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.