An efficient linear GMM estimator for the covariance stationary AR (1)/unit root model for panel data

This paper considers generalized method of moments (GMM) estimation of the inclusive panel AR(1) model that contains the covariance stationary panel AR(1) model and the panel AR(1) model with a unit root as special cases. The paper presents a two-step optimal linear GMM (OLGMM) estimator for the inclusive model that is asymptotically equivalent to the optimal nonlinear GMM estimator of Ahn and Schmidt (1997, Journal of Econometrics 76, 309–321) when the data are covariance stationary. Next the paper derives the asymptotic distribution of the OLGMM estimator when the model has a unit root under a variety of assumptions about the initial observations and the initial estimator. It is shown that in most cases the OLGMM estimator is superconsistent. In addition it is shown that the iterated OLGMM estimator is superefficient when the variance of the initial observations is finite and fixed, i.e., small compared to the cross-sectional dimension of the panel. The paper also conducts a Monte Carlo study in which the finite-sample properties of various GMM estimators for the inclusive panel AR(1) model are compared.I thank Steve Bond and Frank Windmeijer for kindly making one of their computer programs available to me. I also thank two anonymous referees and a co-editor for very helpful comments. This research was funded by the ESRC under grant R000239139