Partial efficient estimation of SUR models

In this paper, we consider efficient estimation of coefficients of interest in seemingly unrelated regressions (SUR) models. Using the GMM interpretation of the usual OLS and GLS/FGLS estimation of regression coefficients in SUR models, we derive the necessary and sufficient condition for the equal asymptotic efficiency of the OLS and FGLS estimators of a subset of regression coefficients. As a result, our paper extends the current SUR literature on the numerical equality of the OLS and GLS/FGLS estimators of the whole coefficient vector (see for example, Dwivedi and Srivastava, 1978) to the asymptotic equivalence of the OLS and GLS/FGLS estimators of a subset of the coefficient vector.