Identification without assuming mean-stationarity: Quasi ML estimation of dynamic panel models with endogenous regressors.

Abstract

Linear GMM estimators for dynamic panel models with predetermined or endogenous regressors suffer from a weak instruments problem when the data are highly persistent. In this paper we propose new random and fixed effects Limited Information Quasi ML estimators (LIQMLEs) for such models. We also discuss LIQMLEs for models that contain time-varying individual effects. Unlike System GMM estimators, the LIQMLEs do not require mean stationarity conditions for consistency. Such conditions often do not hold for the models we consider. Our LIQMLEs are based on a two-step control function approach that includes the first stage model residuals for a predetermined or endogenous regressor in the outcome equation. The LIMLEs are more precise than non-linear GMM estimators that are based on the original outcome equation. The LIQMLEs also compare favourably to various alternative (Q)MLEs in terms of precision, robustness and/or ease of computation.