IDEAS home Printed from https://ideas.repec.org/a/oup/emjrnl/v24y2021i2pc40-c77..html
   My bibliography  Save this article

Low-rank approximations of nonseparable panel models

Author

Listed:
  • Hugo Freeman
  • Martin Weidner

Abstract

SummaryWe provide estimation methods for nonseparable panel models based on low-rank factor structure approximations. The factor structures are estimated by matrix-completion methods to deal with the computational challenges of principal component analysis in the presence of missing data. We show that the resulting estimators are consistent in large panels, but suffer from approximation and shrinkage biases. We correct these biases using matching and difference-in-differences approaches. Numerical examples and an empirical application to the effect of election day registration on voter turnout in the US illustrate the properties and usefulness of our methods.

Suggested Citation

  • Hugo Freeman & Martin Weidner, 2021. "Low-rank approximations of nonseparable panel models," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 40-77.
    • Handle: RePEc:oup:emjrnl:v:24:y:2021:i:2:p:c40-c77.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/ectj/utab007
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Laurent Gobillon & Thierry Magnac, 2016. "Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 535-551, July.
    2. Marc K. Chan & Simon S. Kwok, 2022. "The PCDID Approach: Difference-in-Differences When Trends Are Potentially Unparallel and Stochastic," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1216-1233, June.
    3. Manski, Charles F, 1987. "Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data," Econometrica, Econometric Society, vol. 55(2), pages 357-362, March.
    4. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    5. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    6. 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.
    7. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    8. Cheng Hsiao & H. Steve Ching & Shui Ki Wan, 2012. "A Panel Data Approach For Program Evaluation: Measuring The Benefits Of Political And Economic Integration Of Hong Kong With Mainland China," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(5), pages 705-740, August.
    9. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    10. Xu, Yiqing, 2017. "Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models," Political Analysis, Cambridge University Press, vol. 25(1), pages 57-76, January.
    11. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
    12. Bryan S. Graham & James L. Powell, 2012. "Identification and Estimation of Average Partial Effects in “Irregular” Correlated Random Coefficient Panel Data Models," Econometrica, Econometric Society, vol. 80(5), pages 2105-2152, September.
    13. Silverstein, Jack W., 1989. "On the eigenvectors of large dimensional sample covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 1-16, July.
    14. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    15. Andreas Dzemski, 2019. "An Empirical Model of Dyadic Link Formation in a Network with Unobserved Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 101(5), pages 763-776, December.
    16. Li, Kathleen T. & Bell, David R., 2017. "Estimation of average treatment effects with panel data: Asymptotic theory and implementation," Journal of Econometrics, Elsevier, vol. 197(1), pages 65-75.
    17. Bai, Z. D. & Silverstein, Jack W. & Yin, Y. Q., 1988. "A note on the largest eigenvalue of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 166-168, August.
    18. Victor Chernozhukov & Iván Fernández‐Val & Jinyong Hahn & Whitney Newey, 2013. "Average and Quantile Effects in Nonseparable Panel Models," Econometrica, Econometric Society, vol. 81(2), pages 535-580, March.
    19. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    20. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    21. Dukpa Kim & Tatsushi Oka, 2014. "Divorce Law Reforms And Divorce Rates In The Usa: An Interactive Fixed‐Effects Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(2), pages 231-245, March.
    22. Ruoxuan Xiong & Markus Pelger, 2019. "Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference," Papers 1910.08273, arXiv.org, revised Jan 2022.
    23. Beyhum, Jad & Gautier, Eric, 2019. "Square-root nuclear norm penalized estimator for panel data models with approximately low-rank unobserved Heterogeneity," TSE Working Papers 19-1008, Toulouse School of Economics (TSE).
    24. Silverstein, Jack W., 1989. "On the weak limit of the largest eigenvalue of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 307-311, 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. Hugo Freeman & Martin Weidner, 2021. "Linear Panel Regressions with Two-Way Unobserved Heterogeneity," Papers 2109.11911, arXiv.org, revised Aug 2022.
    2. Anish Agarwal & Vasilis Syrgkanis, 2022. "Synthetic Blip Effects: Generalizing Synthetic Controls for the Dynamic Treatment Regime," Papers 2210.11003, arXiv.org.
    3. Anish Agarwal & Keegan Harris & Justin Whitehouse & Zhiwei Steven Wu, 2023. "Adaptive Principal Component Regression with Applications to Panel Data," Papers 2307.01357, arXiv.org, revised Oct 2023.
    4. Anish Agarwal & Munther Dahleh & Devavrat Shah & Dennis Shen, 2021. "Causal Matrix Completion," Papers 2109.15154, arXiv.org.
    5. Hugo Freeman & Martin Weidner, 2021. "Linear panel regressions with two-way unobserved heterogeneity," CeMMAP working papers CWP39/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Hugo Freeman, 2022. "Multidimensional Interactive Fixed-Effects," Papers 2209.11691, arXiv.org, revised Mar 2023.

    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. Iv'an Fern'andez-Val & Hugo Freeman & Martin Weidner, 2020. "Low-Rank Approximations of Nonseparable Panel Models," Papers 2010.12439, arXiv.org, revised Mar 2021.
    2. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Mar 2024.
    3. Hugo Freeman & Martin Weidner, 2021. "Linear Panel Regressions with Two-Way Unobserved Heterogeneity," Papers 2109.11911, arXiv.org, revised Aug 2022.
    4. Callaway, Brantly & Karami, Sonia, 2023. "Treatment effects in interactive fixed effects models with a small number of time periods," Journal of Econometrics, Elsevier, vol. 233(1), pages 184-208.
    5. Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wuthrich, 2022. "Selection and parallel trends," Papers 2203.09001, arXiv.org, revised Mar 2024.
    6. Hugo Freeman & Martin Weidner, 2021. "Linear panel regressions with two-way unobserved heterogeneity," CeMMAP working papers CWP39/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. 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.
    8. Xavier d'Haultfoeuille & Stefan Hoderlein & Yuya Sasaki, 2013. "Nonlinear difference-in-differences in repeated cross sections with continuous treatments," CeMMAP working papers CWP40/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Chernozhukov, Victor & Fernández-Val, Iván & Hoderlein, Stefan & Holzmann, Hajo & Newey, Whitney, 2015. "Nonparametric identification in panels using quantiles," Journal of Econometrics, Elsevier, vol. 188(2), pages 378-392.
    10. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    11. Bryan S. Graham & Jinyong Hahn & Alexandre Poirier & James L. Powell, 2015. "Quantile regression with panel data," CeMMAP working papers CWP12/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Hyungsik Roger Roger Moon & Martin Weidner, 2013. "Dynamic linear panel regression models with interactive fixed effects," CeMMAP working papers 63/13, Institute for Fiscal Studies.
    13. Hyungsik Roger Roger Moon & Martin Weidner, 2014. "Dynamic linear panel regression models with interactive fixed effects," CeMMAP working papers 47/14, Institute for Fiscal Studies.
    14. Keegan Harris & Anish Agarwal & Chara Podimata & Zhiwei Steven Wu, 2022. "Strategyproof Decision-Making in Panel Data Settings and Beyond," Papers 2211.14236, arXiv.org, revised Dec 2023.
    15. Anish Agarwal & Vasilis Syrgkanis, 2022. "Synthetic Blip Effects: Generalizing Synthetic Controls for the Dynamic Treatment Regime," Papers 2210.11003, arXiv.org.
    16. Xingyu Li & Yan Shen & Qiankun Zhou, 2022. "Confidence Intervals of Treatment Effects in Panel Data Models with Interactive Fixed Effects," Papers 2202.12078, arXiv.org.
    17. Hyungsik Roger Roger Moon & Martin Weidner, 2014. "Linear regression for panel with unknown number of factors as interactive fixed effects," CeMMAP working papers 35/14, Institute for Fiscal Studies.
    18. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    19. Ghanem, Dalia, 2017. "Testing identifying assumptions in nonseparable panel data models," Journal of Econometrics, Elsevier, vol. 197(2), pages 202-217.
    20. 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.

    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:oup:emjrnl:v:24:y:2021:i:2:p:c40-c77.. 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: Oxford University Press (email available below). General contact details of provider: https://edirc.repec.org/data/resssea.html .

    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.