The Consistency of Optimal Policy in Stochastic Rational Expectations Models

This paper extends the work of Barro and Gordon (1983) to general linear models with rational expectations. We examine the question whether the optimal policy rule, i.e. the one that a government which could pre-commit itself would use, can be sustained as a consistent rule in the sense defined by Kydland and Prescott (1977) if the reputational effects similar to those described by Barro and Gordon operate. The analysis is carried out in the context of an infinite horizon game between the government and private sector agents in the economy. We are able to show that, providing the support of the distribution of shocks hitting the economy is bounded, and providing the discount rate in the government objective function is low enough, the optimal policy rule can be sustained as a consistent policy in general. We obtain solutions for the optimal policy rule and the consistent policy rule using straightforward recursive methods and dynamic programming, and show that control theory can be made applicable to economic planning even when expectations are rational (pace Kydland and Prescott, 1977).