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NUCLEAR NORM REGULARIZED QUANTILE REGRESSION WITH INTERACTIVE FIXED EFFECTS

Published online by Cambridge University Press:  24 April 2023

Junlong Feng
Junlong Feng*
Affiliation:
Hong Kong University of Science and Technology
*
Address correspondence to Junlong Feng, Department of Economics, Hong Kong University of Science and Technology, Kowloon, Hong Kong; e-mail: [email protected].
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Abstract

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This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T. We derive an error bound on the estimator that holds uniformly in the quantile level. The order of the bound implies uniform consistency of the estimator and is nearly optimal for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of interactive fixed effects at any quantile level. We demonstrate the performance of the estimator via Monte Carlo simulations.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 6 , December 2024 , pp. 1391 - 1421
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Footnotes

This paper is based on the third chapter of my doctoral dissertation at Columbia. An earlier working paper version of it was circulated under the title “Regularized Quantile Regression with Interactive Fixed Effects.” I am very grateful for helpful comments provided by the Editor, the Co-Editor, and three referees. I thank Jushan Bai, Sokbae (Simon) Lee, and Bernard Salanié, who were gracious with their advice, support, and feedback. I have also greatly benefited from comments and discussions with Songnian Chen, Roger Koenker, José Luis Montiel Olea, Roger Moon, Serena Ng, Jörg Stoye, Peng Wang, Martin Weidner, and participants at the Columbia Econometrics Colloquium, 2021 Econometric Society North American, Asian, and China meetings, and 2021 IAAE. All errors are my own.

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