A Variance Comparison of OLS and Feasible GLS Estimators

Second-order approximations to the variances of OLS and GLS estimators are compared when the covariance matrix is locally nonscalar. Using a result of Rothenberg, the comparison of OLS and GLS variances is shown to be asymptotically equivalent to a weighted mean square error comparison of the error covariance parameter estimators used in those two procedures. When there is only one covariance parameter, this comparison depends only on the noncentrality parameter of a classical hypothesis test for a scalar covariance matrix.