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REGULARIZED ESTIMATION OF DYNAMIC PANEL MODELS

Published online by Cambridge University Press:  28 October 2022

Marine Carrasco  and
Ada Nayihouba
Marine Carrasco*
Affiliation:
University of Montreal
Ada Nayihouba
Affiliation:
World Bank
*
Address correspondence to Marine Carrasco, CIREQ, University of Montreal, Montreal, QC, Canada; e-mail: marine.carrasco@umontreal.ca
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Abstract

In a dynamic panel data model, the number of moment conditions increases rapidly with the time dimension, resulting in a large dimensional covariance matrix of the instruments. As a consequence, the generalized method of moments (GMM) estimator exhibits a large bias in small samples, especially when the autoregressive parameter is close to unity. To address this issue, we propose a regularized version of the one-step GMM estimator using three regularization schemes based on three different ways of inverting the covariance matrix of the instruments. Under double asymptotics, we show that our regularized estimators are consistent and asymptotically normal. These regularization schemes involve a tuning or regularization parameter which needs to be chosen. We derive a data-driven selection of this regularization parameter based on an approximation of the higher-order mean square error and show its optimality. As an empirical application, we estimate a model of income dynamics.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 2 , April 2024 , pp. 360 - 418
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

The authors thank the Editor (P.C.B. Phillips), the Co-Editor (Guido Kuersteiner), three anonymous referees, Ryo Okui, and the participants of the NBER-NSF conference (2016), NY Camp Econometrics (2017), Canadian Economic Association (2018), International Association for Applied Econometrics (2018), and the Econometric Study Group (2019) for their helpful comments. Carrasco thanks SSHRC for partial financial support.

References

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