Estimation of cointegrated models with exogenous variables

We consider a cointegrated vector autoregressive process of integrated order 1, where the process consists of endogenous variables and exogenous variables. Johansen [Cointegration in partial systems and the efficiency of single-equation analysis. J Econometrics. 1992;52:389-402], Harbo et al. [Asymptotic inference on cointegrating rank in partial systems. J Amer Statist Assoc. 1998;16:388-399], and Pesaran et al. [Structural analysis of vector error correction models with exogenous I(1) variables. J Econometrics. 2000;97:293-343] considered inference of such processes assuming that the non-stationary exogenous variables are not cointegrated, and thus they are weakly exogenous. We consider the case where exogenous variables are cointegrated. Parameterization and estimation of the model is considered, and the asymptotic properties of the estimators are presented. The method in this paper is also applicable for the models considered in Mosconi and Giannini [Non-causality in cointegrated systems: representation estimation and testing. Oxford Bull Econ Stat. 1992;54:399-417], Pradel and Rault [Exogeneity in vector error correction models with purely exogenous long-run paths. Oxford Bull Econ Stat. 2003;65:629-653], and Hunter [Cointegrating exogeneity. Econom Lett. 1990;34:33-35]. A real data example is provided to illustrate the methods. Finite sample properties of the estimators are also examined through a Monte Carlo simulation.