TESTING LINEAR RESTRICTIONS ON COINTEGRATING VECTORS: SIZES AND POWERS OF WALD AND LIKELIHOOD RATIO TESTS IN FINITE SAMPLES

Abstract

The Wald test for linear restrictions on cointegrating vectors is compared in finite samples using the Monte Carlo method. The Wald test is calculated within the vector error-correction based estimation methods of Bewley, Orden, Yang, and Fisher (1994, Journal of Econometrics 64, 3–27) and of Johansen (1991, Econometrica 59, 1551–1580), the canonical cointegration method of Park (1992, Econometrica 60, 119–143), the dynamic ordinary least squares method of Phillips and Loretan (1991, Review of Economic Studies 58, 407–436), Saikkonen (1991, Econometric Theory 7, 1–21), and Stock and Watson (1993, Econometrica 61, 783–820), the fully modified ordinary least squares method of Phillips and Hansen (1990, Review of Economic Studies 57, 99–125), and the band spectral techniques of Phillips (1991, in W. Barnett, J. Powell, & G. E. Tauchen (eds.), Nonparametric and Semiparametric Methods in Economics and Statistics, pp. 413–435). The Wald test performance is also compared to that of the likelihood ratio test suggested by Johansen and Juselius (1990, Oxford Bulletin of Economics and Statistics 52, 169–210) and to a Bartlett correction of that test as proposed by Johansen (1998, A Small Sample Test for Tests of Hypotheses on Cointegrating Vectors, European University Institute).