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A third order optimum property of the ML estimator in a linear functional relationship model and simultaneous equation system in econometrics

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Summary

The maximum likelihood (ML) estimator and its modification in the linear functional relationship model with incidental parameters are shown to be third-order asymptotically efficient among a class of almost median-unbiased and almost mean-unbiased estimators, respectively, in the large sample sense. This means that the limited information maximum likelihood (LIML) estimator in the simultaneous equation system is third-order asymptotically efficient when the number of excluded exogenous variables in a particular structural equation is growing along with the sample size. It implies that the LIML estimator has an optimum property when the system of structural equations is large.

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Authors and Affiliations

  1. University of Tokyo, Tokyo, Japan

    Naoto Kunitomo

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  1. Naoto Kunitomo
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Additional information

The research was partly supported by National Science Foundation Grant SES 79-13976 at the Institute for Mathematical Studies in the Social Sciences, Stanford University and Grant-in-Aid 60301081 of the Ministry of Education, Science and Culture at the Faculty of Economics, University of Tokyo. This paper was originally written as a part of the author's Ph.D. dissertation submitted to Stanford University in August, 1981. Some details of the paper were deleted at the suggestion of the associate editor of this journal.

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Kunitomo, N. A third order optimum property of the ML estimator in a linear functional relationship model and simultaneous equation system in econometrics. Ann Inst Stat Math 39, 575–591 (1987). https://doi.org/10.1007/BF02491491

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  • DOI: https://doi.org/10.1007/BF02491491

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