Unit Roots, Cointegration and Pre-Testing in VAR Models


This article investigates the robustness of impulse response estimators to near unit roots and near cointegration in vector autoregressive (VAR) models. We compare estimators based on VAR specifications determined by pretests 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 pretest 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.

VAR Models in Macroeconomics – New Developments and Applications: Essays in Honor of Christopher A. Sims (Advances in Econometrics, Vol. 32), Emerald Group Publishing Limited, pp. 81-115