Nonparametric instrumental variable estimation of quantile structural effects

We study 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 derivative. We derive the asymptotic Mean Integrated Square Error, the rate of convergence and the pointwise asymptotic normality under a regularization parameter depending on sample size. We illustrate our theoretical findings and the small sample properties with simulation results in two numerical examples. We also discuss a data driven selection procedure of the regularization parameter via a spectral representation of the MISE. Finally, we provide an empirical application to estimation of Engel curves.