Econometrica: Mar, 1972, Volume 40, Issue 2
The Exact Finite Sample Properties of the Estimators of Coefficients in the Error Components Regression Models
P. A. V. B. Swamy, S. S. Arora
Wallace and Hussain (1969) considered the use of an error components regression model in the analysis of time series of cross-sections and developed an Aitken estimator of the coefficient vector based on an estimated variance-covariance matrix of error terms. In this paper, we have shown that under the set of assumptions adopted by Wallace and Hussain there are an infinite number of estimators which have the same asymptotic variance-covariance matrix as the Wallace-Hussain estimator and also that it is not possible to choose an estimator on the basis of asymptotic efficiency. We have developed an alternative estimator of the variance-covariance matrix of error terms and have used this estimator in developing a feasible "Aitken" type estimator for the coefficient vector. We have derived some small sample properties of this estimator and have compared them with those of other estimators of the coefficient vector.