Forward Looking Behavior and Learning in Stochastic Control

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Abstract
One drawback of the standard control methods in eco nomics is that they lack the possibility to model for ward looking behavior. We present a method that in corporates forward looking behavior into the stochas tic 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 learn ing. The resulting algorithm is numerically intensive; consequently, vectorization and parallel computing are necessary to compute the optimal solution of the con trol variables. Our first experiments with the algorithm, done with the MacRae model and a modified version of the Sargent and Wallace model, indicate that the standard result of ineffectiveness of monetary policy might not hold in the stochastic control framework. With parameter uncertainty, discretionary policy gener ally performs better than a fixed control rule. The rea son is that when there is parameter uncertainty the learning of these parameters can influence the expec tation effect counteracting the discretionary policy.