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Nonparametric estimation and inference under shape restrictions

Joel L. Horowitz and Sokbae (Simon) Lee ()

Journal of Econometrics, 2017, vol. 201, issue 1, 108-126

Abstract: Economic theory often provides shape restrictions on functions of interest in applications, such as monotonicity, convexity, non-increasing (non-decreasing) returns to scale, or the Slutsky inequality of consumer theory; but economic theory does not provide finite-dimensional parametric models. This motivates nonparametric estimation under shape restrictions. Nonparametric estimates are often very noisy. Shape restrictions stabilize nonparametric estimates without imposing arbitrary restrictions, such as additivity or a single-index structure, that may be inconsistent with economic theory and the data. This paper explains how to estimate and obtain an asymptotic uniform confidence band for a conditional mean function under possibly nonlinear shape restrictions, such as the Slutsky inequality. The results of Monte Carlo experiments illustrate the finite-sample performance of the method, and an empirical example illustrates its use in an application.

Keywords: Conditional mean function; Constrained estimation; Monotonic; Convex; Slutsky condition (search for similar items in EconPapers)
JEL-codes: C13 C14 C21 (search for similar items in EconPapers)
Date: 2017
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Related works:
Working Paper: Nonparametric estimation and inference under shape restrictions (2016) Downloads
Working Paper: Nonparametric estimation and inference under shape restrictions (2015) Downloads
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