Mean Group Estimation in Presence of Weakly Cross-Correlated Estimators

This paper extends the mean group (MG) estimator for random coefficient panel data models by allowing the underlying individual estimators to be weakly cross-correlated. Weak cross-sectional dependence of the individual estimators can arise, for example, in panels with spatially correlated errors. We establish that the MG estimator is asymptotically correctly centered, and its asymptotic covariance matrix can be consistently estimated. The random coefficient specification allows for correct inference even when nothing is known about the weak cross-sectional dependence of the errors. This is in contrast to the well-known homogeneous case, where cross-sectional dependence of errors results in incorrect inference unless the nature of the cross-sectional error dependence is known and can be taken into account. Evidence on small sample performance of the MG estimators is provided using Monte Carlo experiments with both strictly and weakly exogenous regressors and cross-sectionally correlated innovations.