Reputation

As policymaking is not a one-shot process but rather an ongoing repeated interaction with the public, the concept of reputational equilibria involves giving a policymaker an incentive not to deviate from the optimal policy by making deviation costly to the policymaker. The intuition behind this story is the following. If policymaking is defined as a sequential process, an obvious intertemporal trade-off emerges. The current benefit of surprise inflation in terms of boosting output might well be outweighed by the future costs of higher expected inflation, resulting from the current expansionary policy. Thus, the appealing feature of the reputational approach is exactly this intertemporal linkage between current monetary decisions and future consequences of these decisions.⁹

Barro and Gordon (1983b) were the first to apply the concept of reputation to monetary policy. As there are no economic state variables in their set-up, the model can be thought of as a repeated infinite time horizon game.¹⁰ The policymaker now has to balance the short run gains of generating surprise inflation against the cost of higher expected inflation generated by the private sector in the future. The problem of this model, however, is that there are many possible equilibria resulting in the well-known multiplicity problem. The reason for this dilemma is the existence of an infinite number of punishment strategies (Friedman-type trigger strategies)¹¹ which could be adopted. Thus, the model lacks the predictive power expected from a model of monetary policy and inflation. As a result, a second problem emerges. Each possible equilibrium requires that all agents coordinate when the policymaker deviates from the expected rate of inflation. In addition, revisions of expectations take place immediately after observing a deviation. Thus, the expected rate of inflation is discontinuous. This means that if the private sector observes actual inflation being different from its expectations in period t-1, it will revise its expectations for period t. In other words the repeated game is one of complete information and the government takes a certain monetary policy action in equilibrium because it believes it will be punished if it cheats. According to Cripps (1996, p. 522) this use of the term reputation is never found in the game theoretic literature. Hence the appropriate usage would be in an incomplete information framework as, e.g., analyzed by Kreps and Wilson (1982) and Milgrom and Roberts (1982).

Subsequent elaboration of the reputation approach thus focused on alternative informational structures. Canconeri (1985) for example considered a monetary policy model with private information. This necessarily involves a monitoring problem as shocks to inflation are assumed to be neither observable to the private sector ex ante nor ex post. Backus and Driffill (1985) and Barro (1986) particularly focus on incomplete information models of reputation, i.e., in the spirit of Cripps (1996). Barro (1986) for example used the well-known Kreps-Wilson (1982) reputation game (Selten’s (1978) chain-store paradox).¹² The advantage of this framework is that it does not rely on the assumption of an infinite time horizon. As is straightforward from the of Kreps-Wilson (1982) analysis the introduction of uncertainty about the policymakers’ types, i.e., introducing incomplete information, ensures the existence of unique reputational equilibria in a finite time horizon. The private sector is now able to learn about the policymaker’s true type by updating its beliefs according to Bayes rule.

Vickers (1986) instead stressed the problem of signaling a policymaker’s true type to the incompletely informed private sector. In his model a tough policymaker (tough on fighting inflation) might have to go through undesired contractionary policies in order to separate himself from the weak type.

A paper by al Nowaihi and Levine (1994) extended the Barro and Gordon (1983b) framework in an interesting way. The main concern of the authors is to address the problems of the original Barro and Gordon (1983b) reputation framework, namely the multiplicity of equilibria, the coordination problem and what the authors call chisel-prone credibility problem (meaning that a sufficiently small deviation from the optimal policy might not trigger punishment). The problem with pure trigger strategies is that they are not credible because they require a once and for all non-cooperative behavior after one deviation of the opponent. Within a long time horizon this sort of punishment might hurt the punishing player more than not punishing a deviation at all. Hence the private sector has to choose the minimum punishment period that is required to support the most favorable outcome from the private sector’s point of view, i.e., supports the lowest possible rate of inflation in a credible fashion. The resulting coordination problem is solved either by assuming a game between successive monetary authorities with an atomistic private sector or by assuming centralized wage bargaining where a union represents the private agents to coordinate them, forms expectations and punishes the policymaker for observed deviations from the optimal policy. The credibility problem inherent in this game, namely the credible punishment mentioned above is resolved by what the authors call the chisel-proof credibility condition. This simply means that the punishment period of the trigger strategies is endogenized. In other words, by chisel-proof credibility the authors understand the requirement that retaliation be better than acquiescing to any deviation and not just the optimal deviation represented by conducting the discretionary policy.¹³ The idea is to solve for an upper bound of the punishment period up to which punishment for deviation is credible (note that the analysis is off the equilibrium path). This setting is particularly interesting and useful as it addresses and solves an inherent problem in the application of repeated games (with complete information) of monetary policy. It emphasizes the solution to the credibility problem with respect to the punishing party and not only with respect to the policymaker.

Furthermore, Waller (1995) identifies two problems with the reputation approach in the context of central bank policy.¹⁴ As this approach tends to focus on the central banker rather than the central bank as an institution, there appears uncertainty and variability in the policy setting process. This is because central bankers turn over and do not perform their policies forever. Furthermore, if the central bank’s incentives are wrong, resulting in an inflationary bias, it seems to be more appropriate to change the institutional framework, rather than letting the private sector “solve” the problem via punishment strategies. In the light of this critique one might argue that the reputational approach as outlined above is lacking an institutional component. Recently this problem has been addressed—for example, Jensen (1997) and al Nowaihi and Levine (1996)—in the sense that the institutional component of central banking, e.g., via the Walsh (1995a) contract, is merged with the reputational component of appointing central bankers.¹⁵

Delegation

So far the discussion has not distinguished between the policymaker or policymaking institution and the government or society as a whole. The question arising in this context is whether delegation can solve the credibility problem of monetary policy. An often-quoted paper in this context is that by Rogoff(1985). Appointing a “conservative” central banker, that is a person with a low time preference and higher preference for price stability relative to employment targets makes society better off. On the other hand if the central banker only cares about inflation, shocks to the economy would not be stabilized, which is costly in this model. To get a better intuition, assume the following simple Rogoff-type model:¹⁶

Suppose that the social loss function is a quadratic function of two objectives:

where π_t denotes the actual rate of inflation, y_t denotes output, y^* is target output and λ is the policymaker’s weight, placed on the output deviation term. This is standard in the literature.

Without loss of generality and for illustrative purposes output is given by a simple Lucas-type supply function:

where π_t is actual inflation, π_t^e denotes expected inflation conditional on information up to and including period t-1 and ε_t is an i.i.d. distributed supply shock with zero mean and variance σ_ε².

Given (2) and (3) below it is straightforward to see that the “natural” or long run equilibrium of the expected output level is normalized at zero. By combining the assumption that the natural level of output is zero on average and the assumption that y^* > 0, one can capture the idea that distortions in the labor market, such as income taxes, prevent the natural level of output from being at its desired level y^*. In other words y^* would be the long run equilibrium output level in the absence of any distortions. I will come back to this issue further below.

The private sector’s rational expectations can be expressed in the following equation:

The first order condition resulting from minimizing (1) with respect to the rate of inflation (the instrument) subject to (2) and taking rational expectations of the private sector (3) as given, can be solved for inflation and output (time subscripts are dropped):

The first term in (4) is the so called inflation bias, which occurs because the policymaker does not take into account the impact of his or her actions on the expectations of the private sector (see (5)). The second term in (4) captures the extent to which the rate of inflation should respond to an aggregate supply shock. Similarly, (6) is the output response to the supply shock. From (4), (5) and (6) it follows that:

Rogoff (1985) showed that the inflationary bias can be reduced by delegating monetary policy to an agent, who is more conservative than society as a whole such as a central banker who cares less about output relative to inflation. In the present set-up this means that the weight, λ^c say, the agent places on the output deviation term in (1) is smaller than λ, i.e., λ^c < λ. But this reduction comes at the cost of increased output variability, as can easily be verified by inspection of the output variance in (7). Obviously there is a trade-off involved here, namely the trade-off between credibility and flexibility.¹⁷ The issue of credibility versus flexibility in a public finance setting will be discussed in section IV. Concerning the ranking of the different types of equilibria, there are two viable possibilities. Rogoff referred consistently to the equilibrium corresponding to an optimal rule (commitment) as second best because a first best would require removing the distortions responsible for the actual level of output being below its natural level. The equilibrium with the conservative central banker would then be third best, while the discretionary equilibrium is referred to as fourth best. Alternatively one can describe the commitment equilibrium as the first best (policy), the intermediate equilibria as second best and the discretionary equilibrium as third best.¹⁸

A multisector economy with partisanism

Waller (1992) focuses on a variant of the Rogoff (1985) model in a multisector framework. Assuming that the economy consists of a “classical” and a “nonclassical” sector with fully flexible/inflexible wages and prices respectively and that labor supply is immobile between sectors, while goods are treated as mobile between sectors, to allow for spill-over effects, his main results can be summarized as follows. Due to wage rigidities in the nonclassical sector, the output variance will be higher than in the classical sector, although preferences in both sectors are assumed to be the same. Consequently this results in a disagreement between sectors regarding the conservativeness of a potential central banker to be appointed, as the nonclassical sector has to suffer more in terms of a higher output variance than the classical sector starting from the discretionary equilibrium. If two different political parties represent the two sectors, the process of appointing a conservative central banker will be subject to partisan influences.

Escape clauses

Lohmann (1992) elaborated an extension of the Rogoff model to stress the trade-off between credibility and flexibility in central banking.¹⁹ In her model the central bank’s principal has an ex ante choice, not only of which agent to appoint, but also of the ex post cost of “getting rid” of the agent. The result is an equilibrium policy which looks like a rule with an escape clause: under normal circumstances the central bank follows a non-inflationary rule. The monetary authority answers with discretion when the gain of stabilization is particularly high.

The intuition behind this idea is as follows. The central bank acts independently, either credibly committed to a rule or just more conservative than the rest of the society, within an interval for the aggregate supply shock and will be overridden by the government if the observed supply shock falls outside that interval. The width of this interval necessarily depends on the cost of overriding the monetary authority. Consequently, a higher cost is connected with a lower incentive to interfere with the central bank’s decision.

The approaches in the previous sections are illustrated in Figure 1 A-G. Let π be the rate of inflation, ε be the supply shock, c be the cost of overriding the central banker, λ be the weight a normal central banker (as society) places on the output deviation term and λ^c be the weight a conservative central banker places on the output deviation term (as before). The equilibrium will necessarily induce the monetary authority to choose an inflation rate which makes the government just indifferent between overriding the central bank’s decision and accepting it (see, Figure 1 G). Figure 1 B simply captures the situation where the central bank follows a fully state contingent rule. Necessarily there is no inflationary bias (the reaction function intersects the origin) and shocks to the economy are fully accommodated. Comparing graph A and D shows how a more conservative central banker modeled through the lower relative weight on output, λ^c, responds to shocks compared to a central banker who has the same preferences over output and inflation as society has. Obviously the inflationary bias under discretion is higher than with the conservative central banker, but on the other hand Figure 1 D shows that conservativeness results in less stabilization of shocks, i.e., the reaction function is flatter. As easily verified from Figure 1 C, a zero inflation rule results in no shock stabilization at all. Figure 1 E and F contrast the situation of the zero inflation rule (an infinitely conservative central banker) with an escape clause depending on the costs of overriding the central bank’s decision, c, and the zero inflation rule with escape clause but without overriding costs.

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Conservative Central Bankers and Escape Clauses

Citation: IMF Working Papers 2000, 140; 10.5089/9781451856118.001.A001

Source: Lohmann 1992, p. 276–281, modified for the notation here.

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International linkages

Canconeri et al (1995) compare the relatively modern inflation-targeting regime with the ERM. It was generally accepted that prior to the exchange rate crises in 1992 and 1993, the credibility in terms of inflation performance of some European countries was thought to derive from the ERM as well as from the independence of the Bundesbank.²⁰ The reason why this was thought to work is simply that fixing the exchange rate to a low inflation currency serves to import credibility. But fixing the exchange rate to a low inflation currency also means that the foreign inflation rate will be imported. The crucial point here is the following. The shocks by which the foreign sector of the economy is hit will (partly) be accommodated by the foreign monetary policy, i.e., the foreign central bank follows its own objectives and needs. Therefore foreign problems will be transferred to the home country and problems in the home country are not fully accommodated by the foreign monetary policy.²¹ The choice among the different arrangements depends on a number of considerations. Canconeri et al (1995) conclude that targeting inflation is preferable if i) political pressures, which distort the monetary authorities policy are not too big in the first place; ii) the foreign central bank is conducting a very different monetary policy; and iii) the supply shocks are primarily of regional not international magnitude.²²

The Walsh model

The basic idea of Walsh’s (1995a) approach is the use of an optimal contract mechanism to eliminate the inflationary bias mentioned above. The incentive to deviate from the optimal policy by creating surprise inflation is eliminated as the transfer to the policymaker, specified in the contract, adds a cost component to this sort of deviation. This transfer has only to be contingent on observable variables, like the growth rate of the money supply, the inflation rate etc. The signal of a disturbance to the economy is assumed to be the private information of the monetary authority. This does not change the outcome, as the transfer is only contingent on observable variables.^{23 24} So the central bank will choose the optimal policy and the inflationary bias of discretionary monetary policy can be eliminated while leaving the agent free to respond with discretion to the observed, private information, signal. To see this more explicitly, suppose the following simplified version of Walsh’s model:

Let the loss function be as defined as earlier:

Output is given as before:

The informational structure supposes that the monetary authority observes a signal θ=ε+ϕ (where ϕ is a measurement error uncorrelated with the supply shock with zero mean and variance σ_ϕ²) concerning the aggregate supply shock ε (with zero mean and variance σ_ε²) and sets inflation based on this knowledge.²⁵ The signal θ is assumed to be the private information of the central bank, hence its expectation conditional on the signal is given as E_θ(ε)=[σ_ε²/(σ_ε²+σ_ε²)]θ≡sθ, with s≤1.²⁶ As before, y^*>0 captures distortions in the labor market and/or in the tax system and hence is above the expected natural level E(y)=0, which ensures that the monetary authority has an incentive to engage in surprise inflation. Walsh (1995a) assumes a positive natural rate of output (in the absence of any supply shocks or unanticipated inflation), y^c, and denotes the distortion by k ≡ y^* - y^c > 0. In the present simplified set-up I shall simply assume y^* > 0.

The private sector’s rational expectations are still given by:

Suppose now that the principal of the central bank (in the Walsh model this is the government) can chose a transfer payment, conditional on observed inflation,²⁷ to the central banker such that the central banker, to whom monetary policy is delegated, maximizes the following utility function:

We could think of the transfer payment t in several ways: It could be a wage payment or just be thought of as prestige, which the central banker earns for good performance and which increases the probability of a second term or a highly ranked job afterwards. In other words, the central banker is assumed to care about his transfer t and the social loss, which is generated through inflation and output variability. Technically the principal has to design a transfer scheme t that induces the central banker to chose the optimal policy π_t=π_t(θ), while fulfilling his participation constraint E(t-L_t)≥U₀, where U₀ is the central banker’s reservation utility, for simplicity assumed to be zero. Furthermore, to implement the optimal policy, the central banker’s incentive compatibility constraint must be fulfilled, that is π_t(θ) must maximize E_θ(t(π_t)-L_t) for all θ.

Walsh has shown that the optimal policy can be implemented by simply setting the transfer function (in this simplified example, dropping time subscripts):²⁸

It is easy to verify that providing the central banker with this incentive contract removes the inflationary bias λy^* as stated in (4) and implements the optimal policy:²⁹

Another interesting case analyzed by Walsh is where the central bank does not share the same preferences over inflation and output fluctuations. If the agent who implements monetary policy only cares about the transfer income received from the government, the contract based on ex post variables as output and inflation is not unique. One might think that the problem can be solved by paying the agent a fixed amount to “just follow instructions” (dead contract). But as the signal over the shock to the economy is assumed to be private information of the agent, the principal would not be able to verify whether the instructions had in fact been followed; a complete set of contingent instructions cannot possibly be provided. The solution to that problem is a performance based incentive mechanism, which must depend on output and inflation.

Persson and Tabellini

Persson and Tabellini (1993) follow a similar line of reasoning, inspired by an earlier version of Walsh’s (1995a) paper. Accepting that incentive problems may be the major complication to price stability, they ask which institutions may help to resolve these problems. Two directions are of interest in this context. First, the legislative approach to create by law a very independent central bank and second the targeting approach. The latter imposes an explicit inflation target for monetary policy and makes the central bank explicitly accountable to its principals for the success in meeting the target. This approach is more or less followed by New Zealand (1989) and Canada (1991). The basic normative question asked throughout Persson and Tabellini’s paper is what are the features of an optimal contract from the point of view of society’s ex ante preferences: a question of institution design, as the authors call it. As in the paper by Walsh (1995a), the inflationary bias of discretionary monetary policymaking can be eliminated by a simple contract that imposes a linear penalty for inflation on the central bank. This result is shown to be robust to imperfect monitoring by the private sector. If some information is non-verifiable and therefore non-contractual, policy announcements by the central bank become very important. In this case the optimal contract leads to a truthful revelation by the central bank about the stochastic shock to the economy and the ex ante optimal policy will be implemented. If the central bank’s political principals have private interests, that is to say they do not fully represent the preferences of the society, e.g., through partisan or electoral incentives, only incomplete contracts can be written. In this situation there arises a trade-off between information and incentives, i.e., legislative control and targeting. If the central bank controls inflation only indirectly and imperfectly, the incentive contract (which then is an incomplete one) has the property that the agent’s payoff is not based on the principal’s objective.³⁰

Some general insights of this approach are that writing incomplete contracts may still not require a loss of stabilization policies. Furthermore the approach concerns the desirability of inflation targets compared to intermediate targets. Persson and Tabellini (1993) state:

“Why do we observe central banks rarely held accountable for the rate of inflation? …It may be that a commitment to a more readily observable nominal variable, such as a monetary aggregate or the exchange rate, is easier to enforce. A second possible answer is that central bankers would not like to be held accountable for something they do not control tightly, and hence are more liable to miss rather often.”³¹

Monetary policy announcements, if transparent and clear, can serve as a reference point against which to judge central bank behavior now and in the future. Transparent policy making seems especially important since it can serve as a substitute for reputation.³²

Inflation targets versus monetary targets

Cukierman (1995) showed that the choice of a monetary target involves a trade off between visibility and controllability. Targeting a monetary instrument such as the monetary base, because it is easier to control, has a reduced impact on expectations of the private sector, as it is less visible. On the other hand inflation targets are more visible and therefore have a higher impact on the public sector’s expectations. However, the rate of inflation is harder to control by the central bank. In Cukierman’s model the public assigns a certain probability that the policymaker in charge of monetary policy is dependable, i.e., capable to commit himself to a certain policy. If the policymaker is targeting the monetary base, which he can perfectly control, the target is only given attention by a fraction of the public. In contrast to that an inflation target attains full attention by the public, but as mentioned above is not that easy to control. Announcing monetary targets then works as a signaling device, where the dependable policymaker tries to separate himself from the weak policymaker. Cukierman’s main results are that the relative advantage of base targets increases with their visibility. A perfect reputation of being dependable makes inflation targeting always preferable as the public gives it wider attention. The relative advantage of base targeting increases with a decrease of controllability over inflation. Hence the easier it is for the weak policymaker to mimic a tough type the more advantageous are monetary base targets because of their visibility.³⁶

Principal agent or time inconsistency problem?

The key problem with the discussion so far is that providing the central bank with the appropriate incentive scheme, either via the contract or via the inflation target, does actually not resolve the time inconsistency problem; it merely reallocates it as pointed out by McCallum (1995, p. 210).³⁷ However, this unfortunate outcome looks different if it were up to society to implement an inflation contract for the central bank. Waller (1995) argues that the time inconsistency problem and the principal agent problem are not the same thing and this has important repercussions for renegotiation. If the principal (society) has the right preferences (e.g., no output target which is above the natural rate), which would guarantee the optimal policy outcome, renegotiation is not an issue. The reason is that society does not want to be fooled by the policymaker and reacts accordingly. However, we then have to ask, why should society have preferences that involve a temptation for creating surprise inflation without any benefits? Waller (1995) states:³⁸

“But if the performance contract generates the socially optimal outcome regardless of whether society and the central banker have the same output targets, why is it important to classify the problem as a time inconsistency problem, rather than a principal-agent problem?”

This implies that society would not have a reason to renegotiate the inflation contract.

Again time inconsistency

With the government as the framer of the contract things are different. Why should the government act in a time consistent manner and not try to renegotiate the contract when unemployment is higher than desired by the government?³⁹ From the analysis above we know that in absence of a pre-commitment technology the government would suffer from exactly the same incentive problem as the central bank would do without the inflation contract. Therefore al Nowaihi and Levine (1996) followed an interesting approach and actually resolve the dynamic inconsistency problem on the side of the central bank by using Walsh-type contracts in combination with reputational forces as analyzed by Barro (1986) to resolve the time inconsistency problem on the side of the government.⁴⁰ The key feature of their model is that a Walsh-type central bank contract is not renegotiation proof and therefore has no credibility as a commitment device. Allowing for reputational aspects on the side of the government in an infinite horizon game, which means that governments are committed to a non-partisan monetary policy or that successive governments are perfectly correlated in their objectives ensures that the government never renegotiates the Walsh contract. In a finite horizon set-up this result does not hold, as at least at the end of the period of office renegotiation occurs. Both results naturally depend on the parameters of the model such as the discount rate etc. Therefore a first best solution is only possible if successive governments cooperate or if reputation could be passed over to successive governments. As each government has only a finite life and political programs and incentives usually differ, at least over time, this is a quite strong assumption.

The inflation bias

Briault, Haldane and King (1995) mention three further problems with the Walsh contract. The simplicity of the contract solution crucially depends on the non-state-contingency of the inflation bias in the simplistic Barro-Gordon analysis. This means that if the inflation-bias becomes shock dependent, e.g., due to some interest rate targets in the loss function of the central bank as in Canzoneri et al (1995), a simple linear inflation contract can only remove the expected part of the inflationary bias. Except New Zealand, where the governor of the central bank can be dismissed for bad inflation performance, none of the countries which more or less employ performance contracts define explicit penalties in the case of missing the imposed targets. And finally, as most of the targeting procedures in practice have a quadratic (symmetric) nature, one might ask in which way a central bank benefits from undershooting its targets.⁴¹

Introducing the lag effect

Although not much emphasized in the literature, it is common sense that monetary policy operates with relatively long lags. Once accepting this fact, the theoretical literature on resolving the time inconsistency problem of monetary policy becomes inconsistent itself. Goodhart and Huang (1995) state:

“If monetary instruments operate with a lag, than a rational public will observe them, (they can hardly fail to notice interest rate changes), and adjust their expectations accordingly. Hence the public cannot be fooled, and the time inconsistency problem argument vanishes.”⁴²

This is in contrast to the usual assumption that private sector wage contracts are fixed for a longer time than monetary policy needs to take its effects. As the standard set-up normally uses a Lucas type surprise supply function,⁴³ whenever there is a lag in the operating of monetary instruments implies that wage and/or price contracts can be reviewed according to the latest monetary action. In such a setting the monetary authority is unable to fool anyone by creating surprise inflation, which means that there won’t be an inflationary bias, nor can it know the value of future shocks. Thus E(ε_t+1)=0 and the monetary authority is unable to smooth shocks (due to the lag). Goodhart and Huang (1995) suggest that the monetary authority could simply follow Friedman’s proposed k-percent rule, so as to make inflation equal to zero.

Again to see these implications more specifically, especially in the light of the contracting approach, let me set out this approach more formally:

Let the loss function be defined as before:

Also as before the Lucas supply function is:

Monetary policy is now assumed to operate with long lags, thus, the informational structure changes as follows:

This simply means that the private sector fully anticipates and reacts to the actions of the monetary authority before the actions take effect. Suppose now that the central bank maximizes a utility function as in the simplified Walsh model (the signal is left out in order to simplify the analysis). That is to say, the central bank maximizes U_t= t-L_t, with t(π)=t₀ - λy^*π_t, i.e.,:⁴⁴

Due to the lag and the resulting informational structure this optimization problem is a trivial one and the first order condition with respect to inflation for a maximum is given by (dropping time subscripts):

If there were not an incentive problem in the first place, i.e., the contract would not be necessary, therefore t=0 => U=-L, the central banker would set inflation equal to zero in each period which is simply following a k-percent rule a la Friedman. The striking result here is that imposing an inflation contract results in a deflationary bias (the first term in (27)) because there is no time inconsistency problem in the first place. This bias becomes larger if the central banker is less conservative, i.e., the higher is λ and also if the monetary authority aims for higher output y^*. In such a situation the Walsh contract does more bad than good because it tries to correct an incentive problem which does not exist.

Early steps

A natural question which arises in a setting of decentralized policymaking is as follows. Does there exist a trade-off between unemployment and inflation if a government deals with an independent central bank and where the two independent agents, the government and the central bank, have different and conflicting objectives (output/unemployment and inflation)?⁴⁸ Andersen and Schneider (1986) focus their attention on this problem.

“In classical economic policy analysis it is commonly assumed that the choice of fiscal and monetary policy is the outcome of a cooperative political process. ⁴⁹

In contrast to the framework provided in the Andersen and Schneider (1986) paper, the “classical” policy analysis assumes that the central bank is in the same subordinate position as any other department of the government (e.g., Great Britain until May 1997 and France until 1994). In such circumstances, we would expect that the political process yields a coordinated result using fiscal and monetary instruments.⁵⁰ This seems to be plausible as only one authority with only one objective function tries to find the optimal policy mix modeled in a game against the private sector.

In the Andersen-Schneider study the policy interaction is described as a game between the agents where possible actions are determined by the rules of the game.⁵¹ If the two agents, the fiscal authority and monetary authority, set their policies independently, it is clear that different preferences and therefore different weights attached to the targets (inflation and output) result in conflicting objectives. Furthermore coordination problems arise, as a characteristic feature of strategic decision situations.⁵² The authors explicitly model the decision situation of the fiscal authority and the monetary authority as a non-cooperative game under alternative institutional arrangements (the simultaneous Nash game and the sequential Stackelberg game) and under different macroeconomic frameworks (Keynesian and New Classical). Their main results can be summarized as follows: (i) in a pure Keynesian framework, uncoordinated fiscal and monetary policy results in inefficiencies, both in the Nash and the Stackelberg game (with the government as the leader), and cooperation would make both agents better off. More specifically fiscal policy is too expansionary, while monetary policy is too contractionary, compared to any cooperative solution; (ii) in the Stackelberg game, when the monetary authority only cares about inflation, they obtain a cooperative solution; and (iii) in a pure New Classical framework there does not exist a Nash equilibrium, nor a Stackelberg equilibrium. The result of such an interaction is that the player with the higher inflationary preferences rules the game.

Consider Figure 2 for a better illustration of what is happening in this model where the Nash equilibrium is given by the intersection of the two reaction functions (point D).⁵³ Given the government chooses g′ the optimal response of the central bank is m′. But now g′ is no longer an optimal response of the fiscal authority and she chooses g″. In point D these revisions of decisions come to an end and one obtains a Nash equilibrium. One can also see immediately that the Nash and the Stackelberg solution are inefficient, point D and E respectively, as they are not located on the Pareto frontier AB.

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Results of the Policy Game in the Cooperative and the Non-Cooperative Case

Citation: IMF Working Papers 2000, 140; 10.5089/9781451856118.001.A001

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The situation where the central bank is the Stackelberg leader with respect to the government is not analyzed by Andersen and Schneider and thus not depicted in Figure 2.

It is very important to note that the private sector is not modeled explicitly in this framework and therefore the inefficiency of the Nash solution occurs only from the point of view of the two authorities in charge. The key problem of the model is that aggregate supply is totally ignored here. When the fiscal authority is choosing the instrument, whatever this might be, it is unclear how this transmits to the private sector’s behavior. An important question that also arises in that context, is the following: If fiscal policy is too expansionary in the non-cooperative game, how is this policy financed in the light of low inflation? The model of Rankin (1995) gets around the problem of ignoring aggregate supply and shall be briefly discussed in the next paragraph.

Delegation of half demand management

In contrast to the above model, the private sector is modeled explicitly in this contribution. The basic model consists of an IS equation, a LM equation, and the usual Lucas type supply function (without considering supply shocks). The government, in charge of fiscal policy, is assumed to care about inflation, output and the interest rate with the commonly-used quadratic loss function. The central bank is assumed to care only about inflation. From the assumptions so far, it is clear that the central bank always gets its way as it has only one objective. The public sector’s task is to choose the expected price level such as that it is equal to the actual price level, but moves first. Hence the public sector determines the position of the AS (aggregate supply) curve and then the central bank and the government choose their conditional output targets subject to the AS curve.⁵⁴ The main findings of the paper can be summarized as follows. As the central bank only cares about inflation, delegation ensures that the central bank wins the battle. There is no inflation and no raise in output. Unfortunately this comes at the cost of a higher interest rate as the central bank fights the expansionary ambitions of the government. If there is no delegation, the government can raise output at the cost of increased inflation. But as the private sector reoptimizes, i.e., adjusts its expectations, the equilibrium long run level of output will be at its natural rate. In the case where the central bank acts as a Stackelberg leader, the Nash outcome prevails. The reason for this is obvious. The central bank is assumed to care only about inflation. Necessarily the iso loss-curves of the central bank are vertical lines in the i-y (interest rate-output) space; hence the Nash- and the Stackelberg solution are identical. In contrast to this, if the government acts as the Stackelberg leader, the central bank wins the battle but this time at a point where there is no inflation, no rise in output and low interest rates. Clearly this mimics the optimal solution in this framework. Summing up, delegation might induce a higher social loss as it is connected with higher interest rates.

This might explain why Germany experienced high interest rates in the early nineties after reunification.

“The 1990 reunification of East and West was the signal for the German government to increase its spending very substantially, in order to assist the East German economy. This put upward pressure on German inflation, which the Bundesbank countered by tightening monetary policy. The result was a battle for control of aggregate demand, with monetary contraction fighting fiscal expansion. In this battle the main damage was suffered by the German interest rate, which both players’ actions contributed to forcing up. There has been much discussion of the recessionary impact on other countries in the ERM at the time and of the destructive impact on the ERM itself,…”⁵⁵

Time inconsistency and tax distortions

So far the existence of the budgetary constraints which a government faces when engaging in fiscal policies have not been considered explicitly. The model of Alesina and Tabellini (1987) provides an analysis of rules and discretion within an uncoordinated monetary and fiscal policy setting.

“The time inconsistency of optimal monetary policy is due to the effects of tax distortions. Thus the issue of how to improve upon the time-consistent suboptimal monetary policy is related to that of the coordination of monetary and fiscal policy.”⁵⁶

Basically their model consists of three players. The private sector is represented by a trade union, minimizing deviations of the real wage from a positive target υ. The government is in charge of fiscal policy, i.e., choosing an appropriate tax rate, and finally the central bank, in charge of monetary policy, chooses the appropriate rate of inflation. The two authorities are assumed to have preferences over inflation, output and public spending, where the weights placed on these objectives may or may not be equal. The time inconsistency problem in this model is generated through the lack of a non-distortionary fiscal instrument, which results in a reduction of economic activity and hence forces output below its natural level. Total revenue of the firms is taxed at rate τ. Hence the aggregate supply function can be shown to satisfy:⁵⁷

Ignoring public debt and denoting by g the ratio of public expenditures over output, the authors show that the budget constraint of the government can be written as:

The authorities’ loss functions are defined over inflation, output and public spending. Let the superscript M denote monetary authority (central bank) and the superscript F denote fiscal authority, i.e., the government. Then the loss functions are defined as:

The parameters β and θ represent the two authorities’ discount rates, μ_i and δ_i denote the weights the policymakers place on output and public spending, relative to inflation. Additionally π_t, y_t, and g_t represent inflation, output and public spending respectively. It is assumed that the positive public spending targets in (30) and (31) are the same. The key feature of this model is as follows. The strategic behavior of the involved parties arises due to the disagreement of how to achieve optimal financing of public spending. A positive real wage target of the trade union produces downward pressure on output. Furthermore positive spending has to be financed at least partly through taxes according to (29), which results in an additional downward pressure on output according to (28). Hence both authorities would like to create some surprise inflation in order to raise output towards its target, which is assumed to be zero here.⁵⁸ In the discretionary setting the three players act in a Nash fashion, where everybody optimizes taking the decision of the others as given. Alesina and Tabellini show that the resulting equilibrium is characterized by the following conditions (where D stands for discretion):

From (32)-(34) one can establish that inflation is above its zero target, while output and public spending are below their target levels. Clearly this situation worsens when the real wage target of the trade union increases and when the authorities wish to increase public spending. It is also straightforward to show that for μ₂ = δ₂ = 0, output and inflation are at their targets as spending is not an objective for neither authority.

In contrast to the above result the commitment solution is characterized by the following equations (where C stands for commitment):⁵⁹

A straightforward comparison of (32)-(34) with (35)-(37) immediately establishes that inflation, output and public spending are lower in the commitment regime than in the discretionary regime, while taxes in the commitment regime are higher than in the discretionary regime. A more striking result of the paper is that the commitment regime might make the fiscal as well as the monetary authority worse off than the discretionary regime if μ_i≠δ_i. The reason for this result can be summarized as follows. As a committed central bank gives less support to public spending financed via money creation, the fiscal authority has to rely more on distortionary taxes in order to finance public spending. But higher taxes induce output to decrease. Necessarily the government is worse off if the loss in spending and output outweighs the gain from lower inflation. This is likely to be the case if the government places a much higher weight on public spending than the central bank, i.e., μ₂ is low relative to δ₂. The same is true for the central bank if the benefit from the reduced inflation rate, due to the commitment, is outweighed by the output loss resulting from higher taxes. A necessary condition for this to happen is that the central bank cares sufficiently enough about output, i.e., μ₁ is large enough. This is a strong result as it states that tax distortions are not invariant to monetary regime changes.

Nonetheless, a problem of this model can be seen in the fact that it does not analyze the impact of aggregate shocks on the economy, i.e., it is deterministic and not stochastic. Hence an important feature of monetary and fiscal policy, namely to stabilize the economy in the presence of shocks, can not be explained.⁶⁰

Summing up, the model above helps to explain the problem of coordinating monetary and fiscal policies and points out that there might be situations where a committed central bank may result in an Pareto inferior solution, but it does not actually resolve the problem of coordinating policies.

A public debt framework

The main weakness of the models presented so far was that the government did not have the opportunity to issue public debt. The unemployment inflation trade-off example could therefore not explain how the too expansionary fiscal policy together with a too contractionary monetary policy could be financed. The Alesina and Tabellini (1987) approach on the other hand incorporated a government budget constraint, but one that is binding on a period by period basis, i.e., the possibility of issuing debt was ignored. Tabellini (1986) states:

“The government budget constraint provides a dynamic link between fiscal deficits, the creation of monetary base and the time path of public debt.” ⁶¹

As the qualitative results are the same in Tabellini’s (1988) two period framework as in the 1986 infinite horizon analysis, I will only focus on the dynamic case for two reasons: First, in contrast to a finite two-period framework, the dynamic model allows us to say something about the optimal time paths of monetary growth and the growth rate of public debt. Second, it indicates the importance and the implications of real interest rates and real economic growth. As before, the analysis focuses on the strategic interaction between fiscal and monetary policies, but now in a dynamic set-up, explicitly including debt and deficits. The basic framework consists of the following ingredients. The monetary authority has quadratic preferences over the time path of money growth (the instrument) and public debt (the state variable) weighted in the usual way. The fiscal authority also has quadratic preferences but over the time path of the fiscal deficit—its instrument—and the state variable debt, weighted accordingly. Finally we have the usual dynamic budget constraint, the law of motion of public debt. The authorities’ task is to choose a time path for their own instrument subject to the government budget constraint and subject to some presumptions about the time path of the opponent’s instrument. The main findings can be summarized as follows. In the feedback-Nash equilibrium the speed of adjustment towards a steady state value of public debt is lower and the absolute value of public debt is higher than in a cooperative equilibrium.⁶² Symmetric commitments can improve the situation compared to the feedback-Nash equilibrium but are still inferior to the cooperative solution concerning steady state value of debt and the speed of adjustment.⁶³

An interesting feature the model is the impact of changes in the relative weights that the policymakers attach to their targets. If the government cares less about the evolution of public debt relative to its deficit objective, the burden of meeting the government budget constraint and adjusting public debt placed on the central bank increases (recall that the central bank also cares about debt in Tabellini’s model). On the other hand Tabellini (1986) argues that the weight which the central bank places on public debt reflects its independence from the treasury. If the government could choose this weight, it would set it to infinity and hence the central bank’s solely task would be to provide enough revenue from money creation to finance the government’s desired level of the fiscal deficit. In a cooperative setting this would mean that monetary policy needs would be totally neglected.

Taxes, inflation, and the Walsh contract

Huang and Padilla (1995) utilize the Alesina and Tabellini (1987) model to examine how the Walsh contract performs in a public finance model. The government is supposed to optimize by conducting fiscal and monetary policy.

As before the socially optimal policy cannot be time consistent as some surprise inflation allows for higher spending, because for a positive spending target the marginal loss decreases with inflation. As a result, time consistency forces inflation, spending and output to be higher and taxes to be lower than they would be if a credible commitment device existed. If the government imposes a Walsh contract on the central banker this can implement the optimal policy but only if fiscal policy is exogenous, that is, the tax rate is given, which is not surprising. If the government determines fiscal policy endogenously via the tax rate this result no longer holds. Basically one returns to a non-cooperative game. The commitment tax rate is not a best reply of the government to the commitment inflation rate under the contract. The government clearly has an incentive to raise taxes marginally in order to increase spending. Hence this cannot be a Nash equilibrium. Additionally, the commitment inflation rate is no longer a best reply of the central banker. The resulting Nash equilibrium brings about a tax rate, which is higher, and an inflation rate, which is lower than the optimal rates.

Public finances and inflation targets

In my (1999) paper I consider the implications of the interplay between monetary and fiscal policies in an inflation-targeting framework. In this vein, the paper asks whether an inflation target can induce an independent central bank to provide the optimal rate of inflation, resulting in optimal seigniorage, taxes, public spending, and output and whether this would also lead to optimal stabilization of aggregate supply shocks? The aim of this model is thus to merge the two building blocks discussed earlier to derive implications for the optimal policy mix, the optimal policy response to a supply shock, and a way how coordination can actually be achieved.⁶⁴

The analysis is formulated as a game between the private sector, the monetary authority and the fiscal authority. The main results can be summarized as follows. A social planner, when in charge of monetary and fiscal policy, can achieve only a second-best equilibrium as lump-sum taxes are ruled out.⁶⁵ The social planner then has to use alternative sources of finance—distortionary taxes, seigniorage and the shortfall of public expenditure from its desired target. The resulting second-best equilibrium involves optimal positive mean inflation. Therefore, depending on the tax base—that is, the size of real base money holdings—it appears to be optimal to raise seigniorage revenues to some extent, which is in contrast to the various zero inflation rules studied in the literature. Since discretionary policymaking is ruled out, the optimal positive inflation rate derives from optimal revenue considerations and not from a desire to raise output via surprise inflation. Aggregate supply shocks cause inflation, taxes, spending, and output to fluctuate (second best) optimally around their respective means. The policy outcome under the assumption that a benevolent policymaker is in charge of monetary and fiscal policy serves as a benchmark case. Once policies are decentralized, that is, monetary policy is delegated to an independent but committed central bank, both financing and stabilization are distorted. Since the central bank does not optimize subject to the government’s budget constraint and therefore ignores the social value of seigniorage, the entire financing requirement has to be met by the fiscal authority. The central bank does not provide any seigniorage revenues, either through budgetary considerations, or through a desire to boost output closer to its target through surprise inflation. Therefore, the fiscal authority has to rely to a greater extent on taxes—causing output to move further away from its desired target— and a larger expenditure gap. In terms of stabilization, this paper finds that inflation/seigniorage fluctuates less, while output and spending vary more. As a result, the social loss in this scenario is larger than under centralization. A way out of this dilemma is to impose a non-state-contingent inflation target on the central bank. The appealing feature of this target is that it provides the optimal level of expected seigniorage. This result highlights that any output effect in the targeting regime derives from lower taxation since the amount of taxes necessary to finance a given financing requirement depends on the level of seigniorage provided by the central bank. The optimal inflation target is allowed to vary, depending on the base for the inflation tax. At the limit, where real base money holdings tend to zero, the seigniorage motive vanishes and the optimal inflation target becomes zero. In terms of society’s loss, we show that this solution—in which the central bank is independent but subject to an optimal inflation target—dominates the arrangement in which the independent central bank has no inflation target, but is still inferior to the centralized case.

The monetary policy implications and public debt

In his (1996) contribution Dornbusch analyzed the policy issues of monetary policy and public debt. As far as this paper is concerned, I will only focus on the credibility issues as they are linked to the time inconsistency problem of sections II and III. To see why a policymaker with a specific target for the growth rate of the real debt ratio might be tempted to engage in surprise inflation consider the following simple debt dynamics equation:

where d denotes the rate of increase of public debt as a ratio of GDP, y is the growth rate of the economy, b is the ratio of outstanding public debt over GDP, r is the real interest rate and s denotes the fiscal surplus. Two issues concerning equation (38) are important to note. Firstly, the debt growth ratio decreases if the real interest rate is lower than output growth, as servicing the outstanding debt (the first term in (38)) decreases. This obviously gives the government an incentive to engage in surprise inflation to raise output, if defined as a Lucas type logarithmic surprise supply function. Secondly, a higher fiscal deficit or a lower or negative surplus increases the debt ratio for two reasons: (i) directly, as deficits have to be financed by issuing debt, and (ii) indirectly, as the outstanding public debt increases and therefore the debt service increases. Dornbusch (1996) states:

“Deficit finance with a real interest rate that exceeds the growth rate of output leads to rising debt. Rising debt increases deficits and hence leads to ever increasing debt and debt ratios.”⁶⁶

Suppose that the government has the following preferences over the growth rate of the real debt ratio, inflation and the budget surplus. If we think that primary budget surpluses are regarded as negative, a fiscal deficit would enter the following government loss function necessarily with a negative sign. Using Dornbusch’s (1996) notation the loss function is given by:⁶⁷

where a is the weight placed on inflation and c denotes the weight placed on the budget surplus, both relative to the real debt growth target. Assuming that the private sector has rational expectations, i.e., sets π=π^e and the nominal interest rate is determined by r+π^e, the resulting Nash equilibrium for inflation and the primary fiscal budget surplus satisfies:

Since the public sector is assumed to form rational expectations, surprise inflation cannot reduce the real value of debt, because the public embodies this “government disincentive” in nominal interest rates. Clearly, if the government has a strong preference for deficits, i.e., is averse to running a primary budget surplus as captured by the parameter c, inflation tends to be higher. The same is true for higher outstanding debt ratios. This simply means that governments with a bigger debt problem even have a stronger incentive to engage in surprise inflation although it does not help anyone. In contrast, a government caring more about inflation, i.e., placing a higher weight a on inflation, tends to reduce inflation in that Nash equilibrium. Finally, the greater the difference between the real interest rate and the economy’s growth rate, the higher will be inflation. The reason is again that the government’s incentives to create some surprise inflation are stronger in this case, as fooling the public would help to close this gap between the real interest rate and the growth rate of the economy.

The credibility problem appearing in this set-up is the following. According to Dornbusch (1996):

“…we argue that today inflating away debts no longer works; even so, the present discussion underlines that the mere presence of debts and the resulting temptation is a source of inflation unless credible commitments can be made.” ⁶⁸

As suggested by Dornbusch, one way of getting around this problem would be to denote debt in foreign currency (stable and strong) as restrictive monetary policy so that reducing debt service and hence debt growth would no longer be conflicting objectives. Why? The latter could exactly be achieved by tightening monetary policy because this avoids depreciation of the own currency.

A detour to EMU

There are many arguments in favor and against the Maastricht fiscal criteria. Dornbusch (1997) for example argues that the insistence on the Maastricht fiscal criteria are overdone mainly because national debt, say Italian debt, will remain Italian debt after the transition to a single currency. The external debt of Italy is so low that its credit rating (this applies only to dollar debt) is quite high. Even if the Italian debt ratio were to increase and hence its credit risk were to increase, the only thing that would change would be the interest rate spread between Italian bonds and other countries’ bonds. Investors would change their portfolio structure leaving the Italian debt problem an Italian one and not one of the union as a whole. Furthermore, the Maastricht treaty provides the European Central Bank (ECB) with independence, meaning that it is neither allowed to accept guidance of any Union government, nor should it finance any Union government. Wyplosz (1997) also has some doubts about the stability pact as it stands. He argues that a proper definition of fiscal policy must involve the idea of sustainability because excessive debt accumulation today might have to be reversed at some time in the future. He also emphasizes the relevance of the 3 percent deficit ratio and the 60 percent debt ratio outlined in the Maastricht treaty. While the 3 percent deficit ratio is thought of as reflecting investment spending of the public sector it entirely ignores expenditures which have to do with human capital accumulation (e.g., education) as an important determinant of economic growth. Furthermore Wyplosz (1997) states:

“The 60 percent debt/GDP rule was chosen because it was the average of EU countries when the Maastricht Treaty was being negotiated, with or with not even the pretense of any deeper economic justification” ⁶⁹

Although the fiscal criteria reflect the desire of the EU countries to insure the ECB’s independence they bind their hands in terms of fiscal stabilization’s. Together with the loss of monetary control the EMU arrangement might cause serious disruptions at least in some countries especially in the light of a lack of intra European redistribution possibilities. The U.S. currency area for example has a federal government that Europe does not.⁷⁰ McKinnon (1997) on the other hand explores an argument more in favor of the stability pact. Although debt remains a national problem one has to keep in mind that many bonds are in banks, pension funds and other financial institutions. This implies that a debt crisis in one country in EMU might have substantial implications for this particular country and the rest of the union, jeopardizing the ECB’s independence. For that reason, McKinnon (1997) argues that ex ante and ex post fiscal discipline is absolutely necessary.