Analytical Evaluation of the Power of Tests for the Absence of Cointegration

This paper proposes a theoretical explanation to the common empirical results in which different tests for cointegration give different answers. Using local to unity parametrization I compute the analytical power of some tests for the null of no cointegration: The ADF test on the residuals of the cointegration regression, Johansen's maximum eigenvalue test, the t-test on the Error Correction term and Boswijk (1994) Wald test. The tests are shown to be functions of Brownian Motions and Ornstein-Uhlenbeck processes and to depend on a single nuisance parameter, which is, in turn determined by the correlation at frequency zero of the independent variables with the errors of the cointegration regression. Monte Carlo experiments show that the tests can have significantly different performances for different values of the nuisance parameter. An application to the money demand equation is presented.