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 non-stationary 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 non-standard 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. Copyright Royal Economic Society 2007