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Nonparametric Instrumental Variable Estimators of Structural Quantile Effects

Author

Listed:
  • Victor Chernozhukov

    (Massachusetts Institute of Technology)

  • Patrick Gagliardini

    (University of Lugano and Swiss Finance Institute)

  • Olivier Scaillet

    (University of Geneva and Swiss Finance Institute)

Abstract

We study the asymptotic distribution of Tikhonov Regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a minimum distance principle. We show that the minimum distance problem without regularization is locally ill-posed, and consider penalization by the norms of the parameter and its derivatives. We derive pointwise asymptotic normality and develop a consistent estimator of the asymptotic variance. We study the small sample properties via simulation results, and provide an empirical illustration to estimation of nonlinear pricing curves for telecommunications services in the U.S.

Suggested Citation

  • Victor Chernozhukov & Patrick Gagliardini & Olivier Scaillet, 2008. "Nonparametric Instrumental Variable Estimators of Structural Quantile Effects," Swiss Finance Institute Research Paper Series 08-03, Swiss Finance Institute, revised Aug 2009.
    • Handle: RePEc:chf:rpseri:rp0803
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    Citations

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    Cited by:

    1. 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.
    2. Florens, Jean-Pierre & Simon, Guillaume, 2010. "Endogeneity and Instrumental Variables in Dynamic Models," TSE Working Papers 10-178, Toulouse School of Economics (TSE).
    3. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, School of Economics, University of Bristol, UK.
    4. Carrasco, Marine & Florens, Jean-Pierre, 2011. "A Spectral Method For Deconvolving A Density," Econometric Theory, Cambridge University Press, vol. 27(3), pages 546-581, June.
    5. Chen, Xiaohong & Pouzo, Demian, 2008. "Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments," Working Papers 47, Yale University, Department of Economics.
    6. Juan Carlos Escanciano & Wei Li, 2013. "On the identification of structural linear functionals," CeMMAP working papers CWP48/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    Nonparametric Quantile Regression; Instrumental Variable; Ill-Posed Inverse Problems; Tikhonov Regularization; Nonlinear Pricing Curve.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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