A Test for the Null of Multiple Cointegrating Vectors

This paper examines a test for the null of cointegration in a multivariate system based on the discrepancy between the OLS estimator of the full set of n cointegrating relationships in the n + k system and the OLS estimator of the corresponding relationships among first differences without making specific assumptions about the short-run dynamics of the multivariate data generating process.  It is shown that the proposed test statistics are asymptotically distributed as standard chi-square with n + k degrees of freedom and are not affected by the inclusion of deterministic terms or dynamic regressors, thus offering a simple way of testing for cointegration under the null without the need of special tables.  Small sample critical values for these statistics are tabulated using Monte Carlo simulation and it is shown that these non residual-based tests exhibit appropriate size and good power even for quite general error dynamics.  In fact, simulation results suggest that they perform quite reasonably when compared to other tests of the null of cointegration.