Small Sample Properties of Certain Cointegration Test Statistics: A Monte Carlo Study

Abstract

This paper reports on the results of a Monte Carlo study. The latter investigates the performance of various versions of the Conformity test CCT$ for the existence and rank of cointegration, as given in Dhrymes (1996b), the likelihood ratio test LRT as given in Johansen (J) (1988), (1991), and the stochastic trends test (SW), as given in Stock and Watson (1988).

The design of the experiments allows for small, medium and large stationary roots, and one, two, and three unit roots. The largest system investigated is a quadrivariate VAR(4).

Results based on the underlying normal theory indicate that the performance of the CCT is extremely good when the null hypothesis involves the sum of, or individual, (characteristic) roots, some of which are not zero; it does not perform reliably when the sum of the roots under the null involves, in truth,all zero roots.

Results based on non-standard asymptotic theory for estimators of zero roots indicate that the CCT has very good power characteristics in detecting the rank of cointegration, but it exhibits some size distortions that can potentially lead to overestimation of the true cointegrating rank. On the other hand, both versions are robust to non normal and dependent error structures. Such results generally hold for sample sizes 100 and 500.

For samples of size 100, the LR test performs quite well, in terms of size, when the error process is Gaussian and when small and medium stationary roots are employed in the experimental design, but performs rather poorly in terms of power. The problem is magnified with large stationary roots, and/or non-normal errors. The results improve, as expected, for sample size 500.

The SW test performs rather poorly overall, and cannot be recommended for use in empirical applications.

JEL Classification: C4