AbstractLet Σ represent the covariance matrix of the structural disturbances. Following Theil the standard consistent estimator of the elements of Σ is given as the mean 2 SLS residual sum of squares. This paper shows the fact that there is a class of consistent estimators of Σ and that the standard estimator is not a minimum distance estimator. It derives the minimum distance consistent 2 SLS estimator of Σ. Then the paper suggests that the derived estimator be applied in the second stage as well as in the third stage of 3 SLS estimation. Other possible applications are indicated.This paper contains an improvement and reformulation of the results previously derived by the author on a related subject that appeared inMetroeconomica[9]. This paper contains an improvement over the previous result in that the derived estimator in this paper possesses not only consistency but also the minimum distance prope