Nonparametric instrumental variable derivative estimation

The focus of this paper is the nonparametric estimation of the marginal effects (i.e. first partial derivatives) of an instrumental regression function ϕ defined by conditional moment restrictions that stem from a structural econometric model , and involve endogenous variables Y and Z and instruments W. The derivative function is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Landweber–Fridman regularisation. We provide theoretical underpinnings of the proposed approach, examine finite-sample performance, and consider an illustrative application.