Learning and the Complexity of Monetary Policy Rules

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 trite: optimal control is optimal. However, rational expectations can be expected to prevail only in the steady state, since only then will agents have sufficient knowledge to formulate a rational expectation. This means that changes in policy must consider not only the relative merits of the old and prospective new policies, but also the costs along the transition path to the new rule brought about by the induced break from rational expectations. With this in mind, we allow two elements of realism into the exercise that can alter the trite 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 examine the marginal cost of this restriction. 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 pre-commit 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 have to learn the rule? Or would something simpler, and arguably easier to learn, be better in practice? Or would learning a new rule be so costly that an optimizing monetary authority would choose to accept the incumbent rule no matter what it might be? 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 similar to that of Fuhrer and Moore (1995). With this model, we conduct stochastic simulations of a change in the policy rule, with agents learning the structural parameters of the linear rule using recursive least squares, and discounted recursive least squares. Doing these sorts of experiments in an economy that is forward-looking obliges us to exploit modern efficient algorithms for computing state-space representations of the forward-looking model in real time