Forward Looking Behavior and Learning in Stochastic Control

Acknowledgment We would like to thank Sudhakar Achath, Ray Fair and two anonymous referees for their useful comments on an earlier version of this paper. Summary One of drawbacks of the standard control methods in economics is that they lack the possibility to model forward looking behavior. In this paper we present a method that incorporates forward looking behavior into the stochastic control framework by augmenting the system equation with expectational variables. By adapting the Fair-Taylor approach for simulation models, we have constructed an algorithm for solving stochastic linear quadratic control models with expectations and learning. The resulting algorithm is numerically very intensive and consequently supercomputing techniques like vectorization and parallel computing have to be applied to compute the optimal solution of the control variables. Our first experiments with the algorithm have been done with the MacRae model and with a modified version of the Sargent and Wallace model. These experiments indicate that the standard result of ineffectiveness of monetary policy might not hold in the stochastic control framework. If parameter uncertainty is present, discretionary policy generally performs better than a fixed control rule. The reason for this is that when there is parameter uncertainty the learning of these parameters can influence the expectation effect counteracting the discretionary policy.