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Interactions of Monetary and Fiscal Policy via Open Market Operations

Interactions of Monetary and Fiscal Policy via Open Market Operations Abstract We examine interactions of monetary and fiscal policy in a sticky price model where public debt is non‐neutral, as it provides transaction services. This property is brought about by a legal restriction on open market operations by which only government bonds are eligible. Debt creation eases access to money and can therefore induce households to increase purchases of goods. Government expenditures, which are not completely tax financed, and deficit financed tax cuts then tend to stimulate private consumption. However, for these fiscal impulses to raise real activity monetary policy should not too aggressively aim at stabilising the economy. Research on business cycle theory has led to a consensus framework which combines optimising behaviour under rational expectations with nominal rigidities, giving rise to substantial effects of monetary policy measures. These ‘New Keynesian’ models are now widely applied for monetary policy analysis,1 whereas the cyclical effects of fiscal policy are scarcely addressed and seem to be inconsistent with empirical evidence. In particular, Blanchard and Perotti (2002), Fatas and Mihov (2001) and Mountford and Uhlig (2002) find that fiscal policy is able to stimulate private consumption by government spending or tax cuts as implied by the traditional Keynesian view. In contrast, the New Keynesian theory predicts that public spending can at most raise aggregate demand, while private consumption is crowded out due to a neoclassical wealth effect.2 Moreover, as Ricardian equivalence applies in these models, financing decisions of (solvent) fiscal policy regimes are irrelevant. Accordingly, the consensus framework lacks any interaction between monetary policy and public finance and cannot provide a rationale for tight fiscal constraints, as for example imposed by the Stability and Growth Pact for EMU. This paper presents a framework where monetary and fiscal policy interact via government bonds serving as collateral for money in open market operations. According to this property, public debt indirectly provides transaction services and therefore raises households’ willingness to consume. This mechanism is derived in a sticky price model where the central bank supplies money via repurchase agreements and sets the rate by which eligible securities are discounted. Households’ financial wealth comprises private and public debt, while money demand is induced by a cash constraint. Considering that eligible securities are typically required to be of high credit quality,3 we assume that money supply is legally restricted so that only government bonds can be used in open market operations. When, on the other hand, privately issued debt is also accepted as collateral, money supply is de facto unbounded at a given interest rate. Under the legal restriction, households are willing to hold government bonds, even if they earn a lower interest than private debt. In this case, government bonds exhibit a liquidity value in equilibrium and households relate public debt holdings to their demand for money and therefore to their consumption expenditures. Due to its particular role in open market operations public debt provides transaction services, implying that households’ consumption expenditures increase with a larger stock of government bonds outstanding, as it raises the ability to acquire money. Hence, considering transaction services of risk‐free government bonds,4 which might also be rationalised by their potential to serve as collateral for external funds or to relax credit constraints, can be viewed as a general modelling device that induces public debt to be non‐neutral. According to this property debt creation raises private consumption, which qualitatively resembles the impact of public debt in overlapping generations models, where households’ financial wealth increases consumption due to life cycle considerations. As our model further predicts that the cost of money rises with the discount rate, the implied consumption function can be perceived as a particular representation of a generic form, by which households’ consumption increases with financial wealth and decreases with the interest rate.5 The business cycle model developed in this paper, which features staggered price adjustment, a Taylor‐type interest rate rule and a solvent fiscal policy regime, exhibits two fundamentally different versions. When there is no legal restriction, open market operations are irrelevant and the model is isomorphic to the standard New Keynesian model in Clarida et al. (1999). Money supply is unbounded and interest rate setting has an impact on prices and on real activity by shifting the real interest rate which affects households’ willingness to substitute consumption and leisure intertemporally. Ricardian equivalence applies, such that public finance is negligible and monetary policy is solely responsible for macroeconomic stabilisation, as summarised in Clarida et al. (1999). In contrast, money supply and thus private consumption can rise with real public debt and decline with the nominal interest rate when open market operations are legally restricted and government bonds provide transaction services. Accordingly, higher inflation bears a negative feedback on aggregate demand as it reduces the real value of pre‐existing public debt. While this implies that self‐fulfilling inflation expectations cannot occur, the tax policy applied further ensures that public debt evolves on a non‐explosive equilibrium path, such that restrictions on interest rate policy are neither necessary nor sufficient to guarantee saddle path stability.6 The latter version is then applied to examine the transmission of monetary and fiscal policy shocks and to disclose the role of policy interaction. Innovations to the discount rate affect inflation and, by rigid prices, real activity in accordance with interest rate effects in the former version. However, history dependence is now induced by the evolution of public debt, which is responsible for impulse responses not dying out immediately after a shock disappears. The ability of fiscal impulses to stimulate real activity crucially relies on the monetary policy stance. The model predicts inflation and output will rise following an unexpected rise in government consumption, which accords with the results in a standard New Keynesian model. If, however, a sufficiently large amount of government expenditures is debt financed, private consumption can also rise. Similarly, an unexpected tax cut, which is financed by issuance of government bonds, raises the inflation rate and can stimulate private consumption and, thus, real activity. However, whether the expansionary impact of public debt on consumption prevails in both cases, hinges on the extent to which monetary policy aims at stabilising the economy. In particular, strong interest rate adjustments triggered by higher inflation can lead to a contractionary monetary stance which overturns expansionary fiscal policy impulses. Hence, this form of interaction can provide a rationale for fiscal policy effects to vary over time or between countries.7 The remainder of the paper is organised as follows. Section 1 presents a sticky price model with repurchase agreements. In Section 2, we derive fundamental properties of the log‐linear approximation to the model at the steady state. Section 3 examines the role of policy interactions for short‐run effects of monetary and fiscal policy. Section 4 concludes. 1. The Model 1.1. Outline of the Model At the beginning of a period, households are endowed with government bonds and claims on other households carried over from the previous period. There are three sources of aggregate uncertainty: a monetary policy shock, a government spending shock and a tax cut shock. After these shocks materialised, goods are produced and labour remunerations are credited at a financial intermediary. Then the asset market opens, where households can adjust government bond holdings and borrow (lend) from (to) other households. Given that purchases of consumption goods are restricted by a cash constraint, households demand money. The central bank is assumed to supply money exclusively via open market operations, i.e., via repurchase agreements. Households carry over a certain amount of interest bearing assets Bc to the financial intermediary, which engages in repurchase agreements on the behalf of the households. The central bank supplies money M to an amount equal to the value of eligible securities discounted by the nominal interest rate i:M = Bc/(1 + i). Then the goods market opens, where households purchase consumption goods from final goods producing firms. Their cash earnings are then paid to the owners (households), transferred to the intermediary and used to repurchase government bonds from the central bank. Accordingly, money cannot be accumulated, which is not associated with a loss of generality, as the opportunity costs of holding cash from one period to the other would not be lower than the costs of repurchase agreements.8 1.2. Details 1.2.1. Households Lower (upper) case letters denote real (nominal) variables. a caret over a variable denotes log‐deviations from steady state values, while the latter are denoted by symbols without time indices. there is a continuum of identical and infinitely lived households of mass one. at the beginning of period t, the representative household's financial wealth at−1 comprises government bonds bt−1 and private debt dt−1: at−1 = bt−1 + dt−1. before the goods market opens, households enter the asset market, where beginning‐of‐period asset holdings earn (1 + it)bt−1 and and households can adjust their portfolio such that asset holdings are now equal to bt and dt. to acquire money, they carry over securities to a financial intermediary, which participates in repurchase agreements with the central bank. the amount of money mt supplied by the latter equals the discounted value of securities : (1) The discount rate, which is identical to the gross nominal interest rate on government bonds 1 + it, is set by the central bank. Households then enter the goods market. When goods trading has ended, taxes and profits are transferred and securities are repurchased from the central bank such that the cost of money is given by . To account for the fact that central banks demand eligible securities to be of high credit quality (Bank of England, 2002; Meulendyke, 1998),9 we assume that open market operations are restricted in that private debt, which can be freely issued by households, is not accepted as collateral (2) According to (1) and (2), money Mt is the counterpart of the fraction of total government bonds outstanding Bt. When, however, (2) is not imposed, private debt is also accepted in open market operations and money supply would be unbounded, which can be interpreted as an implementation of the real bills doctrine. Households earn income from competitively supplying labour lt and from interest payments on assets, and receive firms’ profits ωt. The budget constraint, which restricts households’ transactions in the asset market, is given by (3) where Pt denotes the aggregate price level, ct consumption, wt the real wage rate, and Ptτt a lump‐sum tax. The representative household holds a checkable account at the financial intermediary. After goods are produced its labour income is credited on this account, while it is charged for wage outlays of firms, which are owned by the households. Entering the goods market, consumption expenditures are restricted by the following liquidity constraint: (4) The standard cash‐in‐advance constraint (Ptct ≤ Mt) is augmented by allowing for accounts, which are given in the round brackets in (4), to be accepted as a means of payment. Hence, an individual labour income, that exceeds the average wage payment of firms indexed with i ∈ [0,1], leads to a relaxation of the cash constraint (4). This specification, which is adopted from Jeanne (1998), is introduced to avoid a cash‐credit good distortion between consumption and leisure, facilitating comparisons with the standard New Keynesian model.10 The objective of a representative household is given by (5) where β ∈ (0,1) denotes the subjective discount factor and E0 the expectation operator conditional on the information in period 0. The utility function u(ct,lt) is assumed to be strictly increasing in consumption c, strictly decreasing in labour l, strictly concave, twice continuously differentiable with respect to both arguments, to satisfy the usual Inada conditions and to be additively separable. As a novelty, we assume that households internalise the legal restriction on open market operations (2), i.e., that their access to money is limited by holdings of government bonds. Hence, the representative household considers an open market constraint (6) when it decides on its optimal plan. Maximising (5) subject to the budget constraint (3), the liquidity constraint (4), the open market constraint (6), and a no‐Ponzi‐game condition, , for a given initial value A−1 > 0, leads to the following first order conditions for consumption, leisure, private debt, government bonds and money: (7) (8) (9) (10) (11) (12) (13) where πt, λt, ηt, and ψt denote the gross inflation rate, πt≡Pt/Pt−1, and the Lagrange multiplier on the constraints for the market for assets (3), money (6), and goods (4). From (10) it can immediately be inferred that a positive expected value for the spread is associated with ηt > 0 and, by (13), with the open market constraint (6) holding with equality. The conditions (11) and (12) further imply that the cash‐in‐advance constraint is always binding if the nominal interest rate it exceeds zero. When open market operations are not legally restricted by (2), the first order conditions change to (14) and (8) and (12). In the optimum the budget constraint (3) further holds with equality and the transversality condition is satisfied (15) 1.2.2. Production sector Differentiated goods are produced by monopolistically competitive firms indexed with i ∈ [0,1]. The final good is produced by perfectly competitive firms, aggregating the differentiated goods. Their production technology is given by: , with ε > 1, where yt is the number of units of the final good, yit the amount of differentiated goods produced by firm i, and ε the constant elasticity of substitution between differentiated goods. Let Pit and Pt denote the price of good i set by firm i and the price index for the final good. Cost minimisation of the final goods producing firms leads to the following demand for each differentiated good yit = (Pit/Pt)−εyt, with . A firm i is assumed to produce yit using a technology which is linear in labour: yit = lit. We introduce a nominal rigidity in the form of staggered price setting as developed by Calvo (1983). In each period monopolistically competitive firms may reset their prices with the probability 1−φ, where φ ∈ (0,1), independent of the time elapsed since the last price setting. The fraction φ of firms is assumed to adjust previous period's prices according to Pit = πPit−1. This rule combined with the optimal condition of firms, who are allowed to reset their prices, is shown by Yun (1996) to imply the following log‐linearised condition for aggregate inflation: (16) where mct denotes real marginal costs. Due to the symmetric structure, aggregate production is given by yt = lt and labour demand satisfies (17) 1.2.3. Public sector The public sector consists of a fiscal and a monetary authority. The monetary authority supplies money Mt in open market operations in exchange for bonds. It further sets the discount rate, i.e., the gross nominal interest rate Rt≡1 + it, according to the following state contingent rule: (18) where the innovation has an expected value of zero and is serially uncorrelated. The reactiveness of interest rate policy, measured by the elasticity , describes the central bank's willingness to stabilise inflation endogenously and, implicitly, output. We assume that the steady state condition on the nominal interest rate has a solution for ρ(π,0) > 1,11 and that the realisations of are small enough that the gross nominal interest rate always exceeds one in the neighbourhood of the steady state. Open market operations are conducted in form of repurchase agreements, i.e., swaps of the ownership over securities at the rate it. Hence, the central bank earns from repurchase agreements such that its budget is given by , where denotes transfers to the fiscal authority. The latter issues risk‐free one period bonds, collects lump‐sum taxes from the households, receives transfers from the monetary authority and purchases the amount Ptgt of the final good (19) The fiscal policy regime is characterised by the following rule which relates consumption expenditures and debt obligations to tax receipts and transfers from the central bank: (20) According to (20), receipts from taxes and transfers are assumed to cover all interest payments on debt, which rules out Ponzi‐games and simplifies the analysis. The policy variable κt, which describes the stance of fiscal policy, governs the portion of consumption expenditures financed by taxes and transfers. By setting κt equal to one the fiscal authority runs a balanced budget policy. A lower value for κt raises the debt financed fraction of government expenditures such that κ can be interpreted as a measure of fiscal feedback. To facilitate an analysis of unexpected changes in the fiscal stance, we assume that realisations of κt are generated by the following process: (21) where has an expected value of zero and is serially uncorrelated. According to (21), the fraction κ is strictly positive in the steady state, whereas κt is not restricted. Further, government expenditures are assumed to follow the stochastic process (22) where the shock has an expected value of zero and is serially uncorrelated. In the steady state, public consumption is, by (22), strictly positive and restricted not to exceed private consumption. Using the fiscal policy rule (20) and the budget constraint (19) gives the following consolidated public sector budget constraint: (23) Given that the sequences of κt and gt are, by (21) and (22), stationary, it can immediately be seen from (23) that our specification of the public sector implies that public debt grows asymptotically with a rate equal to one. The reason is that the fiscal policy rule (20) implies that all debt interest payments are financed by taxes or transfers. For the case where Rt > 1, which will be analysed in what follows, this implies that public sector solvency is guaranteed, i.e.,  lim i→∞EtBt+i is always satisfied.12 1.2.4. Equilibrium In equilibrium private debt is equal to zero dt = 0 such that households’ financial wealth solely consists of government bonds, at = bt. it should further be noted that real financial wealth at−1 = at−1/pt−1 is a predetermined variable, as the initial price level p−1 as well as the initial stock of nominal financial wealth a−1 is given. as we will disregard cases where the cash constraint (4) is not binding, we define the equilibrium of our model for the case where rt > 1. Definition 1. A rational expectations equilibrium of the model forRt > 1 is a set of sequences{λt, ct, lt, yt, πt, satisfying the households’ first order conditions,uc(t)/Rt = λt +, (8), (9), (24) (25) (26)the aggregate production function,yt = lt, optimal price setting approximated by(16), the labour demand condition(17), the consolidated public sector budget constraint(23), the monetary policy rule(18), the law of motion for the fiscal stanceκt(21)and for government expenditures(22), the aggregate resource constraint,yt = ct + gt, asset market clearance,at = bt, and the transversality condition(15)for a given initial valuea−1 > 0. 2. Fundamental Properties In this Section we present the fundamental properties of the model, which will subsequently be applied for the analysis of short‐run monetary and fiscal policy effects. We derive a linear version of the model by log‐linearising the equilibrium conditions listed in Definition 1 at the steady state. The particular steady state conditions depend on the long‐run liquidity value η of government bonds, which determines the relevance of open market operations. When the open market constraint is not binding, η = 0, the nominal interest rates on private and public debt are identical, R = Rd, and inflation solely relies on monetary policy, π = Rβ. Public debt does not affect consumption and inflation, such that the existence of a steady state does not impose a restriction on real debt. In contrast, η > 0 is associated with a binding open market constraint, m = b/R, and a positive spread, Rd − R > 0, where Rd = π/β and R is determined by interest rate policy (18). As public debt is non‐neutral in this case, the economy can only exhibit stationary values for all endogenous variables if public debt is stationary. As a consequence, steady state inflation now depends on fiscal as well as on monetary policy: π = [1 − (1 − κ)g/(cR)]−1 ≥ 1.13 This implies that a fiscal policy regime with a balanced budget target, κ = 1, ensures that the gross steady state inflation rate be equal to one, minimising the average distortion brought about by price rigidity. Otherwise, κ < 1, nominal government debt rises on average for non‐zero government expenditures, see (22), such that steady state inflation has to exceed one to stabilise real public debt. Steady state consumption is, nevertheless, independent of monetary and fiscal policy in both regimes and is pinned down by equating the marginal utility of consumption and leisure, =−ul(c + g). As a consequence, the long‐run relations between inflation and the growth rate of money and real output are consistent with McCandless and Weber's (1995)‘monetary facts’. 2.1. When Open Market Operations are Irrelevant We start the local analysis of the model at the steady state with a brief characterisation of the version where assets traded in open market operations are not restricted by (2). Open market operations are then irrelevant, which corresponds to ηt = 0, and the households’ first order conditions are given in (14). The nominal interest rates on government bonds and on private debt are identical and the amount of open market securities is (recursively) determined by see (24)–(26). Given that the fiscal policy variable κt, which governs the ratio of tax to debt financing, exclusively enters the government budget constraint (23) and public debt does not affect the remaining variables, it can immediately be concluded that κt is irrelevant for the remaining variables. Hence, Ricardian equivalence applies in this version as in the majority of general equilibrium business cycle models with lump‐sum taxes. This result and the log‐linear representation of the model, which can immediately be derived from the equilibrium conditions for ηt = 0 given in Definition 1, are summarised in the following proposition. Proposition 1. If open market operations are irrelevant, then Ricardian equivalence applies and a rational expectations equilibrium of the log‐linear approximation to the model is a set of sequencessatisfying(22), (27) (28) (29)whereγ1≡χ[σ + ϑc/y] > 0, γ2≡χϑg/y > 0, v−1≡ > 0, and the transversality condition for a given initial value for real wealth. The model in Proposition 1 is identical with the consensus monetary business cycle model, the so‐called New Keynesian model; see, e.g., Clarida et al. (1999). The equilibrium sequences of consumption, inflation, the nominal interest rate and government expenditures are solely determined by (22) and (27)–(29). Real financial wealth, which is a predetermined variable and equals real public debt, does not affect these variables and can be recursively determined, by , for given equilibrium sequences of inflation, realisations of the exogenous fiscal variables, κt and gt, and an initial value a−1.14 Accordingly, the fiscal stance κt only matters for the evolution of real wealth, such that public finance is irrelevant. We abstain in what follows from a further analysis of this version and refer to corresponding results provided in the literature. 2.2. When Open Market Operations Matter We now turn to the case where households internalise that their access to money is restricted by (6). The corresponding Lagrange multiplier ηt is larger than zero, implying a binding open market constraint, whenever the spread between the interest rates on private debt and on government bonds is expected to be positive, see (10).15 The existence of a steady state with a positive spread relies on the central bank to choose a sufficiently small average value for the nominal interest rate R. The respective upper bound in particular depends on fiscal policy due to its effect on the steady state inflation rate. Proposition 2. If the central bank sets the nominal interest rate R such that, where, then a steady state exists where the open market constraint is binding, m = b/R. Proof. A steady state with a binding open market constraint requires a positive spread Rd − R > 0 and has to satisfy Rd = π/β and π = [1 − (1 − κ)g/(cR)]−1. Using these conditions, it follows immediately that the existence of this steady state is ensured by , where given that β ∈ (0,1), κ ∈ (0,1], and g ∈ (0,c]. By choosing a sufficiently small average nominal interest rate, , the central bank allows for the existence of a steady state with a positive interest rate spread. The respective upper bound depends on the steady state inflation rate associated with a non‐growing real amount of public debt, which is required for a stationary equilibrium as public debt is non‐neutral. In what follows we assume that the support of and is sufficiently small, such that the log‐linearisation at the steady state with is a suitable approximation of the non‐linear model and the interest rate always exceeds Rt. The open market constraint then always binds, ηt > 0, such that real wealth (public debt) affects access to money and private consumption is determined by ct = mt = at/Rt , see (24)–(26). The following proposition presents the equilibrium of the linear model, which can immediately be derived by log‐linearising the equilibrium conditions for ηt > 0 given in Definition 1. Proposition 3. If the open market constraint is binding, then a rational expectations equilibrium of the log‐linear approximation to the model at the steady state withis a set of sequencessatisfying(21), (22), (29), (30) (31) (32)and the transversality condition for a given initial value for real wealtha0. According to the equilibrium condition (30), private consumption decreases with the nominal interest rate and increases with public debt. While the latter has no impact on real activity and inflation in standard New Keynesian models, it also enters the consumption function in overlapping generation models. Moreover, a binding open market constraint implies that the nominal interest rate, by which open market securities are discounted, affects current consumption via money supply, whereas the consumption Euler equation, which links interest rates to consumption when money supply is unbounded (27), predicts that the expected real interest rate governs the consumption path. Obviously, the consumption Euler equation does not vanish when the open market constraint is binding. However, it features the interest rate on private debt, E, and is therefore irrelevant for the determination of the equilibrium sequences of consumption, inflation and real wealth.16 Given the equilibrium sequences for the latter variables, which are determined by (21), (22), (29) and (30)–(32), the consumption Euler equation now recursively determines the equilibrium sequence for the interest rate on private debt, . The model in Proposition 3 can be reduced to a two dimensional system in inflation and real wealth, where beginning‐of‐period real wealth, , constitutes a relevant endogenous state variable. The equilibrium path of the model is therefore stable and unique if there is exactly one eigenvalue inside the unit circle. It turns out that the assumptions made in the previous Section are sufficient to ensure saddle path stability. In particular, as the nominal interest rate directly affects consumption, equilibrium determinacy does not rely on the behaviour of the real interest rate governed by the inflation elasticity ρ. Proposition 4. If the open market constraint is binding, then the model is saddle path stable. Proof. The deterministic part of the linear model presented in Proposition 3 reads (33) The characteristic polynomial of is given by As F(X) is strictly positive at X = 0, F(0) = (1 + γ1ρ)/(βπ), and strictly negative at X = 1, F(1) = −[γ1 + (π − 1)(1 − β + γ1ρ)]/(βπ), the model (33) exhibits exactly one eigenvalue inside the unit circle. As summarised in Proposition 4, saddle path stability of the rational expectations equilibrium is guaranteed for the monetary (18) and the fiscal policy rule (20). In contrast to the consensus New Keynesian model, pro‐activity, ρ > 1, or the Taylor‐principle (Woodford, 2001), is neither necessary nor sufficient for equilibrium determinacy. To get an intuition for this, consider first the consensus framework where consumption growth is governed by (27). When inflation is expected to rise and the central bank sets the interest rate in a passive way, ρ < 1, the expected real interest rate and consumption growth decline. Given that the model does not exhibit an endogenous state variable, this is consistent with a stable equilibrium path only if current consumption rises on impact, which feeds aggregate consumption and, by (8) and (17), real marginal costs. Hence, inflation in fact rises according to the aggregate supply constraint (16), implying that inflation expectations can be self‐fulfilling. Now, consider the case where the open market constraint is binding. A rise in inflation deflates financial wealth by (32), which tends to reduce consumption by (30). Provided that ρ ≥ 0, interest rate policy does not counteract this mechanism to the extent that aggregate demand declines. This leads to a reduction in real marginal costs and therefore to a decline in inflation, implying that self‐fulfilling expectations cannot occur. It should be noted that the particular choice of the fiscal policy rule (20) is in fact responsible for saddle path stability. When debt obligations are not completely tax financed, debt‐interest spirals, as discussed in Leith and Wren‐Lewis (2000), can occur if the central bank sets the nominal interest rate too aggressively (high ρ). To see this, consider a rise in real wealth brought about by a fundamental shock, for example, a temporary deficit financed tax cut. This leads, by (30), to an increase in private consumption and to a rise in inflation. When the fiscal rule (20) applies, financial wealth will be deflated in the subsequent periods, see (32), causing the economy to converge back to the steady state. If, however, the central bank strongly raises the nominal interest rate with higher inflation and interest payments on public debt are not completely tax financed, real public debt can increase. This rise in real wealth further feeds private consumption, inflation and even higher interest rates so that the economy evolves on an explosive path. In the Appendix, we present an example for a fiscal policy rule, where interest payments on public debt are not entirely tax financed, such that debt interest spirals are not in general precluded.17 3. Monetary and Fiscal Policy Effects As the effects of monetary and fiscal policy shocks in the standard New Keynesian model are already provided in the literature, we focus in what follows on the version with a binding open market constraint given in Proposition 3. By allowing for public debt to be non‐neutral, we expect monetary and fiscal policy interactions to affect the transmission of shocks, facilitating a broader variety of macroeconomic responses than in the case where Ricardian equivalence applies. Nevertheless, the effects of interest rate shocks are consistent with common priors about monetary policy effects. The structural part of monetary and fiscal policy turns out to be decisive for the sign of impulse responses to fiscal policy shocks. In particular, the impact of government spending and tax cut shocks on private consumption and on real activity will be shown to depend on the degree to which government expenditures are debt financed and on the willingness of monetary policy to stabilise the economy endogenously by a reactive interest rate setting. 3.1. The Model's Solution The model in Proposition 3 is reduced to a system in two endogenous variables, real wealth and inflation, with a state space consisting of one endogenous state variable, , and three exogenous, , and . The model's fundamental and unique solution reads (34) (35) As shown in Proposition 4, the coefficient δa in (34) is the single stable eigenvalue of the model and lies between zero and one. Applying the method of undetermined coefficients, the coefficients in (34)–(35) can be expressed as functions of deeper parameters, steady state values, and the stable eigenvalue. Lemma 1. The state space representation (34)–(35) of the model with ηt > 0 is characterised by coefficients δi withi ∈ {a, ag, ar, aκ, πa, πg, πr, πκ}satisfying (i) 0 < δa =and 0 < δπa =  1 − δaπ < 1; (ii) δar = γ1/γ4 > 0 andδπr = − γ1π/γ4 < 0; (iii) δag = [γ3π(1 − κ)(g/a) − γ2]/γ4andδπg = π[(β(1 − δaπ) +γ1)(1 − κ)(g/a) + γ2]/γ4 > 0; and (iv) δaκ = −κπ(g/a)γ3/γ4 < 0 andδπκ = −κπ(g/a) [γ1 + β(1−δaπ)]/γ4 < 0, whereα1≡πγ3 + β + γ1 > 1, , γ3≡1 + γ1ρ ≥ 1, andγ4≡γ3π + β(1 − δaπ) + γ1 > 1. Proof. See Appendix. The cyclical behaviour of inflation and real wealth can immediately be determined by applying the solution presented in Lemma 1. In what follows, we do not restrict our attention on these variables, as we are primarily interested in consumption and output responses. The corresponding coefficients are derived from the solution for inflation and real wealth together with the structural relations and . Note that we assumed, for simplicity, that all policy shocks are transitory. This implies that an economy would be expected to return to the steady state in the after‐shock period, if it lacks any history dependence. Accordingly, the equilibrium conditions of the purely forward looking version of the model, which are given in Proposition 1, are reduced to a set of static relations. In contrast, the model with relevant open market operations exhibits an endogenous state variable, which allows for temporary shocks to affect future expectations. Hence, non‐neutrality of public debt is responsible for an endogenous propagation of shocks, implying that the economy does not immediately jump back to the steady state when a transitory shock disappears. The persistence of shock effects is hereby governed by the stable eigenvalue δa, which can be shown to rise inter alia with the parameters κ and ρ describing the structural part of fiscal and monetary policy. Proposition 5. The stable eigenvalue of the model increases (i) with the fiscal feedback (∂δa/ ∂κ > 0) if, where, and (ii) with the inflation elasticity (∂δa/ ∂ρ > 0). Proof. To establish the first claim, we use the fact that κ affects the eigenvalue δa only via its negative effect on the steady state inflation rate (∂π/∂κ < 0) and that δa is given by . Applying the definitions for α1 and α2 in Lemma 1, the partial derivative of the eigenvalue with respect to inflation is with . It can immediately be shown that is sufficient to ensure ∂δa/∂π < 0 and thus ∂δa/∂κ > 0. The partial derivative of δa with respect to the inflation elasticity ρ is further given by δa/∂ρ = γ1α3/(2β) > 0. The equilibrium condition (32) implies that once real wealth exceeds its long‐run value, the return is speeded up for higher steady state inflation rates by which the pre‐existing stock of wealth is deflated on average. Accordingly, a higher fiscal feedback κ, which solely affects the stable eigenvalue due to its negative impact on steady state inflation, increases ceteris paribus the time required for real wealth to converge back to the steady state.18 Similarly, a high inflation elasticity ρ, which smooths the inflation path, reduces the deflationary impact on wealth and, thus, retards the recovery of real wealth. Hence, the eigenvalue δa and therefore persistence of debt effects increase with the endogenous response of monetary and fiscal policy, measured by ρ and κ, via a reduction in current or in average inflation. 3.2. Responses to Policy Shocks 3.2.1. Interest rate shocks As we derive the effects of policy shocks in what follows, we aim at revealing the role of the structural part of monetary and fiscal policy, ρ and κ, for the sign of the impulse responses. Given that all shocks are assumed to be transitory, we focus on the responses in the impact period. However, the responses in the subsequent periods would be qualitatively unchanged, if we allowed for sufficiently high degrees of autocorrelation in (18), (21) and (22). We start the policy analysis with the case where a nominal interest rate shock hits the economy in period s, while the realisations of the remaining shocks are set equal to zero (). In particular, we assume that the sequence of interest rate rule innovations satisfies and . Proposition 6.A positive innovation to the interest rate rule in periodsleads (i) to a decline in inflation (), (ii) to a rise in real wealth (), and (iii) to a decline in consumption and output (). Proof. The first two claims immediately follow from Lemma 1(ii): and . As also holds, the impact effect on consumption is given by . Applying the solutions in Lemma 1(ii), we obtain and thus . As summarised in Proposition 6, an unanticipated rise in the nominal interest rate causes a decline in inflation, consumption and output. These responses qualitatively accord with the predictions of the standard New Keynesian model. The model additionally predicts that real wealth rises due to a decline in inflation and eases, ceteris paribus, households’ access to money. Subsequent to the impact period s, real wealth exceeds its steady state value and consumption, output and inflation smoothly return to the steady state, while the speed of the recovery is affected by κ and ρ (see Proposition 5). 3.2.2. Government expenditure shocks We now turn to the case where a government expenditure shock hits the economy in period s (, , ). The solutions for the coefficients presented in Lemma 1(iii) reveal that the upward pressure on aggregate demand brought about by a positive innovation to government expenditures always leads to a rise in inflation, while the response of output depends on the central bank's willingness to counteract the inflationary pressure by increasing the nominal interest rate. Proposition 7. A positive government expenditure shock in period s leads to a rise (i) in inflation (), and (ii) in output () if, where. Proof. The first claim immediately follows from the sign restriction for given in Lemma 1(iii). The impact multiplier on output is given by . Using δcg = δag − ρδπg and the definitions for γ1, γ2, γ3, and γ4, we obtain δyg = [g/(c + g)](1/γ4) {π(1−κ)(1/R)[1−ρβ(1 − δaπ)] + π + χσ(1 + ρπ) + β(1 − δaπ)}. Hence, for a rise in a moderate inflation elasticity ρ ≤ 1 = [β(1 − δaπ)]−1 is sufficient, where 1 > 1 given that β < 1 and δaπ < 1. A comparison with the results in Linnemann and Schabert (2003) shows that both results presented in Proposition 7 are consistent with the findings on fiscal policy effects in a standard New Keynesian model given in Proposition 1. The rise in government consumption leads to a price pressure by (31) and tends to raise aggregate demand. However, the rise in inflation has an adverse effect on private consumption and thus on aggregate demand when the central bank endogenously responds to higher inflation by raising the nominal interest rate. A rise in output in response to a government expenditure shock is ensured by a modest interest rate policy, ρ < , where is strictly larger than one. This result immediately leads to probably the most interesting effect of government expenditure shocks, namely, the response of private consumption. Given that the latter rises with real wealth and declines with the nominal interest rate (30), a positive consumption response requires prices not to be too flexible. When government expenditures are not entirely tax financed (small κ) and prices are sufficiently rigid, , where ,19 real public debt can rise, which tends to raise private consumption. A rise in private consumption, however, additionally relies on interest rate policy not to be too reactive (small ρ). Proposition 8. Suppose that prices are sufficiently rigid,. Then a positive innovation to government expenditures in period s leads to a rise (i ) in real wealth () if, whereand, and (ii) in consumptionif, whereandifρ ≤ , whereand2 ∈ [0, ρπ1). Proof. Applying the solution given in Lemma 1(iii), we can write. As R is assumed to be strictly smaller than (see Proposition 2 and 3), it can immediately be shown that is sufficient for δag > 0. To establish the second claim, suppose that ρ < . Using the upper bound and π−1 = 1 − (1−κ)(g/cR), it follows that δcg = {π(1−κ)(g/a)[1 − ρβ(1−δaπ)]−(1 + ρπ)γ2}/γ4 is positive in this case if, but not only if . Further, ρ ≤ (<) ensures that , while is sufficient to guarantee that and are non‐negative. The result presented in the second part of Proposition 8 is, in particular, remarkable, as recent empirical studies (Fatas and Mihov, 2001; Blanchard and Perotti, 2002) find that private consumption rises with government expenditures, while Linnemann and Schabert (2003) show that conventional New Keynesian models cannot generate this effect. The reason is that the neoclassical wealth effect, as described by Baxter and King (1993), prevails in these models even if prices are not completely flexible. Government expenditures induce households to raise labour supply by intertemporal substitution, which is accompanied by an increased willingness to postpone private consumption. The result presented in Proposition 8 reveals that non‐neutrality of public debt is able to reconcile the predictions of a rational expectations business cycle model with the aforementioned empirical findings. As private consumption increases with real public debt, government expenditures do not necessarily lead to crowding out, if they are debt financed to a sufficiently large amount, . However, the existence of a (non‐negative) value for the fiscal feedback, which leads to a rise in private consumption, requires monetary policy not to raise the interest rate too aggressively with inflation, ρ ≤ (<). Otherwise, the increased cost of money can prevail over the stimulating effect of public debt creation on households’ transactions. As the sign of the responses to government expenditure shocks critically depends on the monetary and fiscal stance, the model thus provides a rationale for government spending effects to vary between countries and over time, as for example reported by Perotti (2002). 3.2.3. Temporary fiscal consolidations Finally, we examine the effects of innovations to the fiscal policy variable κt. In particular, we consider a positive shock to 0 ∀t), which can be interpreted as a temporary fiscal consolidation. Obviously, this policy experiment emphasises the main difference from conventional business cycle models. As Ricardian equivalence commonly applies in these models (see Proposition 1), a switch from deficit to tax financing has no impact on the non‐fiscal variables therein. This is clearly inconsistent with recent empirical evidence of Mountford and Uhlig (2002), showing that the most significant fiscal stimulus is brought about by deficit financed tax cuts. When debt is non‐neutral and the average tax financed fraction of government consumption is non‐zero (21), it is in fact possible to reproduce this finding. Proposition 9. An unanticipated and temporary fiscal consolidation in period s leads to a decline (i) in inflationand real financial wealth, and (ii) in consumption and output if and only if ρ < 1. Proof. The claims made in the first part immediately follow from Lemma 1(iv) and . For the second part, we use . Applying the solutions for δaκ and δπκ yields δcκ = −κπ(g/Rc)[1−ρβ(1−δaπ)]/γ4, which is strictly negative if and only if ρ < . A temporary fiscal consolidation () is, by (23), associated with a decline in nominal government bonds outstanding and therefore leads to a decline in inflation and real public debt given that prices are sticky. Thus, consumption and output tend, by (30), to decline as long as interest rate policy is not too reactive. For high inflation elasticities, ρ > , the decline in inflation can cause the central bank to lower the nominal interest rate in an extreme way such that households are willing to increase consumption expenditures if the current discounted value of real wealth exceeds its steady state value, even though real public debt declines. Correspondingly, a deficit financed tax cut can stimulate real activity when monetary policy is conducted in a modest way, ρ < . 4. Conclusion This paper examines the effects of monetary and fiscal policy in an environment where both interact as public debt is non‐neutral. The latter property is induced by allowing for government bonds to provide transactions services such that households’ consumption expenditures increase with real public debt. This mechanism originates in the role of risk‐free government securities in open market operations. We consider two money supply regimes in a sticky price model with interest rate policy, where money, which serves as the means of payment, is the counterpart of securities deposited at the central bank. The first monetary policy regime is characterised by the central bank accepting public and private debt, which can be issued by households in an unbounded way, as collateral for money. In this case open market operations are irrelevant, Ricardian equivalence applies and the model is isomorphic to the standard New Keynesian model. In the second regime, money supply is legally restricted such that only government securities are accepted in open market operations. Given that access to money relies on public debt holdings, households are willing to hold government bonds even if they are dominated in rate of return by private debt. Public debt is non‐neutral in this case as households can increase their (consumption) expenditures with additional holdings of government bonds. Fiscal and monetary policy then interact via the money supply, as the former determines the disposable stock of eligible securities, while the latter is assumed to aim at stabilising the economy by adjusting the nominal interest rate, by which open market securities are discounted. Hence, the response of real balances, private consumption, output and inflation to macroeconomic shocks crucially depends on the degree to which government expenditures are debt financed and on the intensity of endogenous interest rate responses to changes in inflation. Further, as interest payments are assumed to be tax financed, public debt evolves along a stable path and debars non‐fundamental shocks from being able to affect the economy, so that interest rate policy does not need to be restricted for saddle path stability. When this regime applies, a balanced budget target is associated with long‐run price level stability. In the short run, a deficit financed tax cut is able to stimulate real activity if interest rate policy is not too aggressively reacting to the simultaneous rise in inflation. Similarly, government expenditures can in this case also lead to a rise in private consumption if they are debt financed to a sufficiently large extent, that the associated increase in public debt eases households’ access to money. These expansionary fiscal policy effects, which are also found in recent empirical studies, can hardly be reproduced by conventional business cycle models, where public finance is irrelevant and private consumption is crowded out by government spending. Appendix Saddle Path Stability for An Alternative Fiscal Rule Let denote total lump‐sum receipts, which are assumed not to cover interest payments on public debt. In particular, suppose that the fiscal authority sets taxes according to the following rule specified in steady state deviations:20 (36) where r≡R/π denotes the steady state gross real interest rate, α governs the reaction of tax receipts on debt, and α > 0 ensures government solvency. When (36) instead of (20) applies, saddle path stability for ηt > 0 is ensured by a modest interest rate policy , where the upper bound is positive and rises in α if prices are not extremely rigid, , where . Proposition A1. Suppose thatand fiscal policy satisfies (36 ). Then the model with ηt > 0 is saddle path stable if, where, , , and. Proof. Inserting the tax rule (36) into the government budget constraint (19) and using at = bt, leads to , which replaces (32). Given that public debt is non‐neutral, the gross real interest rate r has to satisfy r = 1 + (τl − g)/a. Further suppose that government expenditures are sufficiently small, g < τl, to guarantee r > 1. The matrix M0 in (33) now features the coefficients (M0)11 = r − α and (M0)12 = r(ρ − 1). The characteristic polynomial of therefore reads F(X) = X2 + [(r − 1)γ1ρ − (r − α) β − 1 − γ1r]β−1X + (r − α)γ3β−1. Hence, F(X) is positive at X = 0. It can further be shown that F(1) is negative if the inflation elasticity ρ is sufficiently small, with . The model thus exhibits exactly one stable root if . Further, is strictly positive and increasing in α if, but not only if . Moreover, the upper bound on ρ satisfies As converges for α→0(α→r) to a limiting value which is strictly smaller (larger) than one, we can conclude that neither the Taylor‐principle nor its inverse applies in this model. For , the model can exhibit two unstable eigenvalues indicating an explosive equilibrium path. Proof of Lemma 1 We want to express the coefficients in the solution (34)–(35), δi with i ∈ {a, ag, ar, aκ, πa, πg, πr, πκ}, in terms of parameters and the eigenvalue δa, which lies between zero and one. For this the equilibrium conditions given in Proposition 3 are reduced to (37) (38) Replacing the endogenous variables in (37) and (38) by using the general solution form (34)–(35), leads to the following conditions for the undetermined coefficients (39) (40) (41) (42) Eliminating δπa in the two conditions in (39), leads to the following quadratic equation in the eigenvalue . Exactly one root of this equation lies between zero and one (see Proposition 4) and is given by From (39) we can conclude that δπa is strictly positive, δπa = 1 − πδa > 0, given that πδa can easily be shown to be smaller than one. The conditions in (40) immediately lead to the solutions for δπr and δar given in Lemma 1(ii). Rearranging the conditions in (41), gives the solution for the coefficients δπg and δag presented in Lemma 1(iii). The solution for the remaining coefficients δπκ and δaκ in Lemma 1(iv) immediately follow from the conditions in (42) and δπa = 1 − δaπ. Footnotes 1 " A comprehensive discussion of monetary policy in the New Keynesian model can be found in Clarida et al. (1999) and Woodford (2003). 2 " See Canzoneri et al. (2002a) or Linnemann and Schabert (2003) for an analytical derivation of fiscal policy effects in a New Keynesian model and Baxter and King (1993) for an analysis of the neoclassical wealth effect. 3 " For example, securities accepted by the US Federal Reserve and the Bank of England for open market operations mainly consist of securities issued by the treasury, federal agencies, or local authorities, respectively, as well as of privately issued debt, e.g., acceptances or bank bills, which meet high quality standards; see Bank of England (2002); Meulendyke (1998). 4 " This assumption is made more explicit in Canzoneri and Diba (2000), where it is shown that price level indeterminacy can be avoided by allowing for government bonds to enter a cash‐in‐advance constraint. 5 " One might think of a consumption Euler equation augmented by financial wealth, which, for example, applies in the Blanchard‐Yaari type model of Leith and Wren‐Lewis (2000). 6 " For example, the Taylor principle, which ensures equilibrium determinacy in the standard New Keynesian model (Woodford, 2001), is irrelevant in this case. 7 " See, for example, Perotti (2002) for cross country variations in fiscal policy effects. 8 " Though the duration of holding money is not infinite, the so‐called Hahn (1965) paradox, i.e., the problem about how to guarantee that money has a positive value over a finite horizon, does not apply due to the settlement of open market operations. 9 " Recent asset acquisition policy of the US Federal Reserve is also summarised as ‘Treasuries‐only’; see Broaddus and Goodfriend (2001). 10 " Obviously, one obtains a standard cash‐in‐advance specification in a symmetric equilibrium. 11 " A particular example for the interest rate rule is , where can be set to ensure . 12 " Hence, the fiscal policy regime is not related to specifications applied in the fiscal theory of the price level. See Buiter (2002) for a critical assessment of the latter. 13 " The steady state values g and κ are exogenously determined by (21) and (22). 14 " Note that there is no need for real wealth to be stationary to ensure stable sequences for the remaining variables. Nevertheless, government solvency and the transversality condition are satisfied given that interest rate payments on debt are entirely tax financed, see (23). 15 " When the spread is equal to zero, the model is identical with the one presented in Proposition 1. 16 " This feature relates to Canzoneri et al.'s (2002b) empirical findings, which cast severe doubts on the central role of the consumption Euler equation for the transmission of interest rate policy. 17 " The condition on ρ for saddle path stability is there shown to rely on the feedback from debt on taxes and is not related to the Taylor‐principle. 18 " To be precise, this result applies if, but not only if, prices are not too flexible , which is satisfied for reasonable parameter values. For example, σ = ϑ = 2, β = 0.99, g/y = 0.2, φ = 0.8 and π = 1.01(1.02) imply χ = 0.052 and . 19 " Note that is hardly restrictive for conventional parameter values, as σ = ϑ = 2, β = 0.99, g/y = 0.2, φ = 0.8, imply χ = 0.052 and . 20 " I am indebted to an anonymous referee for suggesting this rule. References Bank of England ( 2002 ). The Bank of England's Operations in the Sterling Money Markets , London: Bank of England Publications . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Baxter , M. and King , R. G. ( 1993 ). ‘Fiscal policy in general equilibrium’ , American Economic Review , vol. 83 , pp. 315 – 34 . OpenURL Placeholder Text WorldCat Blanchard , O. J. and Perotti , R. ( 2002 ). ‘An empirical characterisation of the dynamic effects of changes in government spending and taxes on output’ , Quarterly Journal of Economics , vol. 117 , pp. 1329 – 68 . Google Scholar Crossref Search ADS WorldCat Broaddus , J. A. Jr. and Goodfriend , M. ( 2001 ). ‘What assets should the Federal Reserve buy? , Federal Reserve Bank of Richmond Economic Quarterly , vol. 87 , pp. 7 – 22 . OpenURL Placeholder Text WorldCat Buiter , W. H. ( 2002 ). ‘The fiscal theory of the price level: a critique’ , Economic Journal , vol. 112 , pp. 459 – 80 . Google Scholar Crossref Search ADS WorldCat Calvo , G. ( 1983 ). ‘Staggered prices in a utility‐maximising framework’ , Journal of Monetary Economics , vol. 12 , pp. 383 – 98 . Google Scholar Crossref Search ADS WorldCat Canzoneri , M. B. , Cumby , R. and Diba , B. ( 2002a ). ‘New views on the transatlantic transmission of fiscal policy and macroeconomic policy coordination’, mimeo , Department of Economics, Georgetown University . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Canzoneri , M. B. , Cumby , R. and Diba , B. ( 2002b ). ‘Euler equations and money market interest rates: a challenge for monetary policy models’, mimeo , Department of Economics, Georgetown University . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Canzoneri , M. B. and Diba , B. ( 2000 ). ‘Interest rate rules and price determinacy: the role of transactions services of bonds’, mimeo , Department of Economics, Georgetown University . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Clarida , R. , Galí , J. and Gertler , M. ( 1999 ). ‘The science of monetary policy: a new Keynesian perspective’ , Journal of Economic Literature , vol. 37 , pp. 1661 – 707 . Google Scholar Crossref Search ADS WorldCat Fatas , A. and Mihov , I. ( 2001 ). ‘The effects of fiscal policy on consumption and employment: theory and evidence’ , Centre for Economic Policy Research, Discussion Paper Series, no. 2760. Hahn , F. H. ( 1965 ). ‘On some problems in providing the existence of an equilibrium in a monetary economy’, in ( F. H. Hahn and F. P. R. Brechling, eds.), The Theory of Interest Rates , London: Macmillan . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Jeanne , O. ( 1998 ). ‘Generating real persistent effects of monetary policy: how much nominal rigidity do we really need?’ , European Economic Review , vol. 42 , pp. 1009 – 32 . Google Scholar Crossref Search ADS WorldCat Leith , C. and Wren‐Lewis , S. ( 2000 ). ‘Interactions between monetary and fiscal policy rules’ , Economic Journal , vol. 110 , pp. C93 – 108 . Google Scholar Crossref Search ADS WorldCat Linnemann , L. and Schabert , A. ( 2003 ). ‘Fiscal policy in the new neoclassical synthesis’ , Journal of Money, Credit, and Banking , vol. 35 , pp. 911 – 29 . Google Scholar Crossref Search ADS WorldCat McCandless , G. T. and Weber , W. E. ( 1995 ). ‘Some monetary facts’ , Federal Reserve Bank of Minneapolis Quarterly Review , vol. 19 , pp. 2 – 11 . OpenURL Placeholder Text WorldCat Meulendyke , A. M. ( 1998 ). U.S. Monetary Policy and Financial Markets , New York: Federal Reserve Bank of New York . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Mountford , A. and Uhlig , H. ( 2002 ). ‘What are the effects of fiscal policy shocks?’ , Center for Economic Research, Discussion Paper 2002–31, Tilburg University . Perotti , R. ( 2002 ). ‘Estimating the effects of fiscal policy in OECD countries’ , European Central Bank, Working Paper Series, no. 168. Woodford , M. ( 2001 ). ‘The Taylor rule and optimal monetary policy’ , American Economic Review, Papers & Proceedings , vol. 91 , pp. 232 – 7 . Google Scholar Crossref Search ADS WorldCat Woodford , M. ( 2003 ). Interest and Prices: Foundations of a Theory of Monetary Policy . Princeton, N.J.: Princeton University Press . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Yun , T. ( 1996 ). ‘Nominal price rigidity, money supply endogeneity, and business cycles’ , Journal of Monetary Economics , vol. 37 , pp. 345 – 70 . Google Scholar Crossref Search ADS WorldCat Author notes " I am grateful to Matthew Canzoneri, Campbell Leith, Ludger Linnemann, Jonathan Temple and two anonymous referees for helpful suggestions and comments. © Royal Economic Society 2004 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Economic Journal Oxford University Press

Interactions of Monetary and Fiscal Policy via Open Market Operations

Schabert,, Andreas
The Economic Journal , Volume 114 (494) – Mar 1, 2004
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Oxford University Press
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© Royal Economic Society 2004
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0013-0133
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1468-0297
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10.1111/j.0013-0133.2004.00205.x
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Abstract

Abstract We examine interactions of monetary and fiscal policy in a sticky price model where public debt is non‐neutral, as it provides transaction services. This property is brought about by a legal restriction on open market operations by which only government bonds are eligible. Debt creation eases access to money and can therefore induce households to increase purchases of goods. Government expenditures, which are not completely tax financed, and deficit financed tax cuts then tend to stimulate private consumption. However, for these fiscal impulses to raise real activity monetary policy should not too aggressively aim at stabilising the economy. Research on business cycle theory has led to a consensus framework which combines optimising behaviour under rational expectations with nominal rigidities, giving rise to substantial effects of monetary policy measures. These ‘New Keynesian’ models are now widely applied for monetary policy analysis,1 whereas the cyclical effects of fiscal policy are scarcely addressed and seem to be inconsistent with empirical evidence. In particular, Blanchard and Perotti (2002), Fatas and Mihov (2001) and Mountford and Uhlig (2002) find that fiscal policy is able to stimulate private consumption by government spending or tax cuts as implied by the traditional Keynesian view. In contrast, the New Keynesian theory predicts that public spending can at most raise aggregate demand, while private consumption is crowded out due to a neoclassical wealth effect.2 Moreover, as Ricardian equivalence applies in these models, financing decisions of (solvent) fiscal policy regimes are irrelevant. Accordingly, the consensus framework lacks any interaction between monetary policy and public finance and cannot provide a rationale for tight fiscal constraints, as for example imposed by the Stability and Growth Pact for EMU. This paper presents a framework where monetary and fiscal policy interact via government bonds serving as collateral for money in open market operations. According to this property, public debt indirectly provides transaction services and therefore raises households’ willingness to consume. This mechanism is derived in a sticky price model where the central bank supplies money via repurchase agreements and sets the rate by which eligible securities are discounted. Households’ financial wealth comprises private and public debt, while money demand is induced by a cash constraint. Considering that eligible securities are typically required to be of high credit quality,3 we assume that money supply is legally restricted so that only government bonds can be used in open market operations. When, on the other hand, privately issued debt is also accepted as collateral, money supply is de facto unbounded at a given interest rate. Under the legal restriction, households are willing to hold government bonds, even if they earn a lower interest than private debt. In this case, government bonds exhibit a liquidity value in equilibrium and households relate public debt holdings to their demand for money and therefore to their consumption expenditures. Due to its particular role in open market operations public debt provides transaction services, implying that households’ consumption expenditures increase with a larger stock of government bonds outstanding, as it raises the ability to acquire money. Hence, considering transaction services of risk‐free government bonds,4 which might also be rationalised by their potential to serve as collateral for external funds or to relax credit constraints, can be viewed as a general modelling device that induces public debt to be non‐neutral. According to this property debt creation raises private consumption, which qualitatively resembles the impact of public debt in overlapping generations models, where households’ financial wealth increases consumption due to life cycle considerations. As our model further predicts that the cost of money rises with the discount rate, the implied consumption function can be perceived as a particular representation of a generic form, by which households’ consumption increases with financial wealth and decreases with the interest rate.5 The business cycle model developed in this paper, which features staggered price adjustment, a Taylor‐type interest rate rule and a solvent fiscal policy regime, exhibits two fundamentally different versions. When there is no legal restriction, open market operations are irrelevant and the model is isomorphic to the standard New Keynesian model in Clarida et al. (1999). Money supply is unbounded and interest rate setting has an impact on prices and on real activity by shifting the real interest rate which affects households’ willingness to substitute consumption and leisure intertemporally. Ricardian equivalence applies, such that public finance is negligible and monetary policy is solely responsible for macroeconomic stabilisation, as summarised in Clarida et al. (1999). In contrast, money supply and thus private consumption can rise with real public debt and decline with the nominal interest rate when open market operations are legally restricted and government bonds provide transaction services. Accordingly, higher inflation bears a negative feedback on aggregate demand as it reduces the real value of pre‐existing public debt. While this implies that self‐fulfilling inflation expectations cannot occur, the tax policy applied further ensures that public debt evolves on a non‐explosive equilibrium path, such that restrictions on interest rate policy are neither necessary nor sufficient to guarantee saddle path stability.6 The latter version is then applied to examine the transmission of monetary and fiscal policy shocks and to disclose the role of policy interaction. Innovations to the discount rate affect inflation and, by rigid prices, real activity in accordance with interest rate effects in the former version. However, history dependence is now induced by the evolution of public debt, which is responsible for impulse responses not dying out immediately after a shock disappears. The ability of fiscal impulses to stimulate real activity crucially relies on the monetary policy stance. The model predicts inflation and output will rise following an unexpected rise in government consumption, which accords with the results in a standard New Keynesian model. If, however, a sufficiently large amount of government expenditures is debt financed, private consumption can also rise. Similarly, an unexpected tax cut, which is financed by issuance of government bonds, raises the inflation rate and can stimulate private consumption and, thus, real activity. However, whether the expansionary impact of public debt on consumption prevails in both cases, hinges on the extent to which monetary policy aims at stabilising the economy. In particular, strong interest rate adjustments triggered by higher inflation can lead to a contractionary monetary stance which overturns expansionary fiscal policy impulses. Hence, this form of interaction can provide a rationale for fiscal policy effects to vary over time or between countries.7 The remainder of the paper is organised as follows. Section 1 presents a sticky price model with repurchase agreements. In Section 2, we derive fundamental properties of the log‐linear approximation to the model at the steady state. Section 3 examines the role of policy interactions for short‐run effects of monetary and fiscal policy. Section 4 concludes. 1. The Model 1.1. Outline of the Model At the beginning of a period, households are endowed with government bonds and claims on other households carried over from the previous period. There are three sources of aggregate uncertainty: a monetary policy shock, a government spending shock and a tax cut shock. After these shocks materialised, goods are produced and labour remunerations are credited at a financial intermediary. Then the asset market opens, where households can adjust government bond holdings and borrow (lend) from (to) other households. Given that purchases of consumption goods are restricted by a cash constraint, households demand money. The central bank is assumed to supply money exclusively via open market operations, i.e., via repurchase agreements. Households carry over a certain amount of interest bearing assets Bc to the financial intermediary, which engages in repurchase agreements on the behalf of the households. The central bank supplies money M to an amount equal to the value of eligible securities discounted by the nominal interest rate i:M = Bc/(1 + i). Then the goods market opens, where households purchase consumption goods from final goods producing firms. Their cash earnings are then paid to the owners (households), transferred to the intermediary and used to repurchase government bonds from the central bank. Accordingly, money cannot be accumulated, which is not associated with a loss of generality, as the opportunity costs of holding cash from one period to the other would not be lower than the costs of repurchase agreements.8 1.2. Details 1.2.1. Households Lower (upper) case letters denote real (nominal) variables. a caret over a variable denotes log‐deviations from steady state values, while the latter are denoted by symbols without time indices. there is a continuum of identical and infinitely lived households of mass one. at the beginning of period t, the representative household's financial wealth at−1 comprises government bonds bt−1 and private debt dt−1: at−1 = bt−1 + dt−1. before the goods market opens, households enter the asset market, where beginning‐of‐period asset holdings earn (1 + it)bt−1 and and households can adjust their portfolio such that asset holdings are now equal to bt and dt. to acquire money, they carry over securities to a financial intermediary, which participates in repurchase agreements with the central bank. the amount of money mt supplied by the latter equals the discounted value of securities : (1) The discount rate, which is identical to the gross nominal interest rate on government bonds 1 + it, is set by the central bank. Households then enter the goods market. When goods trading has ended, taxes and profits are transferred and securities are repurchased from the central bank such that the cost of money is given by . To account for the fact that central banks demand eligible securities to be of high credit quality (Bank of England, 2002; Meulendyke, 1998),9 we assume that open market operations are restricted in that private debt, which can be freely issued by households, is not accepted as collateral (2) According to (1) and (2), money Mt is the counterpart of the fraction of total government bonds outstanding Bt. When, however, (2) is not imposed, private debt is also accepted in open market operations and money supply would be unbounded, which can be interpreted as an implementation of the real bills doctrine. Households earn income from competitively supplying labour lt and from interest payments on assets, and receive firms’ profits ωt. The budget constraint, which restricts households’ transactions in the asset market, is given by (3) where Pt denotes the aggregate price level, ct consumption, wt the real wage rate, and Ptτt a lump‐sum tax. The representative household holds a checkable account at the financial intermediary. After goods are produced its labour income is credited on this account, while it is charged for wage outlays of firms, which are owned by the households. Entering the goods market, consumption expenditures are restricted by the following liquidity constraint: (4) The standard cash‐in‐advance constraint (Ptct ≤ Mt) is augmented by allowing for accounts, which are given in the round brackets in (4), to be accepted as a means of payment. Hence, an individual labour income, that exceeds the average wage payment of firms indexed with i ∈ [0,1], leads to a relaxation of the cash constraint (4). This specification, which is adopted from Jeanne (1998), is introduced to avoid a cash‐credit good distortion between consumption and leisure, facilitating comparisons with the standard New Keynesian model.10 The objective of a representative household is given by (5) where β ∈ (0,1) denotes the subjective discount factor and E0 the expectation operator conditional on the information in period 0. The utility function u(ct,lt) is assumed to be strictly increasing in consumption c, strictly decreasing in labour l, strictly concave, twice continuously differentiable with respect to both arguments, to satisfy the usual Inada conditions and to be additively separable. As a novelty, we assume that households internalise the legal restriction on open market operations (2), i.e., that their access to money is limited by holdings of government bonds. Hence, the representative household considers an open market constraint (6) when it decides on its optimal plan. Maximising (5) subject to the budget constraint (3), the liquidity constraint (4), the open market constraint (6), and a no‐Ponzi‐game condition, , for a given initial value A−1 > 0, leads to the following first order conditions for consumption, leisure, private debt, government bonds and money: (7) (8) (9) (10) (11) (12) (13) where πt, λt, ηt, and ψt denote the gross inflation rate, πt≡Pt/Pt−1, and the Lagrange multiplier on the constraints for the market for assets (3), money (6), and goods (4). From (10) it can immediately be inferred that a positive expected value for the spread is associated with ηt > 0 and, by (13), with the open market constraint (6) holding with equality. The conditions (11) and (12) further imply that the cash‐in‐advance constraint is always binding if the nominal interest rate it exceeds zero. When open market operations are not legally restricted by (2), the first order conditions change to (14) and (8) and (12). In the optimum the budget constraint (3) further holds with equality and the transversality condition is satisfied (15) 1.2.2. Production sector Differentiated goods are produced by monopolistically competitive firms indexed with i ∈ [0,1]. The final good is produced by perfectly competitive firms, aggregating the differentiated goods. Their production technology is given by: , with ε > 1, where yt is the number of units of the final good, yit the amount of differentiated goods produced by firm i, and ε the constant elasticity of substitution between differentiated goods. Let Pit and Pt denote the price of good i set by firm i and the price index for the final good. Cost minimisation of the final goods producing firms leads to the following demand for each differentiated good yit = (Pit/Pt)−εyt, with . A firm i is assumed to produce yit using a technology which is linear in labour: yit = lit. We introduce a nominal rigidity in the form of staggered price setting as developed by Calvo (1983). In each period monopolistically competitive firms may reset their prices with the probability 1−φ, where φ ∈ (0,1), independent of the time elapsed since the last price setting. The fraction φ of firms is assumed to adjust previous period's prices according to Pit = πPit−1. This rule combined with the optimal condition of firms, who are allowed to reset their prices, is shown by Yun (1996) to imply the following log‐linearised condition for aggregate inflation: (16) where mct denotes real marginal costs. Due to the symmetric structure, aggregate production is given by yt = lt and labour demand satisfies (17) 1.2.3. Public sector The public sector consists of a fiscal and a monetary authority. The monetary authority supplies money Mt in open market operations in exchange for bonds. It further sets the discount rate, i.e., the gross nominal interest rate Rt≡1 + it, according to the following state contingent rule: (18) where the innovation has an expected value of zero and is serially uncorrelated. The reactiveness of interest rate policy, measured by the elasticity , describes the central bank's willingness to stabilise inflation endogenously and, implicitly, output. We assume that the steady state condition on the nominal interest rate has a solution for ρ(π,0) > 1,11 and that the realisations of are small enough that the gross nominal interest rate always exceeds one in the neighbourhood of the steady state. Open market operations are conducted in form of repurchase agreements, i.e., swaps of the ownership over securities at the rate it. Hence, the central bank earns from repurchase agreements such that its budget is given by , where denotes transfers to the fiscal authority. The latter issues risk‐free one period bonds, collects lump‐sum taxes from the households, receives transfers from the monetary authority and purchases the amount Ptgt of the final good (19) The fiscal policy regime is characterised by the following rule which relates consumption expenditures and debt obligations to tax receipts and transfers from the central bank: (20) According to (20), receipts from taxes and transfers are assumed to cover all interest payments on debt, which rules out Ponzi‐games and simplifies the analysis. The policy variable κt, which describes the stance of fiscal policy, governs the portion of consumption expenditures financed by taxes and transfers. By setting κt equal to one the fiscal authority runs a balanced budget policy. A lower value for κt raises the debt financed fraction of government expenditures such that κ can be interpreted as a measure of fiscal feedback. To facilitate an analysis of unexpected changes in the fiscal stance, we assume that realisations of κt are generated by the following process: (21) where has an expected value of zero and is serially uncorrelated. According to (21), the fraction κ is strictly positive in the steady state, whereas κt is not restricted. Further, government expenditures are assumed to follow the stochastic process (22) where the shock has an expected value of zero and is serially uncorrelated. In the steady state, public consumption is, by (22), strictly positive and restricted not to exceed private consumption. Using the fiscal policy rule (20) and the budget constraint (19) gives the following consolidated public sector budget constraint: (23) Given that the sequences of κt and gt are, by (21) and (22), stationary, it can immediately be seen from (23) that our specification of the public sector implies that public debt grows asymptotically with a rate equal to one. The reason is that the fiscal policy rule (20) implies that all debt interest payments are financed by taxes or transfers. For the case where Rt > 1, which will be analysed in what follows, this implies that public sector solvency is guaranteed, i.e.,  lim i→∞EtBt+i is always satisfied.12 1.2.4. Equilibrium In equilibrium private debt is equal to zero dt = 0 such that households’ financial wealth solely consists of government bonds, at = bt. it should further be noted that real financial wealth at−1 = at−1/pt−1 is a predetermined variable, as the initial price level p−1 as well as the initial stock of nominal financial wealth a−1 is given. as we will disregard cases where the cash constraint (4) is not binding, we define the equilibrium of our model for the case where rt > 1. Definition 1. A rational expectations equilibrium of the model forRt > 1 is a set of sequences{λt, ct, lt, yt, πt, satisfying the households’ first order conditions,uc(t)/Rt = λt +, (8), (9), (24) (25) (26)the aggregate production function,yt = lt, optimal price setting approximated by(16), the labour demand condition(17), the consolidated public sector budget constraint(23), the monetary policy rule(18), the law of motion for the fiscal stanceκt(21)and for government expenditures(22), the aggregate resource constraint,yt = ct + gt, asset market clearance,at = bt, and the transversality condition(15)for a given initial valuea−1 > 0. 2. Fundamental Properties In this Section we present the fundamental properties of the model, which will subsequently be applied for the analysis of short‐run monetary and fiscal policy effects. We derive a linear version of the model by log‐linearising the equilibrium conditions listed in Definition 1 at the steady state. The particular steady state conditions depend on the long‐run liquidity value η of government bonds, which determines the relevance of open market operations. When the open market constraint is not binding, η = 0, the nominal interest rates on private and public debt are identical, R = Rd, and inflation solely relies on monetary policy, π = Rβ. Public debt does not affect consumption and inflation, such that the existence of a steady state does not impose a restriction on real debt. In contrast, η > 0 is associated with a binding open market constraint, m = b/R, and a positive spread, Rd − R > 0, where Rd = π/β and R is determined by interest rate policy (18). As public debt is non‐neutral in this case, the economy can only exhibit stationary values for all endogenous variables if public debt is stationary. As a consequence, steady state inflation now depends on fiscal as well as on monetary policy: π = [1 − (1 − κ)g/(cR)]−1 ≥ 1.13 This implies that a fiscal policy regime with a balanced budget target, κ = 1, ensures that the gross steady state inflation rate be equal to one, minimising the average distortion brought about by price rigidity. Otherwise, κ < 1, nominal government debt rises on average for non‐zero government expenditures, see (22), such that steady state inflation has to exceed one to stabilise real public debt. Steady state consumption is, nevertheless, independent of monetary and fiscal policy in both regimes and is pinned down by equating the marginal utility of consumption and leisure, =−ul(c + g). As a consequence, the long‐run relations between inflation and the growth rate of money and real output are consistent with McCandless and Weber's (1995)‘monetary facts’. 2.1. When Open Market Operations are Irrelevant We start the local analysis of the model at the steady state with a brief characterisation of the version where assets traded in open market operations are not restricted by (2). Open market operations are then irrelevant, which corresponds to ηt = 0, and the households’ first order conditions are given in (14). The nominal interest rates on government bonds and on private debt are identical and the amount of open market securities is (recursively) determined by see (24)–(26). Given that the fiscal policy variable κt, which governs the ratio of tax to debt financing, exclusively enters the government budget constraint (23) and public debt does not affect the remaining variables, it can immediately be concluded that κt is irrelevant for the remaining variables. Hence, Ricardian equivalence applies in this version as in the majority of general equilibrium business cycle models with lump‐sum taxes. This result and the log‐linear representation of the model, which can immediately be derived from the equilibrium conditions for ηt = 0 given in Definition 1, are summarised in the following proposition. Proposition 1. If open market operations are irrelevant, then Ricardian equivalence applies and a rational expectations equilibrium of the log‐linear approximation to the model is a set of sequencessatisfying(22), (27) (28) (29)whereγ1≡χ[σ + ϑc/y] > 0, γ2≡χϑg/y > 0, v−1≡ > 0, and the transversality condition for a given initial value for real wealth. The model in Proposition 1 is identical with the consensus monetary business cycle model, the so‐called New Keynesian model; see, e.g., Clarida et al. (1999). The equilibrium sequences of consumption, inflation, the nominal interest rate and government expenditures are solely determined by (22) and (27)–(29). Real financial wealth, which is a predetermined variable and equals real public debt, does not affect these variables and can be recursively determined, by , for given equilibrium sequences of inflation, realisations of the exogenous fiscal variables, κt and gt, and an initial value a−1.14 Accordingly, the fiscal stance κt only matters for the evolution of real wealth, such that public finance is irrelevant. We abstain in what follows from a further analysis of this version and refer to corresponding results provided in the literature. 2.2. When Open Market Operations Matter We now turn to the case where households internalise that their access to money is restricted by (6). The corresponding Lagrange multiplier ηt is larger than zero, implying a binding open market constraint, whenever the spread between the interest rates on private debt and on government bonds is expected to be positive, see (10).15 The existence of a steady state with a positive spread relies on the central bank to choose a sufficiently small average value for the nominal interest rate R. The respective upper bound in particular depends on fiscal policy due to its effect on the steady state inflation rate. Proposition 2. If the central bank sets the nominal interest rate R such that, where, then a steady state exists where the open market constraint is binding, m = b/R. Proof. A steady state with a binding open market constraint requires a positive spread Rd − R > 0 and has to satisfy Rd = π/β and π = [1 − (1 − κ)g/(cR)]−1. Using these conditions, it follows immediately that the existence of this steady state is ensured by , where given that β ∈ (0,1), κ ∈ (0,1], and g ∈ (0,c]. By choosing a sufficiently small average nominal interest rate, , the central bank allows for the existence of a steady state with a positive interest rate spread. The respective upper bound depends on the steady state inflation rate associated with a non‐growing real amount of public debt, which is required for a stationary equilibrium as public debt is non‐neutral. In what follows we assume that the support of and is sufficiently small, such that the log‐linearisation at the steady state with is a suitable approximation of the non‐linear model and the interest rate always exceeds Rt. The open market constraint then always binds, ηt > 0, such that real wealth (public debt) affects access to money and private consumption is determined by ct = mt = at/Rt , see (24)–(26). The following proposition presents the equilibrium of the linear model, which can immediately be derived by log‐linearising the equilibrium conditions for ηt > 0 given in Definition 1. Proposition 3. If the open market constraint is binding, then a rational expectations equilibrium of the log‐linear approximation to the model at the steady state withis a set of sequencessatisfying(21), (22), (29), (30) (31) (32)and the transversality condition for a given initial value for real wealtha0. According to the equilibrium condition (30), private consumption decreases with the nominal interest rate and increases with public debt. While the latter has no impact on real activity and inflation in standard New Keynesian models, it also enters the consumption function in overlapping generation models. Moreover, a binding open market constraint implies that the nominal interest rate, by which open market securities are discounted, affects current consumption via money supply, whereas the consumption Euler equation, which links interest rates to consumption when money supply is unbounded (27), predicts that the expected real interest rate governs the consumption path. Obviously, the consumption Euler equation does not vanish when the open market constraint is binding. However, it features the interest rate on private debt, E, and is therefore irrelevant for the determination of the equilibrium sequences of consumption, inflation and real wealth.16 Given the equilibrium sequences for the latter variables, which are determined by (21), (22), (29) and (30)–(32), the consumption Euler equation now recursively determines the equilibrium sequence for the interest rate on private debt, . The model in Proposition 3 can be reduced to a two dimensional system in inflation and real wealth, where beginning‐of‐period real wealth, , constitutes a relevant endogenous state variable. The equilibrium path of the model is therefore stable and unique if there is exactly one eigenvalue inside the unit circle. It turns out that the assumptions made in the previous Section are sufficient to ensure saddle path stability. In particular, as the nominal interest rate directly affects consumption, equilibrium determinacy does not rely on the behaviour of the real interest rate governed by the inflation elasticity ρ. Proposition 4. If the open market constraint is binding, then the model is saddle path stable. Proof. The deterministic part of the linear model presented in Proposition 3 reads (33) The characteristic polynomial of is given by As F(X) is strictly positive at X = 0, F(0) = (1 + γ1ρ)/(βπ), and strictly negative at X = 1, F(1) = −[γ1 + (π − 1)(1 − β + γ1ρ)]/(βπ), the model (33) exhibits exactly one eigenvalue inside the unit circle. As summarised in Proposition 4, saddle path stability of the rational expectations equilibrium is guaranteed for the monetary (18) and the fiscal policy rule (20). In contrast to the consensus New Keynesian model, pro‐activity, ρ > 1, or the Taylor‐principle (Woodford, 2001), is neither necessary nor sufficient for equilibrium determinacy. To get an intuition for this, consider first the consensus framework where consumption growth is governed by (27). When inflation is expected to rise and the central bank sets the interest rate in a passive way, ρ < 1, the expected real interest rate and consumption growth decline. Given that the model does not exhibit an endogenous state variable, this is consistent with a stable equilibrium path only if current consumption rises on impact, which feeds aggregate consumption and, by (8) and (17), real marginal costs. Hence, inflation in fact rises according to the aggregate supply constraint (16), implying that inflation expectations can be self‐fulfilling. Now, consider the case where the open market constraint is binding. A rise in inflation deflates financial wealth by (32), which tends to reduce consumption by (30). Provided that ρ ≥ 0, interest rate policy does not counteract this mechanism to the extent that aggregate demand declines. This leads to a reduction in real marginal costs and therefore to a decline in inflation, implying that self‐fulfilling expectations cannot occur. It should be noted that the particular choice of the fiscal policy rule (20) is in fact responsible for saddle path stability. When debt obligations are not completely tax financed, debt‐interest spirals, as discussed in Leith and Wren‐Lewis (2000), can occur if the central bank sets the nominal interest rate too aggressively (high ρ). To see this, consider a rise in real wealth brought about by a fundamental shock, for example, a temporary deficit financed tax cut. This leads, by (30), to an increase in private consumption and to a rise in inflation. When the fiscal rule (20) applies, financial wealth will be deflated in the subsequent periods, see (32), causing the economy to converge back to the steady state. If, however, the central bank strongly raises the nominal interest rate with higher inflation and interest payments on public debt are not completely tax financed, real public debt can increase. This rise in real wealth further feeds private consumption, inflation and even higher interest rates so that the economy evolves on an explosive path. In the Appendix, we present an example for a fiscal policy rule, where interest payments on public debt are not entirely tax financed, such that debt interest spirals are not in general precluded.17 3. Monetary and Fiscal Policy Effects As the effects of monetary and fiscal policy shocks in the standard New Keynesian model are already provided in the literature, we focus in what follows on the version with a binding open market constraint given in Proposition 3. By allowing for public debt to be non‐neutral, we expect monetary and fiscal policy interactions to affect the transmission of shocks, facilitating a broader variety of macroeconomic responses than in the case where Ricardian equivalence applies. Nevertheless, the effects of interest rate shocks are consistent with common priors about monetary policy effects. The structural part of monetary and fiscal policy turns out to be decisive for the sign of impulse responses to fiscal policy shocks. In particular, the impact of government spending and tax cut shocks on private consumption and on real activity will be shown to depend on the degree to which government expenditures are debt financed and on the willingness of monetary policy to stabilise the economy endogenously by a reactive interest rate setting. 3.1. The Model's Solution The model in Proposition 3 is reduced to a system in two endogenous variables, real wealth and inflation, with a state space consisting of one endogenous state variable, , and three exogenous, , and . The model's fundamental and unique solution reads (34) (35) As shown in Proposition 4, the coefficient δa in (34) is the single stable eigenvalue of the model and lies between zero and one. Applying the method of undetermined coefficients, the coefficients in (34)–(35) can be expressed as functions of deeper parameters, steady state values, and the stable eigenvalue. Lemma 1. The state space representation (34)–(35) of the model with ηt > 0 is characterised by coefficients δi withi ∈ {a, ag, ar, aκ, πa, πg, πr, πκ}satisfying (i) 0 < δa =and 0 < δπa =  1 − δaπ < 1; (ii) δar = γ1/γ4 > 0 andδπr = − γ1π/γ4 < 0; (iii) δag = [γ3π(1 − κ)(g/a) − γ2]/γ4andδπg = π[(β(1 − δaπ) +γ1)(1 − κ)(g/a) + γ2]/γ4 > 0; and (iv) δaκ = −κπ(g/a)γ3/γ4 < 0 andδπκ = −κπ(g/a) [γ1 + β(1−δaπ)]/γ4 < 0, whereα1≡πγ3 + β + γ1 > 1, , γ3≡1 + γ1ρ ≥ 1, andγ4≡γ3π + β(1 − δaπ) + γ1 > 1. Proof. See Appendix. The cyclical behaviour of inflation and real wealth can immediately be determined by applying the solution presented in Lemma 1. In what follows, we do not restrict our attention on these variables, as we are primarily interested in consumption and output responses. The corresponding coefficients are derived from the solution for inflation and real wealth together with the structural relations and . Note that we assumed, for simplicity, that all policy shocks are transitory. This implies that an economy would be expected to return to the steady state in the after‐shock period, if it lacks any history dependence. Accordingly, the equilibrium conditions of the purely forward looking version of the model, which are given in Proposition 1, are reduced to a set of static relations. In contrast, the model with relevant open market operations exhibits an endogenous state variable, which allows for temporary shocks to affect future expectations. Hence, non‐neutrality of public debt is responsible for an endogenous propagation of shocks, implying that the economy does not immediately jump back to the steady state when a transitory shock disappears. The persistence of shock effects is hereby governed by the stable eigenvalue δa, which can be shown to rise inter alia with the parameters κ and ρ describing the structural part of fiscal and monetary policy. Proposition 5. The stable eigenvalue of the model increases (i) with the fiscal feedback (∂δa/ ∂κ > 0) if, where, and (ii) with the inflation elasticity (∂δa/ ∂ρ > 0). Proof. To establish the first claim, we use the fact that κ affects the eigenvalue δa only via its negative effect on the steady state inflation rate (∂π/∂κ < 0) and that δa is given by . Applying the definitions for α1 and α2 in Lemma 1, the partial derivative of the eigenvalue with respect to inflation is with . It can immediately be shown that is sufficient to ensure ∂δa/∂π < 0 and thus ∂δa/∂κ > 0. The partial derivative of δa with respect to the inflation elasticity ρ is further given by δa/∂ρ = γ1α3/(2β) > 0. The equilibrium condition (32) implies that once real wealth exceeds its long‐run value, the return is speeded up for higher steady state inflation rates by which the pre‐existing stock of wealth is deflated on average. Accordingly, a higher fiscal feedback κ, which solely affects the stable eigenvalue due to its negative impact on steady state inflation, increases ceteris paribus the time required for real wealth to converge back to the steady state.18 Similarly, a high inflation elasticity ρ, which smooths the inflation path, reduces the deflationary impact on wealth and, thus, retards the recovery of real wealth. Hence, the eigenvalue δa and therefore persistence of debt effects increase with the endogenous response of monetary and fiscal policy, measured by ρ and κ, via a reduction in current or in average inflation. 3.2. Responses to Policy Shocks 3.2.1. Interest rate shocks As we derive the effects of policy shocks in what follows, we aim at revealing the role of the structural part of monetary and fiscal policy, ρ and κ, for the sign of the impulse responses. Given that all shocks are assumed to be transitory, we focus on the responses in the impact period. However, the responses in the subsequent periods would be qualitatively unchanged, if we allowed for sufficiently high degrees of autocorrelation in (18), (21) and (22). We start the policy analysis with the case where a nominal interest rate shock hits the economy in period s, while the realisations of the remaining shocks are set equal to zero (). In particular, we assume that the sequence of interest rate rule innovations satisfies and . Proposition 6.A positive innovation to the interest rate rule in periodsleads (i) to a decline in inflation (), (ii) to a rise in real wealth (), and (iii) to a decline in consumption and output (). Proof. The first two claims immediately follow from Lemma 1(ii): and . As also holds, the impact effect on consumption is given by . Applying the solutions in Lemma 1(ii), we obtain and thus . As summarised in Proposition 6, an unanticipated rise in the nominal interest rate causes a decline in inflation, consumption and output. These responses qualitatively accord with the predictions of the standard New Keynesian model. The model additionally predicts that real wealth rises due to a decline in inflation and eases, ceteris paribus, households’ access to money. Subsequent to the impact period s, real wealth exceeds its steady state value and consumption, output and inflation smoothly return to the steady state, while the speed of the recovery is affected by κ and ρ (see Proposition 5). 3.2.2. Government expenditure shocks We now turn to the case where a government expenditure shock hits the economy in period s (, , ). The solutions for the coefficients presented in Lemma 1(iii) reveal that the upward pressure on aggregate demand brought about by a positive innovation to government expenditures always leads to a rise in inflation, while the response of output depends on the central bank's willingness to counteract the inflationary pressure by increasing the nominal interest rate. Proposition 7. A positive government expenditure shock in period s leads to a rise (i) in inflation (), and (ii) in output () if, where. Proof. The first claim immediately follows from the sign restriction for given in Lemma 1(iii). The impact multiplier on output is given by . Using δcg = δag − ρδπg and the definitions for γ1, γ2, γ3, and γ4, we obtain δyg = [g/(c + g)](1/γ4) {π(1−κ)(1/R)[1−ρβ(1 − δaπ)] + π + χσ(1 + ρπ) + β(1 − δaπ)}. Hence, for a rise in a moderate inflation elasticity ρ ≤ 1 = [β(1 − δaπ)]−1 is sufficient, where 1 > 1 given that β < 1 and δaπ < 1. A comparison with the results in Linnemann and Schabert (2003) shows that both results presented in Proposition 7 are consistent with the findings on fiscal policy effects in a standard New Keynesian model given in Proposition 1. The rise in government consumption leads to a price pressure by (31) and tends to raise aggregate demand. However, the rise in inflation has an adverse effect on private consumption and thus on aggregate demand when the central bank endogenously responds to higher inflation by raising the nominal interest rate. A rise in output in response to a government expenditure shock is ensured by a modest interest rate policy, ρ < , where is strictly larger than one. This result immediately leads to probably the most interesting effect of government expenditure shocks, namely, the response of private consumption. Given that the latter rises with real wealth and declines with the nominal interest rate (30), a positive consumption response requires prices not to be too flexible. When government expenditures are not entirely tax financed (small κ) and prices are sufficiently rigid, , where ,19 real public debt can rise, which tends to raise private consumption. A rise in private consumption, however, additionally relies on interest rate policy not to be too reactive (small ρ). Proposition 8. Suppose that prices are sufficiently rigid,. Then a positive innovation to government expenditures in period s leads to a rise (i ) in real wealth () if, whereand, and (ii) in consumptionif, whereandifρ ≤ , whereand2 ∈ [0, ρπ1). Proof. Applying the solution given in Lemma 1(iii), we can write. As R is assumed to be strictly smaller than (see Proposition 2 and 3), it can immediately be shown that is sufficient for δag > 0. To establish the second claim, suppose that ρ < . Using the upper bound and π−1 = 1 − (1−κ)(g/cR), it follows that δcg = {π(1−κ)(g/a)[1 − ρβ(1−δaπ)]−(1 + ρπ)γ2}/γ4 is positive in this case if, but not only if . Further, ρ ≤ (<) ensures that , while is sufficient to guarantee that and are non‐negative. The result presented in the second part of Proposition 8 is, in particular, remarkable, as recent empirical studies (Fatas and Mihov, 2001; Blanchard and Perotti, 2002) find that private consumption rises with government expenditures, while Linnemann and Schabert (2003) show that conventional New Keynesian models cannot generate this effect. The reason is that the neoclassical wealth effect, as described by Baxter and King (1993), prevails in these models even if prices are not completely flexible. Government expenditures induce households to raise labour supply by intertemporal substitution, which is accompanied by an increased willingness to postpone private consumption. The result presented in Proposition 8 reveals that non‐neutrality of public debt is able to reconcile the predictions of a rational expectations business cycle model with the aforementioned empirical findings. As private consumption increases with real public debt, government expenditures do not necessarily lead to crowding out, if they are debt financed to a sufficiently large amount, . However, the existence of a (non‐negative) value for the fiscal feedback, which leads to a rise in private consumption, requires monetary policy not to raise the interest rate too aggressively with inflation, ρ ≤ (<). Otherwise, the increased cost of money can prevail over the stimulating effect of public debt creation on households’ transactions. As the sign of the responses to government expenditure shocks critically depends on the monetary and fiscal stance, the model thus provides a rationale for government spending effects to vary between countries and over time, as for example reported by Perotti (2002). 3.2.3. Temporary fiscal consolidations Finally, we examine the effects of innovations to the fiscal policy variable κt. In particular, we consider a positive shock to 0 ∀t), which can be interpreted as a temporary fiscal consolidation. Obviously, this policy experiment emphasises the main difference from conventional business cycle models. As Ricardian equivalence commonly applies in these models (see Proposition 1), a switch from deficit to tax financing has no impact on the non‐fiscal variables therein. This is clearly inconsistent with recent empirical evidence of Mountford and Uhlig (2002), showing that the most significant fiscal stimulus is brought about by deficit financed tax cuts. When debt is non‐neutral and the average tax financed fraction of government consumption is non‐zero (21), it is in fact possible to reproduce this finding. Proposition 9. An unanticipated and temporary fiscal consolidation in period s leads to a decline (i) in inflationand real financial wealth, and (ii) in consumption and output if and only if ρ < 1. Proof. The claims made in the first part immediately follow from Lemma 1(iv) and . For the second part, we use . Applying the solutions for δaκ and δπκ yields δcκ = −κπ(g/Rc)[1−ρβ(1−δaπ)]/γ4, which is strictly negative if and only if ρ < . A temporary fiscal consolidation () is, by (23), associated with a decline in nominal government bonds outstanding and therefore leads to a decline in inflation and real public debt given that prices are sticky. Thus, consumption and output tend, by (30), to decline as long as interest rate policy is not too reactive. For high inflation elasticities, ρ > , the decline in inflation can cause the central bank to lower the nominal interest rate in an extreme way such that households are willing to increase consumption expenditures if the current discounted value of real wealth exceeds its steady state value, even though real public debt declines. Correspondingly, a deficit financed tax cut can stimulate real activity when monetary policy is conducted in a modest way, ρ < . 4. Conclusion This paper examines the effects of monetary and fiscal policy in an environment where both interact as public debt is non‐neutral. The latter property is induced by allowing for government bonds to provide transactions services such that households’ consumption expenditures increase with real public debt. This mechanism originates in the role of risk‐free government securities in open market operations. We consider two money supply regimes in a sticky price model with interest rate policy, where money, which serves as the means of payment, is the counterpart of securities deposited at the central bank. The first monetary policy regime is characterised by the central bank accepting public and private debt, which can be issued by households in an unbounded way, as collateral for money. In this case open market operations are irrelevant, Ricardian equivalence applies and the model is isomorphic to the standard New Keynesian model. In the second regime, money supply is legally restricted such that only government securities are accepted in open market operations. Given that access to money relies on public debt holdings, households are willing to hold government bonds even if they are dominated in rate of return by private debt. Public debt is non‐neutral in this case as households can increase their (consumption) expenditures with additional holdings of government bonds. Fiscal and monetary policy then interact via the money supply, as the former determines the disposable stock of eligible securities, while the latter is assumed to aim at stabilising the economy by adjusting the nominal interest rate, by which open market securities are discounted. Hence, the response of real balances, private consumption, output and inflation to macroeconomic shocks crucially depends on the degree to which government expenditures are debt financed and on the intensity of endogenous interest rate responses to changes in inflation. Further, as interest payments are assumed to be tax financed, public debt evolves along a stable path and debars non‐fundamental shocks from being able to affect the economy, so that interest rate policy does not need to be restricted for saddle path stability. When this regime applies, a balanced budget target is associated with long‐run price level stability. In the short run, a deficit financed tax cut is able to stimulate real activity if interest rate policy is not too aggressively reacting to the simultaneous rise in inflation. Similarly, government expenditures can in this case also lead to a rise in private consumption if they are debt financed to a sufficiently large extent, that the associated increase in public debt eases households’ access to money. These expansionary fiscal policy effects, which are also found in recent empirical studies, can hardly be reproduced by conventional business cycle models, where public finance is irrelevant and private consumption is crowded out by government spending. Appendix Saddle Path Stability for An Alternative Fiscal Rule Let denote total lump‐sum receipts, which are assumed not to cover interest payments on public debt. In particular, suppose that the fiscal authority sets taxes according to the following rule specified in steady state deviations:20 (36) where r≡R/π denotes the steady state gross real interest rate, α governs the reaction of tax receipts on debt, and α > 0 ensures government solvency. When (36) instead of (20) applies, saddle path stability for ηt > 0 is ensured by a modest interest rate policy , where the upper bound is positive and rises in α if prices are not extremely rigid, , where . Proposition A1. Suppose thatand fiscal policy satisfies (36 ). Then the model with ηt > 0 is saddle path stable if, where, , , and. Proof. Inserting the tax rule (36) into the government budget constraint (19) and using at = bt, leads to , which replaces (32). Given that public debt is non‐neutral, the gross real interest rate r has to satisfy r = 1 + (τl − g)/a. Further suppose that government expenditures are sufficiently small, g < τl, to guarantee r > 1. The matrix M0 in (33) now features the coefficients (M0)11 = r − α and (M0)12 = r(ρ − 1). The characteristic polynomial of therefore reads F(X) = X2 + [(r − 1)γ1ρ − (r − α) β − 1 − γ1r]β−1X + (r − α)γ3β−1. Hence, F(X) is positive at X = 0. It can further be shown that F(1) is negative if the inflation elasticity ρ is sufficiently small, with . The model thus exhibits exactly one stable root if . Further, is strictly positive and increasing in α if, but not only if . Moreover, the upper bound on ρ satisfies As converges for α→0(α→r) to a limiting value which is strictly smaller (larger) than one, we can conclude that neither the Taylor‐principle nor its inverse applies in this model. For , the model can exhibit two unstable eigenvalues indicating an explosive equilibrium path. Proof of Lemma 1 We want to express the coefficients in the solution (34)–(35), δi with i ∈ {a, ag, ar, aκ, πa, πg, πr, πκ}, in terms of parameters and the eigenvalue δa, which lies between zero and one. For this the equilibrium conditions given in Proposition 3 are reduced to (37) (38) Replacing the endogenous variables in (37) and (38) by using the general solution form (34)–(35), leads to the following conditions for the undetermined coefficients (39) (40) (41) (42) Eliminating δπa in the two conditions in (39), leads to the following quadratic equation in the eigenvalue . Exactly one root of this equation lies between zero and one (see Proposition 4) and is given by From (39) we can conclude that δπa is strictly positive, δπa = 1 − πδa > 0, given that πδa can easily be shown to be smaller than one. The conditions in (40) immediately lead to the solutions for δπr and δar given in Lemma 1(ii). Rearranging the conditions in (41), gives the solution for the coefficients δπg and δag presented in Lemma 1(iii). The solution for the remaining coefficients δπκ and δaκ in Lemma 1(iv) immediately follow from the conditions in (42) and δπa = 1 − δaπ. Footnotes 1 " A comprehensive discussion of monetary policy in the New Keynesian model can be found in Clarida et al. (1999) and Woodford (2003). 2 " See Canzoneri et al. (2002a) or Linnemann and Schabert (2003) for an analytical derivation of fiscal policy effects in a New Keynesian model and Baxter and King (1993) for an analysis of the neoclassical wealth effect. 3 " For example, securities accepted by the US Federal Reserve and the Bank of England for open market operations mainly consist of securities issued by the treasury, federal agencies, or local authorities, respectively, as well as of privately issued debt, e.g., acceptances or bank bills, which meet high quality standards; see Bank of England (2002); Meulendyke (1998). 4 " This assumption is made more explicit in Canzoneri and Diba (2000), where it is shown that price level indeterminacy can be avoided by allowing for government bonds to enter a cash‐in‐advance constraint. 5 " One might think of a consumption Euler equation augmented by financial wealth, which, for example, applies in the Blanchard‐Yaari type model of Leith and Wren‐Lewis (2000). 6 " For example, the Taylor principle, which ensures equilibrium determinacy in the standard New Keynesian model (Woodford, 2001), is irrelevant in this case. 7 " See, for example, Perotti (2002) for cross country variations in fiscal policy effects. 8 " Though the duration of holding money is not infinite, the so‐called Hahn (1965) paradox, i.e., the problem about how to guarantee that money has a positive value over a finite horizon, does not apply due to the settlement of open market operations. 9 " Recent asset acquisition policy of the US Federal Reserve is also summarised as ‘Treasuries‐only’; see Broaddus and Goodfriend (2001). 10 " Obviously, one obtains a standard cash‐in‐advance specification in a symmetric equilibrium. 11 " A particular example for the interest rate rule is , where can be set to ensure . 12 " Hence, the fiscal policy regime is not related to specifications applied in the fiscal theory of the price level. See Buiter (2002) for a critical assessment of the latter. 13 " The steady state values g and κ are exogenously determined by (21) and (22). 14 " Note that there is no need for real wealth to be stationary to ensure stable sequences for the remaining variables. Nevertheless, government solvency and the transversality condition are satisfied given that interest rate payments on debt are entirely tax financed, see (23). 15 " When the spread is equal to zero, the model is identical with the one presented in Proposition 1. 16 " This feature relates to Canzoneri et al.'s (2002b) empirical findings, which cast severe doubts on the central role of the consumption Euler equation for the transmission of interest rate policy. 17 " The condition on ρ for saddle path stability is there shown to rely on the feedback from debt on taxes and is not related to the Taylor‐principle. 18 " To be precise, this result applies if, but not only if, prices are not too flexible , which is satisfied for reasonable parameter values. For example, σ = ϑ = 2, β = 0.99, g/y = 0.2, φ = 0.8 and π = 1.01(1.02) imply χ = 0.052 and . 19 " Note that is hardly restrictive for conventional parameter values, as σ = ϑ = 2, β = 0.99, g/y = 0.2, φ = 0.8, imply χ = 0.052 and . 20 " I am indebted to an anonymous referee for suggesting this rule. References Bank of England ( 2002 ). The Bank of England's Operations in the Sterling Money Markets , London: Bank of England Publications . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Baxter , M. and King , R. G. ( 1993 ). ‘Fiscal policy in general equilibrium’ , American Economic Review , vol. 83 , pp. 315 – 34 . OpenURL Placeholder Text WorldCat Blanchard , O. J. and Perotti , R. ( 2002 ). ‘An empirical characterisation of the dynamic effects of changes in government spending and taxes on output’ , Quarterly Journal of Economics , vol. 117 , pp. 1329 – 68 . Google Scholar Crossref Search ADS WorldCat Broaddus , J. A. Jr. and Goodfriend , M. ( 2001 ). ‘What assets should the Federal Reserve buy? , Federal Reserve Bank of Richmond Economic Quarterly , vol. 87 , pp. 7 – 22 . OpenURL Placeholder Text WorldCat Buiter , W. H. ( 2002 ). ‘The fiscal theory of the price level: a critique’ , Economic Journal , vol. 112 , pp. 459 – 80 . Google Scholar Crossref Search ADS WorldCat Calvo , G. ( 1983 ). ‘Staggered prices in a utility‐maximising framework’ , Journal of Monetary Economics , vol. 12 , pp. 383 – 98 . Google Scholar Crossref Search ADS WorldCat Canzoneri , M. B. , Cumby , R. and Diba , B. ( 2002a ). ‘New views on the transatlantic transmission of fiscal policy and macroeconomic policy coordination’, mimeo , Department of Economics, Georgetown University . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Canzoneri , M. B. , Cumby , R. and Diba , B. ( 2002b ). ‘Euler equations and money market interest rates: a challenge for monetary policy models’, mimeo , Department of Economics, Georgetown University . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Canzoneri , M. B. and Diba , B. ( 2000 ). ‘Interest rate rules and price determinacy: the role of transactions services of bonds’, mimeo , Department of Economics, Georgetown University . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Clarida , R. , Galí , J. and Gertler , M. ( 1999 ). ‘The science of monetary policy: a new Keynesian perspective’ , Journal of Economic Literature , vol. 37 , pp. 1661 – 707 . Google Scholar Crossref Search ADS WorldCat Fatas , A. and Mihov , I. ( 2001 ). ‘The effects of fiscal policy on consumption and employment: theory and evidence’ , Centre for Economic Policy Research, Discussion Paper Series, no. 2760. Hahn , F. H. ( 1965 ). ‘On some problems in providing the existence of an equilibrium in a monetary economy’, in ( F. H. Hahn and F. P. R. Brechling, eds.), The Theory of Interest Rates , London: Macmillan . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Jeanne , O. ( 1998 ). ‘Generating real persistent effects of monetary policy: how much nominal rigidity do we really need?’ , European Economic Review , vol. 42 , pp. 1009 – 32 . Google Scholar Crossref Search ADS WorldCat Leith , C. and Wren‐Lewis , S. ( 2000 ). ‘Interactions between monetary and fiscal policy rules’ , Economic Journal , vol. 110 , pp. C93 – 108 . Google Scholar Crossref Search ADS WorldCat Linnemann , L. and Schabert , A. ( 2003 ). ‘Fiscal policy in the new neoclassical synthesis’ , Journal of Money, Credit, and Banking , vol. 35 , pp. 911 – 29 . Google Scholar Crossref Search ADS WorldCat McCandless , G. T. and Weber , W. E. ( 1995 ). ‘Some monetary facts’ , Federal Reserve Bank of Minneapolis Quarterly Review , vol. 19 , pp. 2 – 11 . OpenURL Placeholder Text WorldCat Meulendyke , A. M. ( 1998 ). U.S. Monetary Policy and Financial Markets , New York: Federal Reserve Bank of New York . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Mountford , A. and Uhlig , H. ( 2002 ). ‘What are the effects of fiscal policy shocks?’ , Center for Economic Research, Discussion Paper 2002–31, Tilburg University . Perotti , R. ( 2002 ). ‘Estimating the effects of fiscal policy in OECD countries’ , European Central Bank, Working Paper Series, no. 168. Woodford , M. ( 2001 ). ‘The Taylor rule and optimal monetary policy’ , American Economic Review, Papers & Proceedings , vol. 91 , pp. 232 – 7 . Google Scholar Crossref Search ADS WorldCat Woodford , M. ( 2003 ). Interest and Prices: Foundations of a Theory of Monetary Policy . Princeton, N.J.: Princeton University Press . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Yun , T. ( 1996 ). ‘Nominal price rigidity, money supply endogeneity, and business cycles’ , Journal of Monetary Economics , vol. 37 , pp. 345 – 70 . Google Scholar Crossref Search ADS WorldCat Author notes " I am grateful to Matthew Canzoneri, Campbell Leith, Ludger Linnemann, Jonathan Temple and two anonymous referees for helpful suggestions and comments. © Royal Economic Society 2004

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The Economic Journal – Oxford University Press

Published: Mar 1, 2004

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