Some identification problems in the cointegrated vector autoregressive model

An analysis of some identification problems in the cointegrated VAR is given. We give a new criteria for identification by linear restrictions on indi- vidual relations which is equivalent to the rank condition. We compare the asymptotic distribution of the estimators of alpha and beta when they are identified by linear restrictions on alpha and when they are identified by linear restrictions on alpha in which case a component of beta is asymptotically Gaussian. Finally we discuss identification of shocks by introducing the contemporaneous and permanent effect of a shock and the distinction between permanent and transi- tory shocks, which allows one to identify permanent shocks from the long-run variance and transitory shocks from the short-run variance