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

We study the asymptotic distribution of Tikhonov Regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a minimum distance principle. We show that the minimum distance problem without regularization is...