The efficiency of panel data estimators: GLS versus estimators which do not depend on variance components

For a balanced panel data regression model with random effects, we discuss the efficiency of the GLS estimator relative to the OLS, the between, and the within estimators. Focus is on how the efficiency responds to changes in (a) the relative variance components and (b) the composition of the regressor covariance matrix which into between and within variation. Both one-way and two-way models are considered. For the one-way, one regressor model, we show that (i) OLS has maximal inefficiency relative to GLS when the within and between individual variation in the regressor account for the same part of the total variation, (ii) the between estimator is always less efficient than the OLS estimator. For the two-way, one regressor model, the between individual (between period) estimator is more efficient than OLS if the between period (between individual) share of the total variation in the regressor and/or the time specific (individual specific) disturbance variance component are sufficiently large. Illustrations relating to marginal budget shares in household consumption are given.