Macro models of monetary policy typically involve forward looking behavior. Except in rare circumstances, we have to apply some numerical method to find the optimal policy and the rational expectations equilibrium. This paper summarizes a few useful methods, and shows how they can be combined with a Kalman filter to estimate the deep model parameters with maximum likelihood. Simulations of a macro model with staggered price setting, interest rate elastic output, and optimal monetary policy illustrate the properties of this estimation approach.
