Granger causality and regime inference in Markov switching Var models with bayesian methods

In this paper, we derive restrictions for Granger noncausality in MS-VAR models and show under what conditions a variable does not affect the forecast of the hidden Markov process. To assess the noncausality hypotheses, we apply Bayesian inference. The computational tools include a novel block Metropolis–Hastings sampling algorithm for the estimation of the underlying models. We analyze a system of monthly US data on money and income. The results of testing in MS-VARs contradict those obtained with linear VARs: the money aggregate M1 helps in forecasting industrial production and in predicting the next period’s state.