  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.
