GMM estimation and inference in dynamic panel data models with persistent data

In this paper we consider GMM based estimation and inference for the panel AR(1) model when the data are persistent and the time dimension of the panel is fixed. We find that the nature of the weak instruments problem of the Arellano-Bond estimator depends on the distributional properties of the initial observations. Subsequently, we derive local asymptotic approximations to the finite sample distributions of the Arellano-Bond estimator and the System estimator, respectively, under a variety of distributional assumptions about the initial observations and discuss the implications of the results we obtain for doing inference. We also propose two LM type panel unit root tests.