Determining the number of cointegrating relations under rank constraints

This paper proposes likelihood-based procedures for determining the number of cointegrating vectors in the presence of constraints on the cointegration rank. The tests can be applied when a priori information suggests a lower bound on the number of common stochastic trends in the system. The likelihood ratio trace and and lambda max tests are obtained as special cases of the present setup. The tests are easy to implement and have comparable asymptotic power with respect to the trace test; it is also shown that the constrained tests are more powerful for some local alternatives.