Comparison of GMM and MD estimators for a panel regression model with endogenous regressors and an AR(1) disturbance

In this paper, we investigate the asymptotic properties of nonlinear GMM and linear MD estimators for a panel regression model with endogenous regressors and an AR(1) disturbance. We demonstrate that the linear MD estimator has a smaller asymptotic variance than the nonlinear GMM estimator when a non-optimal weighting matrix is used. However, when the optimal weighting matrix is used, both the nonlinear GMM and linear MD estimators have the same asymptotic distribution. The simulation results indicate that the linear two-step MD estimator is a practical choice due to its performance and simplicity.