Robust learning stability with operational monetary policy rules

We consider the robust stability of a rational expectations equilibrium, which we define as stability under discounted (constant gain) least-squares learning, for a range of gain parameters. We find that for operational forms of policy rules, ie rules that do not depend on contemporaneous values of endogenous aggregate variables, many interest-rate rules do not exhibit robust stability. We consider a variety of interest-rate rules, including instrument rules, optimal reaction functions under discretion or commitment, and rules that approximate optimal policy under commitment. For some reaction functions we allow for an interestrate stabilization motive in the policy objective. The expectations-based rules proposed in Evans and Honkapohja (2003, 2006) deliver robust learning stability. In contrast, many proposed alternatives become unstable under learning even at small values of the gain parameter.