Nonparametric instrumental variable regression and quantile regression with full independence

The problem of endogeneity in statistics and econometrics is often handled by introducing instrumental variables (IV) which are assumed to be mean independent of some regressors or other observables. When full independence of IV's and observables 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.