Lag-Augmented Two- and Three-Stage Least Squares Estimators for Integrated Structural Dynamic Models

We consider a lag-augmented two- or three-stage least squares estimator for a structural dynamic model of nonstationary and possibly cointegrated variables without the prior knowledge of unit roots or rank of cointegration. We show that the conventional two- and three-stage least squares estimators are consistent but contain nonstandard distributions without the strict exogeneity assumption, hence the conventional Wald type test statistics may not be chi-square distributed. We propose a lag order augmented two- or three-stage least squares estimator that is consistent and asymptotically normally distributed. Limited Monte Carlo studies are conducted to shed light on the finite sample properties of various estimators.