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Shape Constrained Nonparametric Instrumental Regression

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Statistics; Operations research, mathematical programming

video/mp4

Author affiliation: McMaster University

2018-07-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/66603

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/