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One-step smoothing splines instrumental regression

Author

Listed:
  • Jad Beyhum
  • Elia Lapenta
  • Pascal Lavergne

Abstract

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique regularization parameter. We derive rates of the convergence for the estimator and its first derivative, which are uniform in the support of the endogenous variable. We also address the issue of imposing monotonicity in estimation and extend the approach to a partly linear model. Simulations confirm the good performances of our estimator compared to two-step procedures. Our method yields economically sensible results when used to estimate Engel curves.

Suggested Citation

  • Jad Beyhum & Elia Lapenta & Pascal Lavergne, 2023. "One-step smoothing splines instrumental regression," Papers 2307.14867, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2307.14867
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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. Joachim Freyberger, 2017. "On Completeness and Consistency in Nonparametric Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 1629-1644, September.
    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. Xiaohong Chen & Timothy M. Christensen, 2018. "Optimal sup‐norm rates and uniform inference on nonlinear functionals of nonparametric IV regression," Quantitative Economics, Econometric Society, vol. 9(1), pages 39-84, March.
    5. 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.
    6. Denis Chetverikov & Dongwoo Kim & Daniel Wilhelm, 2018. "Nonparametric instrumental-variable estimation," Stata Journal, StataCorp LP, vol. 18(4), pages 937-950, December.
    7. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    8. 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.
    9. Krikamol Muandet & Arash Mehrjou & Si Kai Lee & Anant Raj, 2019. "Dual Instrumental Variable Regression," Papers 1910.12358, arXiv.org, revised Oct 2020.
    10. 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.
    11. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011. "Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator," Econometric Theory, Cambridge University Press, vol. 27(3), pages 522-545, June.
    12. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    13. 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.
    14. Johannes, Jan & Van Bellegem, Sebastien & Vanhems, Anne, 2011. "Convergence rates for ill-posed inverse problems with an unknown operator," LIDAM Reprints ISBA 2011047, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Dreier, I. & Kotz, S., 2002. "A note on the characteristic function of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 221-224, April.
    16. Dunker, Fabian & Florens, Jean-Pierre & Hohage, Thorsten & Johannes, Jan & Mammen, Enno, 2014. "Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression," Journal of Econometrics, Elsevier, vol. 178(P3), pages 444-455.
    17. 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).
    18. 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.
    19. 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.
    20. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    21. 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).
    22. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    23. 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.
    24. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
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