An Autoregressive Distributed Lag Modelling Approach to Cointegration Analysis¤

This paper examines the use of autoregressive distributed lag (ARDL) models for the analysis of long-run relations when the underlying variables are I(1). It shows that after appropriate augmentation of the order of the ARDL model, the OLS estimators of the short-run parameters are p T -consistent with the asymptotically singular covariance matrix, and the ARDL-based estimators of the long-run coe¢cients are super-consistent, and valid inferences on the long-run parameters can be made using standard normal asymptotic theory. The paper also examines the relationship between the ARDL procedure and the fully modi…ed OLS approach of Phillips and Hansen to estimation of cointegrating relations, and compares the small sample performance of these two approaches via Monte Carlo experiments. These results provide strong evidence in favour of a rehabilitation of the traditional ARDL approach to time series econometric modelling. The ARDL approach has the additional advantage of yielding consistent estimates of the long-run coe¢cients that are asymptotically normal irrespective of whether the underlying regressors are I(1) or I(0). JEL Classi…cations: C12, C13, C15, C22. Key Words: Autoregressive distributed lag model, Cointegration, I(1) and I(0) regressors, Model selection, Monte Carlo simulation. ¤This is a revised version of a paper presented at the Symposium at the Centennial of Ragnar Frisch, The Norwegian Academy of Science and Letters, Oslo, March 3-5, 1995. We are grateful to Peter Boswijk, Clive Granger, Alberto Holly, Kyung So Im, Brendan McCabe, Steve Satchell, Richard Smith, Ron Smith and an anonymous referee for helpful comments. Partial …nancial support from the ESRC (Grant No. R000233608) and the Isaac Newton Trust of Trinity College, Cambridge is gratefully acknowledged.