Adaptive estimation for some nonparametric instrumental variable models

TL;DR

This paper develops a new iterative regularization method for nonparametric instrumental variable models with weaker assumptions, achieving improved convergence rates and better numerical performance.

Contribution

It introduces a convergent iterative Newton method for nonlinear integral equations in nonparametric IV models under weaker nonlinearity conditions.

Findings

The method achieves stronger convergence rates.

Numerical simulations show improved accuracy over standard models.

The approach handles weaker assumptions on nonlinearity.

Abstract

The problem of endogeneity in statistics and econometrics is often handled by introducing instrumental variables (IV) which fulfill the mean independence assumption, i.e. the unobservable is mean independent of the instruments. When full independence of IV's and the unobservable is assumed, nonparametric IV regression models and nonparametric demand models lead to nonlinear integral equations with unknown integral kernels. We prove convergence rates for the mean integrated square error of the iteratively regularized Newton method applied to these problems. Compared to related results we derive stronger convergence results that rely on weaker nonlinearity restrictions. We demonstrate in numerical simulations for a nonparametric IV regression that the method produces better results than the standard model.