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Additive Nonparametric Instrumental Regressions: A Guide to Implementation

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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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    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. 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.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    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. Johannes, J. & Van Bellegem, S. & Vanhems, A., 2013. "Iterative regularisation in nonparametric instrumental regression," LIDAM Reprints ISBA 2013003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. 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.
    7. Johannes, Jan & Schwarz, Maik, 2011. "Partially adaptive nonparametric instrumental regression by model selection," LIDAM Reprints ISBA 2011049, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Horowitz, Joel L. & Lee, Sokbae, 2012. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," Journal of Econometrics, Elsevier, vol. 168(2), pages 175-188.
    9. Cardot, Herve & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," LIDAM Reprints ISBA 2010034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. 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.
    11. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2013. "On the Testability of Identification in Some Nonparametric Models With Endogeneity," Econometrica, Econometric Society, vol. 81(6), pages 2535-2559, November.
    12. 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).
    13. 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.
    14. 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.
    15. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    16. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2010. "Iterative Regularization in Nonparametric Instrumental Regression," TSE Working Papers 10-184, Toulouse School of Economics (TSE).
    17. 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.
    18. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    19. 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.
    20. 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.
    21. Andres Santos, 2012. "Inference in Nonparametric Instrumental Variables With Partial Identification," Econometrica, Econometric Society, vol. 80(1), pages 213-275, January.
    22. Cardot, Hervé & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 395-408, February.
    23. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    24. 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.
    25. 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).
    26. Hoderlein, Stefan & Holzmann, Hajo, 2011. "Demand Analysis As An Ill-Posed Inverse Problem With Semiparametric Specification," Econometric Theory, Cambridge University Press, vol. 27(3), pages 609-638, June.
    27. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, School of Economics, University of Bristol, UK.
    28. 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.
    29. Clifford M. Hurvich & Jeffrey S. Simonoff & Chih‐Ling Tsai, 1998. "Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 271-293.
    30. 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. Benatia, David & Carrasco, Marine & Florens, Jean-Pierre, 2017. "Functional linear regression with functional response," Journal of Econometrics, Elsevier, vol. 201(2), pages 269-291.
    2. Babii, Andrii & Florens, Jean-Pierre, 2017. "Are unobservables separable?," TSE Working Papers 17-802, Toulouse School of Economics (TSE).
    3. Escanciano, Juan Carlos & Li, Wei, 2021. "Optimal Linear Instrumental Variables Approximations," Journal of Econometrics, Elsevier, vol. 221(1), pages 223-246.
    4. Liu, Chu-An & Tao, Jing, 2016. "Model selection and model averaging in nonparametric instrumental variables models," MPRA Paper 69492, University Library of Munich, Germany.
    5. Samuele CENTORRINO & Jeffrey S. RACINE, 2017. "Semiparametric Varying Coefficient Models with Endogenous Covariates," Annals of Economics and Statistics, GENES, issue 128, pages 261-295.
    6. Jad Beyhum & Elia Lapenta & Pascal Lavergne, 2023. "One-step nonparametric instrumental regression using smoothing splines," Papers 2307.14867, arXiv.org, revised Sep 2023.
    7. Samuele Centorrino & Jean-Pierre Florens & Jean-Michel Loubes, 2022. "Fairness constraint in Structural Econometrics and Application to fair estimation using Instrumental Variables," Papers 2202.08977, arXiv.org.
    8. Botosaru, Irene, 2023. "Time-varying unobserved heterogeneity in earnings shocks," Journal of Econometrics, Elsevier, vol. 235(2), pages 1378-1393.
    9. Shunan Zhao & Bing Qian & Subal C. Kumbhakar, 2020. "Estimation of productivity and markups with price dispersion: Evidence from Chinese manufacturing during economic transition," Southern Economic Journal, John Wiley & Sons, vol. 87(2), pages 666-699, October.
    10. Beyhum, Jad & Lapenta, Elia & Lavergne, Pascal, 2023. "One-step nonparametric instrumental regression using smoothing splines," TSE Working Papers 23-1467, Toulouse School of Economics (TSE).
    11. Hoshino, Tadao, 2022. "Sieve IV estimation of cross-sectional interaction models with nonparametric endogenous effect," Journal of Econometrics, Elsevier, vol. 229(2), pages 263-275.
    12. Samuele Centorrino & Jean-Pierre Florens, 2014. "Nonparametric Instrumental Variable Estimation of Binary Response Models," Department of Economics Working Papers 14-07, Stony Brook University, Department of Economics.
    13. Irene Botosaru & Chris Muris & Senay Sokullu, 2022. "Time-Varying Linear Transformation Models with Fixed Effects and Endogeneity for Short Panels," Department of Economics Working Papers 2022-01, McMaster University.
    14. Jean-Pierre Florens & Elia Lapenta, 2022. "Partly Linear Instrumental Variables Regressions without Smoothing on the Instruments," Papers 2212.11012, arXiv.org, revised Oct 2023.
    15. Hiroyuki Kawakatsu, 2022. "Local projection variance impulse response," Empirical Economics, Springer, vol. 62(3), pages 1219-1244, March.
    16. Centorrino, Samuele & Florens, Jean-Pierre, 2021. "Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors," Econometrics and Statistics, Elsevier, vol. 17(C), pages 35-63.
    17. Emir Malikov & Shunan Zhao & Subal C. Kumbhakar, 2020. "Estimation of firm‐level productivity in the presence of exports: Evidence from China's manufacturing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 457-480, June.

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    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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