthogonality condition. 2.2.3. Robustness tests Despite my efforts to instrument pollution, one might worry that levels of SO2 concentration reflect local economic activity or air quality more generally. As a first robustness test we include therefore annual unemployment rates at county level and annual mean concentration of total suspended particulates (TSP) as additional controls. From columns I and II of Table 5, I see that the estimates are robust to the inclusion of the local unemployment rate and TSP concentration. The robustness of the conventional estimate contrasts somewhat with the picture that emerges from the difference in the magnitude of conventional and instrumented pollution effects (or rather my interpretation thereof). The ultimate source of concern is a potential correlation between pollution and unobservable characteristics but local economic activity, as captured by local unemployment seems not to bias conventional estimates. Table 5 
Robustness Check Dependent variable . I . II . III . IV . V . VI . Life satisfaction . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.005** −5.78 −0.008* −2.14 −0.002 −1.47 −0.007* −2.10 −0.003(*) −1.74 −0.007(*) −1.70  TSP (μg/m3) −0.001(*) −1.95 −0.001 −0.93 Unemployment rate  Unemployment rate −0.014** −2.95 −0.018** −3.12 Year spec. distance to city effects No No No No Yes Yes Year spec. close to East Germ. effects No No No No Yes Yes HH income  ln(post govt. income) 0.547** 8.35 0.548** 8.36 0.500** 7.34 0.502** 7.36 0.501** 7.35 0.503** 7.37 Personal characteristics Yes Yes Yes Yes Yes Yes City, district size Yes Yes Yes Yes Yes Yes Predicted uncleaned emissions No Yes No Yes No Yes State specific time trends Yes Yes Yes Yes Yes Yes Year specific effects Yes Yes Yes Yes Yes Yes Individual specific effects Yes Yes Yes Yes Yes Yes Prob  >  F 0.000 0.000 0.000 0.000 0.000 0.000 R2 within 0.029 0.029 0.033 0.033 0.033 0.033 R2 between 0.030 0.051 0.048 0.039 0.048 0.033 R2 overall 0.032 0.045 0.047 0.038 0.047 0.033 (b) First stage regressions Dependent variable SO2(μg/m3) Excluded instruments  Predicted ΔSO2 −0.259** −15.49 −0.306** −17.13 −0.283** −13.66  Predicted income 0.019 1.45 0.012 1.30 0.004 0.48  Tenure income earner −0.011* −2.22 0.001 0.24 0.002 0.90 Predicted uncleaned emissions Yes Yes Yes  Predicted uncleaned emissions 0.054 1.14 0.306** 6.12 0.128** 3.84 Included instruments Yes Yes Yes Dependent variable ln(post govt. income) Excluded instruments  Predicted ΔSO2 1.8E‐4 0.92 1.8E‐4 0.88 −1.0E‐6 0.00  Predicted income 0.023** 34.09 0.023** 34.04 0.024** 30.26 0.024** 30.25 0.024** 30.35 0.024** 30.36  Tenure income earner 0.005** 25.01 0.005** 25.10 0.005** 24.10 0.005** 24.09 0.005** 24.08 0.005** 24.08 Included instruments Yes Yes Yes Number of observations 186,628 186,628 147,781 147,781 147,781 147,781 Number of individuals 29,246 29,246 22,881 22,881 22,881 22,881 Avg. no. of obs. per individual 6.4 6.4 6.5 6.5 6.5 6.5 Number of clusters 7,118 7,118 5,540 5,540 5,540 5,540 Shea’s partial R2 for SO2 0.048 0.190 0.169 Bound et al. partial R2 0.048 0.190 0.169 F‐statistics of excluded instruments 85.22 98.64 62.86 Shea’s partial R2 for ln(post govt. inc.) 0.028 0.028 0.030 0.030 0.030 0.031 Bound et al. partial R2 0.028 0.028 0.030 0.030 0.030 0.031 F‐statistics of excluded instruments 1075.23 718.05 918.04 612.72 919.43 613.32 Anderson LR statistic (p‐value) 0.000 0.000 0.000 0.000 0.000 0.000 Hansen’s J statistic (p‐value) 0.172 0.183 0.377 0.391 0.373 0.369 Dependent variable . I . II . III . IV . V . VI . Life satisfaction . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.005** −5.78 −0.008* −2.14 −0.002 −1.47 −0.007* −2.10 −0.003(*) −1.74 −0.007(*) −1.70  TSP (μg/m3) −0.001(*) −1.95 −0.001 −0.93 Unemployment rate  Unemployment rate −0.014** −2.95 −0.018** −3.12 Year spec. distance to city effects No No No No Yes Yes Year spec. close to East Germ. effects No No No No Yes Yes HH income  ln(post govt. income) 0.547** 8.35 0.548** 8.36 0.500** 7.34 0.502** 7.36 0.501** 7.35 0.503** 7.37 Personal characteristics Yes Yes Yes Yes Yes Yes City, district size Yes Yes Yes Yes Yes Yes Predicted uncleaned emissions No Yes No Yes No Yes State specific time trends Yes Yes Yes Yes Yes Yes Year specific effects Yes Yes Yes Yes Yes Yes Individual specific effects Yes Yes Yes Yes Yes Yes Prob  >  F 0.000 0.000 0.000 0.000 0.000 0.000 R2 within 0.029 0.029 0.033 0.033 0.033 0.033 R2 between 0.030 0.051 0.048 0.039 0.048 0.033 R2 overall 0.032 0.045 0.047 0.038 0.047 0.033 (b) First stage regressions Dependent variable SO2(μg/m3) Excluded instruments  Predicted ΔSO2 −0.259** −15.49 −0.306** −17.13 −0.283** −13.66  Predicted income 0.019 1.45 0.012 1.30 0.004 0.48  Tenure income earner −0.011* −2.22 0.001 0.24 0.002 0.90 Predicted uncleaned emissions Yes Yes Yes  Predicted uncleaned emissions 0.054 1.14 0.306** 6.12 0.128** 3.84 Included instruments Yes Yes Yes Dependent variable ln(post govt. income) Excluded instruments  Predicted ΔSO2 1.8E‐4 0.92 1.8E‐4 0.88 −1.0E‐6 0.00  Predicted income 0.023** 34.09 0.023** 34.04 0.024** 30.26 0.024** 30.25 0.024** 30.35 0.024** 30.36  Tenure income earner 0.005** 25.01 0.005** 25.10 0.005** 24.10 0.005** 24.09 0.005** 24.08 0.005** 24.08 Included instruments Yes Yes Yes Number of observations 186,628 186,628 147,781 147,781 147,781 147,781 Number of individuals 29,246 29,246 22,881 22,881 22,881 22,881 Avg. no. of obs. per individual 6.4 6.4 6.5 6.5 6.5 6.5 Number of clusters 7,118 7,118 5,540 5,540 5,540 5,540 Shea’s partial R2 for SO2 0.048 0.190 0.169 Bound et al. partial R2 0.048 0.190 0.169 F‐statistics of excluded instruments 85.22 98.64 62.86 Shea’s partial R2 for ln(post govt. inc.) 0.028 0.028 0.030 0.030 0.030 0.031 Bound et al. partial R2 0.028 0.028 0.030 0.030 0.030 0.031 F‐statistics of excluded instruments 1075.23 718.05 918.04 612.72 919.43 613.32 Anderson LR statistic (p‐value) 0.000 0.000 0.000 0.000 0.000 0.000 Hansen’s J statistic (p‐value) 0.172 0.183 0.377 0.391 0.373 0.369 Notes. IV estimates with individual fixed effects; SO2 concentration is instrumented with the effect of flue gas desulphurisation at power plants; household income is instrumented with the sum of predicted incomes of the household members and job tenure of household of the primary/secondary wage earner. Standard errors are adjusted for clustering on county and year level. **denotes significance at the 99% level, *at the 95% level, and (*) at the 90% level. Open in new tab Table 5 
Robustness Check Dependent variable . I . II . III . IV . V . VI . Life satisfaction . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.005** −5.78 −0.008* −2.14 −0.002 −1.47 −0.007* −2.10 −0.003(*) −1.74 −0.007(*) −1.70  TSP (μg/m3) −0.001(*) −1.95 −0.001 −0.93 Unemployment rate  Unemployment rate −0.014** −2.95 −0.018** −3.12 Year spec. distance to city effects No No No No Yes Yes Year spec. close to East Germ. effects No No No No Yes Yes HH income  ln(post govt. income) 0.547** 8.35 0.548** 8.36 0.500** 7.34 0.502** 7.36 0.501** 7.35 0.503** 7.37 Personal characteristics Yes Yes Yes Yes Yes Yes City, district size Yes Yes Yes Yes Yes Yes Predicted uncleaned emissions No Yes No Yes No Yes State specific time trends Yes Yes Yes Yes Yes Yes Year specific effects Yes Yes Yes Yes Yes Yes Individual specific effects Yes Yes Yes Yes Yes Yes Prob  >  F 0.000 0.000 0.000 0.000 0.000 0.000 R2 within 0.029 0.029 0.033 0.033 0.033 0.033 R2 between 0.030 0.051 0.048 0.039 0.048 0.033 R2 overall 0.032 0.045 0.047 0.038 0.047 0.033 (b) First stage regressions Dependent variable SO2(μg/m3) Excluded instruments  Predicted ΔSO2 −0.259** −15.49 −0.306** −17.13 −0.283** −13.66  Predicted income 0.019 1.45 0.012 1.30 0.004 0.48  Tenure income earner −0.011* −2.22 0.001 0.24 0.002 0.90 Predicted uncleaned emissions Yes Yes Yes  Predicted uncleaned emissions 0.054 1.14 0.306** 6.12 0.128** 3.84 Included instruments Yes Yes Yes Dependent variable ln(post govt. income) Excluded instruments  Predicted ΔSO2 1.8E‐4 0.92 1.8E‐4 0.88 −1.0E‐6 0.00  Predicted income 0.023** 34.09 0.023** 34.04 0.024** 30.26 0.024** 30.25 0.024** 30.35 0.024** 30.36  Tenure income earner 0.005** 25.01 0.005** 25.10 0.005** 24.10 0.005** 24.09 0.005** 24.08 0.005** 24.08 Included instruments Yes Yes Yes Number of observations 186,628 186,628 147,781 147,781 147,781 147,781 Number of individuals 29,246 29,246 22,881 22,881 22,881 22,881 Avg. no. of obs. per individual 6.4 6.4 6.5 6.5 6.5 6.5 Number of clusters 7,118 7,118 5,540 5,540 5,540 5,540 Shea’s partial R2 for SO2 0.048 0.190 0.169 Bound et al. partial R2 0.048 0.190 0.169 F‐statistics of excluded instruments 85.22 98.64 62.86 Shea’s partial R2 for ln(post govt. inc.) 0.028 0.028 0.030 0.030 0.030 0.031 Bound et al. partial R2 0.028 0.028 0.030 0.030 0.030 0.031 F‐statistics of excluded instruments 1075.23 718.05 918.04 612.72 919.43 613.32 Anderson LR statistic (p‐value) 0.000 0.000 0.000 0.000 0.000 0.000 Hansen’s J statistic (p‐value) 0.172 0.183 0.377 0.391 0.373 0.369 Dependent variable . I . II . III . IV . V . VI . Life satisfaction . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.005** −5.78 −0.008* −2.14 −0.002 −1.47 −0.007* −2.10 −0.003(*) −1.74 −0.007(*) −1.70  TSP (μg/m3) −0.001(*) −1.95 −0.001 −0.93 Unemployment rate  Unemployment rate −0.014** −2.95 −0.018** −3.12 Year spec. distance to city effects No No No No Yes Yes Year spec. close to East Germ. effects No No No No Yes Yes HH income  ln(post govt. income) 0.547** 8.35 0.548** 8.36 0.500** 7.34 0.502** 7.36 0.501** 7.35 0.503** 7.37 Personal characteristics Yes Yes Yes Yes Yes Yes City, district size Yes Yes Yes Yes Yes Yes Predicted uncleaned emissions No Yes No Yes No Yes State specific time trends Yes Yes Yes Yes Yes Yes Year specific effects Yes Yes Yes Yes Yes Yes Individual specific effects Yes Yes Yes Yes Yes Yes Prob  >  F 0.000 0.000 0.000 0.000 0.000 0.000 R2 within 0.029 0.029 0.033 0.033 0.033 0.033 R2 between 0.030 0.051 0.048 0.039 0.048 0.033 R2 overall 0.032 0.045 0.047 0.038 0.047 0.033 (b) First stage regressions Dependent variable SO2(μg/m3) Excluded instruments  Predicted ΔSO2 −0.259** −15.49 −0.306** −17.13 −0.283** −13.66  Predicted income 0.019 1.45 0.012 1.30 0.004 0.48  Tenure income earner −0.011* −2.22 0.001 0.24 0.002 0.90 Predicted uncleaned emissions Yes Yes Yes  Predicted uncleaned emissions 0.054 1.14 0.306** 6.12 0.128** 3.84 Included instruments Yes Yes Yes Dependent variable ln(post govt. income) Excluded instruments  Predicted ΔSO2 1.8E‐4 0.92 1.8E‐4 0.88 −1.0E‐6 0.00  Predicted income 0.023** 34.09 0.023** 34.04 0.024** 30.26 0.024** 30.25 0.024** 30.35 0.024** 30.36  Tenure income earner 0.005** 25.01 0.005** 25.10 0.005** 24.10 0.005** 24.09 0.005** 24.08 0.005** 24.08 Included instruments Yes Yes Yes Number of observations 186,628 186,628 147,781 147,781 147,781 147,781 Number of individuals 29,246 29,246 22,881 22,881 22,881 22,881 Avg. no. of obs. per individual 6.4 6.4 6.5 6.5 6.5 6.5 Number of clusters 7,118 7,118 5,540 5,540 5,540 5,540 Shea’s partial R2 for SO2 0.048 0.190 0.169 Bound et al. partial R2 0.048 0.190 0.169 F‐statistics of excluded instruments 85.22 98.64 62.86 Shea’s partial R2 for ln(post govt. inc.) 0.028 0.028 0.030 0.030 0.030 0.031 Bound et al. partial R2 0.028 0.028 0.030 0.030 0.030 0.031 F‐statistics of excluded instruments 1075.23 718.05 918.04 612.72 919.43 613.32 Anderson LR statistic (p‐value) 0.000 0.000 0.000 0.000 0.000 0.000 Hansen’s J statistic (p‐value) 0.172 0.183 0.377 0.391 0.373 0.369 Notes. IV estimates with individual fixed effects; SO2 concentration is instrumented with the effect of flue gas desulphurisation at power plants; household income is instrumented with the sum of predicted incomes of the household members and job tenure of household of the primary/secondary wage earner. Standard errors are adjusted for clustering on county and year level. **denotes significance at the 99% level, *at the 95% level, and (*) at the 90% level. Open in new tab The results in Table 5 imply that TSP concentration is only weakly associated with life satisfaction. However, I do not dwell on these estimates as they may be afflicted by similar simultaneity problems to those I conjecture in the case of conventional SO2 estimates. Local unemployment rates have large negative effects even though I control for respondents’ own employment status – a result that is consistent with earlier findings (Di Tella et al., 2001). Another worry might be that my results are largely driven by the development in East Germany. The retrofitting of power plants in the territory of the former GDR and the associated improvement in air quality were a direct result of the German reunification (see Section 1). As a second robustness I therefore exclude all East German observations. The results are depicted in columns III and IV of Table 5. The size of the conventional decreases by more than 50% and the statistical significance falls below conventional levels. In contrast, the instrumental variable estimate is largely robust to the exclusion of the East German observations (the size of the coefficient decreases by 14%). While people living in East Germany are those most likely to benefit from reunification effects, people in West German counties close to the East‐West German border may benefit as well. Redding and Sturm (forthcoming) show that West German cities located within 75 kilometres of the East‐West German border experienced a substantial decline in population growth relative to other West German cities as a consequence of the German division after the Second World War. Similarly, in the aftermath of the German reunification these cities experienced a relative increase in population growth, although this latter effect is smaller. Following the analysis of Redding and Sturm (forthcoming), I interact a dummy variable with value one for counties within 75 kilometres of the East‐West German border with the full set of year effects. In addition, in order to control for possible urban/trends, I include year specific distance‐to‐city effects.5 The results are depicted in columns V and VI of Table 5. In comparison to column III of Table 5, the coefficient of the conventional estimate in column V increases by 18% in absolute terms and is again narrowly statistically significant. The instrumental variable estimate is again more robust. In absolute terms, the coefficient decreases by around 6%. These changes are the net effect of a decrease in the size of the pollution estimates caused by the inclusion of the interaction of year effects with the dummy variable for counties close to the East‐West border and an increase of the size of the pollution estimates caused by the inclusion of the year specific distance effects. All changes are much more pronounced for the conventional estimate than for the instrumental variable estimate. Including year‐specific distance‐to‐city effects in the whole sample slightly increases the size of the pollution estimates (results are available upon request). Controlling for additional variables and excluding observations is one way to check the robustness and plausibility of the results. Another is to interact the SO2 concentration with subgroups of the population that are expected to suffer disproportionately from exposure to SO2 pollution. In this way, the relatively insensitive group controls for other simultaneous and spatially coincident shocks. I consider two such pollution‐sensitive groups: environmentally concerned individuals and individuals that are at risk with regard to adverse health effects from air pollution. The only variable in the GSOEP for environmental attitudes available in all years asks respondents whether they worry about environmental protection. Possible answers are ‘very concerned’, ‘somewhat concerned’ and ‘not concerned’. Table 6 tabulates row percentages of the number of observations in each category against deciles of SO2 concentration. Generally, the number of very concerned people increases with pollution levels and the number of unconcerned people decreases. Of course, for environmental concerns to be a channel through which air pollution affects life satisfaction, such a positive relationship between objective and perceived environmental degradation is a necessary condition. Although only a few Germans characterise themselves as unconcerned, there are still 1,344 observations in the least populated cell (10th decile of SO2 concentration × unconcerned respondents). In the analysis below, I compare the strongly and moderately concerned individuals against the unconcerned individuals. Table 6 
SO2 Pollution and Environmental Concerns (row percentages) SO2 deciles . Environmental concerns . Very concerned . Somewhat concerned . Not Concerned . 1st 23 62 15 2nd 24 61 15 3rd 26 61 13 4th 28 60 12 5th 33 56 10 6th 40 52 8 7th 47 46 7 8th 49 44 7 9th 49 43 7 10th 47 46 7 Total 37 53 10 SO2 deciles . Environmental concerns . Very concerned . Somewhat concerned . Not Concerned . 1st 23 62 15 2nd 24 61 15 3rd 26 61 13 4th 28 60 12 5th 33 56 10 6th 40 52 8 7th 47 46 7 8th 49 44 7 9th 49 43 7 10th 47 46 7 Total 37 53 10 Notes. N = 185,605. Open in new tab Table 6 
SO2 Pollution and Environmental Concerns (row percentages) SO2 deciles . Environmental concerns . Very concerned . Somewhat concerned . Not Concerned . 1st 23 62 15 2nd 24 61 15 3rd 26 61 13 4th 28 60 12 5th 33 56 10 6th 40 52 8 7th 47 46 7 8th 49 44 7 9th 49 43 7 10th 47 46 7 Total 37 53 10 SO2 deciles . Environmental concerns . Very concerned . Somewhat concerned . Not Concerned . 1st 23 62 15 2nd 24 61 15 3rd 26 61 13 4th 28 60 12 5th 33 56 10 6th 40 52 8 7th 47 46 7 8th 49 44 7 9th 49 43 7 10th 47 46 7 Total 37 53 10 Notes. N = 185,605. Open in new tab Hospitalisation and disability status are the only health variables in the GSOEP available in all years. These variables are not suitable for capturing pollution‐related health effects. Further, on a conceptual level, I am interested in identifying individuals belonging to a risk group rather than actually ill ones. In an auxiliary logit regression, I regress a dummy variable indicating persons suffering from chronic illnesses on a set of 24 sex×age category dummies and 24 corresponding interaction terms with SO2 concentration. The dependent variable is the binary response to the question whether respondents suffered for at least one year or chronically from specific complaints or illnesses, asked in the early waves of the GSOEP. This variable comes closest to representing respiratory and cardiovascular diseases caused by pollution. Using the estimated coefficients, I predict hypothetical probabilities of illnesses upon exposure to high and low pollution levels. I then classify individuals with a predicted difference in the probability of illness between high and low pollution situations above the median as belonging to the risk group. Table 7 reports the average effects of SO2 concentration on the life satisfaction in the various subgroups. Columns I and III depicts the results for the West German sample, columns II and IV for the whole sample. Table 7 
Interaction Effects: Effect of SO2 Pollution on Life Satisfaction for Different Groups Dependent Variable . I . II . III . IV . Life satisfaction . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Pollution and interaction terms  SO2(μg/m3) 0.002  1.14 −3.6E‐4 −0.30 −0.002 −0.94 −0.004** −4.50  SO2· concerned −0.005** −4.15 −0.005** −4.77  SO2· risk group −0.002* −2.34 −0.002** −3.60 Subgroups  Not concerned at all Reference group Reference group  Concerned −0.059** −2.80 −0.051** −2.79  Not in risk group Reference group Reference group  Risk group 0.049** 3.03 0.053** 3.98 HH income  ln(post govt. income) 0.492** 7.17 0.539** 8.18 0.508** 7.46 0.559** 8.54 Personal characteristics Yes Yes Yes Yes City, district size Yes Yes Yes Yes State specific time trends Yes Yes Yes Yes Year specific effects Yes Yes Yes Yes Individual specific effects Yes Yes Yes Yes Number of observations 146,924 185,605 147,781 186,628 Number of individuals 22,881 29,189 22,828 29,246 Avg. no. of obs. per individual 6.5 6.4 6.4 6.4 Number of clusters 5,537 7,115 5,540 7,118 Prob  >  F 0.000 0.000 0.000 0.000 R2 within 0.034 0.031 0.032 0.029 R2 between 0.048 0.026 0.047 0.026 R2 overall 0.048 0.029 0.047 0.029 Dependent Variable . I . II . III . IV . Life satisfaction . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Pollution and interaction terms  SO2(μg/m3) 0.002  1.14 −3.6E‐4 −0.30 −0.002 −0.94 −0.004** −4.50  SO2· concerned −0.005** −4.15 −0.005** −4.77  SO2· risk group −0.002* −2.34 −0.002** −3.60 Subgroups  Not concerned at all Reference group Reference group  Concerned −0.059** −2.80 −0.051** −2.79  Not in risk group Reference group Reference group  Risk group 0.049** 3.03 0.053** 3.98 HH income  ln(post govt. income) 0.492** 7.17 0.539** 8.18 0.508** 7.46 0.559** 8.54 Personal characteristics Yes Yes Yes Yes City, district size Yes Yes Yes Yes State specific time trends Yes Yes Yes Yes Year specific effects Yes Yes Yes Yes Individual specific effects Yes Yes Yes Yes Number of observations 146,924 185,605 147,781 186,628 Number of individuals 22,881 29,189 22,828 29,246 Avg. no. of obs. per individual 6.5 6.4 6.4 6.4 Number of clusters 5,537 7,115 5,540 7,118 Prob  >  F 0.000 0.000 0.000 0.000 R2 within 0.034 0.031 0.032 0.029 R2 between 0.048 0.026 0.047 0.026 R2 overall 0.048 0.029 0.047 0.029 Marginal Effect of SO2 for . M.E. . z‐value . M.E. . z‐value . M.E. . z‐value . M.E. . z‐value .  Not concerned 0.002 1.14 −3.6E‐4 −0.30  Concerned −0.003(*) −1.82 −0.005** −6.21  Not in risk group −0.002 −0.94 −0.004** −4.50  Risk group −0.003* −2.06 −0.006** −6.81 Marginal Effect of SO2 for . M.E. . z‐value . M.E. . z‐value . M.E. . z‐value . M.E. . z‐value .  Not concerned 0.002 1.14 −3.6E‐4 −0.30  Concerned −0.003(*) −1.82 −0.005** −6.21  Not in risk group −0.002 −0.94 −0.004** −4.50  Risk group −0.003* −2.06 −0.006** −6.81 Notes. IV estimates with individual fixed effects; household income is instrumented with the sum of predicted incomes of the household members and job tenure of household of the primary/secondary wage earner. Standard errors are adjusted for clustering on county and year level. **denotes significance at the 99% level, *at the 95% level, and (*) at the 90% level. Open in new tab Table 7 
Interaction Effects: Effect of SO2 Pollution on Life Satisfaction for Different Groups Dependent Variable . I . II . III . IV . Life satisfaction . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Pollution and interaction terms  SO2(μg/m3) 0.002  1.14 −3.6E‐4 −0.30 −0.002 −0.94 −0.004** −4.50  SO2· concerned −0.005** −4.15 −0.005** −4.77  SO2· risk group −0.002* −2.34 −0.002** −3.60 Subgroups  Not concerned at all Reference group Reference group  Concerned −0.059** −2.80 −0.051** −2.79  Not in risk group Reference group Reference group  Risk group 0.049** 3.03 0.053** 3.98 HH income  ln(post govt. income) 0.492** 7.17 0.539** 8.18 0.508** 7.46 0.559** 8.54 Personal characteristics Yes Yes Yes Yes City, district size Yes Yes Yes Yes State specific time trends Yes Yes Yes Yes Year specific effects Yes Yes Yes Yes Individual specific effects Yes Yes Yes Yes Number of observations 146,924 185,605 147,781 186,628 Number of individuals 22,881 29,189 22,828 29,246 Avg. no. of obs. per individual 6.5 6.4 6.4 6.4 Number of clusters 5,537 7,115 5,540 7,118 Prob  >  F 0.000 0.000 0.000 0.000 R2 within 0.034 0.031 0.032 0.029 R2 between 0.048 0.026 0.047 0.026 R2 overall 0.048 0.029 0.047 0.029 Dependent Variable . I . II . III . IV . Life satisfaction . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Coef. . z‐value . Pollution and interaction terms  SO2(μg/m3) 0.002  1.14 −3.6E‐4 −0.30 −0.002 −0.94 −0.004** −4.50  SO2· concerned −0.005** −4.15 −0.005** −4.77  SO2· risk group −0.002* −2.34 −0.002** −3.60 Subgroups  Not concerned at all Reference group Reference group  Concerned −0.059** −2.80 −0.051** −2.79  Not in risk group Reference group Reference group  Risk group 0.049** 3.03 0.053** 3.98 HH income  ln(post govt. income) 0.492** 7.17 0.539** 8.18 0.508** 7.46 0.559** 8.54 Personal characteristics Yes Yes Yes Yes City, district size Yes Yes Yes Yes State specific time trends Yes Yes Yes Yes Year specific effects Yes Yes Yes Yes Individual specific effects Yes Yes Yes Yes Number of observations 146,924 185,605 147,781 186,628 Number of individuals 22,881 29,189 22,828 29,246 Avg. no. of obs. per individual 6.5 6.4 6.4 6.4 Number of clusters 5,537 7,115 5,540 7,118 Prob  >  F 0.000 0.000 0.000 0.000 R2 within 0.034 0.031 0.032 0.029 R2 between 0.048 0.026 0.047 0.026 R2 overall 0.048 0.029 0.047 0.029 Marginal Effect of SO2 for . M.E. . z‐value . M.E. . z‐value . M.E. . z‐value . M.E. . z‐value .  Not concerned 0.002 1.14 −3.6E‐4 −0.30  Concerned −0.003(*) −1.82 −0.005** −6.21  Not in risk group −0.002 −0.94 −0.004** −4.50  Risk group −0.003* −2.06 −0.006** −6.81 Marginal Effect of SO2 for . M.E. . z‐value . M.E. . z‐value . M.E. . z‐value . M.E. . z‐value .  Not concerned 0.002 1.14 −3.6E‐4 −0.30  Concerned −0.003(*) −1.82 −0.005** −6.21  Not in risk group −0.002 −0.94 −0.004** −4.50  Risk group −0.003* −2.06 −0.006** −6.81 Notes. IV estimates with individual fixed effects; household income is instrumented with the sum of predicted incomes of the household members and job tenure of household of the primary/secondary wage earner. Standard errors are adjusted for clustering on county and year level. **denotes significance at the 99% level, *at the 95% level, and (*) at the 90% level. Open in new tab In both samples, environmentally concerned people and people belonging to the risk group are more severely affected by air pollution than the rest of the population. For these subgroups, the effect is negative and statistically significantly in all cases (see bottom rows of Table 7). To sum up the results: first and most importantly, I find negative effects of SO2 concentration on life satisfaction. The size of the effect is larger for the instrumental variable estimate than for the conventional estimate. This difference suggests that pollution is accompanied by factors with a countervailing effect on life satisfaction. Even though an obvious candidate is local economic activity, it is not local unemployment but rather some other unobserved factor. The effects are robust to the inclusion of the local unemployment rate and TSP concentration. Excluding East German observations and controlling for reunification effects in West German counties close to the East‐West German border reduces the size of the effect for the conventional estimate and, conversely, controlling for rural/urban trends increases the size of the effect. The instrumental variable estimate is much more robust to these changes. Finally, differential effects for different groups of respondents imply that it is indeed air pollution that affects life satisfaction and not other simultaneous shocks. 2.3. Effect on Housing Rents 2.3.1. Empirical strategy and explanatory variables In order to calculate the total WTP for air quality, I supplement the results of the life satisfaction approach with housing hedonics (see Appendix A.1. for a theoretical discussion). In contrast to the majority of hedonic market studies, I use rental prices instead of house prices, a deviation that seems justified in the present case for several reasons, in addition to data availability. First, as the life satisfaction approach, hedonic rent regressions yield WTP estimates in the form of (annually) recurring payments. Hence, in summing and comparing estimates based on the two approaches, no assumptions on individuals’ discount rates are necessary. Second, expected changes in air quality are capitalised into sales prices but not into current rents. Given the major air quality regulation were enacted before my sample period, capitalised expectations would bias my estimates downwards. Third, in contrast to other countries, Germany has a well‐developed and relatively loosely regulated, market for rental housing. Nearly 60% of the households live in rented dwellings (compared to around 30% in the US). Rents for vacant dwellings can be freely negotiated between landlords and potential tenants. There are some restrictions on evictions and a ceiling on rent increases for sitting tenants (up to 30% in a three‐year period), but this ceiling is generally not binding (Hoffmann and Kurz, 2002). As a rule, hedonic housing regressions include a large number of time‐invariant housing characteristics. With panel data, these characteristics can be captured by dwelling specific fixed effects; e.g., Mendelsohn (1992) for repeat sale models. In accordance with the life satisfaction regressions, I control for state specific time trends and year effects; state and county specific effects are absorbed by the dwelling effects. Economic theory provides no a priori reason to prefer one functional form for the hedonic price function over others (Rosen, 1974) but, in general, simple forms have proven to outperform more flexible ones (Cropper et al., 1988). Therefore, I estimate semi‐log hedonic rent regressions as specified in (7): (7) where Ricst is the rent of dwelling i in county c and state s at time t, Pcst SO2 pollution, trendst state specific time trends, τt and oi time and dwelling specific fixed effects, and ɛicst the error term. Robust standard errors are adjusted for clustering on county and year level. I exclude owner‐occupied houses from my sample, even though the GSOEP provides owner estimates of rents. Owners may just convert their estimates of the house price into a rent estimate, with associated problems of capitalised expectations and systematic biases in owners’ appraisals (Ihlanfeldt and Martinez‐Vazquez, 1986). I further exclude subsidised dwellings, which are subject to comparatively strict regulation, and institutional households such as nursing homes and barracks. 2.3.2. Results Table 8 presents the hedonic housing regressions, column I the conventional estimate and column II the instrumental variable estimate. Table 8 
Hedonic Housing Regression: Effect of SO2 Pollution on Monthly Rents Dependent variable . I . II . ln(monthly rent, excl. heating costs), 2002 euro . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.009** −4.20 −0.002 −0.45 Predicted uncleaned emissions  Predicted uncleaned emissions 0.001 0.55 State specific time trends Yes Yes Year specific effects Yes Yes Dwelling specific effects Yes Yes Prob  >  F 0.000 0.000 R2 within 0.527 0.508 R2 between 0.002 0.028 R2 overall 0.000 0.019 (b) First stage regressions Dependent variable  SO2(μg/m3) Excluded instrument Predicted ΔSO2 −0.303** −14.55 Predicted uncleaned emissions  Predicted uncleaned emissions 0.091(*) 1.77 Included instruments Yes Number of observations 64,672 64,672 Number of dwellings 17,294 17,294 Avg. no. of obs. per individual 3.7 3.7 Number of clusters 7,111 7,111 Shea’s partial R2 for SO2 0.040 Bound et al. partial R2 0.040 F‐statistics of excluded instruments 211.65 Anderson LR statistic (p‐value) 0.000 Dependent variable . I . II . ln(monthly rent, excl. heating costs), 2002 euro . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.009** −4.20 −0.002 −0.45 Predicted uncleaned emissions  Predicted uncleaned emissions 0.001 0.55 State specific time trends Yes Yes Year specific effects Yes Yes Dwelling specific effects Yes Yes Prob  >  F 0.000 0.000 R2 within 0.527 0.508 R2 between 0.002 0.028 R2 overall 0.000 0.019 (b) First stage regressions Dependent variable  SO2(μg/m3) Excluded instrument Predicted ΔSO2 −0.303** −14.55 Predicted uncleaned emissions  Predicted uncleaned emissions 0.091(*) 1.77 Included instruments Yes Number of observations 64,672 64,672 Number of dwellings 17,294 17,294 Avg. no. of obs. per individual 3.7 3.7 Number of clusters 7,111 7,111 Shea’s partial R2 for SO2 0.040 Bound et al. partial R2 0.040 F‐statistics of excluded instruments 211.65 Anderson LR statistic (p‐value) 0.000 Notes. IV estimates with dwelling fixed effects; SO2 concentration is instrumented with the effect of flue gas desulphurisation at power plants. Standard errors are adjusted for clustering on county and year level. **denotes significance at the 99% level, and (*) at the 90% level. Open in new tab Table 8 
Hedonic Housing Regression: Effect of SO2 Pollution on Monthly Rents Dependent variable . I . II . ln(monthly rent, excl. heating costs), 2002 euro . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.009** −4.20 −0.002 −0.45 Predicted uncleaned emissions  Predicted uncleaned emissions 0.001 0.55 State specific time trends Yes Yes Year specific effects Yes Yes Dwelling specific effects Yes Yes Prob  >  F 0.000 0.000 R2 within 0.527 0.508 R2 between 0.002 0.028 R2 overall 0.000 0.019 (b) First stage regressions Dependent variable  SO2(μg/m3) Excluded instrument Predicted ΔSO2 −0.303** −14.55 Predicted uncleaned emissions  Predicted uncleaned emissions 0.091(*) 1.77 Included instruments Yes Number of observations 64,672 64,672 Number of dwellings 17,294 17,294 Avg. no. of obs. per individual 3.7 3.7 Number of clusters 7,111 7,111 Shea’s partial R2 for SO2 0.040 Bound et al. partial R2 0.040 F‐statistics of excluded instruments 211.65 Anderson LR statistic (p‐value) 0.000 Dependent variable . I . II . ln(monthly rent, excl. heating costs), 2002 euro . Coef. . z‐value . Coef. . z‐value . (a) Second stage regression Pollution  SO2(μg/m3) −0.009** −4.20 −0.002 −0.45 Predicted uncleaned emissions  Predicted uncleaned emissions 0.001 0.55 State specific time trends Yes Yes Year specific effects Yes Yes Dwelling specific effects Yes Yes Prob  >  F 0.000 0.000 R2 within 0.527 0.508 R2 between 0.002 0.028 R2 overall 0.000 0.019 (b) First stage regressions Dependent variable  SO2(μg/m3) Excluded instrument Predicted ΔSO2 −0.303** −14.55 Predicted uncleaned emissions  Predicted uncleaned emissions 0.091(*) 1.77 Included instruments Yes Number of observations 64,672 64,672 Number of dwellings 17,294 17,294 Avg. no. of obs. per individual 3.7 3.7 Number of clusters 7,111 7,111 Shea’s partial R2 for SO2 0.040 Bound et al. partial R2 0.040 F‐statistics of excluded instruments 211.65 Anderson LR statistic (p‐value) 0.000 Notes. IV estimates with dwelling fixed effects; SO2 concentration is instrumented with the effect of flue gas desulphurisation at power plants. Standard errors are adjusted for clustering on county and year level. **denotes significance at the 99% level, and (*) at the 90% level. Open in new tab Pollution has a negative effect on housing rents. However, the instrumental variable estimate is smaller (in absolute terms) compared to the conventional estimate and it is not statistically significant. The relative size of the effect of the conventional and instrumental variable estimates is contrary to prior expectations: as with the life satisfaction regressions, I would expect the instrumental variable estimate to be larger than the conventional estimate. 3. Implicit Willingness‐to‐pay With the estimated coefficients of the life satisfaction regressions for air pollution and household income (, I can calculate the hypothetical WTP for improvements in air quality or implicit utility‐constant trade‐offs between pollution and income. I measure the WTP by the compensating surplus (CS). The CS is the decrease in income necessary to hold utility constant if air quality improves. Given the specification of the micro‐econometric life satisfaction functions expressed in (6), the CS is defined as follows: (8) where mi0 is initial household income and ΔPi the improvement in air quality, Pi0 − Pi1. Based on (8), I estimate the WTP for marginal changes in air quality. In order to calculate the total WTP for improvements in air quality, I add these estimates to the hedonic rent gradients. I calculate the WTP for households that are contained in both samples, i.e. the sample for the life satisfaction regressions and the sample for the hedonic housing regressions. These households have an average household income of €21,462 and average rental costs of €3,871 (in 2002 €). The estimates are based on the coefficients reported in Table 4 for the life satisfaction approach and on the coefficients in Table 8 for the hedonic method. For the life satisfaction approach, I will also report estimates based on other specifications. According to the results in Table 9, the MWTP estimates based on the life satisfaction approach are €183 for the conventional estimate and €313 for the instrumental variable estimate or, in percentage of household income, 0.9% and 1.5%. If I give up the cardinal interpretation of satisfaction scores and use the coefficients based on Probit adjusted OLS estimates (complete results are available upon request), the MWTP estimates increase by between 6% and 8% to €193 (std. err.: €43) and €339 (std. err.: €146) or to 0.9% (std. err.: 0.2%) and 1.6% (std. err.: 0.7%) of household income, respectively. If the effect of pollution on life satisfaction is modelled with the CRRA function in (5) and a risk aversion coefficient of −0.2, the MWTP estimates decrease by between 15% and 22% to €143 (std. err.: €32) and €264 (std. err.: €114) or to 0.7% (std. err.: 0.1%) and 1.2% (std. err.: 0.5%) of household income. Finally, if I use the coefficients for the West German sample reported in columns III and IV of Table 5, the MWTP estimates are between 53% and 94% of the MWTP estimates for the whole sample: €98 (std. err.: €69) or 0.5% (std. err.: 0.3%) of household income for the conventional estimate and €294 (std. err.: €145) or 1.4% (std. err.: 0.7%) of household income for the instrumental variable estimate. Table 9 
WTP Estimates Average household income: €21,462 . Compensating surplus estimates . Life satisfaction approach . Hedonic method . Conventional . IV . Conventional . IV . −1 μg/m3SO2  In euro €183** €313* €34** €6 (€40) (€133) (€8) (€13)  As % of income  0.9**  1.5** 0.2**  0.03** (0.2) (0.6) (0.04) (0.06) Average household income: €21,462 . Compensating surplus estimates . Life satisfaction approach . Hedonic method . Conventional . IV . Conventional . IV . −1 μg/m3SO2  In euro €183** €313* €34** €6 (€40) (€133) (€8) (€13)  As % of income  0.9**  1.5** 0.2**  0.03** (0.2) (0.6) (0.04) (0.06) Notes. Standard errors are estimated using the delta method. **denotes significance at the 99% level, and *at the 95% level. Open in new tab Table 9 
WTP Estimates Average household income: €21,462 . Compensating surplus estimates . Life satisfaction approach . Hedonic method . Conventional . IV . Conventional . IV . −1 μg/m3SO2  In euro €183** €313* €34** €6 (€40) (€133) (€8) (€13)  As % of income  0.9**  1.5** 0.2**  0.03** (0.2) (0.6) (0.04) (0.06) Average household income: €21,462 . Compensating surplus estimates . Life satisfaction approach . Hedonic method . Conventional . IV . Conventional . IV . −1 μg/m3SO2  In euro €183** €313* €34** €6 (€40) (€133) (€8) (€13)  As % of income  0.9**  1.5** 0.2**  0.03** (0.2) (0.6) (0.04) (0.06) Notes. Standard errors are estimated using the delta method. **denotes significance at the 99% level, and *at the 95% level. Open in new tab The implicit prices for clean air reflected in the housing market are much smaller and lie between €6 and €34 or between 0.03% and 0.2% of household income (with only the latter estimate being statistically significant). By summing the estimates in Table 9 from the two methods, I get total MWTP estimates in the range of €218 and €318 (1.0% and 1.5% of household income, respectively). Further, the results in Table 9 suggest that at most around 16% of the total effects of air quality are capitalised in the housing market. This seems to be a very low proportion. At the same time, MWTP estimates based on the life satisfaction approach seem rather high. In the following, I discuss three potential reasons for these interrelated findings: (i) Migration costs and (ii) incomplete information on pollution levels and risks can both explain the low implicit price in the housing markets; (iii) problems associated with estimating the marginal effect of income can explain why the life satisfaction approach estimates are large in absolute terms as well as relative to the hedonic housing estimates. Mobility costs imply that changes in rents understate the true value of a change in air quality. If in a county air quality improves, new residents will be attracted and, as a consequence, rents rise until a new equilibrium is reached. Without mobility costs, the change in the costs of housing fully reflects the value of cleaner air. But if migration is costly, a person will only move to the county with improved air quality if the cleaner air compensates her or him for both higher rents and the costs of moving. This reason for incomplete capitalisation is especially important in the short run and, thus, in panel analyses in which the effect of air quality is identified on the basis of intraregional fluctuations. In a recent study, Bayer et al. (2009) take these mobility costs seriously and estimate a discrete choice model of residential sorting. Their MWTP estimates that allow for mobility costs are 3.5 times higher than the normal hedonic prices (MWTP for a decrease in 1 μg/m3 PM10 increases from $55 to $185). As with mobility costs, the fact that individuals base their moving decisions on the perceived rather than objective effects and levels of air pollution is likely to bias the hedonic estimates downwards. To anticipate the effect of air pollution at a particular location correctly, a prospective house buyer or renter requires adequate knowledge of pollution risks or dose‐response relationships and adequate information about prevailing pollution levels. Distorted risk perceptions may bias hedonic estimates in either direction since people may underestimate or exaggerate the risk of pollution. In contrast, incomplete information about prevailing pollution levels invariably attenuates price gradients towards zero; see Pope (2006) for a theoretical discussion. Several studies suggest that individuals’ information void on location‐specific amenity levels and the resulting downward bias in hedonic estimates may be large. Brookshire et al. (1985) and Troy and Romm (2004) find no price discounts for properties in areas with elevated risks of earthquakes and flooding before laws have been passed that require sellers of property to disclose information on earthquake and flood risks, but large and significant price discounts thereafter. Similarly, Pope (2006) finds the introduction of mandatory disclosure requirements to increase the marginal valuation of airport noise by 36%. Distorted perceptions are of particular importance for the capitalisation of health effects. Smith and Huang (1995) provide evidence consistent with the notion of incomplete capitalisation of health effects. Benefit estimates for improvements in air quality in selected US cities based on dose‐response functions and value of statistical life estimates are around 4 times higher than benefit estimates based on hedonic studies. Of course, incomplete information may not be the only reason for this discrepancy. But the estimate also understates the actual degree of ‘under‐capitalisation’. Reduced mortality risk is only one benefit of clean air. Reduced risk of morbidity, both chronic diseases and minor symptomatic discomforts, reduced material damages and improved visibility are other benefits. The life satisfaction approach is less afflicted by distorted risk perceptions. Most importantly, it can capture indirect effects of externalities that affect individuals’ life satisfaction through a process unnoticed by the individuals themselves. For example, it can capture the utility consequences of health effects even if individuals are ignorant about the causes. Further, long‐term residents of a county are arguably better informed about prevailing pollution levels than prospective house buyers and renters who consider moving to that county. This is not to say that perceptions are completely unimportant for the life satisfaction approach. To the extent that perceptions of local pollution levels have direct effects on life satisfaction, distorted risk perceptions affect life satisfaction estimates as well. However, the above discussion suggests distorted perceptions are much more important for the hedonic method than for the life satisfaction approach. A related aspect is the notion of two different concepts of utility, decision and experienced utility (Kahneman et al., 1997). Welfare measures based on the life satisfaction approach relate to experienced utility. In contrast, welfare measures based on the hedonic method relate to decision utility. Thus, they may be biased estimates of the hedonic experience of the decision as evaluated ex post by the individuals themselves. The third explanation concerns a crucial element of the life satisfaction approach, the estimation of the marginal utility of income. Instrumenting income is inherently difficult and – as discussed in Section 2.2.1– my efforts may fall short of completely resolving all endogeneity and omitted variable problems. Two pieces of evidence suggest that an underestimation of the effect of income on life satisfaction contributes the large MWTP estimates. First, large implicit monetary valuations of intangibles are a prevalent finding in the life satisfaction literature, not only in the case of the valuation of public goods (see references in introduction) but also in the case of the valuation of life events such as unemployment and divorce (Blanchflower and Oswald, 2004). Second, the trade‐off ratios between air pollution and other personal characteristics are not particularly large. To illustrate this point, I look at the effect of changes in air pollution relative to the psychological costs of changes in the local unemployment rate. For an employed individual, the negative effect of an increase in the local unemployment rate is the sum of the general negative effect of high unemployment rates on society shown in Table 5 plus the increase in the likelihood of falling unemployed themselves (Di Tella et al., 2001). In the case of a full‐time employed individual and an increase of the unemployment rate by 1 percentage point, the latter effect is approximately −0.0055(−0.55 × 0.01). Thus a decrease in SO2 concentration by 1 μg/m3 is offset by an increase in the local unemployment rate by between 0.24 percentage points (conventional estimate) and 0.34 percentage points (instrumental variable estimate). Alternatively, the effect on life satisfaction of a decrease in pollution by its mean (16.68 μg/m3) would be between 39% and 56% of the effect of a reduction in the local unemployment rate by its mean (10.16%), the effect of a decrease in pollution by one standard deviation (17.67 μg/m3) would be between 92% and 130% of the effect of a reduction in the local unemployment rate by one standard deviation (4.64%). In interpreting these figures, it is important to note that I only capture the psychological costs of unemployment because German employees are protected by a relatively generous unemployment insurance, because I hold income constant and because fiscal effects cannot be identified in the current empirical setting. Arguably, taking all monetary and fiscal consequences of unemployment into account would make changes in the local unemployment rate much more important than changes in local air pollution. Investigating the relationship between income and life satisfaction is a fast growing area of research; see Clark et al. (2008) for a review. Therefore, better estimates of the marginal utility of income will come forward. However, the question about the effect of income on life satisfaction is not confined to technical problems associated with estimating the marginal utility of income. Rather it raises conceptual questions, which are beyond the scope of this article. A growing body of literature demonstrates that relative motives play an important role. Individuals evaluate their income situation relative to the income of reference groups (Clark and Oswald, 1996; Ferrer‐i‐Carbonell, 2005; Luttmer, 2005; Senik, 2004), own past income (Clark, 1999; Di Tella et al., 2005) and income aspirations (Easterlin, 2001; Stutzer, 2004). Such relative concerns have important implications for the valuation of public goods. If people adapt to income levels, short‐run utility consequences will differ from the long‐run marginal utility of income and, consequently, the short‐run evaluation of public goods will differ from the long‐run evaluation. The realisation of the importance of relative concerns has implications for all non‐market valuation methods and may well speak in favour of the use of the life satisfaction approach instead of standard approaches. For example, Frank (2000) shows that positional concerns bias hedonic market estimates downward.6 The problems associated with estimating the effect of income makes it difficult to give precise benefit estimates in monetary terms and to establish the degree of incompleteness in the capitalisation of the benefits in the housing market exactly. Better estimates of the effect of income will make precise estimates possible. However, in the meantime, at least two unambiguous conclusions can be drawn in the present case. First, the negative relationship between air pollution and life satisfaction indicates that individuals are not fully compensated in private markets. Thus, while the life satisfaction approach may overstate benefits of clean air, the hedonic method clearly understates these benefits. My results suggest that the difference may be large. Second, the evaluation of the large combustion plant ordinance in Germany is unambiguous. Whatever WTP estimate is chosen, the costs of flue gas desulphurisation are dwarfed. Rough estimates of the private compliance costs for Western Germany range between €35 and €180 per year and household (Schärer and Haug, 1990; Schulz, 1985). 4. Conclusion In the Western hemisphere, air quality has improved significantly in the last two decades, at least partly, because of air quality regulations. According to my results, these impressive improvements imply substantial benefits of pollution abatement and large increases in human welfare. Even though most of the first generation regulations were heavy‐handed and costly command‐and‐control regulations and no reliable estimates of the social costs of these regulations are available, they probably had a positive effect on balance. In developing countries, the pollution situation looks less bright and is often getting worse. In the mid‐1990s, Russia and China had SO2 concentrations in urban areas of around 100 μg/m3. This suggests that there are large potential welfare gains from pollution abatement in these countries. Of course the size of the benefits tells us nothing about the means by which air quality should be improved. By relying on incentive‐based approaches with lower compliance costs, the net effect of air quality regulations may well exceed the one experienced by Western countries. Regarding the benefits of air quality, this article contributes to the growing evidence that pollution has larger consequences for the affected population than has previously been recognised. In contrast to other papers that address problems of the hedonic method (Bayer et al., 2009; Chay and Greenstone, 2005), my evidence is based on a new approach, the life satisfaction approach. My analysis corroborates the finding that life satisfaction data contain useful information on individuals’ preferences and hedonic experience of public goods. Therefore, the life satisfaction approach expands economists’ toolbox in the area of non‐market valuation. Advances in estimating the effect of income on life satisfaction will base the monetary benefit estimates on firmer grounds. At present, the life satisfaction approach may overstate the benefits of clean air. At the same time, my results indicate that the hedonic method understates the benefits of clean air. I regard additional and systematic comparisons of the life satisfaction approach to the hedonic method as a priority for future research. Two related questions are: (i) For which goods and under what conditions is capitalisation more or less complete? (ii) How can these differences be explained? Answers to these questions will have important implications beyond the area of non‐market valuation and will, for example, shed light on the validity of the equilibrium assumption in important private markets, on individuals’ risk perceptions and on the difference between various utility concepts. These latter issues also raise difficult questions as to which measure is appropriate for policy evaluation. Footnotes 1 " It is worth noting that the costs of the regulation such as increased electricity prices and secondary benefits such as jobs created in the environmental industry are equally spatially distributed (or at least orthogonal to wind directions). Further, the statutory provisions were enacted before the period considered. Therefore, the actual installation of scrubbers does not reflect a shift in political power from upwind to downwind regions. 2 " In 1994, population per county was between 31,800 in Klingenthal and 2,170,000 in West Berlin with a median of 131,400. The number of counties fell from 543 in 1993 to 439 in 2001 as several counties in the former GDR merged. The polygon data used for aggregation describe the boundaries of the 445 counties existing in 1996. 3 " I exclude self‐employed people both in predicting household income and in the life satisfaction regressions because self‐employed people are more reluctant to state their income and tend to underreport their incomes. 4 " The conventional income estimate lies between 0.150 (std. err.: 0.012) if pollution is instrumented and 0.151 (std. err.: 0.012) if it is not. The results are not shown in Table 4 but are available upon request from the author. 5 " In my analysis, I consider all cities that had 100,000 or more inhabitants at some point over the sample period. 6 " Intriguingly, positional and other relative concerns may have implications not only for the valuation but also for the regulation of externalities. Frank’s (2000) analyses suggests that voluntary and incentive based methods of risk regulation are less effective compared to a situation without positional concerns and that individuals may collectively (and unanimously) agree on binding rules. References Bakkum , A. , Bartelds , H., Duiser , J.A. and Veldt , C. ( 1987 ). Handbook of Emission Factors, Part 3. Stationary Combustion Sources , The Hague: Ministry of Housing, Physical Planning and Environment . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Bayer , P. , Keohane , N.O. and Timmins , C. 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( 2006 ). ‘Environment and happiness: valuation of air pollution using life satisfaction data’ , Ecological Economics , vol. 58 ( 4 ), pp. 801 – 13 . Google Scholar Crossref Search ADS WorldCat Appendix A.1. Relationship Between Hedonic Method and Life Satisfaction Approach This Appendix provides a discussion of what effects can be identified by the hedonic method and the life satisfaction approach and of the relationship between the two methods. In the standard hedonic framework, individuals are assumed to have an indirect utility function, v(·), with clean air, a, household income, m(a), and rental costs, r(a), per unit of housing, h, as arguments (with δv/δa > 0, δv/δm > 0 and δv/δr < 0). In equilibrium, wages and rents must adjust to equalise utility across locations. Otherwise, some individuals would have an incentive to move (Roback, 1982). Hence v(a, m(a), r(a)) = k in all locations. By totally differentiating and rearranging I obtain: (9) Defining the implicit price for clean air reflected in the labour and housing markets, pa, as pa = h(dr/da) − dm/da and using Roy’s identity, h = −(δv/δr)/(δv/δm), one can write: (10) Thus, in equilibrium, the implicit price for clean air equals the marginal willingness‐to‐pay (MWTP). This is the underlying assumption of the hedonic method. If information on pollution levels and risks is complete and the equilibrium condition holds, individuals’MWTP for clean air can be inferred from rent and wage gradients. However, because of migration costs and incomplete information, the effects of air pollution will be incompletely capitalised in wages and rents. In this situation, utility is not equalised across locations with different air quality, i.e. dv/da > 0, and the observed implicit price falls short of individuals’MWTP : (11) The life satisfaction approach does not rely on observed behaviour but regresses life satisfaction, as a proxy for the underlying latent variable utility, on air quality and income. The estimated coefficient for air quality corresponds to the term dv/da in (9). Hence, the coefficient equals the marginal utility of air quality if and only if either wages and rents are held constant or if air quality is not capitalised in private markets, i.e. if dm/da = dr/da = 0. If air quality is capitalised and life satisfaction is regressed only on air quality but neither wages nor rents, a mis‐specified model of the form instead of the true population model v = β0 + β1a + β2m + β3r + ɛ is estimated. The coefficient is a biased estimate of β1 and amounts to , which corresponds to dv/da in (9). Theoretically, housing costs and wages could be included in the set of explanatory variables in life satisfaction regressions and, thus, the full effect could be recovered. However, even if housing rents are available, it may not be advisable to include them in life satisfaction regression if it is not possible to control for all relevant observed and unobserved housing characteristics. This is also the case here. In order to control for unobserved housing characteristics, I would have to include the full set of dwelling specific effects. Even if these effects are absorbed by individual specific effects for individuals that stay put in their dwelling, I would need to include 10,703 dwelling specific effects for movers. Such a model is beyond the memory capacity of the host of a remote access to the GSEOP data (SOEPremote at DIW) I have to use, because German data protection laws do not allow me to have the regional data on my local computer. (Including rents without dwelling specific effects, leaves the coefficient for air pollution virtually unaffected; results are available upon request.) Similarly, since I use instrumental variables for household income, the endogenous part of income is excluded. Thus, the coefficient for air quality captures only the residual effect that is not capitalised in private markets, i.e. dv/da (< δv/δa). The residual effect can be monetised with the marginal utility of income as shown in (12): (12) The sum of the implicit hedonic price in (11) plus the residual shadow benefit in (12) yields the correct MWTP for clean air. As in previous studies (Bayer et al., 2009; Chay and Greenstone, 2005), I find no statistically significant effect of air quality on wages. Thus, total WTP is the sum of the estimates based on the hedonic housing regressions and the life satisfaction approach. A.2. Power Plants and Wind Directions: Data and Data Sources This Appendix provides a detailed description of the data on German power plants and wind directions used to estimate the causal effect of flue gas desulphurisation on annual mean SO2 concentrations at county level. Power plants The data for fossil fuel fired generating units with an electricity capacity of 100 MW and more are from the UBA, information published by the operating companies and the technical literature, a survey mailed to operating companies and statutory provisions. To a list of 396 generating units provided by the UBA, I add 56 units and then reduce the number of units to 390 by combining all units with identical location and characteristics. Of theses 390 units, 7 units have a capacity of less than 100 MW, 351 were active in the period 1985 to 2003 and 303 units were active and are neither nuclear or hydroelectric power plants. The UBA list contains information on the plant name, operator and/or owner, zip code of contact address (which does not necessarily correspond to the plant’s location), the launching year, the year the plant was shut down, capacity and fuel. I complement the data with the location, the year of desulphurisation, fuel efficiency and estimates of annual SO2 emissions. Location: If possible, I establish the exact address using information published by the operating companies, the technical literature or a route planner. Otherwise, the centroid of the zip code is assumed as a plant’s location. I georeference the addresses with a route planner. Year of refit: Published information and responses to my survey of operating companies allows me to determine the year scrubbers were installed for 224 units (61%). For the other units the year can be approximated on the basis of statutory provisions, the launching year, the year the plant was shut down and the capacity. Fuel efficiency (ηj): Published information and survey responses provide information on the fuel efficiency of 196 units (54%). For the other units fuel efficiency is predicted based on the following regression (t‐values in parentheses): Emissions: In order to estimate annual SO2 emissions, I use emission factors, EF, from a time shortly before scrubbers were installed (Bakkum et al., 1987). Emission factors are defined as the industry wide average ratio between the emission rate and the actual load differentiated according to fuel and capacity. Assuming full utilisation of capacities, the annual emission at plant j, Ej, can be estimated as This calculation overstates emissions because the assumption of constant full utilisation is not plausible but I lack data on utilisation rates. Moreover, the procedure allows me to capture the important differences in emissions between fuels and plant sizes. Wind stations Frequencies of wind directions in 12 30‐degree sectors measured wind stations are published in Traup and Kruse (1996). The wind atlas contains data on 107 wind stations of which 12 are not representative for a larger area. For each power plant the wind station closest to the plant is used to describe the wind situation at the plant, restricting the number of wind stations to 43. The frequency distributions are based on measurement series of at least 5 years, in most cases 15 years and in some cases more than 15 years in the period between 1976 and 1995. Author notes " I thank Wolfgang Bräuniger and Wolfgang Müller from the German Federal Environmental Agency for providing the pollution and power plant data, the operating companies for giving confidential information on their generating units, Roland Schmidt and Robert Weibel for their help with GIS, and Jan Goebel for SOEPremote support. For comments and suggestions, I thank Christine Benesch, Bruno Frey, Lorenz Goette, Susanne Neckermann, Katrin Rehdanz, Katja Rost, Alois Stutzer, Christopher Timmins, Hannelore Weck‐Hannemann, Heinz Welsch, seminar participants at the Max Planck Institute for Research on Collective Goods in Bonn, the Swiss Federal Institute of Technology and the universities of Fribourg, Royal Holloway, St. Gallen and Zurich, and participants at the Conference on Policies for Happiness 2007 in Siena, the Royal Economic Society Annual Conference 2008 in Warwick, the 8th International German Socio‐Economic Panel User Conference 2008 in Berlin and the Annual Congress of the European Economic Association 2008 in Milan. I also thank two anonymous referees whose very well‐taken comments greatly improved the article. © The Author(s). Journal compilation © Royal Economic Society 2009

Brunello,, Giorgio;Fort,, Margherita;Weber,, Guglielmo

doi: 10.1111/j.1468-0297.2008.02244.xpmid: N/A

Abstract Using data from 12 European countries and the variation across countries and over time in the changes of minimum school leaving age, we study the effects of the quantity of education on the distribution of earnings. We find that compulsory school reforms significantly affect educational attainment, especially among individuals belonging to the lowest quantiles of the distribution of ability. There is also evidence that additional education reduces conditional wage inequality, and that education and ability are substitutes in the earnings function. Does education affect earnings? This question has attracted enormous attention among labour economists, as reviewed by Card (2001). By and large, the empirical literature has focused on the mean returns to education, with substantial effort devoted to the identification of a causal relationship. Less has been done to investigate how additional education affects the distribution of earnings. Does education reduce (conditional) wage inequality? Are the returns to education heterogeneous and is this heterogeneity correlated to ability? These are important policy questions. If education reduces the dispersion of earnings and equality is valued by the policy maker, then additional schooling can be a powerful tool to combat inequality. It is well known that individual ability is strongly affected by genetic and environmental factors; see Cunha and Heckman (2007). If education and ability are substitutes in the production of human capital and earnings, then additional investment in the former can contribute to reducing the differences generated by the latter; see Ashenfelter and Rouse (1998). How education and ability interact in the generation of earnings and human capital has important implications for optimal education policy. For instance, De Fraja (2002) shows that optimal public policy is more elitist than market provision in the following sense: the difference in educational attainment between bright and less able children is greater than it would be if education were only provided privately. In this case, redistributive education policies that target the less able are bound to have a substantial cost in terms of efficiency. His results, however, require that education and ability are complements in the generation of human capital and earnings. The article addresses these questions by investigating the relationship between the quantity of attained education and the conditional distribution of (gross) hourly earnings in a unique sample of 12 European countries, which we have constructed by pooling together information drawn from three different surveys. Our empirical methodology is an instrumental variable approach to the endogeneity of education in a quantile regression framework, as in recent work by Chesher (2003) and Ma and Koenker (2006). We identify the causal effects of education on earnings by using the country and time variation provided by the compulsory school reforms implemented in Europe after the end of the Second World War.1 The exogenous variation provided by minimum school leaving age laws has been used in the empirical literature since Angrist and Krueger (1991) to identify the causal relationship between education and earnings. Since these laws have been targeted at the less‐educated, who typically belong to the lower quantiles of the distribution of earnings, their use in the current context prompts the question whether the changes in compulsory education observed in Europe after the last war have been particularly beneficial to the targeted population or have spread their effects to the population at large instead. We provide evidence that in a host of European countries the effect of compulsory schooling laws on educational attainment is statistically significant for all but the top deciles of the distribution of male education (all but the very top for females). As expected, the size of this effect declines as we move from the bottom to the top quantile. The statistically significant effect of compulsory school reforms on individuals with higher educational attainment, that is also found for Sweden in Meghir and Palme (2005), suggests that better educated individuals react to increases in compulsory schooling by raising their own attainment, possibly in an effort to maintain their educational advantage over the less educated, who are more directly affected by the reforms. When we treat education as exogenously assigned to individuals, we find that one additional year of schooling increases conditional wage inequality both for males and for females, in line with previous findings in the US (Buchinsky, 1994) and Europe (Martins and Pereira, 2004). In our approach, we allow earnings to depend on both luck and ability, while education depends only on ability. This makes education endogenous in the earnings equation. When we allow for endogeneity, we find instead that conditional (gross) wage inequality is reduced by marginal increases in education for all ability levels. Focusing on the mean quantile treatment effect, we find that assigning an extra year of education to males in the sample marginally reduces the estimated 90–10 conditional wage differential by 0.99 percentage points; the reduction is 1.34 percentage points in the case of females. By conditioning on selected quantiles of the conditional distribution of earnings, we investigate how the returns to education vary as we move from the bottom to the top quantile of the distribution of ability. Our key finding is that returns decrease with ability, which points to substitutability in the relationship between education and ability. Overall, these results do not lend support to the elitist education policy discussed by De Fraja (2002). They are in line with the findings of Ashenfelter and Rouse (1998), in the US context and suggest that education policies which target the less fortunate and/or less talented group in the pursuit of equality of opportunity are not necessarily inefficient. Substitutability also indicates that since ability and parental background are closely intertwined, education policy can contribute to undoing the differences generated by the latter. The article is organised as follows: Section 1 reviews the empirical literature and Section 2 presents the empirical model. Our identification strategy is described in Section 3. Next, we turn to the data in Section 4 and to the results in Section 5. Robustness checks are discussed in Section 6. Conclusions follow. 1. Review of the Literature By using quantile regression techniques one can trace the entire conditional wage distribution and examine how the shape of this distribution is affected by schooling, age and experience. In his pioneering work on the impact of education on the distribution of US wages, Buchinsky (1994) uses quantile regressions and finds that returns to education in the US are higher at the higher quantiles of the conditional distribution of wages. He uses the 0.90–0.10 spread as a measure of within group inequality and finds substantial changes over time. In the European context, Harmon et al. (2003) use UK data and find that the returns to schooling are higher for those at the very top of the wage distribution compared to those at the very bottom. Since individuals with higher talent are more likely to be located in the upper part of the (conditional) wage distribution, this result – they argue – points to complementarity between ability and schooling. Martins and Pereira (2004) use data from 15 European countries and find that individuals who receive higher wages conditional on their characteristics enjoy higher education‐related earnings growth. They suggest that over‐education, poor school quality and the selection of fields of study with limited ex post prospects can explain their results. In contrast with the previous findings, Denny and O’Sullivan (2007) use UK data and find evidence that cognitive and non‐cognitive ability and education are substitutes in the earnings function. On a similar line, Mwabu and Schultz (1996) find complementarity among white South African males and substitutability among black South Africans. The idea that individuals located in the upper part of the conditional wage distributions are of higher ability than those located in the bottom part is plausible but ignores that the allocation of individuals to different points of the distribution could also depend on other factors which are orthogonal to ability itself. Lang (1993), for instance, distinguishes between cognitive ability, which matters for school and the labour market, and the ability which matters mainly for work.2Hornstein et al. (2006) show that ex ante identical individuals could end up with different wages because of random matching with available vacancies. Chesher (2003) calls this labour market fortune. When conditional wages are driven by more than one unobservable factor, the observation that returns to education are higher in the upper quantiles of the conditional distribution of earnings does not suffice to establish complementarity between schooling and ability. The reviewed studies have in common that they do not address the endogeneity of education. Because of this, their results are best interpreted as interesting associations and correlations, with little to say about causal effects. Some recent papers have estimated returns to education within an IV framework. Ichino and Winter Ebmer (1999) and Aakvik et al. (2003), for instance, compare local average treatment effects using different sets of instruments, which allows them to evaluate the returns to education at different levels of education and sometimes at different points in the distribution of individual ability. These studies show that returns of education are heterogeneous, at least at the points where the estimator is defined – a similar conclusion can be reached on the basis of Meghir and Palme’s (2005) careful examination of the impact of the Swedish reforms of the late 1940s on both education and earnings for different groups of individuals. This evidence suggests the need for a more thorough investigation of the impact of education on the whole distribution of earnings – as provided by quantile regressions. The econometric literature provides a few approaches for the identification and estimation of causal effects in quantile regressions. One such approach is due to Chesher,3 who considers non‐parametric identification of a structural model with a recursive structure. Chesher (2001) points out that the continuity of the endogenous regressor is needed for the unambiguous definition of quantiles4 and guarantees the point identification of the quantiles of interest. When the continuity assumption fails, Chesher’s approach can be extended (Chesher, 2003, 2005) but does not generally lead to point identification of the function describing the impact without further assumptions. Importantly, the case of an endogenous binary regressor cannot be dealt within this set‐up. The estimation of the exogenous impact functions and inference in the parametric case are discussed by Ma and Koenker (2006). They assume that the conditional quantile functions are known up to a finite number of parameters and add some technical regularity conditions. In their framework, the conditional quantile functions need not be linear in the parameters and the asymptotic theory is developed for nonlinear quantile regression estimation. Arias et al. (2001) use data on US twins to address the issue of the endogeneity of education in quantile wage regressions. They propose a two stage estimator and find that returns to education increase with the quantiles of the conditional distribution of earnings. They interpret this as evidence that ability and education are complements. Their methodology, however, has been recently questioned by Ma and Koenker (2006), who use Monte Carlo simulations to show that the two‐stage quantile regression which replaces education with predicted education from the ordinary least square (mean) regression of schooling on the set of instruments performs rather badly in terms of simulated bias when compared with Chesher’s WAD (weighted average derivative) estimator and with the control variate approach suggested by Ma and Koenker and implemented in this article. 2. The Empirical Model Following Card (2001) and Ashenfelter and Rouse (1998), assume that individuals – or their parents – choose years of schooling to maximise (1) where wi = g (si) is (net) earnings, si is years of schooling, c(si) is the cost of schooling and the index i is for the individual. At the optimum, individuals select si so as to equate the marginal costs to the (expected) marginal benefits of schooling. Let marginal costs mc(si) be increasing in schooling, decreasing in cognitive ability ai and a function of exogenous controls Xi and z (2) and assume the following Mincerian earnings function (3) where the constant term is included in X, cognitive ability is known to individuals at the time of their choice, and is an idiosyncratic error orthogonal to ability. In the language of Chesher (2003), the latent random variable ui is fortune in the labour market but other interpretations are possible, as discussed in the introduction, and include a zero mean demand shock which affects the relative productivity of jobs and skills (Gosling et al. 2000; Machin and Van Reenen, 1998). The specification in (3) implies that schooling influences both the location and the scale of the earnings distribution. Ability affects earnings both directly and via its interaction with schooling, as in Ashenfelter and Rouse (1998), who distinguish between the absolute and the comparative advantage of higher talent. Education and ability are complements in the production of human capital when λ > 0, and substitutes when λ < 0. Another feature of the selected specification is the possibility that shocks to the composition of labour demand – or random luck ui– have different effects on earnings depending upon the level of accumulated schooling. When φ > 0 these shocks are skill‐biased (Katz and Murphy, 1992). With expected marginal benefits of schooling mb(si) given by (4) optimal schooling is equal to (5) Notice that the relevant variation in ability for the schooling decision involves the slope of the log earnings function, not its intercept.5 In the private optimum, schooling increases with individual ability ai if λ + κ > 0. This is the case either if ability and schooling are complements or if the effect of ability on the marginal costs is large enough to offset the substitutability between ai and si. Two economic models suggest a positive relationship between ability and schooling: the signalling model and a variant of the human capital model (Blackburn and Neumark, 1993). In the former model, more able individuals have lower marginal costs of schooling and self‐select into higher education. In the latter model, ability increases the marginal benefits of education and reduces the marginal costs of schooling. We assume that 1 + φsi > 0, which guarantees that log wages are a monotonic function of the random effect ui. A feature of the model is that schooling in (5) is correlated with ability ai, which affects log earnings both directly and via its effects on education in (3) but not with the random shock ui. Unless we can adequately control for ability, the standard orthogonality condition required for the consistency of ordinary least squares estimation of (3) fails. Consistent estimates can be obtained, however, if there exists a variable z which is correlated with schooling but not with individual ability conditional on schooling; see Card (2001) and Blundell et al. (2005) for extensive discussions. As discussed in detail in the next Section, z in this article is the number of years of compulsory education ycomp. Omitting subscripts for simplicity, the earnings‐cum‐education model presented above can be written in the format of an exactly identified triangular model, as in Chesher’s approach (6) (7) where ξ = (λ + κ)/θ. Define τa = Ga(aτa) and τu = Gu(uτu), where aτa and uτu are the τ–quantiles of the distributions of a and u, respectively. Furthermore define Qw(τu | s, X, z) and Qs(τa | X, z) as the conditional quantile functions corresponding to log wages and years of education. Ma and Koenker (2006) show that recursive conditioning yields the following model (8) (9) Given the restrictions imposed by (6) and (7), the key parameter of interest Π(τa,τu) is a matrix with the following structure (10) which describes the quantile treatment effect of education on earnings. It offers a panoramic view of the stochastic relationship between schooling s and log wages, and describes the effects of a perturbation in the distribution of schooling on the various quantiles of the distribution of earnings. Rather than exogenously altering the value of s, we alter its various quantiles Qs, and study how the quantiles Qw of the distribution of earnings are affected (Ma and Koenker, 2006). If we set τu so that u is fixed at its τu quantile, changes of τa in Π(τa,τu) reflect how the distribution of a affects the τu quantile of the response  ln (w). On the other hand, if we fix τa and allow τu to vary, we can shed light on how the τa quantile of s affects the entire distribution of log wages (Ma and Koenker, 2006). By integrating Π(τa,τu) with respect to τa, we obtain the mean quantile treatment effects, which show how returns to education vary along the distribution of labour market luck for individuals of average ability. Further integration yields the mean treatment effect, which corresponds to the two stages least squares estimate. Conditioning on different values of τu one can investigate whether returns to education increase as we move from lower to higher quantiles of the distribution of ability at different points of the (conditional) wage distribution. Estimation and inference for Π(τa,τu) are discussed extensively by Ma and Koenker (2006), who focus on two approaches, namely the ‘weighted average derivative’ (WAD) approach and the ‘control variate’ (CV) approach. They show that the latter approach yields a more efficient estimator when the model is correctly specified and both estimators have a superior performance compared to alternative parametric estimators; see Ma and Koenker (2006) for details. In this article, we implement the CV approach, which consists of the following three steps. First, we estimate the conditional quantile functions of schooling s and compute the control variate (11) where s is observed schooling and is the estimated conditional quantile. Second, we augment the conditional quantile functions of  ln (w) with the relevant control variate and its interaction with schooling. Finally, we simultaneously estimate the selected quantiles of  ln(s) conditional on Qs(τa | X, z), X and z as in the hybrid model in (8) and obtain the variance–covariance matrix by bootstrapping. 3. Our Empirical Strategy We identify the causal effect of education on the distribution of wages by using the exogenous variation of schooling induced by compulsory school reforms implemented at different times and with different intensity in 12 European countries after the Second World War. The crucial difference between our study and previous literature using the same instruments – see for instance Lang and Kropp (1986), Chevalier et al. (2004), Oreopoulos (2006) and the references therein – is that our analysis is not limited to the exploration of the conditional mean impact of schooling on wages. Rather, we permit heterogeneity in the impact of education at different points of the conditional distribution of earnings. In our empirical application, identification relies on the following assumptions: individuals with higher ability stay in school longer (monotonicity with respect to a in (7)); individuals with a luckier draw from the distribution of wage offers have higher wages (monotonicity with respect to u in (6)); when the schooling decision is made, individuals can only form expectations about their future draw from the distribution of wage offers (triangular structure in the unobservables); years of compulsory schooling ycomp have an exogenous impact on the distribution of years of education and/or the educational attainment of individuals: more education (the treatment) is assigned to individuals on the basis of their date of birth and the latter was not chosen by their parents on the basis of future education‐related wage gains; when the timing of the implementation of school reforms varies across municipalities of the same country, it is uncorrelated with general education levels;6 educational reforms do not affect log wages other than through the individual’s education level, in other words they are excluded from the wage equation (triangular structure in the observables). We use conditional quantile functions as in (8) and (9) and allow the conditional quantiles of years of education to differ across countries up to a constant, holding the value of the other conditioning variables as fixed. We pool data from several countries to increase the number of points on the support of the instrumental variable ycomp.7 By pooling countries, we exploit the fact that the timing of compulsory school reforms varies across countries and by so doing we can distinguish school reform from cohort fixed effects. We return to this assumption in the Section on robustness checks. We select for each country a school reform affecting compulsory education and define as the distance between birth cohort b and the cohort , defined as the first cohort potentially affected by the change in mandatory school leaving age in country k. Since each selected reform occurs at a different point in time, our instrument varies both across countries and over cohorts. For each country, we construct a pre‐treatment and post‐treatment sample composed of the individuals born within the range defined by 7 years before and 7 years after the year of birth of cohort . The breadth of the window is designed to exclude the occurrence of other compulsory school reforms, which would blur the difference between pre and post‐treatment in our data. Our choice also trades off the increase in sample size with the need to reduce the risk that unaccounted confounders affect our results. Borrowing from Angrist et al. (1996), the individuals with t ≥ 0 who have changed their educational attainment as a result of the reforms are defined as ‘compliers’.8Table 1 presents for each country in our sample the selected reform, the year of birth of the first cohort potentially affected by the reform, the change in the minimum school leaving age and in the years of compulsory education induced by the reform, and the expected change in school attainment, expressed in terms of the ISCED classification. Our information is drawn from Eurybase, the Eurydice database on education systems in Europe, from personal communications with national experts and from other country‐specific sources. The description of each reform and the explanation of our choice of for each country are relegated to the Technical Appendix available at http://www.res.org.uk. Table 1 
Selected Compulsory School Reforms, by Country . Reform date . First cohort potentially affected . Change in min. school leaving age . Change in years of comp. school. . Expected change in ISCED . Age at school entry at the time of the reform . Austria 1962 1947 14 to 15 8 to 9 to ISCED 2 6 Belgium 1983 1969 14 to 18 8 to 12 to ISCED 3 6 Denmark 1971 1957 14 to 16 7 to 9 to ISCED 3 7 Finland (Uusimaa) 1977 1966† 13 to 16 6 to 9 to ISCED 3 7 Finland (Etelä‐Suomi) 1976 1965† 13 to 16 6 to 9 to ISCED 3 7 Finland (Itä‐Suomi) 1974 1963† 13 to 16 6 to 9 to ISCED 3 7 Finland (Väli‐Suomi) 1973 1962† 13 to 16 6 to 9 to ISCED 3 7 Finland (Pohjois‐Suomi) 1972 1961† 13 to 16 6 to 9 to ISCED 3 7 France 1959‡ 1953 14 to 16 8 to 10 to ISCED 3 6 Germany(Schleswig‐Holstein) 1956 1941 14 to 15 8 to 9 to ISCED 3 6 Germany(Hamburg) 1949 1934 14 to 15 8 to 9 to ISCED 3 6 Germany(Niedersachsen) 1962 1947 14 to 15 8 to 9 to ISCED 3 6 Germany(Bremen) 1958 1943 14 to 15 8 to 9 to ISCED 3 6 Germany(Nordrhein‐Westphalia) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Hessen) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Rheinland‐Pfalz) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Baden‐Würtemberg) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Bayern) 1969 1955 14 to 15 8 to 9 to ISCED 3 6 Germany(Saarland) 1964 1949 14 to 15 8 to 9 to ISCED 3 6 Greece 1975 1963 12 to 15 6 to 9 to ISCED 2 6 Ireland 1972 1958 14 to 15 8 to 9 to ISCED 3 6 Italy 1963 1949 11 to 14 5 to 9 to ISCED 2 6 Netherlands 1975§ 1959‡ 15 to 16 9 to 10 to ISCED 2 6 Spain 1970 1957* 12 to 14 6 to 8 to ISCED 2 6 Sweden 1962 1950‖ 14/15 to 15/16 8 to 9 to ISCED 3 6 or 7 . Reform date . First cohort potentially affected . Change in min. school leaving age . Change in years of comp. school. . Expected change in ISCED . Age at school entry at the time of the reform . Austria 1962 1947 14 to 15 8 to 9 to ISCED 2 6 Belgium 1983 1969 14 to 18 8 to 12 to ISCED 3 6 Denmark 1971 1957 14 to 16 7 to 9 to ISCED 3 7 Finland (Uusimaa) 1977 1966† 13 to 16 6 to 9 to ISCED 3 7 Finland (Etelä‐Suomi) 1976 1965† 13 to 16 6 to 9 to ISCED 3 7 Finland (Itä‐Suomi) 1974 1963† 13 to 16 6 to 9 to ISCED 3 7 Finland (Väli‐Suomi) 1973 1962† 13 to 16 6 to 9 to ISCED 3 7 Finland (Pohjois‐Suomi) 1972 1961† 13 to 16 6 to 9 to ISCED 3 7 France 1959‡ 1953 14 to 16 8 to 10 to ISCED 3 6 Germany(Schleswig‐Holstein) 1956 1941 14 to 15 8 to 9 to ISCED 3 6 Germany(Hamburg) 1949 1934 14 to 15 8 to 9 to ISCED 3 6 Germany(Niedersachsen) 1962 1947 14 to 15 8 to 9 to ISCED 3 6 Germany(Bremen) 1958 1943 14 to 15 8 to 9 to ISCED 3 6 Germany(Nordrhein‐Westphalia) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Hessen) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Rheinland‐Pfalz) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Baden‐Würtemberg) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Bayern) 1969 1955 14 to 15 8 to 9 to ISCED 3 6 Germany(Saarland) 1964 1949 14 to 15 8 to 9 to ISCED 3 6 Greece 1975 1963 12 to 15 6 to 9 to ISCED 2 6 Ireland 1972 1958 14 to 15 8 to 9 to ISCED 3 6 Italy 1963 1949 11 to 14 5 to 9 to ISCED 2 6 Netherlands 1975§ 1959‡ 15 to 16 9 to 10 to ISCED 2 6 Spain 1970 1957* 12 to 14 6 to 8 to ISCED 2 6 Sweden 1962 1950‖ 14/15 to 15/16 8 to 9 to ISCED 3 6 or 7 † Pekkarinnen (2005) p.5 and his elaborations provided for this article. ‡Reform implemented in 1967, see Grenet (2004). §Reform implemented in 1973, see Oosterbeek et al. (2004). *Pons and Gonzalo (2002), p.753 and Table A.1 p.767. ‖Personal communication with Mårten Palme. Open in new tab Table 1 
Selected Compulsory School Reforms, by Country . Reform date . First cohort potentially affected . Change in min. school leaving age . Change in years of comp. school. . Expected change in ISCED . Age at school entry at the time of the reform . Austria 1962 1947 14 to 15 8 to 9 to ISCED 2 6 Belgium 1983 1969 14 to 18 8 to 12 to ISCED 3 6 Denmark 1971 1957 14 to 16 7 to 9 to ISCED 3 7 Finland (Uusimaa) 1977 1966† 13 to 16 6 to 9 to ISCED 3 7 Finland (Etelä‐Suomi) 1976 1965† 13 to 16 6 to 9 to ISCED 3 7 Finland (Itä‐Suomi) 1974 1963† 13 to 16 6 to 9 to ISCED 3 7 Finland (Väli‐Suomi) 1973 1962† 13 to 16 6 to 9 to ISCED 3 7 Finland (Pohjois‐Suomi) 1972 1961† 13 to 16 6 to 9 to ISCED 3 7 France 1959‡ 1953 14 to 16 8 to 10 to ISCED 3 6 Germany(Schleswig‐Holstein) 1956 1941 14 to 15 8 to 9 to ISCED 3 6 Germany(Hamburg) 1949 1934 14 to 15 8 to 9 to ISCED 3 6 Germany(Niedersachsen) 1962 1947 14 to 15 8 to 9 to ISCED 3 6 Germany(Bremen) 1958 1943 14 to 15 8 to 9 to ISCED 3 6 Germany(Nordrhein‐Westphalia) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Hessen) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Rheinland‐Pfalz) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Baden‐Würtemberg) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Bayern) 1969 1955 14 to 15 8 to 9 to ISCED 3 6 Germany(Saarland) 1964 1949 14 to 15 8 to 9 to ISCED 3 6 Greece 1975 1963 12 to 15 6 to 9 to ISCED 2 6 Ireland 1972 1958 14 to 15 8 to 9 to ISCED 3 6 Italy 1963 1949 11 to 14 5 to 9 to ISCED 2 6 Netherlands 1975§ 1959‡ 15 to 16 9 to 10 to ISCED 2 6 Spain 1970 1957* 12 to 14 6 to 8 to ISCED 2 6 Sweden 1962 1950‖ 14/15 to 15/16 8 to 9 to ISCED 3 6 or 7 . Reform date . First cohort potentially affected . Change in min. school leaving age . Change in years of comp. school. . Expected change in ISCED . Age at school entry at the time of the reform . Austria 1962 1947 14 to 15 8 to 9 to ISCED 2 6 Belgium 1983 1969 14 to 18 8 to 12 to ISCED 3 6 Denmark 1971 1957 14 to 16 7 to 9 to ISCED 3 7 Finland (Uusimaa) 1977 1966† 13 to 16 6 to 9 to ISCED 3 7 Finland (Etelä‐Suomi) 1976 1965† 13 to 16 6 to 9 to ISCED 3 7 Finland (Itä‐Suomi) 1974 1963† 13 to 16 6 to 9 to ISCED 3 7 Finland (Väli‐Suomi) 1973 1962† 13 to 16 6 to 9 to ISCED 3 7 Finland (Pohjois‐Suomi) 1972 1961† 13 to 16 6 to 9 to ISCED 3 7 France 1959‡ 1953 14 to 16 8 to 10 to ISCED 3 6 Germany(Schleswig‐Holstein) 1956 1941 14 to 15 8 to 9 to ISCED 3 6 Germany(Hamburg) 1949 1934 14 to 15 8 to 9 to ISCED 3 6 Germany(Niedersachsen) 1962 1947 14 to 15 8 to 9 to ISCED 3 6 Germany(Bremen) 1958 1943 14 to 15 8 to 9 to ISCED 3 6 Germany(Nordrhein‐Westphalia) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Hessen) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Rheinland‐Pfalz) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Baden‐Würtemberg) 1967 1953 14 to 15 8 to 9 to ISCED 3 6 Germany(Bayern) 1969 1955 14 to 15 8 to 9 to ISCED 3 6 Germany(Saarland) 1964 1949 14 to 15 8 to 9 to ISCED 3 6 Greece 1975 1963 12 to 15 6 to 9 to ISCED 2 6 Ireland 1972 1958 14 to 15 8 to 9 to ISCED 3 6 Italy 1963 1949 11 to 14 5 to 9 to ISCED 2 6 Netherlands 1975§ 1959‡ 15 to 16 9 to 10 to ISCED 2 6 Spain 1970 1957* 12 to 14 6 to 8 to ISCED 2 6 Sweden 1962 1950‖ 14/15 to 15/16 8 to 9 to ISCED 3 6 or 7 † Pekkarinnen (2005) p.5 and his elaborations provided for this article. ‡Reform implemented in 1967, see Grenet (2004). §Reform implemented in 1973, see Oosterbeek et al. (2004). *Pons and Gonzalo (2002), p.753 and Table A.1 p.767. ‖Personal communication with Mårten Palme. Open in new tab The selected reforms increased the minimum school leaving age by one year in Austria, Germany, Ireland, Netherlands and Sweden; by two years in Denmark, France and Spain; by three years in Finland, Greece, Italy and by four years in Belgium.9 In some of these countries, the timing of the introduction of the reform varied by region – this is the case of Germany, Finland and Sweden. Since we do not have access to data at the municipality level, in Finland and Sweden we define the year of the reform in each area as the year when the largest share of municipalities in the area experienced the change in the schooling legislation (see Table B.1 for Finland in the Technical Appendix). In our sample, the modal compulsory number of years of education before the reforms is 8 years. The first cohorts potentially affected by the reforms were born between 1941 and 1969, with a relative concentration between the late 1940s and the late 1950s.10 Furthermore, the most commonly expected change in qualifications is the attainment of ISCED level 3 (upper secondary education). To illustrate the effects of school reforms on years of schooling, we purge the latter from the influence of country effects, country specific trends, individual and macro controls and plot the residuals in Figure 1 for a few years before and after the pivotal cohorts, who were first potentially affected. The upward jump at the time of the reforms is clearly visible and close to 0.3 additional years of schooling. Fig. 1. Open in new tabDownload slide The Effect of School Reforms on Educational Attainment Note. The OLS gender‐specific regressions included a constant, country dummies, q, q2 and their interaction with country dummies, survey dummies, age, age squared, the lagged country specific unemployment rate and GDP per capita, the country and gender specific labour force participation rate at the estimated time of labour market entry, the country specific GDP per head and unemployment rate at the age affected by the country specific reform. Fig. 1. Open in new tabDownload slide The Effect of School Reforms on Educational Attainment Note. The OLS gender‐specific regressions included a constant, country dummies, q, q2 and their interaction with country dummies, survey dummies, age, age squared, the lagged country specific unemployment rate and GDP per capita, the country and gender specific labour force participation rate at the estimated time of labour market entry, the country specific GDP per head and unemployment rate at the age affected by the country specific reform. Tables B.2, B.3 and B.4 in the Technical Appendix summarise the existing empirical evidence on the effects of some of these compulsory school reforms on individual education and earnings as well as the instrumental variable estimates of the average returns to schooling. While the increase in compulsory schooling induced by each reform varies across countries, ranging from 1 additional year of schooling to 3 or 4, the estimated impact on educational attainment (in terms of years of education) is close to 0.3 additional years of schooling, with little cross‐country variation. This number is very close to the one shown in Figure 1. Although the estimates of the effect of compulsory school reforms on educational attainment are broadly similar across European countries, this does not hold when one looks at the effects of longer schooling on wages: while in some countries the evidence suggests zero returns to compulsory schooling, in some other countries returns to longer compulsory schooling are as high as 15%–20%.11 4. The Data We pool data drawn from the 8th wave of the European Community Household Panel (ECHP) for the year 2001, the first wave of the Survey on Household Health, Ageing and Retirement in Europe, or SHARE, for the year 2004, and the waves 1993 to 2002 of the International Social Survey Program (ISSP). The countries included in our study are: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Spain and Sweden. For each country in the dataset Table B.5 (panels a, b, c) in the Technical Appendix shows the sample size for each survey and wave, and the relevant age range.12 Our dependent variable is the log of (gross) hourly earnings expressed at 2000 prices and purchasing power parity units. Additional information on earnings, hours worked and the proportion employed is also in the Technical Appendix, see Table B.6. We measure educational attainment with years of education. Since in some countries and datasets the available information is on the highest attained qualification, we convert it into years of education by assuming that each individual requires the customary number of years to complete a degree.13 The induced measurement error has implications for our estimates which are discussed in the Section devoted to robustness checks. We assume that educational attainment does not change after age 25 and restrict our sample to include only individuals aged 26 to 65.14 The final sample consists of 18,328 individuals; its distribution across the 12 countries is shown in the last column of Table 2, which includes also the sample mean by country of log real earnings, years of schooling, years of compulsory schooling, average age and percentage of males. Educational attainment is highest in Finland (15.15 years) and lowest in Spain (11.05 years). Average age is highest in Sweden (50.41) and lowest in Belgium (33.13), which reflects the different timing of the selected reforms. Table 2 
Means of the Key Variables. Sample Size: 18,328 . Log w . s . ycomp . Age . % Males . Nobs . Austria 2.220 12.181 8.767 50.900 0.492 920 Belgium 2.470 14.887 9.782 33.125 0.465 853 Denmark 2.798 13.667 8.030 44.186 0.477 2235 Finland 2.366 15.133 7.511 37.151 0.496 1409 France 2.399 13.410 9.017 47.074 0.525 1293 Germany 2.439 12.127 8.620 45.649 0.590 1690 Greece 2.005 12.929 7.509 38.270 0.562 984 Ireland 2.265 12.356 8.534 39.330 0.574 1260 Italy 2.367 14.166 7.097 49.066 0.590 1762 Netherlands 2.574 11.049 9.445 37.702 0.592 1294 Spain 2.116 11.049 7.099 43.136 0.626 2284 Sweden 2.328 12.197 8.465 50.410 0.480 2344 . Log w . s . ycomp . Age . % Males . Nobs . Austria 2.220 12.181 8.767 50.900 0.492 920 Belgium 2.470 14.887 9.782 33.125 0.465 853 Denmark 2.798 13.667 8.030 44.186 0.477 2235 Finland 2.366 15.133 7.511 37.151 0.496 1409 France 2.399 13.410 9.017 47.074 0.525 1293 Germany 2.439 12.127 8.620 45.649 0.590 1690 Greece 2.005 12.929 7.509 38.270 0.562 984 Ireland 2.265 12.356 8.534 39.330 0.574 1260 Italy 2.367 14.166 7.097 49.066 0.590 1762 Netherlands 2.574 11.049 9.445 37.702 0.592 1294 Spain 2.116 11.049 7.099 43.136 0.626 2284 Sweden 2.328 12.197 8.465 50.410 0.480 2344 Open in new tab Table 2 
Means of the Key Variables. Sample Size: 18,328 . Log w . s . ycomp . Age . % Males . Nobs . Austria 2.220 12.181 8.767 50.900 0.492 920 Belgium 2.470 14.887 9.782 33.125 0.465 853 Denmark 2.798 13.667 8.030 44.186 0.477 2235 Finland 2.366 15.133 7.511 37.151 0.496 1409 France 2.399 13.410 9.017 47.074 0.525 1293 Germany 2.439 12.127 8.620 45.649 0.590 1690 Greece 2.005 12.929 7.509 38.270 0.562 984 Ireland 2.265 12.356 8.534 39.330 0.574 1260 Italy 2.367 14.166 7.097 49.066 0.590 1762 Netherlands 2.574 11.049 9.445 37.702 0.592 1294 Spain 2.116 11.049 7.099 43.136 0.626 2284 Sweden 2.328 12.197 8.465 50.410 0.480 2344 . Log w . s . ycomp . Age . % Males . Nobs . Austria 2.220 12.181 8.767 50.900 0.492 920 Belgium 2.470 14.887 9.782 33.125 0.465 853 Denmark 2.798 13.667 8.030 44.186 0.477 2235 Finland 2.366 15.133 7.511 37.151 0.496 1409 France 2.399 13.410 9.017 47.074 0.525 1293 Germany 2.439 12.127 8.620 45.649 0.590 1690 Greece 2.005 12.929 7.509 38.270 0.562 984 Ireland 2.265 12.356 8.534 39.330 0.574 1260 Italy 2.367 14.166 7.097 49.066 0.590 1762 Netherlands 2.574 11.049 9.445 37.702 0.592 1294 Spain 2.116 11.049 7.099 43.136 0.626 2284 Sweden 2.328 12.197 8.465 50.410 0.480 2344 Open in new tab Since we intend to identify the causal relationship between the distribution of schooling and the distribution of earnings from the data, we need to control as accurately as possible for additional factors affecting the dependent variable. Therefore, we include in the empirical specification both country and survey dummies, individual age and its square. We also control for country‐specific macroeconomic effects by using the first lags of the unemployment rate, aggregate productivity, measured by real GDP per head and the OECD index of the strictness of employment protection. Because of the existing evidence on gender differences in education and earnings, we estimate gender‐specific years of education equations and allowed a gender dummy to interact with a number of covariates in the earnings equation (as explained below). Trend‐like changes in log wages relative to the time of the reform are controlled with a second order polynomial in q = t + 7 – where t is the distance between each cohort and the first cohort potentially affected by the reform – and its interactions with country dummies.15 Empirical research has shown that individual earnings are significantly affected by the conditions prevailing in the labour market at the time of first labour market entry; see for instance Baker et al. (1994). To capture these effects, we match to each individual the country and gender specific labour participation rate at the age of estimated labour market entry.16 The underlying idea is that entry wages are likely to be higher when the labour market is tight and labour participation rates are high. Changes in educational attainment after a compulsory school reform could be due to the reform itself or to confounding factors, which may alter the incentives to invest in education at the time of the reform but independently of it. To illustrate, take a reform that increases the minimum school leaving age from 14 to 15 in a certain year. If individuals at age 14 – or their parents – find it more attractive to invest in education because of a reduction in the opportunity costs generated by a contemporaneous increase in the unemployment rate, they might invest more independently of the reform. Similarly, the actual implementation of school leaving laws may vary across countries and over time with changes in economic conditions. Implementation is known to be more difficult in poorer countries and, ceteris paribus, in households with a higher number of children. To control for these confounders, we construct two variables, the unemployment rate and the real GDP per head, and match these variables to individuals around the age when the school reform is supposed to have taken place. For instance, assume that the critical age is 14 for Austrian citizens born in 1957. For these individuals the relevant values of the three variables described above are those corresponding to 1971. The inclusion of aggregate income and unemployment at the age when most individuals were in school allows us also to control for the country‐specific macroeconomic factors affecting the access to funds and labour market opportunities, which influence the schooling decision by altering the parameter r in (5). 5. Empirical Evidence We start the presentation of our results with the relationship between education and the conditional distribution of wages when education is treated as exogenous. Treating males and females separately, the estimates in Table 3 show that the returns to a one year in education increase as we move from the lowest to the highest quantile of the distribution. Moreover, returns are consistently higher for females than for males, in line with previous results in the literature – see Harmon et al. (2001). Using the 90–10 log wage differential as a measure of conditional wage inequality, we find that this is increased by 2.0 percentage points for one additional year of education for males and by 2.4 percentage points for females. Table 3 
Quantile Effects When Education is Treated as Exogenous (Sample size: 18,328) By gender (9,936 males and 8,392 females) . τ = 0.10 . τ = 0.30 . τ = 0.50 . τ = 0.70 . τ = 0.90 . Males 0.019*** 0.026*** 0.033*** 0.035*** 0.039*** (0.002) (0.001) (0.001) (0.001) (0.002) Females 0.027*** 0.037*** 0.043*** 0.050*** 0.051*** (0.003) (0.001) (0.001) (0.001) (0.002) . τ = 0.10 . τ = 0.30 . τ = 0.50 . τ = 0.70 . τ = 0.90 . Males 0.019*** 0.026*** 0.033*** 0.035*** 0.039*** (0.002) (0.001) (0.001) (0.001) (0.002) Females 0.027*** 0.037*** 0.043*** 0.050*** 0.051*** (0.003) (0.001) (0.001) (0.001) (0.002) Note. Each regression included a constant, country dummies, q, q2 and their interaction with country dummies, survey dummies, age, age squared, the lagged country specific unemployment rate and GDP per capita, the country and gender specific labour force participation rate at the estimated time of labour market entry, the country specific GDP per head and unemployment rate at the age affected by the country specific reform. Details on these coefficients are available from the authors upon request. τ denotes the quantile of the distribution of wages. Three stars, two stars and one star for statistically significant coefficients at the 1%, 5% and 10% confidence level. Robust standard errors are shown in parentheses. Open in new tab Table 3 
Quantile Effects When Education is Treated as Exogenous (Sample size: 18,328) By gender (9,936 males and 8,392 females) . τ = 0.10 . τ = 0.30 . τ = 0.50 . τ = 0.70 . τ = 0.90 . Males 0.019*** 0.026*** 0.033*** 0.035*** 0.039*** (0.002) (0.001) (0.001) (0.001) (0.002) Females 0.027*** 0.037*** 0.043*** 0.050*** 0.051*** (0.003) (0.001) (0.001) (0.001) (0.002) . τ = 0.10 . τ = 0.30 . τ = 0.50 . τ = 0.70 . τ = 0.90 . Males 0.019*** 0.026*** 0.033*** 0.035*** 0.039*** (0.002) (0.001) (0.001) (0.001) (0.002) Females 0.027*** 0.037*** 0.043*** 0.050*** 0.051*** (0.003) (0.001) (0.001) (0.001) (0.002) Note. Each regression included a constant, country dummies, q, q2 and their interaction with country dummies, survey dummies, age, age squared, the lagged country specific unemployment rate and GDP per capita, the country and gender specific labour force participation rate at the estimated time of labour market entry, the country specific GDP per head and unemployment rate at the age affected by the country specific reform. Details on these coefficients are available from the authors upon request. τ denotes the quantile of the distribution of wages. Three stars, two stars and one star for statistically significant coefficients at the 1%, 5% and 10% confidence level. Robust standard errors are shown in parentheses. Open in new tab Education, however, cannot be treated as exogenous in the presence of unobserved ability. Table 4 presents the results of the first stage regression of years of education against all the exogenous controls plus the instrument ycomp. In most cases this variable attracts a statistically significant and positive coefficient, with the exception of the top decile of the distribution of ability for males. Using the Stock and Staiger rule of thumb, which suggests that when there is a single endogenous variable the selected instrument is weak if the F‐test for its inclusion in the auxiliary regression is lower than 10, we find evidence of weakness for the two top deciles in the case of males and for the top decile in the case of females. Furthermore, the size of the effect of compulsory school leaving laws on attained education is much larger for the lowest quantile of the distribution of ability. Table 4 
First Stage Effect of ycomp on s (Sample size: 18,328) Males . τa = 0.10 . τa = 0.30 . τa = 0.50 . τa = 0.70 . τa = 0.90 . Coeff. (s.e.) 0.354*** 0.056*** 0.120*** 0.078*** 0.026 (0.007) (0.012) (0.006) (0.035) (0.071) F‐test (p‐value) 2146.6 19.1 307.6 4.86 0.13 (0.000) (0.000) (0.000) (.027) (0.714) Males . τa = 0.10 . τa = 0.30 . τa = 0.50 . τa = 0.70 . τa = 0.90 . Coeff. (s.e.) 0.354*** 0.056*** 0.120*** 0.078*** 0.026 (0.007) (0.012) (0.006) (0.035) (0.071) F‐test (p‐value) 2146.6 19.1 307.6 4.86 0.13 (0.000) (0.000) (0.000) (.027) (0.714) Females . τa = 0.10 . τa = 0.30 . τa = 0.50 . τa = 0.70 . τa = 0.90 . Coeff. (s.e.) 0.416*** 0.284*** 0.072*** 0.219*** 0.135*** (0.016) (0.020) (0.007) (0.029) (0.065) F‐test (p‐value) 643.8 195.4 88.7 57.4 4.26 (0.000) (0.000) (0.000) (0.000) (0.039) Females . τa = 0.10 . τa = 0.30 . τa = 0.50 . τa = 0.70 . τa = 0.90 . Coeff. (s.e.) 0.416*** 0.284*** 0.072*** 0.219*** 0.135*** (0.016) (0.020) (0.007) (0.029) (0.065) F‐test (p‐value) 643.8 195.4 88.7 57.4 4.26 (0.000) (0.000) (0.000) (0.000) (0.039) Note. See Table 3. τa denotes the quantile of the distribution of ability. Open in new tab Table 4 
First Stage Effect of ycomp on s (Sample size: 18,328) Males . τa = 0.10 . τa = 0.30 . τa = 0.50 . τa = 0.70 . τa = 0.90 . Coeff. (s.e.) 0.354*** 0.056*** 0.120*** 0.078*** 0.026 (0.007) (0.012) (0.006) (0.035) (0.071) F‐test (p‐value) 2146.6 19.1 307.6 4.86 0.13 (0.000) (0.000) (0.000) (.027) (0.714) Males . τa = 0.10 . τa = 0.30 . τa = 0.50 . τa = 0.70 . τa = 0.90 . Coeff. (s.e.) 0.354*** 0.056*** 0.120*** 0.078*** 0.026 (0.007) (0.012) (0.006) (0.035) (0.071) F‐test (p‐value) 2146.6 19.1 307.6 4.86 0.13 (0.000) (0.000) (0.000) (.027) (0.714) Females . τa = 0.10 . τa = 0.30 . τa = 0.50 . τa = 0.70 . τa = 0.90 . Coeff. (s.e.) 0.416*** 0.284*** 0.072*** 0.219*** 0.135*** (0.016) (0.020) (0.007) (0.029) (0.065) F‐test (p‐value) 643.8 195.4 88.7 57.4 4.26 (0.000) (0.000) (0.000) (0.000) (0.039) Females . τa = 0.10 . τa = 0.30 . τa = 0.50 . τa = 0.70 . τa = 0.90 . Coeff. (s.e.) 0.416*** 0.284*** 0.072*** 0.219*** 0.135*** (0.016) (0.020) (0.007) (0.029) (0.065) F‐test (p‐value) 643.8 195.4 88.7 57.4 4.26 (0.000) (0.000) (0.000) (0.000) (0.039) Note. See Table 3. τa denotes the quantile of the distribution of ability. Open in new tab We include the following controls in all specifications: individual age and its square, country effects, a quadratic polynomial in q and its interactions with country dummies, and macroeconomic variables which include employment protection, GDP per head and the unemployment rate at the time earnings are observed, the gender specific labour force participation rate at the estimated time of labour market entry, and the unemployment rate and GDP per capita around the age when minimum school reforms are implemented. We use F‐tests to verify the joint hypothesis that the included covariates are jointly equal to zero and always reject the null. We interpret this as evidence that schooling and estimated ability are indeed two different variables. These findings suggest that compulsory schooling laws are particularly effective at the lower tail of the distribution of ability: for individuals located below the 10th quantile, a one year increase in compulsory education increases actual attainment by 0.40 years in the case of females and by 0.30 years in the case of males, compared to 0.10 years for individuals with median ability. These results are in line with expectations, which suggest that the bulk of compliers should be among the less able (and wealthy). While for males the impact of school reforms on educational attainment tends to die out at the upper decile of the conditional distribution of ability, for females the effect remains statistically significant above median ability.17 One explanation is that – in conformity with the predictions of the signalling model – better educated individuals, especially females, react to the increase in the minimum school leaving age by upgrading their own education, in an effort to maintain at least in part their relative advantage over the less educated. An additional factor at play could be that, since, in some countries included in the sample, the average educational attainment was very low before compulsory attendance reforms, a large fraction of the population may have been ‘caught up’ by the increase in the minimum school leaving age.18 We apply the control variate approach due to Ma and Koenker (2006) and estimate the full matrix of quantile treatment effects, which describe the impact of education on earnings for different quantiles of the distribution of ability and labour market fortune. We focus for brevity on the following quantiles: 0.10, 0.30, 0.50, 0.70 and 0.90 and proceed as follows: first, we run quantile regressions of (9) separately for males and females and compute the control variate for each selected quantile of the conditional distribution of ability. Second, we augment (8) with each estimated control variate and estimate separate quantile regressions by pooling all data and allowing for the full set of interaction of the explanatory variables with the gender dummy. For each regression, we test whether blocs of interactions with gender are statistically significant and simplify the empirical specification by dropping those blocs which fail to pass the test. Last, we estimate simultaneous quantile regressions for each quantile of the distribution of ability, using the parsimonious specification, and obtain the estimate of the variance–covariance matrix by bootstrapping.19 In all cases, we never reject the hypothesis that the control variate and its interaction with schooling are significantly different from zero, and that education is endogenous in the wage regressions. The estimated percentage increase in log earnings associated with one additional year of education and its standard error are reported separately for males and females in Table 5 for the selected quantiles of the distribution of ability a (τa) and labour market fortune u (τu). The final row in each section of the Table is obtained by integrating the quantile treatment effects with respect to ability, which produces the mean quantile treatment effect. If we compare this effect to the one estimated by treating education as exogenous, we notice that the former is higher than the latter, and that the gap is larger for the lowest decile of the distribution of the random term u. Table 5 
Heterogeneous Returns to Schooling (Quantile Treatment Effects) Males . τu = 0.10 . τu = 0.30 . τu = 0.50 . τu = 0.70 . τu = 0.90 . τa = 0.10 0.0748*** 0.0583*** 0.0555*** 0.0550*** 0.0598*** (0.004) (0.004) (0.003) (0.004) (0.006) τa = 0.30 0.0625*** 0.0476*** 0.0462*** 0.0420*** 0.0503*** (0.007) (0.004) (0.003) (0.005) (0.006) τa = 0.50 0.0665*** 0.0492*** 0.0478*** 0.0432*** 0.0469*** (0.006) (0.004) (0.004) (0.004) (0.006) τa = 0.70 0.0486*** 0.0396*** 0.0448*** 0.0411*** 0.0471*** (0.006) (0.004) (0.004) (0.004) (0.005) τa = 0.90 0.0468*** 0.0329*** 0.0384*** 0.0332*** 0.0452*** (0.006) (0.004) (0.003) (0.004) (0.006) Mean effect+ 0.0598 0.0456 0.0465 0.0429 0.0499 Males . τu = 0.10 . τu = 0.30 . τu = 0.50 . τu = 0.70 . τu = 0.90 . τa = 0.10 0.0748*** 0.0583*** 0.0555*** 0.0550*** 0.0598*** (0.004) (0.004) (0.003) (0.004) (0.006) τa = 0.30 0.0625*** 0.0476*** 0.0462*** 0.0420*** 0.0503*** (0.007) (0.004) (0.003) (0.005) (0.006) τa = 0.50 0.0665*** 0.0492*** 0.0478*** 0.0432*** 0.0469*** (0.006) (0.004) (0.004) (0.004) (0.006) τa = 0.70 0.0486*** 0.0396*** 0.0448*** 0.0411*** 0.0471*** (0.006) (0.004) (0.004) (0.004) (0.005) τa = 0.90 0.0468*** 0.0329*** 0.0384*** 0.0332*** 0.0452*** (0.006) (0.004) (0.003) (0.004) (0.006) Mean effect+ 0.0598 0.0456 0.0465 0.0429 0.0499 Females . τu=0.10 . τu = 0.30 . τu = 0.50 . τu = 0.70 . τu = 0.90 . τa = 0.10 0.0952*** 0.0780*** 0.0788*** 0.0820*** 0.0759*** (0.007) (0.004) (0.004) (0.005) (0.007) τa = 0.30 0.0838*** 0.0701*** 0.0713*** 0.0730*** 0.0702*** (0.007) (0.003) (0.003) (0.004) (0.006) τa = 0.50 0.0847*** 0.0679*** 0.0690*** 0.0707*** 0.0646*** (0.006) (0.004) (0.003) (0.004) (0.006) τa = 0.70 0.0689*** 0.0573*** 0.0588*** 0.0615*** 0.0612*** (0.005) (0.003) (0.003) (0.003) (0.005) τa = 0.90 0.0631*** 0.0502*** 0.0527*** 0.0555*** 0.0567*** (0.006) (0.003) (0.003) (0.004) (0.006) Mean effect+ 0.0792 0.0645 0.0655 0.0655 0.0674 Females . τu=0.10 . τu = 0.30 . τu = 0.50 . τu = 0.70 . τu = 0.90 . τa = 0.10 0.0952*** 0.0780*** 0.0788*** 0.0820*** 0.0759*** (0.007) (0.004) (0.004) (0.005) (0.007) τa = 0.30 0.0838*** 0.0701*** 0.0713*** 0.0730*** 0.0702*** (0.007) (0.003) (0.003) (0.004) (0.006) τa = 0.50 0.0847*** 0.0679*** 0.0690*** 0.0707*** 0.0646*** (0.006) (0.004) (0.003) (0.004) (0.006) τa = 0.70 0.0689*** 0.0573*** 0.0588*** 0.0615*** 0.0612*** (0.005) (0.003) (0.003) (0.003) (0.005) τa = 0.90 0.0631*** 0.0502*** 0.0527*** 0.0555*** 0.0567*** (0.006) (0.003) (0.003) (0.004) (0.006) Mean effect+ 0.0792 0.0645 0.0655 0.0655 0.0674 Note. See Table 3; more details in the text. τu denotes the quantile of the distribution of labour market fortune and τa denotes the quantile of the distribution of ability. Bootstrapped standard errors (100 replications) in parenthesis. + Mean effect: average (over τa) quantile treatment effect. Open in new tab Table 5 
Heterogeneous Returns to Schooling (Quantile Treatment Effects) Males . τu = 0.10 . τu = 0.30 . τu = 0.50 . τu = 0.70 . τu = 0.90 . τa = 0.10 0.0748*** 0.0583*** 0.0555*** 0.0550*** 0.0598*** (0.004) (0.004) (0.003) (0.004) (0.006) τa = 0.30 0.0625*** 0.0476*** 0.0462*** 0.0420*** 0.0503*** (0.007) (0.004) (0.003) (0.005) (0.006) τa = 0.50 0.0665*** 0.0492*** 0.0478*** 0.0432*** 0.0469*** (0.006) (0.004) (0.004) (0.004) (0.006) τa = 0.70 0.0486*** 0.0396*** 0.0448*** 0.0411*** 0.0471*** (0.006) (0.004) (0.004) (0.004) (0.005) τa = 0.90 0.0468*** 0.0329*** 0.0384*** 0.0332*** 0.0452*** (0.006) (0.004) (0.003) (0.004) (0.006) Mean effect+ 0.0598 0.0456 0.0465 0.0429 0.0499 Males . τu = 0.10 . τu = 0.30 . τu = 0.50 . τu = 0.70 . τu = 0.90 . τa = 0.10 0.0748*** 0.0583*** 0.0555*** 0.0550*** 0.0598*** (0.004) (0.004) (0.003) (0.004) (0.006) τa = 0.30 0.0625*** 0.0476*** 0.0462*** 0.0420*** 0.0503*** (0.007) (0.004) (0.003) (0.005) (0.006) τa = 0.50 0.0665*** 0.0492*** 0.0478*** 0.0432*** 0.0469*** (0.006) (0.004) (0.004) (0.004) (0.006) τa = 0.70 0.0486*** 0.0396*** 0.0448*** 0.0411*** 0.0471*** (0.006) (0.004) (0.004) (0.004) (0.005) τa = 0.90 0.0468*** 0.0329*** 0.0384*** 0.0332*** 0.0452*** (0.006) (0.004) (0.003) (0.004) (0.006) Mean effect+ 0.0598 0.0456 0.0465 0.0429 0.0499 Females . τu=0.10 . τu = 0.30 . τu = 0.50 . τu = 0.70 . τu = 0.90 . τa = 0.10 0.0952*** 0.0780*** 0.0788*** 0.0820*** 0.0759*** (0.007) (0.004) (0.004) (0.005) (0.007) τa = 0.30 0.0838*** 0.0701*** 0.0713*** 0.0730*** 0.0702*** (0.007) (0.003) (0.003) (0.004) (0.006) τa = 0.50 0.0847*** 0.0679*** 0.0690*** 0.0707*** 0.0646*** (0.006) (0.004) (0.003) (0.004) (0.006) τa = 0.70 0.0689*** 0.0573*** 0.0588*** 0.0615*** 0.0612*** (0.005) (0.003) (0.003) (0.003) (0.005) τa = 0.90 0.0631*** 0.0502*** 0.0527*** 0.0555*** 0.0567*** (0.006) (0.003) (0.003) (0.004) (0.006) Mean effect+ 0.0792 0.0645 0.0655 0.0655 0.0674 Females . τu=0.10 . τu = 0.30 . τu = 0.50 . τu = 0.70 . τu = 0.90 . τa = 0.10 0.0952*** 0.0780*** 0.0788*** 0.0820*** 0.0759*** (0.007) (0.004) (0.004) (0.005) (0.007) τa = 0.30 0.0838*** 0.0701*** 0.0713*** 0.0730*** 0.0702*** (0.007) (0.003) (0.003) (0.004) (0.006) τa = 0.50 0.0847*** 0.0679*** 0.0690*** 0.0707*** 0.0646*** (0.006) (0.004) (0.003) (0.004) (0.006) τa = 0.70 0.0689*** 0.0573*** 0.0588*** 0.0615*** 0.0612*** (0.005) (0.003) (0.003) (0.003) (0.005) τa = 0.90 0.0631*** 0.0502*** 0.0527*** 0.0555*** 0.0567*** (0.006) (0.003) (0.003) (0.004) (0.006) Mean effect+ 0.0792 0.0645 0.0655 0.0655 0.0674 Note. See Table 3; more details in the text. τu denotes the quantile of the distribution of labour market fortune and τa denotes the quantile of the distribution of ability. Bootstrapped standard errors (100 replications) in parenthesis. + Mean effect: average (over τa) quantile treatment effect. Open in new tab To interpret our findings, select for instance the bottom decile of the distribution of ability, τa = 0.10. We find that the estimated returns to education for males are equal to 7.48% for the individuals at the bottom decile of the distribution of earnings, to 5.55% for the individuals at the median decile and to 5.98% for individuals at the top decile. The corresponding returns for females are higher but follow a similar pattern: the profile of estimated returns is broadly declining, albeit not always monotonically, as we move from the lowest to the highest decile of the distribution of labour market fortune, and independently of the selected decile of the distribution of ability. Table 6 presents tests for equal coefficients for each selected decile of the distribution of ability. Differences in these parameters can be interpreted as measures of education‐induced conditional inequality: one should remember, however, that coefficients on conditioning variables also vary across deciles, thus conditional inequality will also reflect these differences. With this caveat in mind, we can say that education‐related conditional inequality declines with additional education, and significantly so – in a statistical sense – with the exclusion of the index involving the highest decile. When we average returns across the distribution of abilities, we find that the reduction in conditional inequality induced by an additional year of education is close to 1.5 percentage points. With constant marginal returns, this corresponds to about 5 percentage points for a three‐years degree. Table 6 
The Effect of a Marginal Increase in Schooling on the Conditional Log Wage Differential Males . δ30 − δ10 . δ50 − δ10 . δ70 − δ10 . δ90 − δ10 . τa = 0.10 −0.0165 −0.0193 −0.0198** −0.0150 τa = 0.30 −0.0149** −0.0163** −0.0266** −0.0122 τa = 0.50 −0.0172** −0.0187*** −0.0233*** −0.0196** τa = 0.70 −0.0090* −0.0038 −0.0075 −0.0015 τa = 0.90 −0.0139** −0.0084 −0.0136* −0.0016 Mean effect −0.0143 −0.0133 −0.0169 −0.0099 Males . δ30 − δ10 . δ50 − δ10 . δ70 − δ10 . δ90 − δ10 . τa = 0.10 −0.0165 −0.0193 −0.0198** −0.0150 τa = 0.30 −0.0149** −0.0163** −0.0266** −0.0122 τa = 0.50 −0.0172** −0.0187*** −0.0233*** −0.0196** τa = 0.70 −0.0090* −0.0038 −0.0075 −0.0015 τa = 0.90 −0.0139** −0.0084 −0.0136* −0.0016 Mean effect −0.0143 −0.0133 −0.0169 −0.0099 Females . δ30 − δ10 . δ50 − δ10 . δ70 − δ10 . δ90 − δ10 . τa = 0.10 −0.0172*** −0.0164*** −0.0132* −0.0193** τa = 0.30 −0.0137** −0.0125** −0.0108 −0.0136 τa = 0.50 −0.0168*** −0.0158** −0.0140* −0.0201** τa = 0.70 −0.0116** −0.0101** −0.0074 −0.0077 τa = 0.90 −0.0129** −0.0104 −0.0076* −0.0064 Mean effect −0.0144 −0.0130 −0.0106 −0.0134 Females . δ30 − δ10 . δ50 − δ10 . δ70 − δ10 . δ90 − δ10 . τa = 0.10 −0.0172*** −0.0164*** −0.0132* −0.0193** τa = 0.30 −0.0137** −0.0125** −0.0108 −0.0136 τa = 0.50 −0.0168*** −0.0158** −0.0140* −0.0201** τa = 0.70 −0.0116** −0.0101** −0.0074 −0.0077 τa = 0.90 −0.0129** −0.0104 −0.0076* −0.0064 Mean effect −0.0144 −0.0130 −0.0106 −0.0134 Note. See Tables 3 and 5. Legend δτ2 − δτ1 = ∂Qy(τ2,X,s,a)/∂s − ∂Qy(τ1,X,s,a)/∂s. Open in new tab Table 6 
The Effect of a Marginal Increase in Schooling on the Conditional Log Wage Differential Males . δ30 − δ10 . δ50 − δ10 . δ70 − δ10 . δ90 − δ10 . τa = 0.10 −0.0165 −0.0193 −0.0198** −0.0150 τa = 0.30 −0.0149** −0.0163** −0.0266** −0.0122 τa = 0.50 −0.0172** −0.0187*** −0.0233*** −0.0196** τa = 0.70 −0.0090* −0.0038 −0.0075 −0.0015 τa = 0.90 −0.0139** −0.0084 −0.0136* −0.0016 Mean effect −0.0143 −0.0133 −0.0169 −0.0099 Males . δ30 − δ10 . δ50 − δ10 . δ70 − δ10 . δ90 − δ10 . τa = 0.10 −0.0165 −0.0193 −0.0198** −0.0150 τa = 0.30 −0.0149** −0.0163** −0.0266** −0.0122 τa = 0.50 −0.0172** −0.0187*** −0.0233*** −0.0196** τa = 0.70 −0.0090* −0.0038 −0.0075 −0.0015 τa = 0.90 −0.0139** −0.0084 −0.0136* −0.0016 Mean effect −0.0143 −0.0133 −0.0169 −0.0099 Females . δ30 − δ10 . δ50 − δ10 . δ70 − δ10 . δ90 − δ10 . τa = 0.10 −0.0172*** −0.0164*** −0.0132* −0.0193** τa = 0.30 −0.0137** −0.0125** −0.0108 −0.0136 τa = 0.50 −0.0168*** −0.0158** −0.0140* −0.0201** τa = 0.70 −0.0116** −0.0101** −0.0074 −0.0077 τa = 0.90 −0.0129** −0.0104 −0.0076* −0.0064 Mean effect −0.0144 −0.0130 −0.0106 −0.0134 Females . δ30 − δ10 . δ50 − δ10 . δ70 − δ10 . δ90 − δ10 . τa = 0.10 −0.0172*** −0.0164*** −0.0132* −0.0193** τa = 0.30 −0.0137** −0.0125** −0.0108 −0.0136 τa = 0.50 −0.0168*** −0.0158** −0.0140* −0.0201** τa = 0.70 −0.0116** −0.0101** −0.0074 −0.0077 τa = 0.90 −0.0129** −0.0104 −0.0076* −0.0064 Mean effect −0.0144 −0.0130 −0.0106 −0.0134 Note. See Tables 3 and 5. Legend δτ2 − δτ1 = ∂Qy(τ2,X,s,a)/∂s − ∂Qy(τ1,X,s,a)/∂s. Open in new tab In summary, our estimates point to a relationship of substitutability between schooling s and the random effect u: individuals who are less fortunate in the labour market can partially compensate for poor luck with higher returns from investment in education. Therefore, when poor luck depends on circumstances beyond individual control, education policies targeted at the less fortunate which encourage additional schooling contribute to reducing conditional inequality. Next consider Table 5 again but select a decile in the distribution of the random error u. Independently of gender and of the selected decile, there is evidence that the returns to education fall as we move from the bottom to the top decile of the distribution of ability. This qualitative finding remains even if we disregard the two top deciles, because of the weakness of our instrument, especially in the case of males. To illustrate, returns to education fall from 7.88% to 5.88% when we select the median decile in the distribution of error u, focus on females and on the 10th and 70th decile of the distribution of ability. We interpret this as evidence that ability and education are substitutes in the production of human capital. When we increase education by an additional year, individuals located in the upper part of the distribution of ability gain less compared to individuals with less than median ability. Since ability and parental background are closely intertwined – see Cuhna et al. (2005)– our results point to the fact that those better endowed have less to gain from additional education. The size of the gap is again not small and is equal at most to slightly more than 3 percentage points. Since earnings in our model depend both on ability a and on the random error u, an alternative reading of Table 5 is along the main diagonal: as we move from the upper left to the bottom right corner, we consider individuals who are increasingly endowed in both ability and labour market fortune. Independently of gender, our estimates suggest that the better endowed have lower returns to investment in education. Overall, our findings confirm the results by Ashenfelter and Rouse (1998), based on a sample of American twins. Using a different methodology – quantile regressions – and a sample of European individuals, we find – as they do – that better endowed individuals have lower returns to education. The fact that better endowed individuals typically have higher attained education but lower marginal benefits of schooling point either to lower costs of funds or to a negative relationship between the marginal costs of schooling and individual ability, as in (2). Table 5 can also be used to calculate the corresponding structural parameters β,φ and λ, according to (10). All we have to do is to compute the empirical c.d.f.s of the error terms, a and u, and invert them to obtain estimates of and . Then from the estimated values of Π(τa,τu) one can estimate β,φ and λ by GLS. GLS in this context is an optimal minimum distance estimator, but requires estimating the variance–covariance matrix of the whole Π(τa,τu) matrix, something that is beyond the scope of this article. Card and Krueger (1992) show that almost identical estimates of both coefficients and standard errors obtain if a weighted least squares estimator (WLS) is used instead of GLS (that is, if observations are weighed inversely to the estimated variance of the dependent variable, and covariance terms are ignored). We find that the WLS estimated value of β is 0.051 for males and 0.070 for females (see Table 7). Furthermore, λ is negative, statistically significant and in the range −0.0021 to −0.0025, depending on gender. Finally, estimated φ is also negative, and in the range −0.0089 to −0.0119.20 These estimates confirm that both unobserved ability a and labour market luck u are substitutes to education in the production of human capital and earnings. Table 7 
Estimates ofβ, λandφ . Males (1) . Males (2) . Females (3) . Females (4) . β 0.051*** 0.050*** 0.070*** 0.072*** (0.0015) (0.0026) (0.0009) (0.0013) λ −0.0021*** −0.0022*** −0.0025*** −0.0021*** (0.0004) (0.008) (0.003) (0.0016) φ −0.0089*** −0.013*** −0.0091*** −0.0119*** (0.003) (0.0032) (0.0017) (0.0016) Observations 25 15 25 15 R squared 0.680 0.692 0.856 0.836 . Males (1) . Males (2) . Females (3) . Females (4) . β 0.051*** 0.050*** 0.070*** 0.072*** (0.0015) (0.0026) (0.0009) (0.0013) λ −0.0021*** −0.0022*** −0.0025*** −0.0021*** (0.0004) (0.008) (0.003) (0.0016) φ −0.0089*** −0.013*** −0.0091*** −0.0119*** (0.003) (0.0032) (0.0017) (0.0016) Observations 25 15 25 15 R squared 0.680 0.692 0.856 0.836 Note. Columns (1) and (3) are estimates based on the 25 estimated returns in Table 5 (by gender). Columns (2) and (4) are based instead on excluding the bottom two rows of Table 5 and retaining 15 estimated returns (by gender). The regressors and are the estimated deciles of the empirical distributions of the first stage and second stage residuals respectively. Standard errors in parenthesis. Open in new tab Table 7 
Estimates ofβ, λandφ . Males (1) . Males (2) . Females (3) . Females (4) . β 0.051*** 0.050*** 0.070*** 0.072*** (0.0015) (0.0026) (0.0009) (0.0013) λ −0.0021*** −0.0022*** −0.0025*** −0.0021*** (0.0004) (0.008) (0.003) (0.0016) φ −0.0089*** −0.013*** −0.0091*** −0.0119*** (0.003) (0.0032) (0.0017) (0.0016) Observations 25 15 25 15 R squared 0.680 0.692 0.856 0.836 . Males (1) . Males (2) . Females (3) . Females (4) . β 0.051*** 0.050*** 0.070*** 0.072*** (0.0015) (0.0026) (0.0009) (0.0013) λ −0.0021*** −0.0022*** −0.0025*** −0.0021*** (0.0004) (0.008) (0.003) (0.0016) φ −0.0089*** −0.013*** −0.0091*** −0.0119*** (0.003) (0.0032) (0.0017) (0.0016) Observations 25 15 25 15 R squared 0.680 0.692 0.856 0.836 Note. Columns (1) and (3) are estimates based on the 25 estimated returns in Table 5 (by gender). Columns (2) and (4) are based instead on excluding the bottom two rows of Table 5 and retaining 15 estimated returns (by gender). The regressors and are the estimated deciles of the empirical distributions of the first stage and second stage residuals respectively. Standard errors in parenthesis. Open in new tab The policy implications of our results are important. First, suppose that earnings and productivity are closely related, a plausible assumption. Then education policies aimed at raising the educational attainment of the less fortunate and talented are grounded on equity considerations if less lucky individuals are so because of circumstances outside their own control. Equity, however, trades off with efficiency if the marginal returns to schooling are higher for the more talented, because this group has lower marginal costs of education. Our findings that labour market returns to schooling are highest among the less fortunate and talented has the important implication that equity and efficiency need not trade‐off, because these higher returns can more than compensate the higher schooling costs. To illustrate, consider a lump sum fixed subsidy paid to the less privileged that improves access to schooling, funded by a lump sum education tax on the more privileged. Since ability and parental background are strongly correlated, such policy increases equality of opportunity by raising the educational attainment of the less fortunate and reducing that of the more fortunate. If ability and schooling are substitutes, an implication of this policy is that the gain in marginal benefits for the less talented more than compensates the loss for the more talented. Whether this translates into higher efficiency is more difficult to gauge, and requires a careful cost‐benefit analysis that takes into account both the monetary cost of such reforms and the potentially important general equilibrium effects that could arise if compulsory attendance laws were designed to increase the educational attainment of a large fraction of the population.21 Second, the uncovered substitutability between education and ability has implications for the design of an optimal education policy. Such policy should be elitist and favour brighter children only if education and talent are complements in the production of human capital. When this is not the case, as our results suggest, redistributive education that targets the less able and fortunate can pay off both on equity and efficiency grounds. Before drawing too strong conclusions, however, one needs to remember that our results show that less well‐endowed individuals have higher returns to compulsory education than the better endowed. This does not necessarily mean that they would enjoy larger returns for higher levels of education, since the instrumental variable strategy does not allow for identification of the returns to schooling beyond the minimum school leaving age. In order to conclude that elitist policies are not efficient in general, one would need also to show that high‐ability individuals have lower returns to post‐compulsory education than low‐ability individuals. Last but not least, individual ability is strongly affected both by genetic and by environmental factors; see Cunha and Heckman (2007). If education and ability are substitutes in the production of human capital and earnings, then additional investment in the former can contribute to reducing the differences produced by the latter. 6. Robustness Checks Since log hourly wages are only available for employees, our sample is the result of a selection process involving the decision to participate in the labour market and having an employee job. Unless we take this selection process explicitly into account, the error term in (6) is unlikely to have zero mean. More important for our purposes is the concern that selection into employment may be affected by the number of years of compulsory education. If this was the case, the validity of our instrument would fail to hold. We investigate this by defining B as a dummy variable equal to 1 if log earnings are observed and to 0 otherwise. Failure to observe wages could be due to the participation decision, to the choice between employment, unemployment and self‐employment or to the presence of missing wage data. We estimate a probit model for variable B using all the controls described above plus the predicted years of schooling from the first stage regression of years of schooling on compulsory years of education. If the latter affected the selection process, we would expect that predicted years attract a statistically significant coefficient. It turns out that the estimated coefficient is equal to 0.023 for males, with a bootstrapped standard error equal to 0.076 (p‐value: 0.300) and to 0.088 for females (standard error: 0.055 and p‐value: 0.107). Therefore, there is no evidence in our data supporting the view that the years of compulsory education are significantly associated to the endogenous selection of workers into paid employment, and we conclude that our instrument is not invalidated by failure to explicitly consider such selection. An important assumption of model (6)–(7) is that it contains no more than two latent variables, ability and luck (no excess variation). A first issue here is measurement error, that is particularly likely to occur when years of education are indirectly predicted using the information on the highest qualification, as occasionally happens in this article. This is not the case, however, with the ECHP data, because years of education are computed there by using the information on the age when full time education was stopped. We re‐estimate our model for the ECHP sub‐sample, which does not include valid information for France, the Netherlands and Sweden, and check whether our key qualitative results are preserved. As shown in Table B.7 in the Technical Appendix – available at http://www.res.org.uk– the findings that ability and education are substitutes and that the better endowed have lower returns to schooling still hold.22 A second issue is whether ability is the sole source of unobserved heterogeneity in schooling decisions. Many factors other than individual ability may indeed explain differences in educational attainment: family background, credit constraints and different labour market opportunities. Partly, the last two factors are affected by differences in country–specific macroeconomic conditions, and we control for these with the unemployment rate and the GDP per capita at schooling age. Unfortunately, our data do not allow us to construct fully satisfactory measures of parental background and credit constraints at the individual level. In an attempt to gauge the importance of omitting these controls, we use information on co‐habitation patterns in the ECHP to retrieve one such measure, the education of parents – a dummy equal to 1 if at least one parent has ISCED 3 education or higher. Given the well‐known correlation between education and income, this measure is also a good proxy of individual access to funds. Due to the numerous missing values, we are forced to restrict our sample to four countries, Italy, Spain, Greece and Belgium. If parental background does explain a substantial part of unobserved heterogeneity, we would expect that omitting it from the first stage quantile regressions significantly affects the distribution of residuals. Yet we find that the correlation of residuals with and without controlling for parental background is never smaller than 93% and that the two distributions closely track each other.23 A key assumption in this article is that we can treat the pooled data from multiple countries as one population and therefore treat the timing of the natural experiment in different countries as regional variation in the timing in the same way as US researchers would use state‐by‐state variation in implementation. One aspect of this assumption is that the conditional impact of school reforms on education and earnings does not vary within the sample of 12 countries under study. To verify this, we start with the ECHP sub‐sample of 9 countries, as we have already shown that omitting France, the Netherlands and Sweden does not affect our qualitative results in a significant way. Next, we rank countries according to the average educational attainment of individuals aged between 30 and 50 and classify them in two groups, a ‘low education’ group – composed of Spain, Italy, Austria and Ireland – and a ‘high education’ group – consisting of Germany, Finland, Belgium and Denmark. Finally, we interact years of schooling and the first stage residuals with a dummy equal to 1 for the ‘high education’ group and to 0 for the other group, and test whether these interactions are jointly different from zero. Table B.8 in the Appendix reports the p‐values of the tests: with a few exceptions in the case of females, the general pattern is that we cannot reject the hypothesis that the estimated returns are the same across the two groups of countries. Next, notice that Chesher’s model requires that outcomes and covariates exhibit continuous variation. In the specification adopted in this article, wages are indeed continuous but the schooling variable and the instruments are not. We investigate whether this problem affects our estimates with the help of Monte Carlo simulations and find the effects to be negligible (see Table C.1 in the Technical Appendix for details). Finally, we check whether our findings are sensitive to the selected bandwidth and find that they are not. 7. Conclusions In this article, we use data from twelve European countries and the variation across countries and over time in the changes of minimum school leaving age to study the effects of the quantity of education on the distribution of earnings. We treat the countries of Europe as regions of a single country, and country‐specific compulsory school reforms as episodes of a broad European reform, which has taken place in each region at a different point in time. By so doing, we are able to generate the country and time variation that was absent in previous European research; see Harmon and Walker (1995). Confirming that there are no free lunches, we make this progress at the price of pooling together data from three fairly heterogeneous surveys, which is likely to lower the precision of our estimates. There are three main results: first, we find evidence that additional schooling reduces conditional wage dispersion. Second, compulsory school reforms affect mainly the individuals at the lower end of the distribution of educational attainment: for these individuals one additional year of compulsory education is estimated to translate into 0.30 to 0.40 years of additional education or higher. This figure falls to 0.10 or below for the rest of the population. Third, there is evidence that education and ability are substitutes in the generation of earnings. We believe that the policy implications of our results are rather clear. First, compulsory schooling law reforms have had a rather pervasive effect, highest among the less talented but present also – albeit to a substantially lower extent – among the better endowed, especially females. Second, the pursuit of an elitist education policy because of efficiency considerations is open to question, because the basic assumption of complementarity between education and ability fails to hold for the individuals affected by changes in the minimum school leaving age. Third, education policies which focus on the equality of opportunity for the less fortunate and less talented can be justified not only on equity but also on efficiency grounds if the additional benefits – which we have shown to be higher than for the more talented – are sufficiently large to offset the additional costs and the potentially important general equilibrium effects. Footnotes 1 " Moretti and Lochner (2004), Lleras‐Muney (2005) and Oreopoulos (2006) use a similar approach by exploiting regional variation within a single country. 2 " Lang’s approach is different from that of Heckman et al. (2006), who distinguish between cognitive ability and social skills. For these authors, both types of ability affect schooling and earnings. 3 " Alternative approaches have been developed by Abadie et al. (2002) and Chernozhukov et al. (2005). The first methodology cannot be applied in our context because it requires that both the instrument and the endogenous regressors be binary variables. The approach by Chernozhukov et al. (2005) assumes that there is a single latent factor, unaffected by the treatment variable (schooling, in our application), that determines the relative ranking of individuals in the outcome distribution: individuals who are ‘highly ranked’ earners without additional schooling remain ‘highly ranked’ earners after achieving higher qualifications. We find the assumption too restrictive in our setting since we cannot condition on a large number of individual characteristics. 4 " In Chesher (2001), there is no requirement on the scale of the regressors and of the instruments but a completeness condition has to be met. 5 " As discussed in Card (1995), ‘..individuals with higher earnings opportunities at each level of education (i.e. with higher intercepts in their log earnings functions) may well invest less in schooling, since they have a higher opportunity cost of attending school..’. 6 " Black et al. (2003) test this hypothesis in the case of Norway and find no systematic relationship. 7 " The support of this variable consists of 7 points. 8 " Individuals whose nationality is unknown and/or who are not citizens of the country in which they live at time of the interview are excluded from the analysis. The relative share of compliers is affected by migration flows within Europe. If for instance a German citizen belongs to the first cohort potentially affected but migrated as an adult from Italy, where he received his education, we cannot expect his education to be affected by the change in German schooling laws. 9 " Notice that in Italy, Belgium, Finland, France and in the Netherlands, these reforms were accompanied by a change in school design, typically the postponement of tracking. In the UK – a country not included in our analysis – two major compulsory schooling reforms were enacted in 1947 and 1973. Both reforms have been shown to have been very effective in raising educational standards and have been extensively studied in the literature. 10 " Close to 83% of the individuals belonging to the first cohorts affected by the reforms were born between 1947 and 1959. 11 " As discussed by Pischke and Watcher (2005), for the case of (West) Germany the following factors may lead to finding no returns to compulsory schooling: (i) measurement errors; (ii) wage rigidity; (iii) the role of apprenticeship; (iv) the heterogeneity of returns, with individuals affected by compulsory schooling being the low‐return group; (v) the type of skills learned in school around the time of school leaving age and the relevance of these skills for the labour market. Another reason might be that returns to education depend on the qualification individuals achieve, regardless of whether the issued certification has legal value, or of the actual time spent in full‐time education. As Grenet (2008) suggests for France, the actual quantity of education attained is far less important than the qualifications held by individuals in determining these returns. 12 " The European Community Household Panel data used in this article are from the December 2003 release (contract 14/99 with the Department of Economics, University of Padova). This article uses data from SHARE 2004. The SHARE data collection has been primarily funded by the European Commission through the 5th framework programme (project QLK6‐CT‐2001‐00360 in the thematic programme Quality of Life). Additional funding came from the US National Institute on Aging (U01 AG09740‐13S2, P01 AGO05842, P01 AGO8291, P30 AG12815, Y1‐AG‐4553‐01 and OGHA 04‐064). Data collection in Austria (through the Belgian Science Policy Office) and Switzerland (through BBW/OFES/UFES) was nationally funded. The SHARE data set is introduced in Börsch‐Supan et al.(2005); methodological details are in Börsch‐Supan and Jürges (2005). 13 " The ECHP measures years of schooling by the age when full time education was stopped. This measure in not available for the UK. The conversion of categorical variables into years of schooling is applied to SHARE data and to part of ISSP data. Since the UK is not included in the SHARE dataset and the quality of the ISSP data for that country is rather poor, we have decided to omit it from our sample of European countries. See the Technical Appendix for further details. 14 " We also exclude individuals with more than 30 years of schooling. We repeated the analysis by considering only individuals who were aged at least 28 at the time of the interview. Results are robust and are not reported for brevity. We prefer not to exclude individuals aged between 26 and 28 since this procedure would lead to drop from the analysis individuals potentially affected by the reforms in some countries, for instance in Spain and Finland. 15 " The relatively low order of the polynomial follows the suggestions by Lee and Card (2008). Compared to higher order polynomials, the second order specification is the most parsimonious and provides adequate fit of the data. 16 " We estimate entry to occur after the completion of schooling. We use a three‐years moving average of the macro variables to smooth out measurement errors in the date of labour market entry. 17 " When we examine the distribution of educational attainment in the three years before and after the reforms, we notice that the combined reduction in the frequency of low attainment and increase in the frequency of higher than average attainment is more pronounced for females than for males. 18 " More than a quarter of the Spaniards and Greeks and close to one fifth of Italians in our sample had less than 8 years of education before compulsory reforms were enacted which raised minimum school leaving age, to ensure 8 or more years were achieved. 19 " To facilitate the convergence of the estimates in the bootstrapping exercise in the presence of a large number of regressors, we operate as follows: define the relevant regression as Q(y) = ΓX + ΩY, where X and Y are suitable matrices of variables. We first estimate each quantile regression separately and compute the index . Next, we redefine the dependent variable as and estimate quantile regressions for different quantiles of the distribution of wages simultaneously using STATA built in functions. In practice, the vector X includes two survey dummies, the polynomial in the second order in q and its interactions with country dummies. 20 " These results do not significantly change when we omit the two top quantiles of the distribution of ability – see columns (2) and (4) in Table 7. The estimates of φ suggest that the constraint 1 + φs is always verified. 21 " For instance, a large shift in the labour supply of educated workers could reduce the wages of the low‐skilled workers who were educated before the enforcement of the new compulsory schooling level. 22 " Arias et al. 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Winter‐Ebmer, F. Wagner, L. Deutsch, S. Perelman, V. Perin, V. Vandenberghe, A. Pill Damm, K. Andersen Ranberg, S. Nurmi, T. Pekkarinnen, A. Laferrére, F. Papadopoulis, G. Psacharopoulos, A. van Soest, H. Oosterbeek, D. Webbink, P. Hootnout, M. Palme, D. Hallberg, A. Klevmarken, K. Denny and L. Romero for help with the country‐specific education institutions and data; to J. Angrist, E. Battistin, D. Coviello, M. El‐Attar, A. Ichino, E. Rettore, R. Spady, two anonymous referees and to the participants at seminars in Berlin, Bologna, Florence (EUI), UCL (ESPE), Padova, Salerno (Brucchi Luchino) and Warwick (RES) for comments on this and an earlier version (Brunello et al., 2007). The usual disclaimer applies. Fort gratefully acknowledges financial support from AMANDA (Advanced Multidisciplinary Analysis of New Data on Ageing) contract no. QLK6‐2002‐002426, project ‘Issues in population ageing: an economic analysis’ (Pr. RBAU01YYHW003), and to the Max Weber Programme, as well as the hospitality of the Dept. of Statistical Sciences at the University of Padova. Brunello and Fort acknowledge financial support from the EEEPE Research and Training Network, funded by the European Commission. © The Author(s). Journal compilation © Royal Economic Society 2009