Tikhonov Regularization for Nonparametric Instrumental Variable Estimators

62 Pages Posted: 26 Nov 2006 Last revised: 23 Aug 2011

See all articles by Patrick Gagliardini

Patrick Gagliardini

USI Università della Svizzera italiana; Swiss Finance Institute

O. Scaillet

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

Date Written: August 2011

Abstract

We study a Tikhonov Regularized (TiR) estimator of a functional parameter identified by conditional moment restrictions in a linear model with both exogenous and endogenous regressors. The nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by the norms of the parameter and its derivative. After showing its consistency in the Sobolev norm we derive the expression of the asymptotic Mean Integrated Square Error. The convergence rate with optimal value of the regularization parameter is characterized in two examples. We illustrate our theoretical findings and the small sample properties with simulation results. Finally, we provide an empirical application to estimation of an Engel curve, and discuss a data driven selection procedure for the regularization parameter.

Keywords: Nonparametric Estimation, Ill-posed Inverse Problems, Tikhonov Regularization, Endogeneity, Instrumental Variable

JEL Classification: C13, C14, C15, D12

Suggested Citation

Gagliardini, Patrick and Scaillet, Olivier, Tikhonov Regularization for Nonparametric Instrumental Variable Estimators (August 2011). Swiss Finance Institute Research Paper 06-30. Available at SSRN: https://ssrn.com/abstract=947094 or http://dx.doi.org/10.2139/ssrn.947094

Patrick Gagliardini

USI Università della Svizzera italiana ( 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

Olivier Scaillet (Contact Author)

University of Geneva GSEM and GFRI ( email )

40 Boulevard du Pont d'Arve
Geneva 4, 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

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