This note shows that adding monotonicity or convexity constraints on the regression function does not restore well-posedness in nonparametric instrumental variable regression. The minimum distance problem without regularisation is still locally ill-posed

In econometrics some nonparametric instrumental regression models and nonparametric demand models with endogeneity lead to nonlinear integral equations with unknown integral kernels. We prove convergence rates of the risk for the iteratively regularized Newton method applied to these problems....