The Size and Power of Bootstrap Tests for Linear Restrictions in Misspecified Cointegrating Relationships

Abstract

This paper considers computer intensive methods for inference on cointegrating vectors in maximum likelihood analysis. It investigates the robustness of LR , Wald tests and an F-type test for linear restrictions on cointegrating space to misspecification on the number of cointegrating relations. In addition, since all the distributional results within the maximum likelihood cointegration model rely on asymptotic considerations, it is important to consider the sensitivity of inference procedures to the sample size. In this paper we use bootstrap hypothesis testing as a way to improve inference for linear restriction on the cointegrating space. We find that the resampling procedure is a very useful device for tests that lack the invariance property such as the Wald test, where the size distortion of the bootstrap test converges to zero even for a sample size T=50. Moreover, it turns out that when the number of cointegrating vectors are correctly specified the bootstrap succeeds where the asymptotic approximation is not satisfactory, that is, for a sample size T