On the Efficiency of Ordinary Least-Squares in Regression Models

Abstract

For all regression models containing a common subset of explanatory variables, a necessary and sufficient condition for the ordinary least-squares estimators to be also best linear-unbiased estimators is given. The stochastic properties of the variances and covariances estimated by ordinary least-squares are derived. Five examples, especially useful in economic applications, are studied. The relevance of the basic result of this article for regression models containing a set of dummy variables is stressed.