Nonparametric Instrumental Variable Estimators of Structural Quantile Effects

32 Pages Posted: 4 Feb 2008 Last revised: 23 Feb 2018

See all articles by Victor Chernozhukov

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics

O. Scaillet

University of Geneva GSEM and GFRI; Swiss Finance Institute; University of Geneva - Research Center for Statistics

Patrick Gagliardini

University of Lugano; Swiss Finance Institute

Date Written: September 7, 2011

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.

Keywords: Nonparametric Quantile Regression, Instrumental Variable, Ill-Posed Inverse Problems, Tikhonov Regularization, Nonlinear Pricing Curve.

JEL Classification: C13, C14, D12, G12

Suggested Citation

Chernozhukov, Victor and Scaillet, Olivier and Gagliardini, Patrick, Nonparametric Instrumental Variable Estimators of Structural Quantile Effects (September 7, 2011). Swiss Finance Institute Research Paper No. 08-03, Available at SSRN: https://ssrn.com/abstract=1090151 or http://dx.doi.org/10.2139/ssrn.1090151

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-262f
Cambridge, MA 02142
United States
617-253-4767 (Phone)
617-253-1330 (Fax)

HOME PAGE: http://www.mit.edu/~vchern/

Olivier Scaillet (Contact Author)

University of Geneva GSEM and GFRI ( email )

40 Boulevard du Pont d'Arve
Geneva 4, Geneva 1211
Switzerland
+ 41 22 379 88 16 (Phone)
+41 22 389 81 04 (Fax)

HOME PAGE: http://www.scaillet.ch

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva - Research Center for Statistics

Geneva
Switzerland

Patrick Gagliardini

University of Lugano ( email )

Via Buffi 13
Lugano, TN 6900
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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