Further evidence on the size and power of the Bierens and Johansen cointegration procedures

Although both the Johansen (1991, 1994) trace test and Bierens (1997a,b) nonparametric lambda-min test for cointegration have good size properties in Monte Carlo studies by Hubrich, Lutkepohl, and Saikkonen (2001) and Boswijk, Lucas, and Taylor (2000), the Bierens test has very low power. In contrast, Bierens reports good power for his procedure. Meanwhile, Hubrich et al. and Boswijk et al. do not include Bierens' companion method for estimating the number of cointegrating vectors, nor do they investigate the effect of serial correlation on Bierens'' test. In the present paper, inclusion of the estimation step does not significantly degrade size of the Bierens procedure, even with serial correlation, but power is not improved. Serial correlation does degrade the size of the Johansen test, but it remains superior. Analysis of Bierens'' (1997b) Monte Carlo results suggests that their indication of high power reflects the test''s lack of scale invariance.