IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1911.00166.html
   My bibliography  Save this paper

Regularized Quantile Regression with Interactive Fixed Effects

Author

Listed:
  • Junlong Feng

Abstract

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 fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of the) 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 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 fixed effects at any quantile level. To derive the error bound, we develop new theoretical arguments under primitive assumptions and new results on random matrices that may be of independent interest. We demonstrate the performance of the estimator via Monte Carlo simulations.

Suggested Citation

  • Junlong Feng, 2019. "Regularized Quantile Regression with Interactive Fixed Effects," Papers 1911.00166, arXiv.org, revised Mar 2021.
  • Handle: RePEc:arx:papers:1911.00166
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1911.00166
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    2. Ivan A. Canay, 2011. "A simple approach to quantile regression for panel data," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 368-386, October.
    3. Abrevaya, Jason & Dahl, Christian M, 2008. "The Effects of Birth Inputs on Birthweight," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 379-397.
    4. Hyungsik Roger Moon & Martin Weidner, 2018. "Nuclear Norm Regularized Estimation of Panel Regression Models," Papers 1810.10987, arXiv.org, revised Jun 2023.
    5. Victor Chernozhukov & Christian Hansen & Yuan Liao & Yinchu Zhu, 2019. "Inference for heterogeneous effects using low-rank estimations," CeMMAP working papers CWP31/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Harding, Matthew & Lamarche, Carlos, 2014. "Estimating and testing a quantile regression model with interactive effects," Journal of Econometrics, Elsevier, vol. 178(P1), pages 101-113.
    7. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    8. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.
    9. Antonio F. Galvao & Carlos Lamarche & Luiz Renato Lima, 2013. "Estimation of Censored Quantile Regression for Panel Data With Fixed Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1075-1089, September.
    10. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    11. Lamarche, Carlos, 2010. "Robust penalized quantile regression estimation for panel data," Journal of Econometrics, Elsevier, vol. 157(2), pages 396-408, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Belloni, Alexandre & Chen, Mingli & Madrid Padilla, Oscar Hernan & Wang, Zixuan (Kevin), 2019. "High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing," The Warwick Economics Research Paper Series (TWERPS) 1230, University of Warwick, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liang Chen & Juan J. Dolado & Jesús Gonzalo, 2021. "Quantile Factor Models," Econometrica, Econometric Society, vol. 89(2), pages 875-910, March.
    2. Liang Chen & Yulong Huo, 2019. "A Simple Estimator for Quantile Panel Data Models Using Smoothed Quantile Regressions," Papers 1911.04729, arXiv.org.
    3. Ruofan Xu & Jiti Gao & Tatsushi Oka & Yoon-Jae Whang, 2022. "Quantile Random-Coefficient Regression with Interactive Fixed Effects: Heterogeneous Group-Level Policy Evaluation," Papers 2208.03632, arXiv.org, revised Nov 2024.
    4. Belloni, Alexandre & Chen, Mingli & Madrid Padilla, Oscar Hernan & Wang, Zixuan (Kevin), 2019. "High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing," The Warwick Economics Research Paper Series (TWERPS) 1230, University of Warwick, Department of Economics.
    5. Ruofan Xu & Jiti Gao & Tatsushi Oka & Yoon-Jae Whang, 2022. "Estimation of Heterogeneous Treatment Effects Using Quantile Regression with Interactive Fixed Effects," Monash Econometrics and Business Statistics Working Papers 13/22, Monash University, Department of Econometrics and Business Statistics.
    6. Andres Sagner, 2020. "High Dimensional Quantile Factor Analysis," Working Papers Central Bank of Chile 886, Central Bank of Chile.
    7. Harding, Matthew & Lamarche, Carlos, 2019. "A panel quantile approach to attrition bias in Big Data: Evidence from a randomized experiment," Journal of Econometrics, Elsevier, vol. 211(1), pages 61-82.
    8. Paulo M.M. Rodrigues & Matei Demetrescu, 2022. "Cross-Sectional Error Dependence in Panel Quantile Regressions," Working Papers w202213, Banco de Portugal, Economics and Research Department.
    9. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    10. Galvao, Antonio F. & Wang, Liang, 2015. "Efficient minimum distance estimator for quantile regression fixed effects panel data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 1-26.
    11. Callaway, Brantly & Li, Tong & Oka, Tatsushi, 2018. "Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods," Journal of Econometrics, Elsevier, vol. 206(2), pages 395-413.
    12. Antonio F. Galvao & Thomas Parker & Zhijie Xiao, 2024. "Bootstrap Inference for Panel Data Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 628-639, April.
    13. Frantisek Cech & Jozef Barunik, 2017. "Measurement of Common Risk Factors: A Panel Quantile Regression Model for Returns," Working Papers IES 2017/20, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Sep 2017.
    14. Linton, O. B. & Rücker, M. & Vogt, M. & Walsh, C., 2024. "Estimation and Inference in High-Dimensional Panel Data Models with Interactive Fixed Effects," Janeway Institute Working Papers 2429, Faculty of Economics, University of Cambridge.
    15. Zongwu Cai & Meng Shi & Yue Zhao & Wuqing Wu, 2020. "Testing Financial Hierarchy Based on A PDQ-CRE Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202011, University of Kansas, Department of Economics, revised Jul 2020.
    16. Chen, Mingli & Fernández-Val, Iván & Weidner, Martin, 2021. "Nonlinear factor models for network and panel data," Journal of Econometrics, Elsevier, vol. 220(2), pages 296-324.
    17. Denis Chetverikov & Bradley Larsen & Christopher Palmer, 2016. "IV Quantile Regression for Group‐Level Treatments, With an Application to the Distributional Effects of Trade," Econometrica, Econometric Society, vol. 84, pages 809-833, March.
    18. Ye, Xiaoqing & Xu, Juan & Wu, Xiangjun, 2018. "Estimation of an unbalanced panel data Tobit model with interactive effects," Journal of choice modelling, Elsevier, vol. 28(C), pages 108-123.
    19. Battagliola, Maria Laura & Sørensen, Helle & Tolver, Anders & Staicu, Ana-Maria, 2022. "A bias-adjusted estimator in quantile regression for clustered data," Econometrics and Statistics, Elsevier, vol. 23(C), pages 165-186.
    20. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1911.00166. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.