Constructing panel data estimators by aggregation

A regression equation for panel data with two-way random or fixed effects and a set of individual specific and period specific 'within individual' and 'within period', estimators of its slope coefficients are considered. They can be given Ordinary Least Squares (OLS) or Instrumental Variables (IV) interpretations. A class of estimators, obtained as an arbitrary linear combination of these 'disaggregate' estimators, is defined and an expression for its variance-covariance matrix is derived. Nine familiar 'aggregate' estimators which utilize the entire data set, including two between, three within, three GLS, as well as the standard OLS, emerge by specific choices of the weights. Other estimators in this class which are more robust to simultaneity and measurement error bias than the standard aggregate estimators and more efficient than the 'disaggregate' estimators, are also considered. An empirical illustration of robustness and efficiency, relating to manufacturing productivity, is given.