On the Solution of Markov-switching Rational Expectations Models

Abstract

This paper describes a method for solving a class of forward-looking Markov-switching Rational Expectations models under noisy measurement, by specifying the unobservable expectations component as a general-measurable function of the observable states of the system, to be determined optimally via stochastic control and filtering theory. Solution existence is proved by setting this function to the regime-dependent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight autoregressive Markov jump state motion. As the exact expression of the conditional (rational) expectations term is derived both in finite and infinite horizon model formulations, no (asymptotic) stationarity assumptions are needed to solve forward the system, for only initial values knowledge is required. A simple sufficient condition for the mean-square stability of the obtained rational expectations equilibrium is also provided.Rational Expectations, Markov-switching dynamic systems, Dynamic programming, Time-varying Kalman filter