The Granger Non-Causality Test in Cointegrated Vector Autoregressions

The usual Wald test for the Granger non-causality in cointegrated vector autoregressive (VAR) processes is known to have the asymptotically non-standard distribution. There have been proposed a few alternative (inefficient) methods which give the asymptotically standard distribution. However, their power of test is relatively low because of their inefficiency. In this paper, we propose a procedure that always gives the asymptotically standard distribution with higher power of test than the alternative ones, by suitably combining the usual Wald test and the alternative ones, based upon the certain rank condition of the submatrix of the cointegration matrix. We also propose a simple modifications to the test statistics in order to obtain reasonable empirical size of test in finite samples. The relevant Monte Carlo experiment reveals that our proposed procedure works favorably in finite samples in comparison with conventional tests.