ON ILL-POSEDNESS OF

NONPARAMETRIC INSTRUMENTAL VARIABLE REGRESSION

UNDER CONVEXITY CONSTRAINTS

SCAILLET, O. *

* University of Geneva and Swiss Finance Institute

 

Abstract

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.

Keywords : Nonparametric Estimation, Instrumental Variable, Ill-Posed Inverse Problems.

JEL : C13, C14, C26.