Model Mis-Specification and Johansen's Cointegration Analysis : An Application to the U.S. Money Demand

This paper examines the consequences of mis-specifying the deterministic components of a cointegration model estimated with the Johansen's multivariate maximum likelihood approach. Using the U.S. long-run money demand model as our example, we show that when a linear deterministic time trend is excluded from the cointegration model, we obtain very robust results suggesting the cointegration 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 cointegration 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 cointegrated 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