The Asymptotic Properties of the System GMM Estimator in Dynamic Panel Data Models When Both N and T are Large

Abstract

In this paper, we derive the asymptotic properties of the system GMM estimator in dynamic panel data models with individual and time effects when both N and T, the dimensions of cross section and time series, are large. We first show that the two-step level GMM estimator with an optimal weighting matrix is consistent under large N and T asymptotics, whereas that with a non-optimal one is not. We then show that the two-step system GMM estimator is consistent even if a sub-optimal weighting matrix where off-diagonal blocks are set to zero is used. Such consistency results theoretically support the use of the system GMM estimator in large N and T contexts even though it was originally developed for large N and small T panels. Simulation results indicate that the large N and large T asymptotic results approximate the finite sample behavior reasonably well unless persistency of data is strong and/or the variance ratio of individual effects to the disturbances is large.