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Ancillarity and the Limited Information Maximum-Likelihood Estimation of a Structural Equation in a Simultaneous Equation System

Published online by Cambridge University Press:  18 October 2010

Yuzo Hosoya ,
Yoshihiko Tsukuda  and
Nobuhiko Terui
Yuzo Hosoya
Affiliation:
Tohoku University
Yoshihiko Tsukuda
Affiliation:
Tohoku University
Nobuhiko Terui
Affiliation:
Yamagata University
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Abstract

The concepts of the curved exponential family of distributions and ancillarity are applied to estimation problems of a single structural equation in a simultaneous equation model, and the effect of conditioning on ancillary statistics on the limited information maximum-likelihood (LIML) estimator is investigated. The asymptotic conditional covariance matrix of the LIML estimator conditioned on the second-order asymptotic maximal ancillary statistic is shown to be efficiently estimated by Liu and Breen's formula. The effect of conditioning on a second-order asymptotic ancillary statistic, i.e., the smallest characteristic root associated with the LIML estimation, is analyzed by means of an asymptotic expansion of the distribution as well as the exact distribution. The smallest root helps to give an intuitively appealing measure of precision of the LIML estimator.

Type
Articles
Information
Econometric Theory , Volume 5 , Issue 3 , December 1989 , pp. 385 - 404
Copyright
Copyright © Cambridge University Press 1989

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