Comment on "Adaptive Learning and Monetary Policy Design"

The original motivation for investigating the stability of rational expectations equilibria (REE) under learning was to provide a microfoundation for how agents might come to hold rational expectations. "Learnability" (or expectational stability) of REE was later proposed as an equilibrium selection criterion in environments with multiple equilibria. In this paper, Evans and Honkapohja survey and address frontier issues in a very promising new application of learning analysis: the design of monetary policy rules.

This new application has been made possible by the introduction of a simple, linear, microfounded "New Keynesian" model (described, e.g., in Clarida, Galí, and Gertler 1999), where monetary policy plays a critical role in determining the nominal interest rate. The model of the private sector consists of two equations:

The "IS" equation (Equation 1) has the output gap, x_t, depending on the nominal interest rate, i_t, as well as on expectations of future inflation Eπ_t+1, the future output gap, Ex_t+1, and a demand shock, g_t. The price-setting equation (Equation 2) derives from the staggered sticky price literature and has current inflation, π_t, dependent on the current output gap, expected future inflation, and a supply shock, u_t. The model is closed by the addition of a policy rule that the monetary authority uses to set the nominal interest rate, i_t.

The presence in this model of expectations of future inflation and output leads naturally to questions regarding the determinacy or indeterminacy of the REE. But, it leads just as naturally to questions concerning the stability of REE under adaptive learning behavior. Evans and Honkapohja rightfully place learnability of REE at the same level of importance as determinacy, though the two are independent criteria.

Satisfaction of both criteria is highly desirable. Determinacy means that an REE is locally unique so that standard comparative statics exercises can be conducted. Learnability implies that agents need not initially know the REE so long as their model specification—their "perceived law of motion"—nests the REE solution as a special case. If the parameter-updating procedure leads agents to the REE, this equilibrium is pronounced learnable, otherwise it is not learnable (it is expectationally unstable). Learnability of REE under a particular monetary policy rule can be further distinguished from transparency of monetary policy; the latter is concerned with how well the private sector understands the goals and instruments of monetary policy. By contrast, in the learning analysis of Evans and Honkapohja, private sector agents need not be aware that a monetary authority even exists so long as their perceived laws of motion are of the same form as the reduced form equations of the model environment.

Evans and Honkapohja primarily focus on determinacy and learnability of REE in the New Keynesian model under optimal monetary policy rules, i.e., rules derived from minimization of a policy loss function over an infinite horizon with discounting, where the loss function in period t is , and is a target level of inflation. They also examine an interest rate rule introduced by McCallum and Nelson (2000) that seeks to approximate optimal monetary policy—which they call the "approximate targeting" (AT) rule. By contrast, Bullard and Mitra (2002) consider the determinacy and learnability of REE under "instrument rules," consisting of versions of Taylor's rule. Optimal policy rules are derived under assumptions that the policy maker can or cannot commit to maintenance of the policy in future periods. In either case, optimal policy rules are shown to come in two varieties, "fundamentals based" (FB) and "expectations based" (EB); the EB rule nests the FB rule, but adds private sector expectations of future inflation and output. Evans and Honkapohja find that FB rules do not always lead to determinate REE, and furthermore, these REE are never expectationally stable. The latter finding means that if agents did not initially possess knowledge of the REE and monetary policy followed the FB rule, then the agents' parameter-updating process would, over time, lead them further away from the REE, an undesirable outcome. On the other hand, the EB rules, as well...