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Identification and Estimation by Penalization in Nonparametric Instrumental Regression

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  • Florens, Jean-Pierre
  • Johannes, Jan
  • Van Bellegem, Sébastien

Abstract

The nonparametric estimation of a regression function from conditional moment restrictions involving instrumental variables is considered. The rate of convergence of penalized estimators is studied in the case where the regression function is not identified from the conditional moment restriction. We also study the gain of modifying the penalty in the estimation, considering derivatives in the penalty. We analyze the effect of this modification on the identification of the regression function and the rate of convergence of its estimator.
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Suggested Citation

  • Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2009. "Identification and Estimation by Penalization in Nonparametric Instrumental Regression," TSE Working Papers 09-076, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:22276
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    References listed on IDEAS

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    1. Xiaohong Chen & Markus Reiss, 2007. "On Rate Optimality for Ill-posed Inverse Problems in Econometrics," Cowles Foundation Discussion Papers 1626, Cowles Foundation for Research in Economics, Yale University.
    2. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    3. Jean‐Pierre Florens & Jan Johannes & Sébastien Van Bellegem, 2012. "Instrumental regression in partially linear models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 304-324, June.
    4. 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.
    5. P. Gagliardini & O. Scaillet, 2006. "Tikhonov Regularization for Functional Minimum Distance Estimators," Swiss Finance Institute Research Paper Series 06-30, Swiss Finance Institute, revised Nov 2006.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    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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