This paper analyses three Granger noncausality hypotheses within a conditionally Gaussian MS-VAR model. Noncausality in mean is based on Granger´s original concept for linear predictors by defining noncausality from the 1-step ahead forecast error variance for the conditional expectation. Noncausality in mean-variance concerns the conditional forecast error variance, while noncausality in distribution refers to the conditional distribution of the forecast errors. Necessary and sufficient parametric conditions for noncausality are presented for all hypotheses. As an illustration, the hypotheses are tested using monthly postwar U.S. data on money and income. We find that money is not Granger causal in mean for income, but Granger causal in mean-variance, i.e there is unique information in money for predicting the next period regime and the regime affects the uncertainty about the income forecast.
Granger causality Markov process Regime switching Vector autoregression