Tests for long-run Granger non-causality in cointegrated systems

In this article, 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 covariance matrix associated with the usual Wald-type test by proposing a generalized inverse procedure. A test for the ranks of submatrices of the cointegration matrix and its orthogonal matrix plays a vital role in our procedure. 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 nations.