Perturbation Methods for Markov-Switching Models

This paper develops a methodology for approximating rational expectations models with Markov Switching. Specifically, we consider how to do both linear and higher-order approximations, including cases when each individual regime is associated with it's own steady state. We document the importance of using higher-order approximations in economies that have parameter switching that affects variances. We illustrate our algorithm by considering a standard real business cycle economy with Markov switching in total factor productivity drift and variance and assess the accuracy of our approximations. Our method allows for further empirical analysis of economies with Markov switching.