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NONLINEAR PANEL DATA MODELS WITH DISTRIBUTION-FREE CORRELATED RANDOM EFFECTS

Published online by Cambridge University Press:  25 January 2021

Yu-Chin Hsu  and
Ji-Liang Shiu
Yu-Chin Hsu
Affiliation:
Institute of Economics, Academia Sinica National Central University National Chengchi University
Ji-Liang Shiu*
Affiliation:
Jinan University
*
Address correspondence to Ji-Liang Shiu, Institute for Economic and Social Research, Jinan University, Guangzhou, China; e-mail: jishiu.econ@gmail.com.
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Abstract

Under a Mundlak-type correlated random effect (CRE) specification, we first show that the average likelihood of a parametric nonlinear panel data model is the convolution of the conditional distribution of the model and the distribution of the unobserved heterogeneity. Hence, the distribution of the unobserved heterogeneity can be recovered by means of a Fourier transformation without imposing a distributional assumption on the CRE specification. We subsequently construct a semiparametric family of average likelihood functions of observables by combining the conditional distribution of the model and the recovered distribution of the unobserved heterogeneity, and show that the parameters in the nonlinear panel data model and in the CRE specification are identifiable. Based on the identification result, we propose a sieve maximum likelihood estimator. Compared with the conventional parametric CRE approaches, the advantage of our method is that it is not subject to misspecification on the distribution of the CRE. Furthermore, we show that the average partial effects are identifiable and extend our results to dynamic nonlinear panel data models.

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Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 6 , December 2021 , pp. 1075 - 1099
Copyright
© Cambridge University Press 2021

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Footnotes

The authors are grateful to the co-editor, three anonymous referees, Arthur Lewbel, and Matthew Shum for valuable comments and suggestions on previous versions of the paper. The authors are indebted to the editor Peter Phillips for constructive advice and comments, which have considerably improved the presentation of the paper. The authors are solely responsible for any remaining errors. Yu-Chin Hsu gratefully acknowledges research support from the Ministry of Science and Technology of Taiwan (MOST107-2410-H-001-034-MY3) and Career Development Award of Academia Sinica, Taiwan. Ji-Liang Shiu acknowledges support from the China National Science Foundation (Project No. 72073050).

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