IDENTIFICATION AND DICHOTOMIZATION OF LONG- AND SHORT-RUN RELATIONS OF COINTEGRATED VECTOR AUTOREGRESSIVE MODELS

We show that the usual rank condition is necessary and sufficient to identify a vector autoregressive process whether the variables are I(0) or I(d) for d = 1,2,... We then use this rank condition to demonstrate the interdependence between the identification of short-run and long-run relations of cointegrated process. We find that both the short-run and long-run relations can be identified without the existence of prior information to identify either relation. But if there exists a set of prior restrictions to identify the short-run relation, then this same set of restrictions is sufficient to identify the corresponding long-run relation. On the other hand, it is in general not possible to identify the long-run relations without information on the complete structure. The relationship between the identification of a vector autoregressive process and a Cowles Commission dynamic simultaneous equations model is also clarified.