THE POWER OF SINGLE EQUATION TESTS FOR COINTEGRATION WHEN THE COINTEGRATING VECTOR IS PRESPECIFIED

Eric Zivot

Econometric Theory, 2000, vol. 16, issue 03, pages 407-439

Abstract: In this paper I present an alternative derivation of the asymptotic distribution of Kremers, Ericsson, and Dolado s (1992, Oxford Bulletin of Economics and Statistics 54, 325 348) conditional error correction model (ECM) based t-test for cointegration with a single prespecified cointegrating vector. This alternative distribution, which is identical to the distribution of Hansen s (1995, Econometric Theory 11, 1148 1171) covariate augmented t-test for a unit root, is valid for weakly exogenous regressors and depends on a consistently estimable nuisance parameter that takes on values in the unit interval. I show analytically, using asymptotic power functions based on near-cointegrated alternatives, that the ECM t-test with a prespecified cointegrating vector can have much higher power than single equation tests for cointegration based on estimating the cointegrating vector. I also characterize situations in which the ECM t-test computed with a misspecified cointegrating vector will have high power.

Date: 2000
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