Testing for Cointegration in Misspecified Systems - A Monte Carlo Study of Size Distortions

When dealing with time series that are integrated of order one, the concept of cointegration becomes crucial for the specification of a model. Using the best available tests, one can reduce the probability of estimating econometric models that are misspecified. This paper investigates the small sample performance of four well-known cointegration tests when a system has been misspecified by leaving out one relevant explanatory variable from a system with one cointegrating vector. In a Monte Carlo study, the size distortions of the Augmented Engle-Granger (Engle and Granger, 1987), Johansen's (1988) maximum eigenvalue, Johansen's (1991) trace and the Boswijk (1989) Wald tests are examined. The Johansen trace test adjusted by the finite sample correction of Reinsel and Ahn (1988) is found to have the most robust performance when lag length in the test equations is chosen according to traditional information criteria.