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 identi fy a vector autoregressive process whether the variables are I(0) or I(d) f or d = 1,2..... We then use this rank condition to demonstrate the interdep endence between the identification of short-run and long-run relations of c ointegrated process. We find that both the short-run and long-run relations can be identified without the existence of prior information to identify e ither relation. But if there exists a set of prior restrictions to identify the short-run relation, then this same set of restrictions is sufficient t o identify the corresponding long-run relation. On the other hand, it is in general not possible to identify the long-run relations without informatio n on the complete structure. The relationship between the identification of a vector autoregressive process and a Cowles Commission dynamic simultaneo us equations model is also clarified.