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Partly linear instrumental variables regressions without smoothing on the instruments

Author

Listed:
  • Jean-Pierre Florens

    (Toulouse School of Economics)

  • Elia Lapenta

    (CREST and ENSAE)

Abstract

We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the Landweber–Fridman regularization scheme to the estimation of this semiparametric model. We then show the asymptotic normality of the parametric estimator and obtain the convergence rate for the nonparametric estimator. Our estimator that does not smooth on the instruments coincides with a typical estimator that does smooth on the instruments but keeps the respective bandwidth fixed as the sample size increases. We propose a data driven method for the selection of the regularization parameter, and in a simulation study we show the attractive performance of our estimators.

Suggested Citation

  • Jean-Pierre Florens & Elia Lapenta, 2024. "Partly linear instrumental variables regressions without smoothing on the instruments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 897-920, September.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:3:d:10.1007_s11749-024-00931-z
    DOI: 10.1007/s11749-024-00931-z
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    References listed on IDEAS

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    1. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 14/17, Institute for Fiscal Studies.
    2. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    3. Juan Carlos Escanciano, 2018. "A simple and robust estimator for linear regression models with strictly exogenous instruments," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 36-54, February.
    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. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    6. Lavergne, Pascal & Patilea, Valentin, 2013. "Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory," Journal of Econometrics, Elsevier, vol. 177(1), pages 47-59.
    7. Birke, Melanie & Van Bellegem, Sebastien & Van Keilegom, Ingrid, 2017. "Semi-parametric Estimation in a Single-index Model with Endogenous Variables," LIDAM Reprints ISBA 2017022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Denis Chetverikov & Dongwoo Kim & Daniel Wilhelm, 2018. "Nonparametric instrumental-variable estimation," Stata Journal, StataCorp LP, vol. 18(4), pages 937-950, December.
    9. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    10. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    11. 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.
    12. Melanie Birke & Sebastien Van Bellegem & Ingrid Van Keilegom, 2017. "Semi-parametric Estimation in a Single-index Model with Endogenous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 168-191, March.
    13. 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.
    14. Andrii Babii & Jean-Pierre Florens, 2017. "Is completeness necessary? Estimation in nonidentified linear models," Papers 1709.03473, arXiv.org, revised Jan 2025.
    15. Centorrino Samuele & Feve Frederique & Florens Jean-Pierre, 2017. "Additive Nonparametric Instrumental Regressions: A Guide to Implementation," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-25, January.
    16. Jinho Choi & Juan Carlos Escanciano & Junjie Guo, 2022. "Generalized band spectrum estimation with an application to the New Keynesian Phillips curve," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 1055-1078, August.
    17. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    18. Chen, Qihui, 2021. "Robust and optimal estimation for partially linear instrumental variables models with partial identification," Journal of Econometrics, Elsevier, vol. 221(2), pages 368-380.
    19. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sebastien, 2012. "Instrumental regression in partially linear models," LIDAM Reprints ISBA 2012017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. 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.
    21. J. P. Florens & J. S. Racine & S. Centorrino, 2018. "Nonparametric instrumental variable derivative estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 368-391, April.
    22. FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2012. "Instrumental regression in partially linear models," LIDAM Reprints CORE 2456, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    23. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    24. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    25. 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.
    26. Escanciano, Juan Carlos, 2022. "Semiparametric Identification And Fisher Information," Econometric Theory, Cambridge University Press, vol. 38(2), pages 301-338, April.
    27. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
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