This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model. This is illustrated in computed examples with simulated data.
Ill-posed integral equation; Landweber iteration; IV quantile; Kernel smoothing;
- C13: Estimation: General
- C14: Semiparametric and Nonparametric Methods: General
- C30: General
- C31: Cross-Sectional Models • Spatial Models • Treatment Effect Models • Quantile Regressions • Social Interaction Models
Journal of Econometrics, vol. 178, n. 3, January 2014, pp. 444–455