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Additive Nonparametric Instrumental Regressions: A Guide to Implementation

Author

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  • Samuele Centorrino
  • Frederique Feve
  • Jean-Pierre Florens

Abstract

We present a review on the implementation of regularization methods for the estimation of additive nonparametric regression models with instrumental variables. We consider various versions of Tikhonov, Landweber-Fridman and Sieve (Petrov-Galerkin) regularization. We review data-driven techniques for the sequential choice of the smoothing and the regularization parameters. Through Monte-Carlo simulations, we discuss the finite sample properties of each regularization method for different smoothness properties of the regression function. Finally, we present an application to the estimation of the Engel curve for food in a sample of rural households in Pakistan, where a partially linear specification is described that allows one to embed other exogenous covariates.

Suggested Citation

  • Samuele Centorrino & Frederique Feve & Jean-Pierre Florens, 2017. "Additive Nonparametric Instrumental Regressions: A Guide to Implementation," Department of Economics Working Papers 17-06, Stony Brook University, Department of Economics.
  • Handle: RePEc:nys:sunysb:17-06
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    References listed on IDEAS

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    1. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    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. Florens, Jean-Pierre & Simoni, Anna, 2012. "Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior," Journal of Econometrics, Elsevier, vol. 170(2), pages 458-475.
    4. Deniz Ozabaci & Daniel J. Henderson & Liangjun Su, 2014. "Additive Nonparametric Regression in the Presence of Endogenous Regressors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 555-575, October.
    5. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    6. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
    7. JOHANNES, Jan & VAN BELLEGEM, Sébastien & VANHEMS, Anne, 2010. "Iterative regularization in nonparametric instrumental regression," CORE Discussion Papers 2010055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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(03), pages 472-496, June.
    9. Hoderlein, Stefan & Holzmann, Hajo, 2011. "Demand Analysis As An Ill-Posed Inverse Problem With Semiparametric Specification," Econometric Theory, Cambridge University Press, vol. 27(03), pages 609-638, June.
    10. Sonia Bhalotra & Cliff Attfield, 1998. "Intrahousehold resource allocation in rural Pakistan: a semiparametric analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 463-480.
    11. 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.
    12. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, Department of Economics, University of Bristol, UK.
    13. Horowitz, Joel L., 2014. "Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter," Journal of Econometrics, Elsevier, vol. 180(2), pages 158-173.
    14. 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. Liu, Chu-An & Tao, Jing, 2016. "Model selection and model averaging in nonparametric instrumental variables models," MPRA Paper 69492, University Library of Munich, Germany.
    2. Samuele CENTORRINO & Jeffrey S. RACINE, 2017. "Semiparametric Varying Coefficient Models with Endogenous Covariates," Annals of Economics and Statistics, GENES, issue 128, pages 261-295.
    3. repec:eee:econom:v:201:y:2017:i:2:p:269-291 is not listed on IDEAS

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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