Critical values for an F-test for cointegration in a multivariate model

Abstract

Critical values for a test for cointegration are generated based on the joint significance of the levels terms in an error-correction equation. It is shown that the appropriate critical values are higher than those derived from the standard F-distribution. The power properties of this test are compared with those of the Engle–Granger (Econometrica, 55, 251–76, 1987 Ericsson, NR and MacKinnon, JG. 2002. Distributions of error-correction tests for cointegration. Econometrics Journal, 5: 285–318. [Crossref] , [Google Scholar]) test and Kremers et al.'s (Oxford Bulletin of Economics and Statistics, 54(3), 325–48, 1992 Kremers, JJM, Ericsson, N and Dolado, JJ. 1992. The power of cointegration tests. Oxford Bulletin of Economics and Statistics, 54(3): 325–48. [Crossref], [Web of Science ®] , [Google Scholar]) t-test based on the t-statistic from an error-correction equation. The F-test has higher power than the Engle–Granger test but lower power than the t-form of the error-correction test. However, the F-form of the test has the advantage that its distribution is independent of the parameters of the problem being considered. Finally, a test is considered for cointegration between UK and US interest rates. It is shown that the F-test rejects the null of no cointegration between these variables although the Engle–Granger test fails to do so.

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