Estimation of dynamic panel data models with a lot of heterogeneity

The commonly used 1-step and 2-step System GMM estimators for the panel AR(1) model are inconsistent under mean stationarity when the ratio of the variance of the individual effects to the variance of the idiosyncratic errors is unbounded when N -> infinity. The reason for their inconsistency is that their weight matrices select moment conditions that do not identify the autoregressive parameter. This paper proposes a new 2-step System estimator that is still consistent in this case provided that T > 3. Unlike the commonly used 2-step System estimator, the new estimator uses an estimator of the optimal weight matrix that remains consistent in this case. We also show that the commonly used 1-step and 2-step Arellano-Bond GMM estimators and the Random Effects Quasi MLE remain consistent under the same conditions. To illustrate the usefulness of our new System estimator we revisit the growth study of Levine et al. (2000).