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Partly Linear Instrumental Variables Regressions without Smoothing on the Instruments

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  • Jean-Pierre Florens
  • Elia Lapenta
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, 2022. "Partly Linear Instrumental Variables Regressions without Smoothing on the Instruments," Papers 2212.11012, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2212.11012
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    References listed on IDEAS

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    6. 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).
    7. JOHANNES, Jan & VAN BELLEGEM, Sébastien & VANHEMS, Anne, 2010. "Iterative regularization in nonparametric instrumental regression," LIDAM Discussion Papers CORE 2010055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. 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.
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    12. 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.
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