Efficient estimation of panel data models with strictly exogenous explanatory variables

With panel data, exogeneity assumptions imply many more moment conditions than standard estimators use. However, many of the moment conditions may be redundant, in the sense that they do not increase efficiency; if so, we may establish the standard estimators' efficiency. We prove efficiency results for GLS in a model with unrestricted error covariance matrix, and for 3SLS in models where regressors and errors are correlated, such as the Hausman-Taylor model. For models with correlation between regressors and errors, and with unrestricted error covariance structure, we provide a simple estimator based on a GLS generalization of deviations from means.