سادگی در مقابل بهینگی : انتخاب قواعد سیاست پولی که ماموران باید یاد بگیرند

The normal assumption of full information is dropped and the choice of monetary policy rules is instead examined when private agents must learn the rule. A small, forward-looking model is estimated and stochastic simulations conducted with agents using discounted least squares to learn of a change of preferences or a switch to a more complex rule. We find that the costs of learning a new rule may be substantial, depending on preferences and the rule that is initially in place. Policymakers with strong preferences for inflation control incur substantial costs when they change the rule in use, but are nearly always willing to bear the costs. Policymakers with weak preferences for inflation control may actually benefit from agents’ prior belief that a strong rule is in place.

In recent years, there has been a renewed interest in the governance of monetary policy through the use of rules. This has come in part because of academic contributions including those of Hall and Mankiw (1994),McCallum (1987),Taylor, 1993 and Taylor, 1994, and Henderson and McKibbin (1993). It has also arisen because of adoption in a number of countries of explicit inflation targets. New Zealand (1990), Canada (1991), the United Kingdom (1992), Sweden (1993) and Finland (1993) have all announced such regimes. The academic papers noted above all focus on simple ad hoc rules. Typically, very simple specifications are written down and parameterized either with regard to the historical experience, such as Taylor (1993), or through simulation experiments as in Henderson and McKibbin (1993), or McCallum (1987). Both the simplicity of these rules, and the evaluation criteria used to judge them stand in stark contrast to the earlier literature on optimal control. Optimal control theory wrings all the information possible out of the economic model, the nature of the stochastic shocks borne by the economy, and policymakers’ preferences. This, however, may be a mixed blessing. As a tool for monetary policy, optimal control theory has been criticized on three related grounds. First, the optimization is conditional on a large set of parameters, some of which are measured imperfectly and the knowledge of which is not shared by all agents. Some features of the model are known to change over time, often in imprecise ways. The most notable example of this is policymakers’ preferences which can change either `exogenously’ through the appointment process, or `endogenously’ through the accumulation of experience.1 Second, optimal control rules are invariably complex. The arguments to an optimal rule include all the state variables of the model. In working models used by central banks, state variables can number in the hundreds. The sheer complexity of such rules makes them difficult to follow, difficult to communicate to the public, and difficult to monitor. Third, in forward-looking models, it can be difficult to commit to a rule of any sort. Time inconsistency problems often arise. Complex rules are arguably more difficult to commit to, if for no reason other than the benefits of commitment cannot be reaped if agents cannot distinguish commitment to a complex rule and mere discretion. Simple rules are claimed to avoid most of these problems by enhancing accountability, and hence the returns to precommitment, and by avoiding rules that are optimal only in idiosyncratic circumstances. At the same time, simple rules still allow feedback from state variables over time, thereby avoiding the straightjacket of `open-loop’ rules, such as Friedman's k-percent money growth rule. The costs of this simplicity include the foregone improvement in performance that a richer policy can add. This paper examines the friction between simplicity and optimality in the design of monetary policy rules. With complete information, rational expectations, and full optimization, the correct answer to the question of the best rule is obvious: optimal control is optimal. However, the question arises of how expectations come to be rational in the first place. Rational expectations equilibria are sometimes justified as the economic structure upon which the economy would eventually settle down once a given policy has been in place for a long time.2 But if learning is slow, a policymaker must consider not only the relative merits of the old and prospective new policies in steady state, but also the costs along the transition path to the new rule. Conceivably, these costs could be high enough to induce the authority to select a different new rule, or even to retain the old one despite misgivings as to its steady-state performance. With this in mind, we allow two elements of realism into the exercise that can alter the basic result. First, we consider optimal rules subject to a restriction on the number of parameters that can enter the policy rule – a simplicity restriction. We measure the cost of this restriction by examining whether transitions from 2-parameter policy rules to 3-parameter rules are any more difficult than transitions to other 2-parameter rules. Second we restrict the information available to private agents, requiring them to learn the policy rule that is in force. In relaxing the purest form of the rational expectations assumptions, we follow the literature on learning in macroeconomics associated with Taylor (1975) and Cripps (1991) and advanced by Sargent (1993). We are then in a position to ask the question: if the Fed were to precommit to a rule in the presence of a skeptical public, what form should the rule take? If the Fed knew the true structure of the economy, would the rule that is optimal under full information still be optimal when private agents would have to learn the rule? Or would something simpler, and arguably easier to learn, be better in practice? In typical examinations of the design of monetary policy rules, such as Taylor (1979),Levin et al. (1998),Rudebusch and Svensson (1999) and Williams (1999), the transition costs of migrating to the proposed new rule are ignored. Instead, the focus is entirely on alternative steady states. Similarly, the simplicity of rules is exogenously assumed. One of the aims of this paper is to remedy this oversight. To examine these questions, we estimate a small forward-looking macro model with Keynesian features and model the process by which agents learn the features of the policy rule in use. The model is a form of a contracting model, in the spirit of Taylor (1980) and Calvo (1983), and is broadly similar to that of Fuhrer and Moore (1995b). We construct the state-space representation of this model and conduct stochastic simulations of a change in the policy rule, with agents learning the structural parameters of the linear monetary policy rule using recursive least squares, and discounted recursive least squares. Solving for the state-space representation of a forward-looking model with learning represents a bit of a numerical hurdle because the model, as perceived by private agents, changes every period. Thus an additional contribution of this paper is the adaptation and exploitation of efficient methods for rapidly solving and manipulating linear rational expectations models. The rest of this paper proceeds as follows. In Section 2 we discuss the simple, macroeconomic model. Section 3 outlines our methodological approach. Section 4 provides our results. The fifth and final section offers some concluding remarks.

This paper has examined the implications for the design of monetary policy rules of the complexity of rules and the interaction of complexity and preferences with the process of learning by private agents of the inflation-targeting rule that is in place. In particular, we took a small New Keynesian macroeconometric model and computed optimal simple rules for two sets of preferences: strong preferences for inflation control, where a substantial penalty is attached to inflation variability and only a small weight on output or instrument variability; and weak preferences for inflation control, where the same substantial weight is placed on output variability. Then we compared the stochastic performance of these policies that would have been optimal within a single regime to two types of transition experiments. The first was the transition to more complex rules from simpler rules, within a single regime. The second was the transition between regimes for a simple optimal rule of given complexity. Our four basic findings are: (1) learning should be expected to be a slow process. Even when agents `forget’ the past with extraordinary haste, it takes more than 10 years for agents to learn the correct parameters of a new rule. (2) The costs of these perceptual errors can vary widely, depending on the rule that is initially in force, and on the preferences of the monetary authority. In particular, a strong inflation-targeting monetary authority tends to find high costs associated with the need for agents to learn a new (strong) rule that has been put in place. It follows that such a policymaker should be willing to take steps to identify his policy preferences to private agents. Paradoxically, a weak policymaker will sometimes benefit from being misperceived, posting a better economic performance than would have been the case if the optimal rule had been in place all along. This sharp contrast in results has to do with the multiplicity of sources of shocks to inflation, the nature of inflation in this model being a forward-looking variable, and the fact that inflation appears later in the chain of the monetary policy transmission mechanism than does output. (3) The performance, in steady state, of optimal two-parameter policy rules is not much worse than the performance of optimal three-parameter policy rules, at least for this model. Largely for this reason, some policymakers that would like to move from a suboptimal rule would be better off moving to the optimal 2-parameter rule, and forsaking the 3-parameter rule, than bearing the incremental costs of private agents having to learn the more complicated rule. (4) Faster learning is not necessarily better. When the monetary authority takes steps to `actively teach’ private agents that the rule has changed, agents’ expectations converge more rapidly on the new and true parameters, but economic performance does not necessarily improve. This is because the policymaker himself must add instrument variability to the system in order to hasten the learning, and because initial benefits of more rapid learning are `given back’ when learning slows down later on.