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Computation of Zellner-Theil's Three Stage Least Squares Estimates
R. Narayanan
Abstract
In their paper on the three stage least squares method of estimation of a simultaneous equation system, Zellner and Theil [5] make the interesting observation that the large sample efficiency of the estimates of the parameters in the group of over-identified equations is unaffected if the three stage method is applied to this subsystem alone, ignoring all the exactly identified equations. It is shown in this paper that the estimates themselves--not just their large sample efficiency--are unaffected if one follows the above mentioned simplified procedure. This result is established for the general case of a simultaneous equation system subject to linear homogeneous a priori restrictions, whereas many other known properties of the three stage least squares method have been demonstrated only for the special case of "simple restrictions" on the structural coefficients. An error in the expression giving the estimates for the exactly identified equations in Zellner-Theil's paper is also corrected. The results of this paper have obvious significance for the problem of developing an efficient computer program for finding the three stage least squares estimates.
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