Simulating competing cointegration tests in a bivariate system

In this paper, we consider the size and power of a set of cointegration tests in a number of Monte Carlo simulations. The behaviour of the competing methods is investigated in diff erent situations, including diff erent levels of variance and correlation in the error processes. The impact of violations of the common factor restriction (CFR) implied by the Engle-Granger framework is studied in these situations. The reactions to changes in the CFR condition depend on the error correlation. When the correlation is non-positive, the power increases with increasing CFR violations for the error correction model (ECM) test, while the other tests react in the opposite direction. We also note the reaction to diff erences in the error variances in the data-generating process. For positive correlation and equal variances, the reaction to changes in the CFR violations diff ers somewhat between the tests. We conclude that the ECM and the Z-tests show the best performance over diff erent parameter combinations. In most situations the ECM is best. Therefore, if we had to recommend a unit root test, it would be the ECM, especially for small samples. However, we do not think that one should use just one test, but two or more. Of course, the portfolio of tests we have considered here only represents a subset of the possible tests.