Efficient perturbation methods for solving regime-switching DSGE models

In an environment where economic structures break, variances change, distributions shift, conventional policies weaken and past events tend to reoccur, economic agents have to form expectations over different regimes. This makes the regime-switching dynamic stochastic general equilibrium (RS-DSGE) model the natural framework for analyzing the dynamics of macroeconomic variables. We present effcient solution methods for solving this class of models, allowing for the transition probabilities to be endogenous and for agents to react to anticipated events. The solution algorithms derived use a perturbation strategy which, unlike what has been proposed in the literature, does not rely on the partitioning of the switching parameters. These algorithms are all implemented in RISE, a exible object-oriented toolbox that can easily integrate alternative solution methods. We show that our algorithms replicate various examples found in the literature. Among those is a switching RBC model for which we present a third-order perturbation solution.