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Nonparametric Instrumental Regression

Author

Listed:
  • Serge Darolles

    (DRM-Finance - DRM - Dauphine Recherches en Management - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Pierre Florens

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRA - Institut National de la Recherche Agronomique - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées)

  • Yanqin Fan

    (Department of Economics - Vanderbilt University [Nashville])

  • Eric Renault

    (Department of Economics - Brown University)

Abstract

The focus of this paper is the nonparametric estimation of an instrumental regression function f defined by conditional moment restrictions that stem from a structural econometric model E[Y − f (Z) | W] = 0, and involve endogenous variables Y and Z and instruments W. The function f is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyzes identification and overidentification of this model, and presents asymptotic properties of the estimated nonparametric instrumental regression function.

Suggested Citation

  • Serge Darolles & Jean-Pierre Florens & Yanqin Fan & Eric Renault, 2011. "Nonparametric Instrumental Regression," Post-Print halshs-00677716, HAL.
  • Handle: RePEc:hal:journl:halshs-00677716
    DOI: 10.3982/ECTA6539
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00677716
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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.
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    6. 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.
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    14. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, July.
    15. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
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    More about this item

    Keywords

    integral equation; Instrumental variables; ill-posed problem; Tikhonov regularization; kernel smoothing;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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