[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2206.12152.html
   My bibliography  Save this paper

Estimation and Inference in High-Dimensional Panel Data Models with Interactive Fixed Effects

Author

Listed:
  • Oliver Linton
  • Maximilian Ruecker
  • Michael Vogt
  • Christopher Walsh
Abstract
We develop new econometric methods for estimation and inference in high-dimensional panel data models with interactive fixed effects. Our approach can be regarded as a non-trivial extension of the very popular common correlated effects (CCE) approach. Roughly speaking, we proceed as follows: We first construct a projection device to eliminate the unobserved factors from the model by applying a dimensionality reduction transform to the matrix of cross-sectionally averaged covariates. The unknown parameters are then estimated by applying lasso techniques to the projected model. For inference purposes, we derive a desparsified version of our lasso-type estimator. While the original CCE approach is restricted to the low-dimensional case where the number of regressors is small and fixed, our methods can deal with both low- and high-dimensional situations where the number of regressors is large and may even exceed the overall sample size. We derive theory for our estimation and inference methods both in the large-T-case, where the time series length T tends to infinity, and in the small-T-case, where T is a fixed natural number. Specifically, we derive the convergence rate of our estimator and show that its desparsified version is asymptotically normal under suitable regularity conditions. The theoretical analysis of the paper is complemented by a simulation study and an empirical application to characteristic based asset pricing.

Suggested Citation

  • Oliver Linton & Maximilian Ruecker & Michael Vogt & Christopher Walsh, 2022. "Estimation and Inference in High-Dimensional Panel Data Models with Interactive Fixed Effects," Papers 2206.12152, arXiv.org, revised Nov 2024.
    • Handle: RePEc:arx:papers:2206.12152
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2206.12152
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hansen, Christian & Liao, Yuan, 2019. "The Factor-Lasso And K-Step Bootstrap Approach For Inference In High-Dimensional Economic Applications," Econometric Theory, Cambridge University Press, vol. 35(3), pages 465-509, June.
    2. 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.
    3. 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.
    4. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    5. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    6. Kapetanios, G. & Pesaran, M. Hashem & Yamagata, T., 2011. "Panels with non-stationary multifactor error structures," Journal of Econometrics, Elsevier, vol. 160(2), pages 326-348, February.
    7. Alexandre Belloni & Victor Chernozhukov & Christian Hansen & Damian Kozbur, 2016. "Inference in High-Dimensional Panel Models With an Application to Gun Control," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 590-605, October.
    8. Kapetanios, George, 2010. "A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 397-409.
    9. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso," Journal of Econometrics, Elsevier, vol. 191(1), pages 86-109.
    10. Chudik, Alexander & Pesaran, M. Hashem, 2015. "Common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors," Journal of Econometrics, Elsevier, vol. 188(2), pages 393-420.
    11. Pesaran, M. Hashem & Tosetti, Elisa, 2011. "Large panels with common factors and spatial correlation," Journal of Econometrics, Elsevier, vol. 161(2), pages 182-202, April.
    12. Kock, Anders Bredahl, 2013. "Oracle Efficient Variable Selection In Random And Fixed Effects Panel Data Models," Econometric Theory, Cambridge University Press, vol. 29(1), pages 115-152, February.
    13. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    14. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    15. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    16. Hyungsik Roger Moon & Martin Weidner, 2018. "Nuclear Norm Regularized Estimation of Panel Regression Models," Papers 1810.10987, arXiv.org, revised Jun 2023.
    17. Joakim Westerlund & Yana Petrova & Milda Norkute, 2019. "CCE in fixed‐T panels," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 746-761, August.
    18. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    19. Kock, Anders Bredahl, 2016. "Oracle inequalities, variable selection and uniform inference in high-dimensional correlated random effects panel data models," Journal of Econometrics, Elsevier, vol. 195(1), pages 71-85.
    20. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    21. 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.
    22. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    23. Kock, Anders Bredahl & Tang, Haihan, 2019. "Uniform Inference In High-Dimensional Dynamic Panel Data Models With Approximately Sparse Fixed Effects," Econometric Theory, Cambridge University Press, vol. 35(2), pages 295-359, April.
    24. 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).
    25. repec:hal:journl:peer-00796743 is not listed on IDEAS
    26. Juodis, Artūras & Karabiyik, Hande & Westerlund, Joakim, 2021. "On the robustness of the pooled CCE estimator," Journal of Econometrics, Elsevier, vol. 220(2), pages 325-348.
    27. Joakim Westerlund, 2018. "CCE in panels with general unknown factors," Econometrics Journal, Royal Economic Society, vol. 21(3), pages 264-276, October.
    Full references (including those not matched with items on IDEAS)

    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. Vogt, M. & Walsh, C. & Linton, O., 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Janeway Institute Working Papers 2218, Faculty of Economics, University of Cambridge.
    2. Vogt, M. & Walsh, C. & Linton, O., 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Cambridge Working Papers in Economics 2242, Faculty of Economics, University of Cambridge.
    3. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.
    4. Freeman, Hugo & Weidner, Martin, 2023. "Linear panel regressions with two-way unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 237(1).
    5. Stauskas, Ovidijus & De Vos, Ignace, 2024. "Handling Distinct Correlated Effects with CCE," MPRA Paper 120194, University Library of Munich, Germany.
    6. Su, Liangjun & Ju, Gaosheng, 2018. "Identifying latent grouped patterns in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 554-573.
    7. 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.
    8. Juodis, Artūras & Karabiyik, Hande & Westerlund, Joakim, 2021. "On the robustness of the pooled CCE estimator," Journal of Econometrics, Elsevier, vol. 220(2), pages 325-348.
    9. 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.
    10. Juodis, Artūras & Sarafidis, Vasilis, 2022. "An incidental parameters free inference approach for panels with common shocks," Journal of Econometrics, Elsevier, vol. 229(1), pages 19-54.
    11. Alexander Chudik & M. Hashem Pesaran, 2013. "Large panel data models with cross-sectional dependence: a survey," Globalization Institute Working Papers 153, Federal Reserve Bank of Dallas.
    12. 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.
    13. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    14. 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.
    15. Evan Totty, 2017. "The Effect Of Minimum Wages On Employment: A Factor Model Approach," Economic Inquiry, Western Economic Association International, vol. 55(4), pages 1712-1737, October.
    16. Jiang, Bin & Yang, Yanrong & Gao, Jiti & Hsiao, Cheng, 2021. "Recursive estimation in large panel data models: Theory and practice," Journal of Econometrics, Elsevier, vol. 224(2), pages 439-465.
    17. Hugo Freeman & Martin Weidner, 2021. "Linear Panel Regressions with Two-Way Unobserved Heterogeneity," Papers 2109.11911, arXiv.org, revised Aug 2022.
    18. Hsiao, Cheng, 2018. "Panel models with interactive effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 645-673.
    19. Luca Margaritella & Joakim Westerlund, 2023. "Using information criteria to select averages in CCE," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 405-421.
    20. Hou, Lei & Li, Kunpeng & Li, Qi & Ouyang, Min, 2021. "Revisiting the location of FDI in China: A panel data approach with heterogeneous shocks," Journal of Econometrics, Elsevier, vol. 221(2), pages 483-509.

    More about this item

    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:2206.12152. 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.