Panel data estimators and aggregation

For a panel data regression equation with two-way unobserved heterogeneity, individual-specific and period-specific, 'within-individual' and 'within-period' estimators, which can be given Ordinary Least Squares (OLS) or Instrumental Variables (IV) interpretations, are considered. A class of estimators defined as linear aggregates of these estimators, is defined. Nine aggregate estimators, including between, within, and Generalized Least Squares (GLS), are special cases. Other estimators are shown to be more robust to simultaneity and measurement error bias than the standard aggregate estimators and more efficient than the 'disaggregate' estimators. Empirical illustrations relating to manufacturing productivity are given.