Optimal Monetary Policy in Markov-Switching Models with Rational Expectations Agents

In this paper we consider the optimal control problem of models with Markov regime shifts and forward-looking agents. These models are very general and flexible tools for modelling model uncertainty. An algorithm is devised to compute the solution of a linear rational expectations model with random parameters or regime shifts. This algorithm can also be applied in the optimisation of any arbitrary instrument rule. A second algorithm computes the time-consistent policy and the resulting Nash-Stackelberg equilibrium. Similar methods can be easily employed to compute the optimal policy under commitment. Furthermore, the algorithms can also handle the case in which the policymaker and the private sector hold different beliefs. We apply these methods to compute the optimal (non-linear) monetary policy in a small open economy subject to random structural breaks in some of its key parameters