Bayesian Inference of Multivariate Regression Models with Endogenous Markov Regime-Switching Parameters*

Abstract

This study introduces a multivariate regression model with endogenous Markov regime-switching parameters, in which the regression disturbances and regime switches are allowed to be instantaneously correlated. For the estimation and model comparison, we develop a posterior sampling algorithm for the parameters, regimes, and marginal likelihood calculation. We demonstrate the reliability of the proposed method using simulation and empirical studies. The simulation study shows that neglecting the endogeneity leads to inaccurate parameter estimates, and that our marginal likelihood comparison chooses a correctly specified model. In the business cycle application, we find that the joint dynamics of the U.S. industrial production index (IPI) growth and unemployment rates are subject to three-state endogenous regime shifts. Another application to stock and bond return data suggests that negative shocks to the stock return seem to cause regime shifts from a low volatility state to a high volatility state of the financial markets. (JEL: C11, C53, E43, G12)