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+