Abstract :
In this note, based on the generalized method of moments ~GMM! interpretation
of the usual ordinary least squares ~OLS! and feasible generalized least squares
~FGLS! estimators of seemingly unrelated regressions ~SUR! models, we show
that the OLS estimator is asymptotically as efficient as the FGLS estimator if and
only if the cross-equation orthogonality condition is redundant given the withinequation
orthogonality condition+ Using the condition for redundancy of moment
conditions of Breusch, Qian, Schmidt, and Wyhowski ~1999, Journal of Econometrics
99, 89–111!, we then derive the necessary and sufficient condition for the
equal asymptotic efficiency of the OLS and FGLS estimators of SUR models+ We
also provide several useful sufficient conditions for the equal asymptotic efficiency
of OLS and FGLS estimators that can be interpreted as various mixings of
the two famous sufficient conditions of Zellner ~1962, Journal of the American
Statistical Association 57, 348–368!+
