Size properties of cointegration tests in misspecified systems

Abstract

The small sample size properties of three frequently used cointegration tests when a system has been misspecified are investigated. Specifically, the misspecification consists of one relevant variable being omitted from a system with one cointegrating vector. A Monte Carlo study shows that the Johansen (1991) trace test, adjusted by a simple finite sample correction, has the most robust behaviour when lag length in the test equations is chosen according to traditional information criteria.

Acknowledgements

I am grateful to Meredith Beechey, Michael Jansson, Per Jansson, Rolf Larsson, Thomas Lindh and seminar participants at Uppsala University for valuable comments on this paper. Financial support from Sparbankernas Forskningsstiftelse and Jan Wallander's and Tom Hedelius’ foundation is gratefully acknowledged.

Notes

See for instance Engle and Granger (1987).

In this paper only the essential equations will be presented and for a detailed discussion of the different tests, the reader is referred to the articles cited above.

T refers to sample size, n to the number of variables in the VAR and p to the number of lags.

Lag length for the Johansen test is established by applying the information criteria to the VAR in levels with a maximum lag length of four, thereby determining p. Rewriting the VAR in the form of Equation 6, this translates into a maximum lag length of p−1 equal to three.

See Österholm (2003) for a detailed description of the results.