IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/125634.html
   My bibliography  Save this paper

Factor and factor loading augmented estimators for panel regression

Author

Listed:
  • Beyhum, Jad
  • Gautier, Eric

Abstract

This paper considers linear panel data models where the dependence of the regressors and the unobservables is modelled through a factor structure. The asymptotic setting is such that the number of time periods and the sample size both go to infinity. Non-strong factors are allowed and the number of factors can grow to infinity with the sample size. We study a class of two-step estimators of the regression coefficients. In the first step, factors and factor loadings are estimated. Then, the second step corresponds to the panel regression of the outcome on the regressors and the estimates of the factors and the factor loadings from the first step. Different methods can be used in the first step while the second step is unique. We derive sufficient conditions on the first-step estimator and the data generating process under which the two-step estimator is asymptotically normal. Assumptions under which using an approach based on principal components analysis in the first step yields an asymptotically normal estimator are also given. The two-step procedure exhibits good finite sample properties in simulations.

Suggested Citation

  • Beyhum, Jad & Gautier, Eric, 2021. "Factor and factor loading augmented estimators for panel regression," TSE Working Papers 21-1219, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:125634
    as

    Download full text from publisher

    File URL: https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2021/wp_tse_1219.pdf
    File Function: Full Text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Pesaran, M. Hashem, 2015. "Time Series and Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780198759980.
    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. Greenaway-McGrevy, Ryan & Han, Chirok & Sul, Donggyu, 2012. "Asymptotic distribution of factor augmented estimators for panel regression," Journal of Econometrics, Elsevier, vol. 169(1), pages 48-53.
    5. Simon Reese & Joakim Westerlund, 2018. "Estimation of factor-augmented panel regressions with weakly influential factors," Econometric Reviews, Taylor & Francis Journals, vol. 37(5), pages 401-465, May.
    6. Gagliardini, Patrick & Gouriéroux, Christian, 2017. "Double instrumental variable estimation of interaction models with big data," Journal of Econometrics, Elsevier, vol. 201(2), pages 176-197.
    7. 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.
    8. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    9. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    10. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    11. 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).
    12. George Kapetanios & M. Hashem Pesaran, 2005. "Alternative Approaches to Estimation and Inference in Large Multifactor Panels: Small Sample Results with an Application to Modelling of Asset Returns," CESifo Working Paper Series 1416, CESifo.
    13. George Kapetanios & M. Hashem Pesaran, 2005. "Alternative Approaches to Estimation and Inference in Large Multifactor Panels: Small Sample Results with an Application to Modelling of Asset Returns," CESifo Working Paper Series 1416, CESifo.
    14. Jushan Bai & Peng Wang, 2016. "Econometric Analysis of Large Factor Models," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 53-80, 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. Guowei Cui & Milda NorkutÄ— & Vasilis Sarafidis & Takashi Yamagata, 2022. "Two-stage instrumental variable estimation of linear panel data models with interactive effects [Eigenvalue ratio test for the number of factors]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 340-361.
    2. 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.
    3. Westerlund, Joakim & Urbain, Jean-Pierre, 2013. "On the implementation and use of factor-augmented regressions in panel data," Journal of Asian Economics, Elsevier, vol. 28(C), pages 3-11.
    4. Kazuhiko Hayakawa & Shuichi Nagata & Takashi Yamagata, 2018. "A robust approach to heteroskedasticity, error serial correlation and slope heterogeneity for large linear panel data models with interactive effects," ISER Discussion Paper 1037, Institute of Social and Economic Research, Osaka University.
    5. Jörg Breitung & Philipp Hansen, 2021. "Alternative estimation approaches for the factor augmented panel data model with small T," Empirical Economics, Springer, vol. 60(1), pages 327-351, January.
    6. George Kapetanios & Laura Serlenga & Yongcheol Shin, 2019. "Testing for Correlated Factor Loadings in Cross Sectionally Dependent Panels," SERIES 02-2019, Dipartimento di Economia e Finanza - Università degli Studi di Bari "Aldo Moro", revised Jun 2019.
    7. Westerlund, Joakim & Urbain, Jean-Pierre, 2015. "Cross-sectional averages versus principal components," Journal of Econometrics, Elsevier, vol. 185(2), pages 372-377.
    8. Matthew Harding & Carlos Lamarche & Chris Muris, 2022. "Estimation of a Factor-Augmented Linear Model with Applications Using Student Achievement Data," Papers 2203.03051, arXiv.org.
    9. 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.
    10. 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.
    11. 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.
    12. Norkutė, Milda & Sarafidis, Vasilis & Yamagata, Takashi & Cui, Guowei, 2021. "Instrumental variable estimation of dynamic linear panel data models with defactored regressors and a multifactor error structure," Journal of Econometrics, Elsevier, vol. 220(2), pages 416-446.
    13. Guowei Cui & Kazuhiko Hayakawa & Shuichi Nagata & Takashi Yamagata, 2018. "A robust approach to heteroskedasticity, error serial correlation and slope heterogeneity for large linear panel data models with interactive effects," ISER Discussion Paper 1037r, Institute of Social and Economic Research, Osaka University, revised Jun 2019.
    14. Michael Vogt & Christopher Walsh & Oliver Linton, 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Papers 2206.12152, arXiv.org.
    15. Simon Reese & Joakim Westerlund, 2018. "Estimation of factor-augmented panel regressions with weakly influential factors," Econometric Reviews, Taylor & Francis Journals, vol. 37(5), pages 401-465, May.
    16. Lu'is A. V. Cat~ao & Jan Ditzen & Daniel Marcel te Kaat, 2023. "Global Factors in Non-core Bank Funding and Exchange Rate Flexibility," Papers 2310.11552, arXiv.org, revised Jan 2024.
    17. 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.
    18. Jörg Breitung & In Choi, 2013. "Factor models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 11, pages 249-265, Edward Elgar Publishing.
      • In Choi & Jorg Breitung, 2011. "Factor models," Working Papers 1121, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy), revised Dec 2011.
    19. Wang,Dieter, 2021. "Natural Capital and Sovereign Bonds," Policy Research Working Paper Series 9606, The World Bank.
    20. Joakim Westerlund, 2020. "A cross‐section average‐based principal components approach for fixed‐T panels," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(6), pages 776-785, September.

    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:tse:wpaper:125634. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.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.