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 phi defined by conditional moment restrictions that stem from a structural econometric model E[Y - phi(Z) vertical bar W] = 0, and involve endogenous variables Y and Z and instruments W. The derivative function phi' 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.