State Space Models With Endogenous Regime Switching

This article studies the estimation of state space models whose parameters are switching endogenously between two regimes, depending on whether an autoregressive latent factor crosses some threshold level. Endogeneity stems from the sustained impacts of transition innovations on the latent factor, absent from which our model reduces to one with exogenous regime switching. Due to the flexible form of state space representation, this class of models is broad, including classical regression models and the popular dynamic stochastic general equilibrium (DSGE) models as special cases. We develop a computationally efficient filtering algorithm to estimate the nonlinear model. The algorithm is shown to be accurate in approximating both the likelihood function and filtered state variables. We also apply the filter to estimate a small-scale DSGE model with threshold-type switching in monetary policy rule, and find that the Bayes factor decisively favors the endogenous switching version of the DSGE model over the fixed regime case. Overall, our approach provides a greater scope for understanding the complex interaction between regime switching and measured economic behavior