Rules vs. discretion under computability constraints

I describe a class of models for monetary policy in which rationality is bounded by the requirement of algorithmic computability. Essentially, I add a computability constraint to the canonical model of Barro and Gordon (1983b). Discretionary policy increases uncertainty for the public and makes it difficult for the policymaker to anticipate the public's reactions to policy. With discretionary policy and computability-constrained agents the public and the policymaker are unable to outguess one another, and there is no rational procedure that ensures the convergence of expectations. When the policymaker follows a rule, however, expectations converge and uncertainty is reduced for both the public and the policymaker.