## Abstract

The merits of rules and discretion for monetary policy are considered when the structure of the macroeconomic model and the probability distributions of disturbances are not well defined. When it is costly to delay policy reactions to seldom-experienced shocks until formal algorithmic learning has been accomplished, and when time-consistency problems are significant, a mixed strategy that combines a simple verifiable rule with discretion is attractive. The paper also discusses mechanisms for mitigating credibility problems and emphasizes that arguments against some types of simple rules lose their force under a mixed strategy.[JEL 310, 311]

**T**his paper addresses issues that are relevant to the design and implementation of monetary policy strategies. A simple framework is developed that can be used to analyze different types of strategies for an open economy in which social welfare depends negatively on both price level instability and deviations of output from its full employment level (Section I). To set the stage for discussing different strategies, it is initially assumed—unrealistically—that the structure of the economic model is known completely and that disturbances to the economy can be characterized as having well-understood probability distributions (Section II). The traditional distinction is drawn between discretion (that is, policies derived from conditional optimization) and rules (that is, policies derived from unconditional optimization); a further distinction is drawn between fully state-contingent rules and partially state-contingent rules.

The paper then turns to the realistic case in which knowledge about the structure of the economy and the nature of economic disturbances is incomplete, and in which it may be costly for society to delay policy reactions until new events are fully understood. It is argued that such considerations make fully state-contingent rules irrelevant in practice, and it is demonstrated that partially state-contingent rules are not necessarily superior to policies derived from conditional optimization. The paper then explores the possibilities arising under a hybrid policy in which a partially state-contingent rule is mixed with discretion (Section II). In addition to demonstrating that such mixed strategies can dominate both complete discretion and rigid adherence to the partially state-contingent rule, we investigate the appropriate setting of parameters in a partially state-contingent policy when it is acknowledged that the rule will not be followed on all occasions—that is, that sometimes the monetary authority will resort to discretion.

The results of this section have general applicability to the design and evaluation of policy rules. The typical design and evaluation strategy in economics involves setting an initial rule and then simulating the coun-terfactual path that a model economy would have taken had the proposed rule been in place and had agents expected the rule to be in place forever. In this methodology the parameters in the proposed rule are then “fine-tuned” to give desirable properties to the counterfactual path. To the extent, however, that the rule evaluated using such methodology is not fully state-contingent, it is possible that policymakers, had they actually been confronted with the counterfactual history, would have chosen to respond to contingencies not specified in the rule. In general, the possibility of such responses by the policymaker, which would have been recognized ex ante by rational market participants, renders inappropriate the parameter settings obtained by using a methodology that does not account for the nonzero probability of occasional discretionary reactions to unspecified contingencies. It thus becomes interesting to explore conditions, in a particular model environment, under which the usual policy evaluation methodology gives the “right answers” even though the evaluation problem is only partially specified. In doing so, our approach to the problem of setting optimal rules that are not fully state-contingent draws on the “process-switching” literature (for example, see Rood and Garber (1980, 1983)).

One further issue that deserves serious consideration is the question of how to design institutional arrangements for mitigating the credibility problems that could arise under a hybrid policy that left the monetary authorities with some discretion (Section IV). Concluding remarks are provided in Section V, which notes that the relative merits of different choices of variables for a monetary rule may depend on whether the policy strategy calls for rigid adherence to the rule or for mixing the rule without discretion.

### I. Analytic Framework

This section develops a simple analytic framework that illustrates several issues that arise in adopting a monetary policy strategy for an open economy. Following conventional practice, we consider an economy in which society dislikes deviations of output from its full employment level and also dislikes price level instability. In this context, it is assumed for simplification that the objective of monetary policy is to minimize the quadratic loss function:

where *y _{t}*is the logarithm of output in period

**is the logarithm of full employment output,**

*t*,*y**p*is the logarithm of the price level, and a is a strictly positive weight that society places on price level stabilization relative to output stabilization.

_{t}^{1}

Following Gray (1976), Canzoneri (1985), and others, we assume that output is produced by labor, that the nominal wage rate is set in a contract negotiated before the realization of the price level, and that the employment contract calls for workers to supply whatever amount of labor is demanded by firms at the negotiated wage rate. These assumptions are taken to imply that, in combination, the production function and the labor demand function yield a relationship in which output is a decreasing function of the real cost of a unit of labor:

Here, *w _{t}*is the logarithm of the wage rate,

*c*and

*d*are parameters, and

*μ*, is a mean-zero productivity shock.

_{t}^{2}It is also convenient to assume that wage setters know the output supply function and act to minimize the expected squared deviation of output (employment) from some implicit target level (ӯ) that may differ from the full employment concept that enters the social loss function.

^{3}Thus, the wage level is determined from the first-order condition

which, together with equation (2), implies that

Substitution of equation (4) into equation (2) yields an output supply relationship,

that is similar to the standard rational expectations supply function introduced by Lucas (1972). Substitution of equation (5) into equation (1) implies that

or

where ϵ_{t}= *p _{t}—p_{t-1 }* is the rate of inflation and where

is the difference between the social concept of full employment output and the level of output that wage setters implicitly target when negotiating their wage contracts. The existence of “distortions” such as unemployment compensation or income taxation—or of incentives for wage setters to maximize the welfare of some subset of the labor force that is already employed (or that has seniority rights to employment)—may give rise to a situation in which *k* is positive.^{7}

To address monetary policy issues for an open economy, it is convenient to use the relationship

where π^{*}_{t} is the foreign rate of inflation, *s _{t}* is the rate of change of the nominal exchange rate (the rate of change of the domestic currency price of foreign exchange), and ϕ

_{t}is a shock to the purchasing power parity relation. It is assumed that monetary authorities control base-money growth and that the nominal rate of depreciation of the domestic currency can be decomposed into one component that varies systematically with the differential between the domestic base-money growth rate

*(b*and the foreign inflation rate (π

_{t}^{*}

_{t}), a second component (ϕ

_{t}) corresponding to the purchasing power parity shocks, and a third part (v

_{t}) that reflects other elements responsible for nominal exchange rate movements. This relationship is given by

^{4}

To simplify the later algebra, it is assumed that *E _{t-1} v_{t}=0*. Thus, under the additional assumptions that

*v*is exogenous to domestic pohcy and uncorrelated with μ

_{t}_{t}

^{5}, and that the distortion term, k , is time and policy invariant, equations (9) and (10) can be combined to yield

^{6}

and

To simplify notation further, it is convenient to transform variables and to express the policy problem as that of minimizing the social loss function.

where

Note that, although our primary interest lies in analyzing monetary policy for an open economy, equations (11)-(13) apply not only to an open economy with stochastic terms in the purchasing power parity relation and the nominal exchange rate equation, but also to a closed economy with white noise in the relationship between inflation and base-money growth.

### II. Comparisons of Alternative Strategies

The analytic framework developed in the previous section will now be used to compare social welfare—as measured by the expected value of the social loss function (13)—under a regime that allows the monetary authorities to exercise discretion and under two regimes in which monetary policy is governed by rules. One of the rules is fully state-contingent, and the other is partialiy state-contingent. For the discretion regime, we assume that the authorities attempt to minimize the value of the social loss function, and—consistently—under the two different rule regimes we solve for parameter values under which the expected value of the social loss function is minimized.

A central consideration in any discussion of the optimal design of monetary policy is the extent to which the structure of the macroeconomic model is known, the relevant economic variables are observable, and the disturbances to the economy can be characterized in terms of well-defined probability distributions. In this regard, we assume initially that both the monetary authorities and the private sector know the macroeconomic structure, can deduce“, and *v _{t}* from observable variables and their knowledge of the parameters of the model ex post, and have accurate ex ante information about the probability distributions from which

*u*and

_{t}*v*are drawn.

_{t}In reality, of course, monetary policy strategies must be designed for an environment in which there is incomplete information ex ante about both the macroeconomic structure and the probability distributions of disturbances. Moreover, the problem of optimal policy design is complicated by the fact that it can be costly to delay pohcy reactions until new information is fully assimilated from those events that contain new information. Section III will attempt to address the problem formally in such an environment. The purpose of considering a partially state-contingent rule in this section, where we adopt the assumption of “complete” ex ante information, is to provide the groundwork for Section III. Furthermore, to avoid semantic confusion at a later stage, we will use the term “conditional optimization” as a synonym for “discretion” and the term “unconditional optimization” as a synonym for “rules.”

#### Discretion, or Conditional Optimization

Under a strategy of discretion or conditional optimization—henceforth denoted *CO* —the monetary authority sets *b _{t}* to minimize equation (13) subject to the observed values of

*u*and

_{t}*v*and, most important

_{t}*, subject to predetermined expectations of base-money growth*,

*E*. The first-order condition for a minimum of equation (13) with respect to

_{t-1}*b*is

_{t}Private agents understand the monetary authority’s motives, so they form their expectations of base-money growth by talking the expectation of *b*, in equation (14). Combining this expectation with the expectation of equation (11) yields

This expression hliks the inflationary bias that arises under *CO* to the distortion term *k*. If *k* were zero, deviations of output from its full employment level would also be zero in the absence of inflation surprises and productivity shocks (recall conditions (5) and (8)), and there would be no inflationary bias.

To evaluate social welfare, substitute equation (15) into equation (14) to obtain

where *b _{t}CO* is base growth under conditional optimization (discretion). Thus, from equation (5), the realized loss from

*CO*is

and the expected loss is

where*V(u)* is the variance of *u*, conditional on information from period *t-1*.^{8} The first term on the right-hand side of equation (18) reflects the expected loss associated with whatever output or labor market distortions are responsible for the inflation bias, whereas the second term reflects the loss associated with fluctuations in productivity.

#### Rules, or Unconditional Optimization

Next consider the implications of following a rule or an unconditional optimization strategy—henceforth denoted*UO*. Given the functional form of a rule that is known to the public, the optimal parameter values for the rule are derived under the condition that *E ^{t-1}b^{t}*, is not a predetermined variable.

##### Fully State-Contingent Unconditional Optimization (UOF)

The optimal fully state-con tin gent rule— *UOF* —can be derived by postulating that base-money growth is given by^{9}

and then minimizing the expected value of the loss function with respect to λ_{0}, λ_{1}, and λ_{2}. The resutring optimal policy is

which mimics the *CO* policy (16) without including a response to the distortion term *k*. Under the *UOF* policy.

##### Partially State-Contingent Unconditional Optimization (UOP)

Next consider the case of a partially state-contingent rule— *UOP* —in which base money reacts to the *u _{t}* disturbances but not to the v

_{t}disturbances. The optimization problem is analogous to the

*UOF*case, except τ

_{0}and τ

_{1}that minimize the expected loss for rules having the form

The optimal policy of this form is

Thus,

#### Discussion

If time-consistency issues are ignored for a moment, it is evident from equations (18), (21), and (24) that the *UOF* policy dominates both the *CO* policy and the *UOP* policy. It is also evident that the *CO* and *UOP* policies are not unambiguously ranked. The *CO* policy is advantageous relative to the *UOP* policy when *V(v)* is large, whereas *UOP* is advantageous relative to *CO* when *k* is large.^{10} This reflects the fact that discretion has the desirable consequence of allowing the monetary authority to react to shocks that are not allowed for in the partially state-contingent rule but has the undesirable consequence of generating an inflationary bias whenever there are distortions affecting the determination of output.^{11}

The time-consistency issue arises in an environment in which a policy authority announces its intention to follow either the *UOF* or *UOP* policy but is tempted actually to follow the *CO* policy (see Kydland and Prescott (1977)). The source of temptation is that when private agents believe that the policymakers will follow either *UOF or UOP*, the monetary authority can achieve a welfare gain in the short run by exploiting the agents’ predetermined expectations and following the *CO* policy instead. Accordingly, agents in the economy, understanding this point, will expect the authority to follow the *CO* policy no matter what policy is announced. Thus, the only time-consistent equilibrium in this example is the *CO* policy.

Despite widespread awareness of this time-consistency issue, many economists favor the adoption of a *UOP* policy (for example, see McCallum (1987, 1988)), These individuals must believe either that time-consistency problems are not likely to be important in practice or that such problems can be avoided through institutional mechanisms that precommit the authorities to adhere to the *UOP* rule. For example, some form of penalty-—either formal or informal—could be imposed on the authority or on society to remove the incentive for the monetary authority to exploit the predetermined expectations,^{12} Such institutional arrangements are discussed in Section IV.

### III. The Strategy of Mixing a Partially State-Contingent Rule with Discretion

If it were feasible and costless to specify and follow a fully state-contingent monetary rule, and if appropriate institutional mechanisms could be estabhshed for precommitting the authorities to follow the rule, then there would be no justification for relying on either discretion or a partially state-contingent rule in the conduct of monetary policy. As illustrated in the previous section, it is clear in theory that both discretion and partially state-contingent rules are “second-best” strategies.

As a practical matter, however, a fully state-contingent rule for monetary policy is simply not a relevant possibility in a world in which (1) knowledge about the macroeconomic structure and the nature of disturbances is incomplete, (2) it takes time and other resources to assimilate new information from those events that contain new information, and (3) it can be very costly to society to delay policy reactions until new information is fully assimilated. Consistently, the various types of “simple rules” that have actually been proposed for monetary policy are not fully state-contingent *UOF policits*.

When fully state-contingent rules are discarded as irrelevant alternatives, new scope emerges for advancing the analysis of rules versus discretion. Indeed, given that discretion (that is, *CO* policies) and partially state-contingent rules (that is, *UOP* pohcies) cannot be unambiguously ranked, it is natural to investigate strategies that optimally mix a partially state-contingent rule with discretion.

In focusing on this issue, it may be helpful to keep the semantics precise in this section by referring to *CO* and *UOP* policies rather than to discretion and partially state-contingent rules. Our intuition at the outset is that the advantage of mixing a *UOP* policy with a *CO* policy is that the *CO* policy all rows reactions to disturbances not incorporated in the *UOP* policy. The disadvantage is that, under the mixed strategy, part of the inflationary consequences of the *CO* policy will be built into agents’ inflation expectations even during periods when the monetary authority is actually following the *UOP* policy. The goal is to weight the advantages and disadvantages appropriately in selecting the optimal degree of mixing.

The remaining parts of this section have two objectives: to derive the optimal values of the coefficients in the *UOP* policy, given that the authority is actually following a mixed pohcy; and to show that a mixed strategy can be socially preferable to both the *CO* and the *UOP* policies. In connection with the first objective, it is important to note that the typical evaluation methodology used for *UOP* policies is not generally valid when a monetary authority adopting a *UOP* pohcy occasionally “bails out” of the policy to react to the realization of some state that had not been prescribed in the *UOP* policy. In particular, the typical methodology for evaluating proposed *UOP* policies, and for deriving optimal parameter values for such pohcies, is based on the assumption that the policies will be followed indefinitely. Accordingly, we are interested in finding conditions such that the parameters obtained through traditional methodology are also optimal when the *UOP* policy is recognized to be part of a mixed strategy that includes occasional reliance on *CO* policy.

#### Setting Optimal *VOP* Parameter Values as Part of a Mixed Strategy

Consider the problem of finding the optimal values of τ_{0} and τ_{1} in the policy *b _{t} = τ_{t} + τ_{1} μ_{t}* (as defined in equation (22)), where these values solve

Here *q* denotes the probability that the *UOP* policy will be followed during period t, whereas 1 - q is the probability that the *CO* policy wih be followed. For now, we will take *q* to be an exogenous constant (0≤ q ≤ 1). In the next subsection we will begin to model *q*.

To solve this problem it is convenient to first obtain *E _{t-1} b_{t}* which enters into the loss function under both branches of the policy. If

*UOP*is followed,

*b*if

_{t}= τ_{0}+ τ_{1}u_{t}*CO*is followed (recall equation (14)),

*b*. Accordingly, since

_{t}=(1-a)^{-1}(E_{t-1}b_{t}-u_{t}+k)-v_{t}*E*,

_{t-1}b_{t}=qE_{t-1}(b_{t}/UOP)+(1-q)E_{t-1}(b_{t}/CO)To obtain the optinnat values of τ_{0} and τ_{1x} , first substitute equation (22) and equation (26) into equation (13) and obtain the appropriate expression for *E _{t-1}(L_{t}|UOP)* next, substitute equation (H) and equation (26) into equation (13) and obtain the appropriate expression for

*E*; finally, substitute these expressions into the policy problem (25) and obtain through optimization two equations in τ

_{t-1}(L_{t}|UOP)_{0}and τ

_{1}. In general, the optimal values of τ

_{0}and τ

_{1}will depend on the conditional expectations of w and v. However, for the case in which the

*CO*pohcy is used symmetrically in the sense that

*E*=

_{t-1}(u_{t}|CO)*E*=

_{t-1}(u_{t}|UOP)*E*=0 then the optimal parameter values are

_{t-1}(v_{t}|CO)*τ*, which are identical to the optimal values of the policy parameters obtained for the pure

_{0}and τ_{1}=-1/(1+a)*UOP*pohcy (recall equation (23)). This “symmetric” case is of interest because it provides a plausible environment in which the typical policy evaluation methodology delivers the correct pohcy rule parameterization even when the policy rule will sometimes be violated.

#### The Optimality of a Mixed Strategy

This section of the paper demonstrates that rigid adherence to a simple rule may be inferior to the strategy of mixing a simple rule with discretion. We illustrate the possible gains from a mixed strategy using the above framework. Fohowing the results of the previous subsection, the mixed strategy that we study combines the pohcy resulting from conditional optimization *(CO)* with the partially state-contingent policy *(UOP)* that is optimal when it is known that the *CO* policy will sometimes be apphed.

To capture the idea that society wants the central bank to exercise discretion only when there are relatively large payoffs in terms of the social loss function, we assume that the central bank has been motivated to minimize the sum of the social loss function L (as specified by condition (13)) plus a cost that arises whenever policy settings deviate from the *UOP* rule.^{13} For purposes of providing a simple illustration, we consider the analytic framework developed in Section I under the assumption that *u _{t}*= 0. We further assume that the distribution of v

_{t}shocks is symmetric and that society wants the monetary authorhies to follow the

*UOP*rule

*b*

_{t}—*0*for small

*v*shocks and to switch to the

_{t}*CO*policy for shocks that exceed (in absolute value) a threshold size θ, As shown in the previous subsection, b

_{t}= 0 is the optimal

*UOP*policy under these circumstances. If society has established the appropriate incentives for the monetary authority (that is, made the cost of overriding the rule large enough but not too large), then society can expect that the rule wih be overridden if and only if the shock is large in the sense that it is outside the θ boundaries. Thus, the probability of following the

*UOP*policy is

For this case, it is straightforward to show that for some parameter values the mixed strategy is preferable to (that is, results in a smaller expected loss than) both the *UOP* policy (the rule) and the *CO* policy (discretion). The first step in the demonstration is to note that

where *E _{t-1}b_{t}|UOP* is the period

*t-1*conditional expectation of base-money growth given that

*UOP*is being followed, and

*E*is thet-1 conditional expectation of

_{t-1}b_{t}|CO*b*given that

_{t}*CO*is being followed. Recall that a

*CO*policy must satisfy the first-order condition (14); it therefore follows that

where we have used *u _{t}=0* Next, use equation (17) and the condition

*b*to derive

_{t}/UOP=0The probability of following *UOP*—that is, *q*—shows up in equation (30) because this scheme modifies agents’ rational expectations of base-money growth. As long as *q* is positive, the scheme reduces expected base growth conditional on discretion and will therefore reduce the inflationary bias. Unconditional expected base-money growth, which is obtained from equations (30) and (28), is

Next, consider that the expected value of the loss function under the mixed strategy is

From equations (13) and (32) it can be seen that

and

where *V(v|UOP)* is the variance of v conditional on the *UOP* policy, which is equivalent to being conditional on v being “small.” Similarly, from equations (13), (14), and (31) it can be seen that

Combining these two branches of the loss function yields

So far, our demonstration is simply a formalism. What we will show next is that under a range of parameter values the mixed strategy is superior to both the optimal *UOP* rule and discretion. Because we simply want to show a possibility, an example will suffice. Recall equation (27) and consider a situation in which *v*, is uniformly distributed on the interval [-γ, γ] such that *q =θ/γ* for any choice of θ on the relevant interval. For this distribution, *V(v)=γ ^{2}/3* and

*V(v\UOP) = q*. Furthermore, by substituting the conditional variance into equation (36) and minimizing

_{2}γ^{2}/3*E*with respect to

_{t-1}L_{t}*q*it can be shown that the optimal value of

*q*must satisfy the condition

^{14}

The probability *q* need not be an object of choice—we simply want to illustrate that it is feasible for the optimal*q* to take on a value between zero and unity. Such a case arises when *k/γ<1+a*, which provides an example in which the mixed strategy dominates both *UOP* (rule) and *CO* (discretion).

Note that the mixed strategy is not always optimal. Indeed, if *k* is large or if y is small, the rule wih dominate (that is, *q* = 1 will be optimal as a corner solution). But note also that if *y* is extremely large relative to *k*, then discretion has an advantage relative to the rule. Although a large value of *y* makes *CO* (discretion) attractive in this example, the mixed strategy always dominates *CO* (that is, q = 0 is never optimal as long as *k* *>0)* but does not always dominate *UOP* (the rule).

As a general point, it should be emphasized that the support that such analysis provides for strategies that combine rules and discretion requires careful interpretation. In particular, the analysis does not support the strategy of announcing a rule but not taking the rule seriously, as has sometimes appeared to have been the practice in the past. Rather, as we interpret the analysis, the mixed strategy calls for the monetary authorities to follow a precisely defined rule in normal circumstances but to be prepared to override the rule in abnormal circumstances. In implementing such a strategy, society would have to think carefully about how it wants to define “abnormal circumstances.” Our example interpreted abnormal circumstances as synonymous with large v shocks, but it might also be appropriate for the central bank to override the rule temporarily whenever the ultimate target variables have drifted too far from their intended course.

### IV. Institutional Arrangements for Mitigating Credibility Problems

Because we know from the literature on time consistency that even authorities concerned solely with maximizing social welfare may be tempted to deviate from the optimal rule in the presence of distortions (recall the third subsection of Section II), it is important to establish mechanisms for overcoming problems of the credibility of monetary policy. In some countries the existence of independent central banks, and the practice of granting long and overlapping tenures to central bank governors, may provide an institutional framework within which an announced monetary policy strategy has more credibility than would be the case if monetary policy was controlled by elected officials with shorter terms of office. Nevertheless, even independent central banks have credibility problems in the sense that their policy announcements are not always accepted at face value.

As emphasized above, problems of monetary policy credibihty can easily be resolved if the structure of the macroeconomic model is well known to all economic agents, if all relevant economic variables are observable, and if all disturbances to the economy can be characterized as having well-defined probability distributions. In that case, an optimal fully state-contingent rule would be well defined, society would derive no benefit from allowing the central bank to exercise discretion, and, conversely, society would have nothing to lose from resolving the problems of monetary policy credibility by requiring the central bank to adhere rigidly to the optimal fully state-contingent rule. By contrast, when information is incomplete, and when the central bank has the opportunity to base the settings of its policy instruments on better information about the economy than private agents have (or had) in making contracts for wages and other relevant variables, eliminating monetary pohcy discretion can have the undesirable consequence of preventing central banks from performing a beneficial stabilization role.

In analyzing the difficulties that can arise in resolving problems of monetary policy credibility when central banks have “private information”—that is, information different from what other economic agents can obtain or verify—Canzoneri (1985) has noted that “private information” includes both superior information about the economy and information about the policymaking process that the private sector cannot reconstruct. We think it is important to recognize that the pohcy-maker’s environment includes seldom-experienced events—such as wars, commodity price shocks, asset market panics, or horizon-expanding inventions—that are not amenable to any ex ante codification of policy reactions. In our view, this environment—superimposed on a world in which private agents find it rational (based on transaction and negotiation costs) to enter into contracts for wages and other variables for fixed periods of time in forms that are not fully state-contingent or subject to continuous revision—creates the possibility that discretionary central bank responses to seldom-experienced events might play a valuable stabilization role.

In considering the strategy of mixing a simple rule with discretion in the manner defined in the previous section, one of the important issues that arises is how to limit the exercise of central bank discretion when the very circumstances in which discretionary responses are desired cannot be defined precisely in advance. Our formal analysis relied on the assumption that the central bank was induced to minimize the sum of the social loss function plus a fixed cost that it incurred whenever it deviated from the rule. In practice, the achievement of an appropriate mix of rule and discretion seems likely to depend on (1) the selection of a clearly defined rule that can be expected to steer the economy in a direction broadly consistent with social preferences, (2) the appointment of central bankers whose preferences are closely aligned with those of society at large, and (3) the imposition of an appropriate penalty for deviating from the rule.

With regard to the first of these factors, many countries have allowed their central banks to operate with imprecisely defined rules for monetary growth. For example, most monetary targets have been specified as ranges, few countries have adopted rules that preclude “drift” between targets for successive years, some countries have shifted their targeting strategies from one measure of money to another, and other countries have specified simultaneous targets for several monetary aggregates that cannot easily be controlled independently. Thus, in the context of the political viability that would come from an explicit understanding that rules would be mixed with discretion, there is scope for all countries to define their monetary rules more precisely. There also may be scope for adopting more sensible types of simple rules—for example, rules that prescribe explicit countercyclical behavior.

For some countries, the achievement of an optimal mix of rule and discretion might also be facilitated by changes in the process for selecting central bank governors. Rogoff (1985) has emphasized that, in the context of a time-consistency problem, society can sometimes make itself better off by leaving monetary pohcy to the discretion of central bankers with preferences that attach more weight than the preferences of society at large to price level stabilization relative to output stabilization. By contrast, under the mixed strategy envisioned in this paper, society wants its central bankers to adhere rigidly to a rule under “normal” circumstances, and only to deviate from the rule when doing so provides a sufficient reduction in the value of the social loss function. Accordingly, in this setup it seems desirable to appoint central bankers whose preferences are similar to those of society at large.

Finally, the issue of how severely to penalize central banks for exercising discretion to override the rule may be a matter that can be decided only through experimentation. At present, some countries subject their central bankers to regular cross-examinations by elected officials, but it is difficult for such procedures to discipline central bankers effectively when announced rules for monetary pohcy are not precisely defined. With a precisely defined monetary rule, the costs imposed by public cross-examinations and protestations might well dissuade central bankers from overriding the rule with much frequency. Regardless of whether public cross-examination is sufficient for this purpose, however, the severity of the penalty (or the cross-examination) should be inversely related, other things being equal, to the level of confidence with which it is expected that the rule will steer the economy in a direction consistent with social preferences.

### V. Concluding Remarks

During the 1980s, monetary authorities in the major industrial countries have become more tolerant of variability in monetary growth rates relative to preannounced targets or projections, while giving increasing consideration to exchange rate objectives.^{15} Although these authorities have not modified their broad objective of maintaining appropriate conditions for sustained noninflationary growth, there are important unresolved questions about the appropriate strategy for pursuing that objective, particularly in the largest countries.

This paper has used a simple analytic framework to review and reconsider some of the basic issues that arise in designing and implementing a strategy for monetary policy. Among the main points made are the following.

Under the unrealistic assumprion that both the monetary authoriries and the private sector know the macroeconomic structure, can observe all relevant economic variables accurately ex post, and have accurate ex ante information about the probability distributions of disturbances to the economy, the optimal strategy is a fully state-contingent rule rather than the type of non-state-contingent monetary targets that countries have adopted in the past.

^{16}To the extent that time-consistency problems exist in such a situation, the optimal state-contingent rule can be made credible through institutional mechanisms to insure precommitment.The resolution of credibility problems and the design of an optimal strategy become more complicated when there is incomplete information about the economic structure and the nature of disturbances. On the one hand, the environment generates new information that can be used to re-evaluate continuously the structure or structural parameters of the economy and the nature of economic disturbances; thus, there are important potential gains from allowing the central bank to make use of the latest available information in its attempts to stabilize the economy. On the other hand, when the environment includes seldom-experienced events that are not amenable to any ex ante codification of policy reactions, and when it takes time and other resources to assimilate the new information that such events provide, it would seem virtually impossible to formalize the policymaking process—let alone to formalize

*it*in a way that the private sector could reconstruct and monitor. Thus, the credibility of monetary policy would be questionable if the central bank announced a complicated state-contingent procedure for setting its pohcy instruments and was allowed to use new information to make period-by-period revisions of the structural model, of the parameter estimates on which its instrument settings were based, or of both. In practice, a complicated state-contingent rule that included period-by-period revisions could not be adequately distinguished from discretion.Although the problems associated with comphcated state-contingent strategies have led some economists to propose the adoption of simple policy rules, a mixed strategy of combining a simple rule with discretion may be preferable both to rigid adherence to the rule and to complete discretion. The type of mixed strategy we are referring to here is not a strategy of announcing a rule but not taking the rule seriously, as has sometimes appeared to have been the practice in the past, but rather a strategy that calls for the authorities to follow a precisely defined (but simple) rule in “normal circumstances” and to override the rule only under certain conditions.

Institutional mechanisms that penalized central banks for exercising discretion under “normal” conditions might be important for resolving credibility problems under a mixed strategy, just as they might be for precommitting the authorities to adhere rigidly to a rule in all circumstances. In this context, existing institutional oversight arrangements (usually involving regular cross-examinations of central bankers by elected officials) might be more effective if the rule component of the mixed strategy was defined precisely.

In the context of a mixed strategy involving a simple rule that can be overridden under certain conditions, many of the arguments against some types of monetary rules lose their force. A rule for targeting nominal gross national product, for example, becomes more attractive when the rule can be overridden in response to supply shocks.

The typical procedure for designing and evaluating policy rules based on counterfactual historical simulations is flawed when the rules under investigation are not fully state-contingent. In particular, it is not generally valid to base counterfactual simulations on the assumption that rational market participants would have expected the authorities to adhere rigidly to a partialiy state-contingent rule when policymakers, had they actually been confronted with the counterfactual history, would have sometimes had incentives to deviate from the rule.

## REFERENCES

Barro, Robert J., and David B. Gordon, “Rules, Discretion and Reputation in a Model of Monetary Policy,”

(Amsterdam), Vol. 12 (1983), pp. 101–21.*Journal of Monetary Economics*Canzoneri, Matthew B., “Monetary Policy Games and the Role of Private Information,”

(Nashville, Tennessee), Vol. 75 (1985), pp. 1056–70.*American Economic Review*Fischer, Stanley,

*“Rules Versus Discretion in Monetary Policy,” NBER Working Paper*2518 (Cambridge, Massachusetts: National Bureau of Economic Research, 1987).Flood,Robert P., and Peter M. Garber, “An Economic Theory of Monetary Reform,”

(Chicago), Vol. 88 (1980), pp. 22–58.*Journal of Political Economy*Flood,Robert P., and Peter M. Garber, “A Model of Stochastic Process Switching,”

(Evanston, Illinois), Vol. 51 (1983), pp. 537–51.*Econometrica*Gray, Jo Anna, “Wage Indexation: A Macroeconomic Approach,”

(Amsterdam), Vol. 2 (1976), pp. 221–35.*Journal of Monetary Economics*Isard, Peter, and Liliana Rojas-Suarez, “Velocity of Money and the Practice of Monetary Targeting: Experience, Theory, and the Policy Debate,” in International Monetary Fund,

(Washington, D.C., 1986), pp. 73–114.*Staff Studies for the World Economic Outlook*,Knight, Frank H.,

(Chicago: University of Chicago Press, 1985).*Risk, Uncertainty, and Profit*Kydland,Finn E., and Edward C. Prescott, “Rules Rather Than Indiscretion: The Inconsistency of Optimal Plans,”

(Chicago), Vol, 85 (1977), pp. 473–92.*Journal of Political Economy*Lucas, Robert E., Jr., “Expectations and the Neutrality of Money,”

(New York), Vol. 4 (1972), pp. 103–24.*Journal of Economic Theory*McCallum, Bennett T., “The Case for Rules in the Conduct of Monetary Policy: A Concrete Example,” in

(September-October 1987), pp. 10–18.*Federal Reserve Bank of Richmond Economic Review*,McCallum, Bennett T., “Robustness Properties of a Rule for Monetary Policy,” in

, Vol. 29, ed. by Karl Brunner and Bennett T. McCallum (Amsterdam and New York: North-Holland, 1988), pp. 173–203.*Money*,*Cycles, and Exchange Rales: Essays in Honor of Allan H. Meltzer*, Carnegie-Rochester Conference Series in Public PolicyRogoff, Kenneth, “The Optimal Degree of Commitment to an Intermediate Monetary Target,”

(Cambridge, Massachusetts), Vol. 100 (1985), pp. 1169–89.*Quarterly Journal of Economics*Rogoff, Kenneth, “Reputation, Coordination and Monetary Policy” (1987);

*forthcoming in*ed. by Robert J. Barro (New York: Cambridge University Press).*Handbook of Modern Business Cycle Theory*,

^{}*

Mr. Flood is a Senior Economist in the Financial Studies Division of the Research Department. He holds graduate degrees from the University of Rochester.

Mr. Isard is an Advisor in the Research Department. He holds degrees from the Massachusetts Institute of Technology and Stanford University.

The authors are grateful to Kenneth Rogoff, Elhanan Heipman, Dale Henderson, and seminar participants at the University of Michigan and the Fund for helpful comments and reactions.

^{}1

This single-period optimization framework abstracts from issues involving the “reputation” of the policymaker. See Rogoff (1987) for a survey of issues concerning reputation. See also Barro and Gordon (1983).

^{}2

If it is assumed that the logarithm of the production function is *y _{t}— λ+ θl_{t} + x_{t}* where l

_{t}is the logarithm of labor input,

*x*is the shock to the production function, and 0< θ < 1, then

_{t}*μ*

_{t}= x_{t}/

*(1*- θ)^{}3

See Rogoff (1985) for one possible elaboration of this approach. Rogoff defined *y* as the level of output (employment) that would arise if contracts could be negotiated after observing the productivity shock and alt other period-f information.

^{}5

Allowing correlations of the various shocks would introduce covariances into the later analysis but would not change any of the basic conclusions. We have refrained from analyzing exchange rate regimes in this setup because of the key role played in the literature on the choice of exchange rate regime by the covariances we are assuming away.

^{}6

” Ahhough the main points are robust to many relaxations of the white noise and independence assumptions about the shocks, things would be much more complicated in the realistic setting where the coefficient attached to fr, in equation (10) is not known with certamty.

^{}7

“In our view, much of the attraction of partially state-contingent rules—such as constant money growth rules, or nominal income targeting rules—stems from economists’ (apparently invincible) ignorance about many aspects of the relevant economic environment. In earher versions of this paper we attempted to discuss such ignorance in terms of Knight’s (1985) classic distinction between risk and uncertainty. These attempts reflected our conviction that it is important to emphasize the existence of Knightian uncertainty—or, as Fischer (1987) puts it, of contingencies that cannot be foreseen or described when formulating a rule— but also convinced us of the difficulty of incorporating such a concept, in a satisfactory way, into a formal economic model.

^{}8

It is assumed that policy strategies in this uncertain environment are evaluated by using the expectation of the loss function.

^{}9

From the structure of the model and the assumption of uncorrelated disturbances, it is intuitively clear that the optimal fully state-contingent rule must have a linear form.

^{}11

We are ignoring additional “accountability” considerations that would arise if the central bank had different preferences than society at large and thus would not seek to minimize the social loss function if left to its own discretion.

^{}12

” Formally, imposing the penalty on the private sector would work as well as imposing costs on the monetary authority, since the monetary authority is assumed to care about the well-being of the private sector.

^{}13

From the point of view of this example, it makes little difference whether society imposes the cost on itself (perhaps in the form of a costly institutional adjustment) or imposes the cost directly on the central bank (perhaps in the form of reduced bonuses or endless congressional testimony). We adopt the simplest structure by assuming that the cost is imposed on the monetary authority, and we assume that the cost is not a deadweight loss to society as a whole. Other examples can be constructed with alternative cost assumptions.

^{}14

To obtain this condition, substitute the conditional variance into equation (36) and set the derivative of this expression with respect to *q* equal to zero. Rearrange the resulting expression so that it becomes *k ^{2}=(a+q)^{2}q^{2}γ^{2}* Equation (37) then follows from taking the square root of each side of the above and rearranging.

^{}15

In recent years, monetary policy strategies have involved policy coordination among countries to encourage the depreciation of the U.S. dollar during a period following the Piaza Meeting of the Group of Five countries in September 1985, and to resist further large changes in exchange rates during the period since the Louvre Accord was announced in February 1987. See Isard and Rojas-Suarez (1986) for a review of the experience with targeting monetary aggregates.