Nonparametric Instrumental Variable Estimators of Structural Quantile Effects

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