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

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) test and Kremers et al.’s (Oxford Bulletin of Economics and Statistics, 54(3), 325–48, 1992) 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.