Unit Roots, Cointegration and Pre-Testing in VAR Models∗

This chapter investigates the robustness of impulse response estimators to near unit roots and near cointegration in VAR models. We compare estimators based on VAR specifications determined by pre-tests for unit roots and cointegration as well as unrestricted VAR specifications in levels. Our main finding is that the impulse response estimators obtained from the levels specification tend to be most robust when the magnitude of the roots is not known. The pre-test specification works well only when the restrictions imposed by the model are satisfied. Its performance deteriorates even for small deviations from the exact unit root for one or more model variables. We illustrate the practical relevance of our results through simulation examples and an empirical application. ∗We would like to thank the participants at the 12th Annual Advances in Econometrics Conference for useful feedback. We are particularly indebted to Lutz Kilian for numerous detailed comments and insightful suggestions that substantially improved the presentation of the chapter. Nikolay Gospodinov gratefully acknowledges financial support from FQRSC and SSHRC. †Department of Economics, Concordia University, Montreal, QC H3G 1M8, Canada; e-mail: [email protected] ‡Department of Economics, University of Kentucky, Lexington, KY 40506-0034, USA; e-mail: [email protected] §Department of Economics, Emory University, Atlanta, GA 30322-2240, USA; e-mail: [email protected]