Coordination of monetary and fiscal policies - CiteSeerX

SWEDISH ECONOMIC POLICY REVIEW 15 (2008) 89-124

Coordination of monetary and fiscal policies: A fresh look at the issue Stefan Niemann and Jürgen von Hagen*

Summary A large literature has studied the coordination of monetary and fiscal policies in the context of macroeconomic stabilization. The general result from this literature is that coordination is desirable but that the welfare gains which can be achieved from it are negligible. In this paper, we take a fresh look at the issue. We consider coordination in the context of the longer-term orientation of monetary and fiscal policies and, hence, their impact on the economy’s steady state. We present a dynamic game, in which a fiscal authority sets its budgetary targets while the monetary authority sets its inflation target, and study the interaction between the two. We find that policy externalities between the two authorities are potentially large. Excessive central bank conservatism leads to high levels of public debt and reduced welfare. This speaks in favor of coordination in the sense that the institutional design of the central bank should be devised taking into account the characteristics of the fiscal authority.

JEL classification: E61, E63, E58. Key words: monetary-fiscal interaction, nominal government debt, time-consistency, dynamic game.

* Stefan Niemann is a Lecturer at the Department of Economics, University of Essex and University of Bonn. Jürgen von Hagen is Professor at the University of Bonn, Indiana University, and CEPR.

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SWEDISH ECONOMIC POLICY REVIEW 15 (2008) 89-124

Coordination of monetary and fiscal policies: A fresh look at the issue Stefan Niemann and Jürgen von Hagen* During the past two decades, two paradigms have conquered monetary policy in the developed world and a number of developing countries and emerging market economies: central bank independence and inflation targeting. While monetary policy was controlled by the finance ministries in many countries until the 1970s and 1980s, numerous central banks are now independent from their governments in the sense that they do not take orders from them regarding the conduct of monetary policy. While monetary policy was busy managing the macro-economy and pursuing price stability, full employment and external balance all at the same time before, it is now charged with pursuing price stability as its primary goal in most developed countries (and many emerging economies), with stabilization of cyclical movements as a secondary goal at best. The combination of these two paradigms has led to an increasing disassociation of monetary from fiscal policies, which are now generally regarded as two distinct branches of macroeconomic policy, each pursuing its own goals independently of the other. In this context, an exemplary institutional arrangement is given by the European Monetary Union, where the authority over monetary policy lies solely with the European Central Bank, a supranational agency, while fiscal policies continue to be the prerogatives of individual national governments. The view behind these developments is that a monetary authority can successfully implement society’s most desirable target path for inflation when it has a clear mandate for price stability and is independent in its choices about how to conduct monetary policy. Of course, independent central banks could still coordinate their policies with the fiscal authorities, but they seem generally reluctant to do so. For example, the first president of the ECB, Wim Duisenberg, clearly rejected the idea of policy coordination between the ECB and the fis* This paper has been prepared for the conference on Fiscal Rules and Institutions organized by the Economic Council of Sweden, October 22, 2007. We thank our discussant Anna Larsson, Martin Flodén, an anonymous referee and seminar participants for very helpful comments.

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COORDINATION OF MONETARY AND FISCAL POLICIES: A FRESH LOOK AT THE ISSUE, Stefan Niemann and Jürgen von Hagen

cal authorities in the European Monetary Union, stating that (Duisenberg, 2003): ”Fiscal policy should contribute to maintaining an environment of macroeconomic stability. At the same time, the monetary policy of the ECB takes into account the fiscal policy stance, as one of the factors which contribute to the outlook for price stability over the medium term. ... An open exchange of views between individual policy actors can assist the overall outcome, if this enhances an understanding of the objectives and strategies to pursue them. However, there cannot be any scope for active co-ordination of fiscal and monetary policies.”

In contrast, fiscal policy makers call for coordination with monetary authorities more frequently, especially in the context of exchange rate policies and in calling for lower interest rates; witness the recent (2007) remarks by the new French President Sarkozy. The argument that separating monetary policy from fiscal policy is best rests on the assumption that the actions of one do not affect the target variables of the other in important ways. Specifically, this requires (i) that fiscal policy is not a major source of inflation, while (ii) the effects of monetary policy on the government budget are small (Woodford, 2001). These two conditions assure that policy externalities between the actors, which are at the heart of the problem of policy coordination, are negligible. If such externalities are strong, a lack of coordination leads to inefficient policy outcomes in the sense that both actors could achieve better outcomes by taking into account the effects their actions have on the targets of the other actor. At the same time, however, the case for separating monetary and fiscal institutions is based on the experience that leaving both monetary and fiscal policy in the hands of the government leads to an inefficient inflation bias because of the well-known time-consistency problem. Governments will then try to use monetary policy to correct the distortions created by taxes and subsidies in terms of permanently lower levels of output and employment by means of surprise inflation. Anticipating this, the private sector will expect higher inflation rates; in equilibrium, inflation will be positive with no permanent gains in output nor inflation (Kydland and Prescott, 1977; Barro and Gordon, 1983a, b). Most of the literature on monetary and fiscal policy coordination has focused on the problem of optimal macroeconomic stabilization policies. For example, Wim Duisenberg, in the speech quoted above, continues by saying (italics added): “Such active co-ordination is bound to be 92


ineffective given the inability of both fiscal and monetary policy-makers to finetune economic developments.” In this context, the policy problem is to find the optimal response to fluctuations of key macroeconomic variables around a given steady state characterized by long-run trends for output, employment, and the price level. Here, fiscal policy is typically regarded as governed by microeconomic and distributional concerns. Its effectiveness to stabilize short-run macroeconomic fluctuations is seen as very limited due to the lags involved in recognizing such fluctuations and in adjusting fiscal policy instruments, since the latter requires legislative actions. Monetary policy then carries the brunt of macroeconomic stabilization, and, to avoid the time-consistency problem plaguing discretionary policy making, does so by committing to policy rules. Such rules typically prescribe the adjustment of short-term interest rates to macroeconomic variables such as the rate of inflation and the output gap (Taylor, 1993). As noted by Canzoneri (2007), though, even in this context there is a potential for fiscal policy to provide macroeconomic stabilization through fiscal policy rules tying changes in fiscal policy instruments such as the budget deficit to fluctuations in macroeconomic variables. This raises the issue of a coordinated design of optimal policy rules for both monetary and fiscal policy, which remains a largely unexplored research issue at this time.1 Even so, however, the focus on macroeconomic stabilization puts this perspective on monetary and fiscal policy coordination under the verdict of Lucas (2003), namely that it is by its very nature dealing with issues which are of second-order magnitude in terms of welfare considerations. Lucas argues that stabilization policies are concerned with relatively small fluctuations around the steady state, and that eliminating these fluctuations will yield gains which can only be of second-order magnitude, too. In this paper, therefore, we adopt a different perspective: By asking to what extent the coordination of macroeconomic policies affects the steady-state equilibrium of the economy, we approach the issue of policy coordination in terms of first-order effects. The existence of significant amounts of government debt may give rise to important externalities between monetary and fiscal policies. Since the largest part of government debt is in nominal terms, moneSee Canzoneri (2007) for a brief review of the small existing literature on this issue. 1

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tary policy can affect its real value and therefore the tax burden required to finance it; this establishes a channel through which monetary policy can affect the government budget, an important element in the set of fiscal objectives. Table 1. General government gross financial liabilities and net debt interest payments

Australia Austria Belgium Canada b) Czech Republic Denmark Finland France Germany Greece c) Hungary Iceland d) Ireland Italy Japan Korea Luxembourg Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland UK US Euro area Total OECD

Gross financial a) liabilities 1996199620012006 2001 2006 24.8 30.7 18.5 69.3 68.7 69.9 111.3 121.5 101.3 83.4 91.5 75.1 34.9 n.a. 34.9 57.3 65.7 48.5 54.1 58.1 49.4 69.3 66.7 71.0 63.8 60.5 66.4 94.7 92.1 98.6 65.6 65.4 64.7 42.1 48.0 36.8 39.7 47.7 34.1 122.7 126.1 118.9 141.6 120.1 163.6 16.8 12.6 21.0 9.2 9.8 8.5 68.3 74.3 60.7 34.8 40.3 29.5 39.0 32.8 44.2 47.3 45.0 48.0 65.9 63.4 67.6 46.1 47.4 46.6 62.5 70.2 54.7 68.8 76.3 60.6 55.4 52.8 57.4 46.7 49.0 43.5 61.6 62.2 59.9 76.2 77.0 75.0 73.2 71.5 74.3

Net debt interest a) payments 1996199620012006 2001 2006 1.7 2.1 1.3 2.7 3.0 2.4 5.9 6.9 4.9 3.0 4.2 1.9 0.2 0.2 0.2 2.5 3.2 1.8 0.7 1.3 0.1 2.6 2.8 2.5 2.6 2.8 2.5 5.4 6.6 4.2 n.a. n.a. n.a. 0.6 0.9 0.2 1.0 1.7 0.1 6.0 7.3 4.6 1.3 1.4 1.1 -0.9 -0.9 -0.9 -0.8 -0.8 -0.9 2.8 3.6 2.0 0.0 0.4 -0.4 -7.4 -6.2 -8.8 2.6 3.2 2.0 3.2 3.6 2.8 1.2 1.5 1.0 2.8 3.6 1.9 0.8 1.3 0.2 0.7 0.7 0.6 2.3 2.7 1.9 2.5 2.9 2.0 3.4 3.9 2.8 2.4 2.8 1.9

Notes: a) Percent of nominal GDP. Averages based on yearly data. b) Data on gross financial liabilities only for 2002-2006. c) No data available on net debt interest payments. d) Data on gross financial liabilities only for 1998-2006. Source: OECD (2007).

Table 1 presents data on the ratio of public debt to GDP and the GDP share of governments’ net interest payments for a number of 94


OECD countries. Averaging across years, it demonstrates that debt burdens are indeed large in most OECD economies and that there is no clear trend towards debt consolidation. In addition, the figures on net interest payments illustrate that the budgetary effects of reducing the debt burden can indeed be substantial. Thus, the potential externalities from monetary to fiscal policy should not be neglected. Regarding the reverse channel, the seminal insights are due to Sargent and Wallace’s (1981) unpleasant monetarist arithmetic. Building on their paper, the fiscal theory of the price level (Leeper, 1991) has argued that government deficits can trigger wealth effects which generate inflationary dynamics. However, this theoretical proposition rests on the admissibility of non-Ricardian fiscal policies, i.e., fiscal policy rules which do not necessarily guarantee that the intertemporal government budget constraint is satisfied. Moreover, inference with respect to the empirical validity of the fiscalist arguments is problematic (Kocherlakota and Phelan, 1999). Nevertheless, with nominal debt (and unindexed bonds), the incentives facing monetary policy to resort to surprise inflation are an increasing function of the government’s debt burden; in an environment of rational expectations, the prediction then is a positive inflation bias which is systematically related to the stock of debt. Indeed, empirically, Campillo and Miron (1997) find a significant effect of the debt-to-GDP ratio in accounting for cross-country inflation variation. Thus, since the accumulation of public debt is primarily the result of fiscal budget decisions, fiscal policy may exert externalities on monetary policy by shaping the environment in which the latter operates. In this paper, we take a fresh look at the issue. Our approach is in line with the traditional view in that it admits only Ricardian policies, but at the same time it produces outcomes similar to those of the fiscal theory. To arrive there, we borrow from two different branches of the literature. The first one builds on the unpleasant monetarist arithmetic due to Sargent and Wallace (1981). Taking the government’s intertemporal budget constraint as its central building block, it argues that the future path of fiscal policy can impose restrictions on the inflation path monetary policy can achieve. However, a drawback with this literature is that it takes no explicit stand on the policy regimes (monetary versus fiscal dominance) that can emerge and whether or not they are sustainable. Thus, Sargent and Wallace (1981) state: ”...monetary and fiscal policies simply have to be coordinated. The question is,

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which authority moves first, the monetary authority or the fiscal authority? In other words, who imposes discipline on whom?” The second branch pursues these questions in frameworks where monetary and fiscal policies are the result of explicit optimizing exercises with well-defined constraints. This literature, however, generally assumes that there is one unified actor setting monetary and fiscal policies simultaneously.2 Alternatively, it assumes an independent monetary or fiscal authority, but takes fiscal or monetary policy as non-existent or exogenous. Thus, this literature has little to say about dynamic monetary-fiscal interactions and the pertinent coordination problems. Combining these two branches of the literature, we build a dynamic general equilibrium model of monetary and fiscal policy making which features two separate policy actors entrusted with the conduct of macroeconomic policy. Since we are not interested in shortterm stabilization issues, we analyze a simple monetary economy with flexible prices and study the interaction between the fiscal and the monetary authority as a dynamic game. This sheds light also on normative aspects of institutional design: The question here is to what extent the design of one authority exerts externalities on the other and, hence, ought to be taken into account when the latter is being designed. Our model is closely related to Díaz-Giménez et al. (2008) and Niemann (2006a,b). Díaz-Giménez et al. (2008) look at the dynamic interaction of monetary and fiscal policies from an optimal taxation perspective and consider a single policy maker controlling both fiscal and monetary instruments. Focusing on sequential decision making, they show that the optimal policy without commitment is to deplete any outstanding stock of nominal government debt gradually over time. The rationale for this is that, for given nominal interest rates, the inflationary erosion of the real stock of public liabilities allows to economize on the distortions needed to comply with the intertemporal government budget constraint. Only when there is no more nominal debt, the incentive for surprise inflation disappears and zero inflation can be sustained in equilibrium. Niemann (2006a) extends this 2 See e.g. Chari and Kehoe (1999) or Benigno and Woodford (2003) for prominent papers in this literature. The papers by Dixit and Lambertini (2003) and by Adam and Billi (2007) are exceptions in that there monetary and fiscal policies are implemented by separate agencies; however, the papers make simplifying assumptions which help to abstract from the dynamics of government debt.

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model to two separate policy makers and studies the dynamic interaction between a fiscal and a monetary policy actor who both are benevolent in the sense that they share the representative agent’s utility function. He shows that the separation of fiscal and monetary policy leads to multiple (self-confirming) equilibria and may sustain a zeroinflation equilibrium with positive levels of nominal public debt. In this paper, we build on Niemann (2006b) and study more closely the institutional design of the two policy agencies. We assume that both authorities have utility functions which differ from that of the representative agent. More specifically, we assume that the central bank is designed to be “conservative” in the sense that it puts more weight on inflation than the representative agent. This assumption has been common in the literature on the design of independent central banks since Rogoff (1985) and is interpreted as an institutional device reducing the inflation bias of monetary policy. In our context, the divergence of the policy authorities’ respective objective functions, which is implied by monetary conservatism, can also be interpreted as an institutional safeguard against the temptation of the two authorities to coordinate their policies. This is because with identical preferences the two agencies would have an incentive to collude each period and, as a result, succumb to the time-consistency problem of monetary policy. Furthermore, we assume that the fiscal authority is more impatient than the central bank and the representative agent, i.e., it values the future relatively less than the latter. Such relative impatience is a standard feature of governments in models of political economy and can be interpreted as a result of electoral uncertainty or other politicoeconomic frictions.3 It gives rise to a tendency of profligate fiscal policies and introduces a strategic conflict between the two agencies. This strategic conflict assures that, in contrast to the benchmark case discussed in Niemann (2006a), the policy game between the two authorities has a unique equilibrium outcome in terms of the equilibrium dynamics of consumption and government debt.

3 For example, Malley et al. (2007) predict that fiscal incumbents with uncertain prospects of reelection find it optimal to follow shortsighted fiscal policies; using US data, they find a statistically and economically significant link between electoral uncertainty and macroeconomic policy outcomes. For a discussion of other politico-economic mechanisms shaping the conduct of fiscal policy, see Persson and Tabellini (2000).

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The strategic game we consider proceeds within the framework of a dynamic general equilibrium model, where government policies are implemented sequentially over time and the two actors move simultaneously each period. In contrast, the literature focusing on short-run stabilization issues often assumes that—due to the constraints of the parliamentary decision making process—fiscal policy is more sluggish than monetary policy and, therefore, their interaction should be modeled as a dynamic Stackelberg game with fiscal policy as the leader.4 As noted above, we abstract from short-term stabilization and focus on the determination of inflation and government debt over the medium-to-long-run, instead. This makes the assumption of simultaneous moves more appropriate. A convenient interpretation of our game is that the two actors simultaneously set annual inflation targets and budgetary targets. In this game, a measure of real government debt serves as an endogenous state variable that can be dynamically manipulated by the two authorities. We solve this game using the concept of Markov-perfect equilibrium. While the use of a dynamic general equilibrium model comes at some cost in terms of modeling effort, it is appropriate in a context where both fiscal and monetary policy are considered endogenous, and it has a number of advantages. First, our model allows for meaningful policy interaction in the sense of a dynamic game with a nontrivial state variable played between the two actors. In contrast, the earlier literature studying monetary institutions such as conservative central bankers (Rogoff, 1985; Lohmann, 1992), incentive contracts for central bankers (Walsh, 1995; Waller et al., 1997), or inflation targeting (Svensson, 1997) has taken fiscal policy as either non-existent or exogenous. Second, our model comprises dynamic, forwardlooking behavior of all agents, such that current economic outcomes are influenced by expectations about future policies; the formation of these expectations, in turn, varies along with the dynamics of the endogenous state variable. To reduce the complexity of the analysis, in this paper we present a numerical example of the more general game studied in Niemann (2006b). Since we abstract from short-term stabilization problems, the model is deterministic. The central result from our analysis is that the impatient fiscal actor can strategically exploit the monetary authority’s inability to commit to zero inflation in the presence of nominal public debt. This 4

See e.g. Alesina and Tabellini (1987) or Dixit and Lambertini (2003).

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makes the inflation bias reappear even under decentralized policies and has important implications for the dynamics of government debt. The reason why fiscal policy affects inflation in our otherwise monetarist world is that, although it has no direct impact on inflation, it affects the monetary authority’s incentives to create surprise inflation. In this sense, inflation emerges as a fiscal phenomenon in our analysis. Moreover, being explicit about the welfare costs of partial commitment by the central bank, our analysis sheds some new light on the role of central bank conservatism. While the direct effect of central bank conservatism is to enable the central bank to commit to a lower rate of inflation for any given level of public debt, the implication that any level of real government debt can be sustained at a lower rate of inflation is fully internalized and exploited by the fiscal authority. Doing so, fiscal policy runs larger deficits and accumulates more debt with a more conservative monetary regime. Hence, due to the requirement to finance the higher level of debt by higher distortionary taxes, central bank conservatism has an indirect cost in terms of consumer welfare. The rest of this paper is organized as follows. In Section 1, we set up our model of dynamic monetary and fiscal policy interaction. Section 2 specifies the policy game between the central bank and the fiscal authority. In section 3, we study the properties of the equilibrium outcomes. Section 4 draws out some policy implications and concludes. Technical details are relegated to the Appendix.

1. The model We consider a dynamic monetary general equilibrium economy with public debt, but without capital.5 The economy is made up of a private sector and a government sector which consists of two distinct authorities: a monetary authority (central bank) and a fiscal authority. The central bank enjoys both goal independence and instrument independence (Debelle and Fischer, 1994). Accordingly, the central bank’s objectives may differ from those of the fiscal authority, and the central bank is free to set its policy instruments such as to achieve these objectives. Similar models have been analyzed in Lucas and Stokey (1983), Díaz-Giménez et al. (2008), Martin (2007) and Niemann (2006a,b). 5

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There is no uncertainty, time is discrete, and in each period t , the policy instrument controlled by the central bank is the supply of money M ta+ 1 (the superscript a is used to distinguish an aggregate variable from an individual variable). Equivalently, monetary policy in period t can be characterized in terms of the rate of aggregate money growth µ t ≡ M ta+ 1 M ta − 1 . The fiscal authority faces the task of collecting consumption taxes6 τ tc in order to finance an exogenously given stream of public expenditures g t . As a means to defer taxation, the fiscal authority can also issue nominal one-period bonds Bta+ 1 ; hence, the government faces an optimal taxation problem. For simplicity, we let public spending be constant over time such that g t = g for all periods. The two authorities interact via the consolidated budget constraint of the government sector. Seignorage revenues from money creation by the monetary authority accrue to the consolidated government budget. Thus, we restrict attention to the public finance role of monetary policy. The money price of one unit of consumption c t prevailing at time t is Pt , while R t is the nominal interest rate from period

t − 1 to period t . Starting from an initial stock of money M 0a and initial gross-of-interest debt liabilities B0a (1 + R 0 ) , the government sector has to satisfy the following sequence of period-by-period budget constraints:

M ta+1 − M ta + Bta+1 + Pt τ tc c t ≥ Bta (1 + Rt ) + Pt g ,

(1)

requiring that the sum of revenues from seignorage, the issuance of public debt and taxation are sufficient to cover the liabilities from maturing debt as well as current expenditure needs. The economy’s private side consists of a continuum of identical infinitely-lived households who discount the future with the factor

6

Our arguments could also be formalized in terms of a wage tax.

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β ∈ ( 0,1) and derive utility from consumption c t and labor n t according to the following expression:7 ∞

∑ β t {log( c t ) − αnt } .

(2)

t =0

In any period, each household faces the following budget constraint:

M t +1 + Bt +1 + Pt (1 + τ tc )c t ≥ M t + Bt (1 + Rt ) + Wt n t ,

(3

which requires that current gross-of-tax consumption expenditure Pt (1 + τ tc )ct and the portfolio of nominal assets—consisting of government debt Bt +1 and money M t +1 —to be taken into the next period are financed out of nominal wealth brought into the period plus the current wage earnings. Moreover, each household’s asset position must remain bounded, which rules out explosive Ponzi-schemes. Households face a transaction restriction which requires that their gross-of-tax consumption expenditure in period t must be financed using currency carried over from period t − 1 . This gives rise to the following cash-in-advance (CIA) constraint (Svensson, 1985):

M t ≥ Pt (1 + τ tc )c t

(4)

The timing structure underlying this CIA constraint is such that fresh cash injections generate an immediate reaction of the price level, but are not disposable for purchasing private consumption until the next period. Due to the absence of physical capital, the production side of the model economy is very simple. In each period, labor nt can be transformed into private consumption ct or public consumption g at a 7 Our particular specification of preferences implies (i) that, as far as the source of the monetary time-consistency problem is concerned, we abstract from seignorage on base money and focus on the inflationary implications of changing the real value of nominal debt (by log utility from consumption) and (ii) that the real interest rate cannot be affected by public policies (by linear disutility from labor).

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constant rate, which we assume to be unitary. It follows that the equilibrium real wage is w t ≡ Wt Pt = 1 , and aggregate feasibility is reflected by the following linear resource constraint: c t + g ≥ nt .

(5)

We are now ready to characterize a competitive equilibrium for a given sequence of government policy choices {τ tc , M ta+1 , Bta+1 , g}t∞= 0 . In particular, the government budget constraint (1) and the aggregate resource constraint (5) hold at equality, and the CIA constraint (4) is binding whenever Rt +1 > 0 . It is important to recall that the economy under consideration is entirely deterministic; as a consequence, households’ rational expectations with respect to the future dictate that they have perfect foresight about the policies to be implemented by the monetary and fiscal agencies, even though the latter cannot commit to specific future rules or actions. The competitive equilibrium allocation can then be determined from the following conditions which must hold for all periods: M t = Pt (1 + τ tc )c t , ( 1 + Rt +1 ) =

(6)

1 Pt +1 , β Pt

(7)

1 = (1 + Rt )(1 + τ tc ) . αc t

(8)

The first expression is a simple restatement of the (binding) CIA constraint and implies that there is a quantity-theoretic relation between money, output and gross-of-tax prices. Relation (7) is the Fisher equation relating the nominal interest rate to the real interest rate and inflation. Equation (8) is a static optimality condition and establishes that the distortions due to fiscal ( τ tc ) and monetary ( Rt ) policies are equivalent with respect to their effect on private households’ decision margins for consumption and leisure. In order to obtain explicit solutions for a private household’s decisions in period t, not only the sequence of macroeconomic policies

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from that date onwards is relevant, but also information about the household’s asset position at the beginning of the period is necessary. The latter piece of information can be condensed into a single state variable zt ≡ Bt (1 + Rt ) M t , which summarizes the composition of the nominal asset portfolio with which the household enters the period and, importantly, also indicates the real gross-of-interest value of the maturing government bonds held. Aggregation across households yields the aggregate state variable a zt ≡ Bta (1 + Rt ) M ta . The aggregate state will be seen to shape the incentives faced by the authorities when implementing their policies: On the one hand, due to the CIA constraint only money is available for households’ current consumption expenditure such that the composition of their nominal asset portfolios provides information about their consumption possibilities. On the other hand, the real gross-ofinterest value of the maturing liabilities is an indicator for the government’s real debt burden inherited from the past, which must be met by distortionary revenue generation from taxation or seignorage such as to balance the intertemporal government budget. Hence, when considering the use of their policy instruments τ tc and M ta for public revenue generation, the authorities must trade off the decrease in current consumption with the future gains due to a relaxed debt burden.

2. The policy game We consider a policy game between the fiscal and the monetary authority which is played sequentially over time. Neither authority has a commitment technology. Each period, policies are determined according to a rule ϕ ( z a ) = {ϕ m ( z a ),ϕ f ( z a )} consisting of a monetary and a fiscal policy component, each of which is determined independently by the relevant authority. The rule maps the current aggregate state of the economy into policy choices.8 History does not matter except via its influence on the current state. Since the environment in which the two authorities interact is stationary except for the aggregate state variable, we consider only time-invariant functions. In each period, monetary and fiscal policies are chosen simultaneously. The Subsequently, non-indexed variables pertain to a generic current period and primes denote variables relating to the corresponding next period. 8

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objective of our subsequent analysis is to determine the equilibrium policy rule ϕ ∗ ( z a ) = {ϕ m∗ ( z a ), ϕ ∗f ( z a )} adopted by the two authorities. The fiscal authority is assumed to be benevolent, but impatient due to political uncertainty. Its objective function is: ∞

∑ δ {log(c ) − αn }, t

t

t =0

t

where δ < β . The divergence of the fiscal authority’s discount factor from the one employed by private agents creates a systematic tendency towards myopic fiscal policy choices. The central bank is assumed to be conservative in the sense of pursuing price stability as a goal of its own in addition to maximizing household welfare. Its objective function is:   P  2  β − γ  t  + (1 − γ )[log(ct ) − αnt ] . ∑ t =0   Pt   ∞

t

Here, γ ∈ (0,1) is the weight on price stability. Specifically, γ balances the relative impacts on the monetary authority’s payoff of general welfare and a loss term resulting from unanticipated deviations of the realized price level Pt from the level Pt that was expected by the public.9 The central bank’s aversion against surprise inflation implies a reluctance to use the inflation tax as a lump-sum instrument. The two authorities choose their policies in a non-cooperative manner, taking their respective counterpart’s current behavior as well as the policy rules employed in the future as given. The government budget constraint (1) constitutes a restriction facing monetary and fiscal authorities when they choose their policies. Since the objectives pursued by the authorities are defined in terms of the macroeconomic allocation, it is useful to solve the authorities’ optimization problem in terms of macroeconomic allocations rather than policy instruments (primal approach). On the basis of this reformulation, we now pro9 Note that, although any government policy will be perfectly anticipated in a rational expectations equilibrium, it is nevertheless possible to define the monetary authority’s objective function in terms of deviations from arbitrary predetermined expectations.

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ceed to analyze the Markov-perfect equilibrium outcomes of the dynamic game played between the monetary and the fiscal authority. Without going into details, we mention that the Markov-perfect equilibrium concept encodes the requirement that the two agencies employ time-consistent policy rules. A number of technical aspects underlying the primal approach as well as a formal description of the Markov-perfect equilibrium are laid out in the Appendix. The requirement of time-consistency dictates that the equilibrium policy rule ϕ ∗ ( z a ) , if it is in place in the future, must be replicated via the current policies. Note, however, that this requirement relates to the policy functions, not to policy outcomes. Thus, the actual policy choices may differ across periods along with the dynamics of the aggregate state z a . Indeed, the evolution of the endogenous state variable z a plays a crucial role for the dynamics of monetary-fiscal interaction. Specifically, as an indicator for the tightness of the intertemporal government budget constraint, z a provides information with respect to the amount of distortions to be imposed on the economy. Given the authorities’ conflict with respect to the intertemporal pattern of these distortions and future policy makers’ lack of commitment, future state variables will be strategically manipulated such as to shape the incentive constraints facing the latter.

3. Markov-perfect equilibrium outcomes 3.1. Equilibrium conditions

Consider the two authorities’ first order conditions with respect to their primal choice variables c and z a ' , which characterize the current agencies’ behavior conditional on a given future policy rule ϕ ( z a ) . For the fiscal authority, the implemented allocation must obey the following optimality condition: 1 δ −α = c β

  −1 1  a − α  1 − ε µ ( z a ' ; ϕ ) ,  c (z ' ; ϕ ) 

[

]

(9)

where ε µ ( z a ; ϕ ) ≡ [ ∂(1 + µ( z a ' ; ϕ )) ∂z a ' ] [(1 + µ ( z a ' ; ϕ )) z a ' ] denotes the elasticity of the (gross) rate of monetary expansion in re105


[

]

−1

sponse to changes in the aggregate state z a and 1 − ε µ ( z a ' ; ϕ ) > 1. This latter term reflects the adverse expectational effects of the increased future nominal public debt z a ' resulting from higher current consumption: A higher debt burden increases the central bank’s incentives to resort to the inflation tax in the future, which is anticipated by the public and leads to an upward distortion in the nominal interest rate. This, in turn, constitutes an opportunity cost of future consumption and makes it more valuable. In analogy to the fiscal optimality condition (9), a condition characterizing the optimal behavior by the monetary authority can be derived. Due to the additional inflationary loss term, it is slightly more complicated; therefore, its explicit statement is relegated to the Appendix. To build intuition, it is sufficient to note that the underlying logic again reflects a trade-off between current and future distortions. Accordingly, the marginal benefit from current consumption as perceived by the monetary authority is such that it attaches the relative weights (1 − γ ) and γ to private agents’ utility and the inflationary loss term, respectively. However, in contrast to the fiscal optimality condition, the combined benefit from increased consumption is discounted because—by virtue of the CIA constraint—higher consumption requires the current monetary policy maker to forego the inflation tax and leave future policy makers with the task of satisfying the intertemporal budget constraint by distortionary revenue generation. Finally, the evaluation of the marginal benefit of higher consumption in the next period involves the same aspects, and again the future benefits are amplified since the commitment problems faced by future policy makers are taken into account by the current policy maker. 3.2. Monetary and fiscal policy interdependence

In the economy under consideration, government debt crowds out private consumption because it has to be serviced via distortionary taxation. Thus, the function c( z a ) is decreasing, and the fiscal optimality condition (9) reveals that the fiscal authority is not willing to balance the budget, but prefers to accumulate debt as long as

δ β [1 − ε µ ( z a ' ;ϕ )] < 1 . For the long run, the model predicts a sta−1

tionary

level

of

debt

z a∗

implicitly

characterized

by

δ β [1 − ε µ ( z a* ;ϕ )] = 1 . Since δ β < 1 , it follows that the steady −1

106


state must be characterized by ε µ ( z a * ;ϕ ) = (1 − δ β ) > 0 . In other words, despite its inflation aversion, monetary policy will respond to variations in the stock of liabilities z a . In particular, around the steady state, it will let the rate of money growth co-vary with the government sector’s real indebtedness. Result 1: For δ < β and γ ∈ (0,1) , money growth co-varies positively with changes in the real amount of public debt around the steady state.

Note that this result does not follow from the assumption of a specific feedback function, but is an implication of the sequential implementation of monetary and fiscal policies. The normative content is that, facing a fiscal authority which refuses to run balanced budgets, a monetary policy maker will never find it optimal to undertake a deflation because doing so would increase the real value of the inherited stock of nominal debt, thus tightening the intertemporal government budget constraint.10 Thus, there is a lower bound on the rate of money growth of the form µ ( z a* ;ϕ ) ≥ 0 . Together with the strictly positive elasticity of the money growth rate, this implies that the steady state rate of money growth µ ( z a* ;ϕ ) and hence the steadystate rate of inflation are strictly positive. While such positive inflation per se does not lead to welfare losses, the systematic dependence of money growth on the stock of real liabilities has adverse consequences because of the expectational effects and associated interest rate distortions it gives rise to. Hence, we call a policy rule characterized by ε µ ( z a ;ϕ ) > 0 subject to an inflation bias. Result 2: For δ < β and γ ∈ (0,1) , any time-consistent policy rule is subject to an inflation bias. The steady-state inflation bias ε µ ( z a* ;ϕ ) = (1 − δ β ) > 0 is entirely determined via fiscal institutions.

10 Note that the validity of this argument requires the time t monetary policy maker to neglect the influence of current policies on the formation of expectations at time t - 1 and hence on the nominal interest rate R t .

107


This result suggests that inflation is ultimately a fiscal phenomenon. Specifically, as implied by (9), the degree of fiscal impatience determines the steady-state degree of monetary responsiveness to the stock of debt. This result obtains despite the fact that fiscal policy itself has no direct inflationary effects; by running deficits and accumulating public debt, though, fiscal policy can strategically manipulate the monetary authority’s willingness to inflate the economy. In order to illustrate the dynamics of our economy in the presence of nominal government debt, we now employ a simple numerical example. Since the time period is meant to be a year, we choose β = 0.98 , corresponding to an annual real interest rate of approximately 2 percent. In want of informative data, we set δ = 0.96 and γ = 0.5 ; these parameters reflect an impatient fiscal authority, which discounts the future at a rate of 4.17 percent compared to the real interest rate of 2.04 percent, and a central bank, which puts equal weight on economic welfare and the inflationary loss term. Given these parameters, α and g are chosen such as to generate model statistics in line with empirical data for spending-to-GDP ratios;11 this implies α = 0.45 and g = 0.5 . In order to facilitate the interpretation of the model’s predictions for debt-to-GDP ratios, we report the relevant statistics not in terms of the aggregate state zta , but in terms of bta ≡ Bta (1 + Rt ) Pt −1 = β α zta .12 The parameterization of our model economy is summarized in Table 2. Table 2. Model parameters α

β

γ

δ

g

0.45

0.98

0.5

0.96

0.5

Based on these parameters, we simulate our model to locate its steady state. The key results of this exercise are displayed in Figures 1 and 2. Figure 1 shows the dynamic evolution of the end-of-period The average (1989-2006) of the ratio of general government total outlays to GDP is at 41.0 percent; compare OECD (2005). The ratio general government final consumption expenditure to GDP is significantly lower at around 20 percent. 12 To make welfare comparisons across different monetary and fiscal institutions, we also endogenize the initial nominal interest rate R0 via a rational expectations consistency condition. 11

108


stock of real government debt bta ' = β α zta ' . The stock of real debt grows at a decreasing rate and converges to a debt ceiling at bta * = β α zta* , corresponding to a debt-to-GDP ratio of 1.067.13 The increasing distortions associated with the accumulation of debt— direct ones due to the need to service the debt via distortionary tax instruments and indirect ones stemming from the additional interest rate distortions—affect the pattern of consumption displayed in Figure 2. Figure 1. Path of real debt in benchmark example

As hinted above, the debt ceiling z a* is determined by the fiscal optimality condition (9), but it is important to realize that this condition is contingent on the complete equilibrium policy rule ϕ ( z a ) and thus depends on monetary policy, too. In particular, according to the monetary optimality condition (cf. equation (A3) in the Appendix), it must be the case that, at z a* , the marginal losses incurred due to inflation and the marginal benefits from stabilizing the level of debt by monetizing fiscal deficits via the inflation tax are equal from the monetary authority’s perspective. At the same time, the responsiveThroughout, the model significantly overpredicts steady state debt-to-GDP ratios. A more flexible specification of the preferences in (2) is promising to generate improvements along this dimension; compare Martin (2007).

13

109


ness of monetary policy to the level of debt makes the accumulation of debt increasingly unattractive for the fiscal authority, since it also suffers from the distortionary effects caused by the public’s increasing inflation expectations. Thus, the fiscal authority has an incentive not to let debt go out of hands. In other words, the steady-state level z a* of public liabilities must be such that the motives for debt accumulation and decumulation exactly balance each other from both authorities’ perspectives. Figure 2. Path of consumption in benchmark example

3.3. Institutional interdependence

The parameters of the loss functions of the two policy authorities reflect their institutional characteristics. The fiscal discount factor reflects the political uncertainty of the incumbent government and its inability to devise a long-run fiscal policy perspective, while the weight on surprise inflation in the central bank’s loss function reflects its conservatism. Against the background of the above insights, it is interesting to see how changes in the institutional characteristics of the two authorities impinge on the properties of the steady-state equilibrium outcomes. First, consider the effect of a lower fiscal discount factor δ . The associated drop in the ratio δ β implies an increased degree of monetary responsiveness ε µ ( z a ;ϕ ) at any given level of 110


real indebtedness z a . Starting from an equilibrium allocation, an increase in the fiscal authority’s impatience induces a tax cut. However, since the monetary authority’s preferences over the allocation remain unchanged, the best monetary policy response to this is a higher rate of monetary expansion in order to contain the incipient accumulation of real debt. This requires the monetary authority to compromise its previous inflation target. Current consumption is higher than in the original equilibrium, but more liabilities are accumulated. The result is a decrease in the marginal rate of substitution between current and future consumption, though by less that the drop in δ . Inspection of (9) then reveals that ε µ ( z a ;ϕ ) increases for any given level of z a . Hence, the more impatient fiscal authority triggers a monetary policy which is more responsive to variations in the stock of debt. Since the required money expansions are well-anticipated by the public, the indirect liability costs of government debt are accentuated. Hence, the welfare losses associated with any given level of outstanding debt z a increase, which is internalized even by an impatient fiscal authority. The implications for the long-run level of debt z a* are ambiguous: On the one hand, greater fiscal profligacy generates a tendency to accumulate more debt, but on the other hand, the extra liability costs of outstanding debt are globally increased such that the resulting level of debt may be higher or lower than in the original steady state. Thus, while it remains true that government debt is a means to defer taxation and thereby shift distortions into the future, an increase in fiscal impatience does not necessarily result in a higher steady-state level of government debt. We can establish the following result: Result 3: A more impatient fiscal authority, characterized by a lower δ , triggers a more responsive monetary policy as measured by a higher ε µ ( z a ; ϕ ) for all z a > 0 . The effect on the steady-state level of

debt z a* is ambiguous. Next, we turn to the implications of an increase in the monetary authority’s aversion against surprise inflation. By Result 2 above, the steady-state inflation bias is pinned down by δ β and thus remains unchanged in the long run, although the direct effect of a more conservative central bank is that any given level of real liabilities goes along with a reduced incentive for inflation. However, since this is internal111


ized by the fiscal policy maker, the indirect effect is that more debt is accumulated in equilibrium. Hence, a more conservative central bank will merely be less successful in containing the accumulation of public debt. Thus we have the following: Result 4: With a more inflation-averse monetary authority, characterized by a higher γ ∈ (0,1) , an impatient fiscal policy triggers a less responsive monetary policy as measured by a lower ε µ ( z a ; ϕ ) for all

z a > 0 , but the steady-state level of debt z a* is higher. This finding is illustrated numerically by Figure 3 which compares the dynamic evolution of real debt for a set of alternative economies. The basic parameterization is as summarized in Table 2, but the monetary authority’s inflation aversion parameter γ varies in the set {0.5;0.7;0.9} . The plotted paths for real debt illustrate that an increase in γ is associated with higher steady-state levels of government debt. Figure 3. Debt dynamics for different degrees of monetary conservatism

Monetary conservatism is a successful commitment device to constrain the monetary accommodation of fiscal profligacy for any given real value of nominal government debt, but at the same time results in 112


a higher stock of debt in equilibrium. The direct effect implies that, during the transition to the new steady state, consumption is higher with a more conservative central bank, as the interest rate distortions due to the anticipated inflation tax are lower. This generates positive welfare effects. In contrast, consumption is lower in the new steady state, since the equilibrium stock of debt is higher. This generates a reduction in welfare. To evaluate the effects of increased central bank conservatism, one must therefore weigh the transitional welfare gains against the steady-state welfare losses. Numerically, it turns out that the transitory gains from monetary conservatism are overcompensated by the long-run costs: Result 5: With an impatient fiscal authority (δ < β ) , the higher the degree γ ∈ (0,1) of the monetary authority’s inflation aversion, the lower the level of welfare enjoyed by the representative household.

This assessment of the welfare implications of monetary conservatism is graphically illustrated in Figure 4, which plots the representative household’s lifetime utility as a function of real debt for the same variation of the monetary authority’s inflation aversion parameter γ as in the experiment underlying Figure 3. Increased monetary conservatism has negative welfare effects. Figure 4. Representative household’s welfare for different degrees of monetary conservatism

113


Table 3 presents the steady-state statistics for consumption and real debt as well as for the output shares of government spending and debt; moreover, the graphical exposition of the pertinent welfare implications in Figure 4 is converted into steady-state consumption equivalents. Table 3. Steady-state statistics for alternative economiesa) δ = 0.96 γ = 0.5

δ = 0.96 γ = 0.7

δ = 0.96 γ = 0.9

δ = 0.95 γ = 0.5

δ = 0.95 γ = 0.5

δ = 0.95 γ = 0.5

1.631 2.275

1.627 2.502

1.624 2.652

1.619 2.892

1.612 3.245

1.607 3.486

0.235

0.235

0.235

0.236

0.237

0.237

1.067

1.176

1.249

1.365

1.537

1.655

-0.532 -0.083

-0.608 -0.093

-0.658 -0.101

-0.739 -0.148

-0.860 -0172

-0.944 -0.189

c b a) g c+g

b a) c+g b)

welfare loss A B

Notes: a) Throughout, α = 0.45 , β = 0.98 , g = 0.5 as in the benchmark parameterization. b) Welfare losses are converted in consumption equivalents and calculated in percentage terms relative to steady-state consumption in an economy with indexed debt and non-impatient fiscal policy δ = β . Row A compares steady-state alloca-

b

g

tions only; row B takes into account the transition, starting from b 0a = 0.002 .

The first three and the last three columns, respectively, each consider the effects of increased monetary conservatism for a given degree of fiscal impatience. As predicted by above results, steady-state real indebtedness increases with the degree of monetary inflation aversion, while the consumption allocation changes very little. The spending-to-GDP ratio remains virtually unchanged, whereas the debt-to-GDP ratio increases. While the debt ratio in column 3 is 17 percent larger than the debt ratio in column 1, the debt ratio in column 6 is 20 percent larger than the ratio in column 4. This indicates that an increase in the degree of fiscal impatience amplifies the effects of greater monetary policy conservatism on the debt ratio. Finally, for the current parameterization an increase in fiscal impatience also leads to significantly higher levels of real debt in the steady state. The two last rows of Table 3 display the welfare losses of the alternative policy regimes compared to an ideal economy without fiscal 114


impatience (δ = β ) that has access to inflation-indexed debt, i.e., an economy where the monetary time-consistency problem is absent by construction. Two measures of welfare losses are presented: Row A compares steady-state allocations only, while row B incorporates the effects of the transition. The welfare losses in row A are larger than those in row B because they do not take into account the transition to the steady state during which policy distortions are partially shifted into the future by means of debt accumulation. For both measures, we find that monetary conservatism is harmful and that increased fiscal impatience accentuates the welfare costs of such conservatism. The endogenous determination of macroeconomic policies implies that the respective economies differ from the ideal benchmark economy not merely in terms of feedback rules in the neighborhood of a given reference point, but in their selection of distinct steady states. Thus, in contrast to the welfare effects associated with pure stabilization policies, the welfare losses associated with the design of fiscal and monetary policy authorities are considerable.14 A tentative conclusion to be drawn at this stage is that the welfare costs associated with increased monetary conservatism due to the excessive accumulation of public debt have the potential to more than outweigh the benefits that might be reaped from superior stabilization policies under inflation-averse monetary policy institutions. Our discussion so far has been centered on the dynamics of the allocation in terms of consumption and real debt. However, little has been said about the details of how this allocation is decentralized via the relevant policy instruments, the tax rate, τ c , and the monetary growth rate, µ . Recall from equation (8) that the two instruments are equivalent with respect to the margins they distort. Thus, there are infinitely many combinations of the policy instruments supporting the same policy rule and the same real allocation. Without a mechanism that pins down the specific combination of monetary and fiscal policy instruments, there is scope for coordination failure. To illustrate the effects of changing monetary and fiscal policy institutions on the determination of macroeconomic policies, we fix the consumption tax τ c at a given level and ask how changes in the authorities’ preference parameters δ and γ affect the rate of inflation Using log-utility, the prototype calculation in Lucas (2003) implies welfare gains from elimination of consumption fluctuations via pure stabilization policies of around 0.05 percent of steadystate consumption. 14

115


prevailing in steady state. Some information regarding this question is summarized in Table 4. Table 4. Real debt and inflation across steady statesa)

b a)

δ = 0.96 γ = 0.5

δ = 0.96 γ = 0.7

δ = 0.96 γ = 0.9

δ = 0.95 γ = 0.5

δ = 0.95 γ = 0.7

δ = 0.95 γ = 0.9

2.275

2.502

2.652

2.892

3.245

3.486

Inflation in percentage points 11.375 11.585 11.923 12.424

12.768

τ c = 0.20

11.059

τ = 0.25

6.581

c

6.884

7.085

7.410

7.890

8.221

τ c = 0.30

2.450

2.742

2.935

3.247

3.709

4.027

τ = 0.35

-1.373

-1.092

-0.906

-0.606

-0.161

0.145

c

Notes: a) Throughout, α = 0.45 , β = 0.98 , g = 0.5 as in the benchmark parameterization.

The parameter variations considered here are the same as in Table 3, and the first row restates the relevant implications for the steadystate level of real indebtedness. Regarding the inflationary consequences associated with the different parameter constellations under the assumption of a fixed tax rate, we note that increased monetary conservatism induces higher rates of inflation. The reason for this is that the economy settles at a higher level of real debt which gives rise to increased debt service requirements; with τ c fixed, this necessitates higher inflation. The inflation effect of increased monetary policy conservatism is slightly greater for lower levels of the consumption tax rate. If the degree of fiscal impatience increases, the inflation effect of increased monetary policy conservatism is amplified. Finally, increased fiscal impatience causes the inflation rate to rise for each degree of monetary policy conservatism.

4. Policy implications: Coordinated design of monetary and fiscal institutions The main implication from the present analysis is that, once the implications of nominal debt are taken into consideration, fiscal policy and monetary policy can indeed exert large externalities on each other. This is in sharp contrast to the conventional literature on macroeconomic stabilization. The externalities we have studied here affect the steady-state equilibrium of the economy and give rise to substantial 116


welfare effects. Thus, there is a case for reconsidering the coordination of monetary and fiscal policies. The nature of these externalities is institutional in the sense that the preferences of the monetary authority and the fiscal authority are at the heart of the problem. A first implication from our analysis is, therefore, that the effects of changing the objectives or operational procedures of one institution cannot be evaluated without taking into account the properties of the other. In particular, disregarding the implications of fiscal impatience, one is tempted to conclude that increased monetary policy conservatism generates benefits in terms of lower inflation. Our analysis shows that this conclusion is overturned once the strategic interaction between fiscal and monetary policy is taken into account. On theoretical grounds, the result is of a secondbest nature: Given the fiscal friction which leads to the accumulation of public debt, provisions which make the monetary time-consistency problem less acute are not guaranteed to enhance welfare. Thus, to appropriately assess the advantages of central bank independence and low inflation targets, it is necessary to take into account their effects on the formation of fiscal policy. Indeed, our analysis illustrates that having an independent and conservative central bank is not enough to ensure low inflation. On the contrary, even under decentralized authority over monetary and fiscal policy, the long-run properties of monetary policy are determined via the fiscal side. The deterministic nature of our model and the complete absence of nominal rigidities obviously imply that there is no scope for macroeconomic stabilization at all in our economy. As a result, monetary policy conservatism is a nuisance if we take the model at face value. Yet, we can draw further policy implications by assuming that such conservatism has welfare benefits arising from the reduction of a conventional inflation bias not explicitly modeled here. Suppose that these benefits increase and that society wishes to make its central bank more conservative. Our model then indicates that the institutional characteristics of the fiscal authority should be changed at the same time to assure that the desired benefits of increased monetary conservatism can be reaped. Specifically, the degree of fiscal impatience should be reduced, such that the fiscal authority is less tempted to exploit the more conservative central bank. Implementing electoral reforms or changes in parliamentary rules that reduce political uncertainty or dynamic common pool problems would be one way of achieving this. Increasing the government’s ability to 117


devise long-term fiscal plans, e.g., by introducing better budgetary institutions, offers another way to do the same. An alternative approach would be to leave the degree of fiscal impatience unchanged, but to impose constitutional constraints on fiscal policy. Such constraints should then be designed to provide a ceiling to the maximum admissible amount of real debt. Establishing limits on fiscal deficits can help as an auxiliary device, because, under a binding constraint on primary deficits, the transition to the long-run steady state proceeds along a path featuring lower rates of inflation. However, deficit rules alone turn out to be insufficient: They require taxes to be responsive to variations in the stock of debt; thus, they automatically induce an upper bound on the degree of monetary responsiveness, which implies that the extra liability cost from distorted nominal interest rates is lower at any given real stock of debt. Our analysis then shows that the steady-state equilibrium may involve the accumulation of higher amounts of debt (cf. Result 3). A final implication comes from the fact that the degree of monetary policy conservatism affects not only the steady-state debt level, but also the speed at which the economy converges to the steady-state equilibrium. If the initial debt level is higher than the steady-state level, a less conservative central banks leads to faster reduction of the stock of real debt than a more conservative central bank. Suppose that the economy is hit by a one-time shock increasing its stock of nominal public debt by a large amount, such as a banking crisis or a natural disaster. Suppose, further, that the government wishes to regain the original steady state and the original level of public debt, e.g., for financial stability reasons. Under those circumstances, it may be beneficial for the government to temporarily reduce the degree of monetary conservatism to go back to the original debt level at a faster pace and with a higher rate of inflation. Once the old level of debt has been reached again, the government would then restore the original degree of monetary conservatism; the reason is that, with a less conservative central bank, the economy would converge to a different steady state otherwise. Thus, an optimal response to a debt shock may entail a series of reforms of the monetary authority in order to attain the desired fiscal policy outcomes. This is similar in spirit to Lohmann’s (1992) suggestion that a temporary suspension of central bank independence may be appropriate in the face of large supply shocks.

118


In conclusion, our analysis points to a new interpretation of the coordination of monetary and fiscal policies, namely in terms of institutional design rather than in terms of the use of monetary policy instruments in response to macroeconomic shocks. It suggests that the benefits hoped for from institutional reforms in one area of macroeconomic policy must be secured by appropriate reforms in the other area.

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COORDINATION OF MONETARY AND FISCAL POLICIES: A FRESH LOOK AT THE ISSUE, Stefan Niemann and Jürgen von Hagen Duisenberg, W. (2003), Monetary and fiscal policy in the euro area, Introduction by Dr. Willem F. Duisenberg, President of the European Central Bank, at the International Monetary Conference, Berlin, 3 June 2003 (http://www.ecb.int/press/key/date/2003/html/sp030603.en.html). Kocherlakota, N. and Phelan, C. (1999), Explaining the fiscal theory of the price level, Federal Reserve Bank of Minneapolis Quarterly Review 23, 14-23. Kydland, F. and Prescott, E. (1977), Rules rather than discretion: The inconsistency of optimal plans, Journal of Political Economy 85, 473-492. Leeper, E. (1991), Equilibria under “active” and “passive” monetary and fiscal policies, Journal of Monetary Economics 27, 129-147. Lohmann, S. (1992), Optimal commitment in monetary policy: Commitment versus flexibility, American Economic Review 82, 273-286. Lucas (2003), Macroeconomic priorities, American Economic Review 93, 1-14. Lucas, R. and Stokey, N. (1983), Optimal fiscal and monetary policy in an economy without capital, Journal of Monetary Economics 12, 55-93. Malley, J., Philippopoulos, A. and Woitek, U. (2007), Electoral uncertainty, fiscal policy and macroeconomic fluctuations, Journal of Economic Dynamics and Control 31, 1051-1080. Martin, F. (2007), A positive theory of government debt, Mimeo, Simon Fraser University. Niemann, S. (2006a), On the time consistency of optimal policies with interacting authorities, Mimeo, University of Bonn. Niemann, S. (2006b), Dynamic monetary-fiscal interactions and the role of monetary conservatism, Mimeo, University of Bonn. OECD (2005), Central Government Debt: Statistical Yearbook 1994-2003: 2005 Edition, OECD Publishing, Paris. OECD (2007), OECD Economic Outlook 81, Paris. Persson, T. and Tabellini, G. (2000), Political Economics: Explaining Economic Policy, MIT Press, Cambridge. Rogoff, K. (1985), The optimal degree of commitment to an intermediate monetary target, Quarterly Journal of Economics 100, 1169-1190. Sargent, T. and Wallace, N. (1981), Some unpleasant monetarist arithmetic, Federal Reserve Bank of Minneapolis Quarterly Review 5, 1-17. Svensson, L. (1985), Money and asset prices in a cash-in-advance economy, Journal of Political Economy 93, 919-944. Svensson, L. (1997), Optimal inflation targets, “conservative” central banks, and linear inflation contracts, American Economic Review 87, 98-114.

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COORDINATION OF MONETARY AND FISCAL POLICIES: A FRESH LOOK AT THE ISSUE, Stefan Niemann and Jürgen von Hagen Taylor, J. (1993), Discretion versus policy rules in practice, Carnegie-Rochester Conference Series on Public Policy 39, 195-214. Waller, C., Fratianni, M. and von Hagen, J. (1997), Central banking as a political principal agent problem, Economic Inquiry 35, 378-94. Walsh, C. (1995), Optimal contracts for central bankers, American Economic Review 85, 150-167. Woodford, M. (2001), Fiscal requirements for price stability, Journal of Money, Credit and Banking 33, 669-728.

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Appendix A.1. Primal approach As hinted in the main text, it is convenient to solve the authorities’ optimization problem in terms of macroeconomic allocations rather than policy instruments. For that purpose, we reformulate the consolidated government budget constraint as a dynamic restriction on the set of allocations which can be implemented via the policy instruments. Making use of the definition of the aggregate state variable z a as well as of the private sector optimality conditions (6), (7) and (8), we obtain the following implementability constraint:

β − g + β z a ' c ( z a ' ; ϕ )( 1 + τ c ( z a ' ; ϕ )) − c − z a c (1 + τ c ) = 0, α

(A.1)

which can be reformulated as: za' β β β za c − g+β − − = 0. α α (1 + µ ( z a ' ; ϕ )) α (1 + µ )

(A.2)

While current variables can be chosen by the government authorities, future variables are determined by functions of the future state z a ' which are beyond the control of current policy makers. Since constraint (A1) is conditional also on the current consumption tax, we associate it with the monetary authority which chooses the level of current consumption c for a given level of τ c . Constraint (A2) corresponds to the fiscal authority which chooses c subject to the restrictions imposed by the current rate of money expansion µ . Given the aggregate state z a and the policy instrument chosen by the respective other authority, there is a one-to-one mapping between each authority's own instrument choice and c. Hence, the respective authorities’ instrument choices are only consistent with equilibrium if both authorities choose the same level of current consumption c. In this case, the implementability constraints (A1) and (A2) coincide and therefore imply also the same z a ' . 122


A.2. Markov-perfect equilibrium A Markov-perfect equilibrium is defined as a profile of time-invariant strategies for the two authorities that yields a Nash equilibrium in each period’s subgame, whereby the period t subgame is indexed via the aggregate state zta inherited from the past and the policy rule characterizing the future play of the policy game. The optimal policy rule in the current period when future policies are determined by some arbitrary policy rule ϕ ( z a ) is denoted π ∗ ( z a ;ϕ ) . Formally, the stage game (Nash) equilibrium of the current period is then a pair of functions π ∗ ( z a ;ϕ ) = {π m∗ ( z a ;ϕ ), π ∗f ( z a ;ϕ )} such that (i) π ∗f ( z a ; ϕ ) maximizes the current fiscal authority’s payoff, given π m∗ ( z a ;ϕ ) , and (ii) π m∗ ( z a ;ϕ ) maximizes the current monetary authority’s payoff, given

π ∗f ( z a ; ϕ ) .

Finally,

the

pair

of

functions

ϕ ∗ ( z a ) = {ϕ m∗ ( z a ), ϕ ∗f ( z a )} is a Markov-perfect (time-consistent) equilibrium, if it is the Nash solution of the period stage game when the two authorities rationally expect the rule ϕ ∗ ( z a ) to determine future policies. Formally, the equilibrium policy must satisfy a fixedpoint property in the sense of being a best response to itself: π i∗ ( z a ;ϕ ∗ ) = ϕi∗ ( z a ) for i = f , m . The requirement of timeconsistency therefore dictates that the equilibrium policy rule ϕ ∗ ( z a ) , if it is in place in the future, must be replicated via the current policies.

A.3. Optimal monetary policy The condition characterizing optimal monetary policy reads as follows: a c a     1 − ε µ ( z a ' ; ϕ ) [1 + z ' (1 + τ ( z ' ; ϕ ))]    a c a     + 1 z ' ( 1 τ ( z ' ; ϕ ))      (1 − γ ) c (z a ' ; ϕ ) − α  + 2γ  c (z a ' ; ϕ )     1  1  (1 − γ ) − α  + 2γ   c    1 − ε ( z a ' ; ϕ ) −1 c  =   µ [ 1 + z a (1 + τ c )] [1 + z a ' (1 + τ c ( z a ' ; ϕ ))]            

[

123

]

(A.3)


Accordingly, the marginal benefit from current consumption as perceived by the monetary authority consists of three components: First, there is the effect via current household utility as reflected by the expression (1 − γ )(1 c − α ) . Second, for a given fiscal policy, higher current consumption necessitates lower inflation and hence impacts on the inflationary loss term. Third, the benefits from increased consumption are discounted by the term [1 + z a (1 + τ c )] > 1 because—by virtue of the CIA constraint—higher consumption requires the current monetary policy maker to forego the inflation tax and leave future policy makers with the task of satisfying the intertemporal budget constraint by distortionary revenue generation. The evaluation of the marginal benefit of higher consumption in the next period also comprises these three components; however, the effect via the inflationary loss term is diminished because of the endogenous variation in the publicly expected price level P( z a ' ) . Finally, as in the fiscal optimality condition, the commitment problems faced by future policy makers are taken into account and reflected by

[

the amplification term 1 − ε µ ( z a ' ; ϕ )

]

124

−1

> 1.