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A Linear Estimator for FactorAugmented Fixed-T Panels with Endogenous Regressors

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  • Arturas Juodis
  • Vasilis Sarafidis

Abstract

A novel method-of-moments approach is proposed for the estimation of factor-augmented panel data models with endogenous regressors when T is fixed. The underlying methodology involves approximating the unobserved common factors using observed factor proxies. The resulting moment conditions are linear in the parameters. The proposed approach addresses several issues which arise with existing nonlinear estimators that are available in fixed T panels, such as local minima-related problems, a sensitivity to particular normalisation schemes, and a potential lack of global identification. We apply our approach to a large panel of households and estimate the price elasticity of urban water demand. A simulation study confirms that our approach performs well in finite samples.

Suggested Citation

  • Arturas Juodis & Vasilis Sarafidis, 2020. "A Linear Estimator for FactorAugmented Fixed-T Panels with Endogenous Regressors," Monash Econometrics and Business Statistics Working Papers 5/20, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2020-5
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/wp05-2020.pdf
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    References listed on IDEAS

    as
    1. Andrews, Donald W. K., 1987. "Asymptotic Results for Generalized Wald Tests," Econometric Theory, Cambridge University Press, vol. 3(3), pages 348-358, June.
    2. Artūras Juodis & Vasilis Sarafidis, 2018. "Fixed T dynamic panel data estimators with multifactor errors," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 893-929, September.
    3. Robertson, Donald & Sarafidis, Vasilis, 2015. "IV estimation of panels with factor residuals," Journal of Econometrics, Elsevier, vol. 185(2), pages 526-541.
    4. 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.
    5. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    6. Ahn, Seung C. & Lee, Young H. & Schmidt, Peter, 2013. "Panel data models with multiple time-varying individual effects," Journal of Econometrics, Elsevier, vol. 174(1), pages 1-14.
    7. Hsiao, Cheng & Hashem Pesaran, M. & Kamil Tahmiscioglu, A., 2002. "Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods," Journal of Econometrics, Elsevier, vol. 109(1), pages 107-150, July.
    8. 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.
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    Citations

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    Cited by:

    1. Jiaqi Xiao & Artūras Juodis & Yiannis Karavias & Vasilis Sarafidis & Jan Ditzen, 2023. "Improved tests for Granger noncausality in panel data," Stata Journal, StataCorp LP, vol. 23(1), pages 230-242, March.
    2. 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.
    3. Freeman, Hugo & Weidner, Martin, 2023. "Linear panel regressions with two-way unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 237(1).
    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. Artūras Juodis & Yiannis Karavias & Vasilis Sarafidis, 2021. "A homogeneous approach to testing for Granger non-causality in heterogeneous panels," Empirical Economics, Springer, vol. 60(1), pages 93-112, January.
    6. Hugo Freeman & Martin Weidner, 2021. "Linear Panel Regressions with Two-Way Unobserved Heterogeneity," Papers 2109.11911, arXiv.org, revised Aug 2022.
    7. 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.
    8. Artūras Juodis, 2022. "A regularization approach to common correlated effects estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(4), pages 788-810, June.
    9. 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.
    10. 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.
    11. Li, Qi & Sarafidis, Vasilis & Westerlund, Joakim, 2020. "Essays in Honor of Professor Badi H Baltagi: Editorial," MPRA Paper 104751, University Library of Munich, Germany.
    12. Jianqing Fan & Kunpeng Li & Yuan Liao, 2020. "Recent Developments on Factor Models and its Applications in Econometric Learning," Papers 2009.10103, arXiv.org.
    13. Ignace De Vos & Gerdie Everaert & Vasilis Sarafidis, 2021. "A method for evaluating the rank condition for CCE estimators," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 21/1013, Ghent University, Faculty of Economics and Business Administration.
    14. Yan Sun & Wei Huang, 2022. "Quasi-maximum likelihood estimation of short panel data models with time-varying individual effects," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 93-114, January.
    15. Juodis, Arturas & Sarafidis, Vasilis, 2020. "Online Supplement to An Incidental Parameters Free Inference Approach for Panels with Common Shocks," MPRA Paper 104908, University Library of Munich, Germany.
    16. Robert F. Phillips & Benjamin D. Williams, 2024. "A Simple Interactive Fixed Effects Estimator for Short Panels," Papers 2410.12709, arXiv.org.
    17. Qian Sun, 2023. "SOE wage premium in China: new evidence," Empirical Economics, Springer, vol. 64(3), pages 1121-1147, March.
    18. 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.

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    More about this item

    Keywords

    panel data; common factors; fixed T consistency; moment conditions; urban water management;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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