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Iterative estimation of nonparametric regressions with continuous endogenous variables and discrete instruments

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  • Centorrino, Samuele
  • Fève, Frédérique
  • Florens, Jean-Pierre

Abstract

We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. Although this framework is very relevant for applied research, its implementation is challenging, as the regression function becomes the solution to a nonlinear integral equation. We propose a simple iterative procedure to estimate such models and showcase some of its asymptotic properties. In a simulation experiment, we detail its implementation in the case when the instrumental variable is binary. We conclude with an empirical application to returns to education.

Suggested Citation

  • Centorrino, Samuele & Fève, Frédérique & Florens, Jean-Pierre, 2025. "Iterative estimation of nonparametric regressions with continuous endogenous variables and discrete instruments," Journal of Econometrics, Elsevier, vol. 247(C).
    • Handle: RePEc:eee:econom:v:247:y:2025:i:c:s0304407625000041
    DOI: 10.1016/j.jeconom.2025.105950
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    More about this item

    Keywords

    Nonparametric; Instrumental variables; Landweber-Fridman; Returns to education;
    All these keywords.

    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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