On the efficiency of two-stage and three-stage least squares estimators

This paper utilizes the results of Kruskal (1968), Zyskind (1967), and more recently Milliken and Albohali (1984) to derive a simple necessary and sufficient condition for 3SLS to be equivalent to 2SLS. This condition depends upon the inverse of the variance:covariance matrix of the disturbances, and the set of second stage regressors of each structural equation. More importantly, this condition should prove useful for econometric students and provides an easy method for checking sufficiency.