Shape Constrained Nonparametric Instrumental Regression

We consider nonparametric kernel estimation of an instrumental regression function φ defined by conditional moment restrictions that stem from a structural econometric model E(Y − φ(Z)|W ) = 0, and involve endogenous variables Y and Z and instruments W . The function φ is the solution to an ill-posed inverse problem. Our primary focus lies in shape constrained estimation, and we present a simple and robust approach towards shape constrained local nonparametric instrumental regression. The constraints can be imposed on the estimated function $\hat \varphi$, its derivatives, or combinations thereof. Our approach facilitates imposing, say, axioms of consumer/producer theory on an otherwise unrestricted but smooth estimate. Theoretical underpinnings are provided and applications are considered.Non UBCUnreviewedAuthor affiliation: McMaster UniversityFacult