The power of single equation tests for cointegration

Abstract

In recent research, Kanioura and Turner (2005) have proposed an F-test for cointegration based upon the joint significance of the level terms in an error correction model. In the present study, the analysis of this test is extended via comparison with the GLS-based cointegration test of Perron and Rodriguez (mimeo, 2001). The simulation evidence presented indicates that for the data generation process considered by Kanioura and Turner, the F-test possesses greater power than both the Engle-Granger and the GLS-based cointegration tests. An empirical examination of the relationship between UK non-durable consumers' expenditure and disposable income illustrates the findings of the simulation analysis, with the F-test alone able to reject the null of no cointegration between the series.

Notes

¹ In the present study, the properties of the alternative tests for cointegration are considered in a bivariate setting. However, all of the tests can be extended to the multivariate case.

² The critical values for this section are derived for the exact number of observations used. This is achieved via Monte Carlo simulation for the GLS-based and F-tests, and use of the response surface analysis of MacKinnon (1991) for the Engle-Granger test. The second stage of the Engle-Granger and GLS-based tests employ fifth order augmented Dickey-Fuller tests to avoid proeblems of serial correlation.

³ Following Kanioura and Turner (2005), a Newey-West heteroscedasticity and autocorrelation consistent variance-covariance matrix estimator is employed when performaing the cointegration F-test.