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One-step nonparametric instrumental regression using smoothing splines

Author

Listed:
  • Jad Beyhum

    (KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven)

  • Elia Lapenta

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Pascal Lavergne

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing es-timators, the resulting estimator is one-step and relies on a unique regularization parameter. We derive uniform rates of the convergence for the estimator and its first derivative. We also address the issue of imposing monotonicity in estimation. Sim-ulations confirm the good performances of our estimator compared to some popular 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 nonparametric instrumental regression using smoothing splines," Working Papers hal-04971401, HAL.
    • Handle: RePEc:hal:wpaper:hal-04971401
    Note: View the original document on HAL open archive server: https://hal.science/hal-04971401v1
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