Tests for Long-Run Granger Non-Causality in Cointegrated Systems

In this paper, we propose a new approach to test the hypothesis of long-run Granger non-causality in cointegrated systems. We circumvent the problem of singularity of the variance-covariance matrix associated with the usual Wald type test by proposing a generalized inverse procedure, and an alternative simple procedure which can be approximated by a suitable chi-square distribution. A test for the ranks of submatrices of the cointegration matrix and its orthogonal matrix plays a vital role in the former. The relevant small sample experiments indicate that the proposed method performs reasonably well in finite samples. As empirical applications, we examine long-run causal relations among long-term interest rates of three and five nations.