A Note on Johansen’s Cointegration Procedure when Trends are Present

Abstract

This note discusses some issues that arise when Johansen’s (1991) framework is used to analyze cointegrating relationships among variables with deterministic linear time trends. We distinguish “stochastic” and “deterministic” cointegration, arguing that stochastic cointegration is sufficient for the existence of an error correction representation and that it is often the hypothesis of interest in empirical applications. We show that Johansen’s (1991) method, which includes only a constant term in the estimated regression system, does not allow for stochastic cointegration. We propose to modify Johansen’s method by including a vector of deterministic linear trends in the estimated model. We present tabulated critical values of the maximal eigenvalue and trace statistics appropriate for this case. We discuss the circumstances under which our modification may be useful.

Financial support from the National Science Foundation and the Fonds pour la Formation de Chercheurs et l’Aide à la Recherche du Québec (F.C.A.R.) is acknowledged. We wish to thank Sangjoon Kim for computational assistance, Serena Ng for comments and Hiro Y. Toda for pointing out an error in a previous draft.