Large sample properties of an IV estimator based on the Ahn and Schmidt moment conditions

We propose an instrumental variables (IV) estimator based on nonlinear (in param- eters) moment conditions for estimating linear dynamic panel data models and derive the large sample properties of the estimator. We assume that the only explanatory variable in the model is one lag of the dependent variable and consider the setting where the absolute value of the true lag parameter is smaller or equal to one, the cross section dimension is large, and the time series dimension is either fixed or large. Estimation of the lag parameter involves solving a quadratic equation and we find that the lag parameter is point identified in the unit root case; otherwise, two distinct roots (solutions) result. We propose a selection rule that identifies the consistent root asymptotically in the latter case and derive the asymptotic distribution of the estimator for the unit root case and for the case when the absolute value of the lag parameter is smaller than one.