OLS or GLS in the presence of specification error? : An expected loss approach

Abstract

Omitted variables in regression analysis can lead to the erroneous conclusion that autocorrelation or heteroscedasticity is present. The common response is to use the suggested GLS procedure, even if it is suspected that the error is a non-zero disturbance mean. The question addressed here is whether one is better off with the GLS or with the OLS estimator when the omitted portion of the regression cannot be incorporated into the regression. Using a loss function this paper relates the seriousness of OLS and GLS loss to identifiable parameters. With consistent estimators of these parameters the researcher can choose between OLS and GLS.