Stochastic Policy Design for Models with Rational Expectations and Time-Varying Parameters

In this paper, we present a method for using rational expectations in a stochastic linear-quadratic optimization framework in which the unknown parameters are updated through a learning scheme. We use the QZ decomposition as suggested by Sims (1996) to solve the rational-expectations part of the model. Parameter updating is done with a Kalman filter, and the optimal control is calculated using the variances and covariances of the uncertain time-varying parameter.