Asymptotic Theory and Finite Sample Properties of GMM Estimators in Dynamic Panel Settings with Persistent Regressors

Abstract

Dynamic panel data models with persistent regressors present significant challenges for econometric estimation, particularly when the autoregressive parameter approaches unity and instruments exhibit weak correlation with endogenous variables. This paper develops a comprehensive asymptotic theory for Generalized Method of Moments (GMM) estimators in dynamic panel settings where regressors display high persistence, extending beyond the traditional framework of stationary processes. We establish the limiting distribution of both difference and system GMM estimators under sequences of local-to-unity asymptotics, demonstrating that standard asymptotic approximations fail when the autoregressive coefficient approaches one. Our theoretical analysis reveals that the rate of convergence deteriorates from the standard $\sqrt{NT}$ to $\sqrt{N}T^{-1/2}$ when persistence increases, fundamentally altering the statistical properties of conventional estimators. Through extensive Monte Carlo simulations across varying degrees of persistence, cross-sectional dimensions, and time series lengths, we document substantial finite sample biases that persist even in moderately large samples. The simulation results demonstrate that bias-corrected estimators and alternative identification strategies significantly improve performance in persistent settings. We propose a modified GMM framework that incorporates bias correction mechanisms and develops robust inference procedures that maintain adequate size control under high persistence. The practical implications extend to applications in macroeconomic panel studies where persistence is prevalent, offering guidance for empirical researchers working with dynamic panel models featuring near-unit root behavior.