Ancillarity and the limited information maximum-likelihood estimation of a structural equation in a simultaneous equation system

Yuzo Hosoya, Yoshihiko Tsukuda, Nobuhiko Terui

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)385-404
Number of pages20
JournalEconometric Theory
Volume5
Issue number3
DOIs
Publication statusPublished - 1989 Dec

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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