Further consequences of viewing LIML as an iterated Aitken estimator

Following an approach originally suggested by Pagan (1979. Economics Letter s 3, 369-372) we have explored some additional consequences of viewing LIML as an iterated Aitken estimator. A curious result we derive in this contex t is that the Aitken estimator based on 2SLS residuals produces 2SLS estima te of the structural parameters. We derive a simple expression for the diff erence between 2SLS and LIML in finite samples, which turns out to be very similar to an expression for the approximate bias of 2SLS in small samples (Nagar, 1959. Econometrica 27, 575-595; Buse, 1992. Econometrica 60, 173-18 0; Bound et al., 1995. Journal of American Statistical Association 90, 443- 450). The expression pinpoints the gain from iteration. Our analytical form ula yields many of the results on the difference between 2SLS and LIML that Anderson and Sawa (1979. Econometrica 47, 163-182) and Anderson et al. (19 82. Econometrica 50, 1009-1027) have obtained through extensive numerical s imulations in a model with two endogenous variables. The robustness of 2SLS and LIML with respect to certain deviations from normality is also examine d. (C) 2000 Elsevier Science S.A. All rights reserved. JEL classification: C30.