Markov-Switching Models with Unknown Error Distributions: Identification and Inference Within the Bayesian Framework

Abstract

The basic Markov-switching model has been extended in various ways ever since the seminal work of Hamilton (1989. “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.” Econometrica 57: 357–84). However, the estimation of Markov-switching models in the literature has relied upon parametric assumptions on the distribution of the error term. In this paper, we present a Bayesian approach for estimating Markov-switching models with unknown and potentially non-normal error distributions. We approximate the unknown distribution of the error term by the Dirichlet process mixture of normals, in which the number of mixtures is treated as a parameter to estimate. In doing so, we pay special attention to the identification of the model. We then apply the proposed model and MCMC procedure to the growth of the postwar U.S. industrial production index. Our model can effectively control for irregular components that are not related to business conditions. This leads to sharp and accurate inferences on recession probabilities.