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Identification and estimation by penalization in nonparametric instrumental regression

Author

Listed:
  • FLORENS, Jean-Pierre
  • JOHANNES, Jan
  • VAN BELLEGEM, Sébastien

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

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

Suggested Citation

  • FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2007. "Identification and estimation by penalization in nonparametric instrumental regression," LIDAM Discussion Papers CORE 2007085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2007085
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    4. 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.
    5. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
    6. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    7. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    instrumental variable; nonparametric estimation; ill-posed inverse problem; identification; penalized estimator; Tikhonov regularization; Sobolev norm;
    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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