Model mis-specification and Johansen's co-integration analysis: an application to the US money demand

Abstract

This paper examines the consequences of mis-specifying the deterministic components of a co-integration model estimated with the Johansen's multivariate maximum likelihood approach. Using the US long-run money demand model as our example, we show that when a linear deterministic time trend is excluded from the co-integration model, we obtain very robust results, suggesting the co-integration of the real M1 and the real M2 with their determinants. When a linear deterministic time trend is included, however, we find generally unfavorable results. Next, using a procedure discussed in Johansen (1992) that jointly determines the co-integration rank and the deterministic components of a model, we find that the preferred models for the real M1 and the real M2 are generally not co-integrated with their determinants. Our study suggests that great care should be exercised in the initial stages of model specification. The inclusion or exclusion of the linear deterministic time trend should be justified formally. Otherwise, the results may be misleading.