Efficiency of Alternative Estimators in Generalized Seemingly Unrelated Regression Models

Joint estimation of the parameters of systems of multiple equations by Zellner’s (1962) method of seemingly unrelated regressions (SUR) will in general lead to efficiency gains relative to single equation estimation. The original work of Zellner (1962, 1963) and Zellner and Huang (1962) investigated the magnitude of these efficiency gains. In particular they showed that there is no gain if either the explanatory variables are the same in each equation or if the error covariances are all zero. Further characterizations and extensions of these results have appeared in the work of Schmidt (1978), Dwivedi and Srivastava (1978), Theil and Fiebig (1979) and Kapteyn and Fiebig (1981). In summary, the conventional wisdom, as represented by say Judge et al. (1985, p. 468), is that: ‘efficiency gains from joint estimation tend to be higher when the explanatory variables in different equations are not highly correlated but the disturbance terms corresponding to different equations are highly correlated’.