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Identifying Distributional Characteristics in Random Coefficients Panel Data Models

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  • Manuel Arellano
  • Stéphane Bonhomme

Abstract

We study the identification of panel models with linear individual-specific coefficients when T is fixed. We show identification of the variance of the effects under conditional uncorrelatedness. Identification requires restricted dependence of errors, reflecting a trade-off between heterogeneity and error dynamics. We show identification of the probability distribution of individual effects when errors follow an Autoregressive Moving Average process under conditional independence. We discuss Generalized Method of Moments estimation of moments of effects and errors and construct non-parametric estimators of their densities. As an application, we estimate the effect that a mother smoking during pregnancy has on her child's birth weight. Copyright , Oxford University Press.

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  • Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 987-1020.
    • Handle: RePEc:oup:restud:v:79:y:2012:i:3:p:987-1020
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    1. Patrick GAGLIARDINI & Elisa OSSOLA & Olivier SCAILLET, "undated". "Time-Varying Risk Premium In Large Cross-Sectional Equidity Datasets," Swiss Finance Institute Research Paper Series 11-40, Swiss Finance Institute.
    2. Manuel Arellano & Stéphane Bonhomme, 2015. "Nonlinear panel data estimation via quantile regressions," CeMMAP working papers CWP40/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Lychagin, Sergey, 2016. "Spillovers, absorptive capacity and agglomeration," Journal of Urban Economics, Elsevier, vol. 96(C), pages 17-35.
    4. Evdokimov, Kirill & White, Halbert, 2012. "Some Extensions Of A Lemma Of Kotlarski," Econometric Theory, Cambridge University Press, vol. 28(04), pages 925-932, August.
    5. Hoderlein, Stefan & Sherman, Robert, 2015. "Identification and estimation in a correlated random coefficients binary response model," Journal of Econometrics, Elsevier, vol. 188(1), pages 135-149.
    6. Hoderlein, Stefan & Holzmann, Hajo & Meister, Alexander, 2017. "The triangular model with random coefficients," Journal of Econometrics, Elsevier, vol. 201(1), pages 144-169.
    7. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    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. Magnac, Thierry & Pistolesi, Nicolas & Roux, Sébastien, 2013. "Post schooling human capital investments and the life cycle variance of earnings," IDEI Working Papers 765, Institut d'Économie Industrielle (IDEI), Toulouse.
    10. 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.
    11. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Shosei Sakaguchi, 2017. "Estimation of Average Treatment Effects Using Panel Data when Treatment Effects Are Heterogeneous by Unobserved Fixed Effects," KIER Working Papers 970, Kyoto University, Institute of Economic Research.
    13. William H Greene & Mark N Harris & Christopher Spencer, 2013. "Estimating the Standard Errors of Individual-Specific Parameters in Random Parameters Models," Bankwest Curtin Economics Centre Working Paper series WP1309, Bankwest Curtin Economics Centre (BCEC), Curtin Business School.
    14. Ryo Okui & Takahide Yanagi, 2018. "Kernel Estimation for Panel Data with Heterogeneous Dynamics," Papers 1802.08825, arXiv.org, revised Mar 2018.
    15. Gao, Yichen & Li, Cong & Liang, Zhongwen, 2015. "Binary response correlated random coefficient panel data models," Journal of Econometrics, Elsevier, vol. 188(2), pages 421-434.
    16. Stéphane Bonhomme & Elena Manresa, 2012. "Grouped Patterns of Heterogeneity in Panel Data," Working Papers wp2012_1208, CEMFI.
    17. Stefan Hoderlein & Yuya Sasaki, 2011. "On the role of time in nonseparable panel data models," CeMMAP working papers CWP15/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Emine Boz & Gita Gopinath & Mikkel Plagborg-Møller, 2017. "Global Trade and the Dollar," NBER Working Papers 23988, National Bureau of Economic Research, Inc.
    19. Sung Jae Jun & Yoonseok Lee & Youngki Shin, 2016. "Treatment Effects With Unobserved Heterogeneity: A Set Identification Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 302-311, April.
    20. repec:gnv:wpaper:unige:76321 is not listed on IDEAS
    21. Patrick Gagliardini & Elisa Ossola & Olivier Scaillet, 2016. "Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets," Econometrica, Econometric Society, vol. 84, pages 985-1046, May.
    22. repec:cup:etheor:v:34:y:2018:i:01:p:134-165_00 is not listed on IDEAS

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    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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