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A NOTE ON GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATION OF SEMIPARAMETRIC CONDITIONAL MOMENT RESTRICTION MODELS

Published online by Cambridge University Press:  19 September 2016

Naoya Sueishi
Naoya Sueishi*
Affiliation:
Kobe University
*
*Address correspondence to Naoya Sueishi, Graduate School of Economics, Kobe University, Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan; e-mail: sueishi@econ.kobe-u.ac.jp.
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Abstract

This paper proposes an empirical likelihood-based estimation method for semiparametric conditional moment restriction models, which contain finite dimensional unknown parameters and unknown functions. We extend the results of Donald, Imbens, and Newey (2003, Journal of Econometrics 117, 55–93) by allowing unknown functions to be included in the conditional moment restrictions. We approximate unknown functions by a sieve method and estimate the finite dimensional parameters and unknown functions jointly. We establish consistency and derive the convergence rate of the estimator. We also show that the estimator of the finite dimensional parameters is $\sqrt n$-consistent, asymptotically normally distributed, and asymptotically efficient.

Type
MISCELLANEA
Information
Econometric Theory , Volume 33 , Issue 5 , October 2017 , pp. 1242 - 1258
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

Early versions of this paper were titled “Generalized Empirical Likelihood Estimation via Conditional Moment Restrictions Containing Unknown Functions.” This paper is based on part of my dissertation at the University of Wisconsin. I would like to thank Bruce Hansen and Jack Porter for their helpful comments and suggestions. The comments from a co-editor and two referees improved the paper. I also thank Yoshihiko Nishiyama, Kohtaro Hitomi, Qingfeng Liu, Ryo Okui, and seminar participants at Kobe University, Kyoto University, and University of Wisconsin. All remaining errors are mine.

References

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