Robustifying Learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought after goals of policy design. And while some contributions to the literature (for example Bullard and Mitra (2001) and Evans and Honkapohja (2002)) have made significant headway in establishing certain features of monetary policy rules that facilitate learning, a comprehensive treatment of policy design for learnability has yet to surface, especially for cases in which agents have potentially misspecified their learning models. This paper provides such a treatment. We argue that since even among professional economists a generally acceptable workhorse model of the economy has not been agreed upon, it is unreasonable to expect private agents to have collective rational expectations. We assume instead that agents have an approximate understanding of the workings of the economy and that their task of learning true reduced forms of the economy is subject to potentially destabilizing errors. We then ask: can a central bank set policy that accounts for learning errors but also succeeds in bounding them in a way that allows eventual learnability of the model, given policy. For different parameterizations of a given policy rule applied to a New Keynesian model, we use structured singular value analysis (from robust control) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE. A parallel set of experiments seeks to determine the optimal stance (strong inflation as opposed to strong output stabilization) that allows for the greatest scope of errors in learning without leading to expectational instabilty in cases when the central bank designs both optimal and robust policy rules with commitment. We compare the features of all the rules contemplated in the paper with those that maximize economic performance in the true model, and we measure the performance cost of maximizing learnability under the various conditions mentioned here.