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January 1964 - Volume 32 Issue 1 Page 51 - 56


p.51


On the Efficiency of Three-Stage Least-Squares Estimation

Albert Madansky

Abstract

A recent contribution to estimation of the coefficients of a system of simultaneous linear equations is the three-stage least-squares procedure of Zellner and Theil. This paper points out the relationship between this procedure and the method of instrumental variables, thus simplifying the exposition of the procedure. It further shows that the procedure yields estimates which are asymptotically at least as efficient as two-stage least-squares estimates, and that iteration of the procedure does not improve its asymptotic efficiency.

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