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Non parametric analysis of panel data models with endogenous variables

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  • Fève, Frédérique
  • Florens, Jean-Pierre

Abstract

This paper considers the estimation of panel data models by first differences in the presence of endogenous variables and under an instrumental variables condition. This framework leads to the resolution of linear inverse problems solved using a Tikhonov regularization with L2 or Sobolev penalty. Rates of convergence and data driven selection of the regularization parameters are proposed. The practical implementation of our estimators is presented and some Monte Carlo simulations show the potential of the method.

Suggested Citation

  • Fève, Frédérique & Florens, Jean-Pierre, 2014. "Non parametric analysis of panel data models with endogenous variables," Journal of Econometrics, Elsevier, vol. 181(2), pages 151-164.
    • Handle: RePEc:eee:econom:v:181:y:2014:i:2:p:151-164
    DOI: 10.1016/j.jeconom.2014.03.009
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    References listed on IDEAS

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    1. Frédérique Fève & Jean-Pierre Florens, 2010. "The practice of non-parametric estimation by solving inverse problems: the example of transformation models," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 1-27, October.
    2. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    3. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(3), pages 497-521, June.
    4. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    5. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    6. Hu, Yingyao & Shiu, Ji-Liang, 2018. "Nonparametric Identification Using Instrumental Variables: Sufficient Conditions For Completeness," Econometric Theory, Cambridge University Press, vol. 34(3), pages 659-693, June.
    7. Joel L. Horowitz, 2007. "Asymptotic Normality Of A Nonparametric Instrumental Variables Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1329-1349, November.
    8. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2011. "Identification And Estimation By Penalization In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 27(3), pages 472-496, June.
    9. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sebastien, 2011. "Identification and estimation by penalization in Nonparametric Instrumental Regression," LIDAM Reprints ISBA 2011046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    11. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011. "Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator," Econometric Theory, Cambridge University Press, vol. 27(3), pages 522-545, June.
    12. J. P. Florens & J. S. Racine & S. Centorrino, 2018. "Nonparametric instrumental variable derivative estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 368-391, April.
    13. Andrews, Donald W.K., 2017. "Examples of L2-complete and boundedly-complete distributions," Journal of Econometrics, Elsevier, vol. 199(2), pages 213-220.
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    15. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    16. Patrick Gagliardini & Olivier Scaillet, 2012. "Nonparametric Instrumental Variable Estimation of Structural Quantile Effects," Econometrica, Econometric Society, vol. 80(4), pages 1533-1562, July.
    17. Breunig, Christoph & Johannes, Jan, 2013. "Adaptive estimation of functionals in nonparametric instrumental regression," LIDAM Discussion Papers ISBA 2013058, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Joel L. Horowitz, 2006. "Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables," Econometrica, Econometric Society, vol. 74(2), pages 521-538, March.
    19. FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2011. "Identification and estimation by penalization in nonparametric instrumental regression," LIDAM Reprints CORE 2320, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    21. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
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    Cited by:

    1. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2020. "Robust frontier estimation from noisy data: A Tikhonov regularization approach," Econometrics and Statistics, Elsevier, vol. 14(C), pages 1-23.
    2. Centorrino Samuele & Feve Frederique & Florens Jean-Pierre, 2017. "Additive Nonparametric Instrumental Regressions: A Guide to Implementation," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-25, January.
    3. Daniel Wilhelm, 2015. "Identification and estimation of nonparametric panel data regressions with measurement error," CeMMAP working papers CWP34/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. De Monte Enrico, 2024. "Nonparametric Instrumental Regression with Two-Way Fixed Effects," Journal of Econometric Methods, De Gruyter, vol. 13(1), pages 49-66, January.

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    More about this item

    Keywords

    Panel data; Endogeneity; Instrumental variables; Inverse problems;
    All these keywords.

    JEL classification:

    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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