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SECOND-ORDER BIAS REDUCTION FOR NONLINEAR PANEL DATA MODELS WITH FIXED EFFECTS BASED ON EXPECTED QUANTITIES

Published online by Cambridge University Press:  25 April 2022

Martin Schumann
Martin Schumann*
Affiliation:
Maastricht University
*
Address correspondence to Martin Schumann, School of Business and Economics, Maastricht University, 6211 LM Maastricht, The Netherlands; e-mail: m.schumann@maastrichtuniversity.nl.
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Abstract

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In many nonlinear panel data models with fixed effects maximum likelihood estimators suffer from the incidental parameters problem, which often entails that point estimates are markedly biased. While the recent literature has mostly generated methods that yield a first-order bias reduction relative to maximum likelihood, we derive a first- and second-order bias correction of the profile likelihood based on “expected quantities” which differs from the corresponding correction based on “sample averages” derived in Dhaene and Sun (2021, Journal of Econometrics 220, 227–252). While consistency and asymptotic normality of our estimator are derived in a setting where both the number of individuals and the number of time periods grow to infinity, we illustrate in a simulation study that our second-order bias reduction indeed yields an estimator with substantially improved small sample properties relative to its first-order unbiased counterpart, especially when less than 10 time periods are available.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 4 , August 2023 , pp. 693 - 736
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

I thank the Co-Editor Guido Kuersteiner and two anonymous referees for various helpful comments. Further, I thank Gautam Tripathi, Thomas A. Severini, and seminar participants at Dortmund, Bochum, Maastricht, the 11th International Conference of the ERCIM WG on Computational and Methodological Statistics and seminar participants of the Asian meeting of the Econometric Society 2019. The simulation experiments reported in this paper were carried out using the HPC facilities of the University of Luxembourg (Varrette et al. (2014), http://hpc.uni.lu). An earlier version of this paper has been circulated under the title “Second-Order Analytical Bias Reduction for Nonlinear Panel Data Models with Fixed Effects.”

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