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Nonparametric estimation and inference under shape restrictions

Authors: Joel L. Horowitz and Sokbae (Simon) Lee
Date: 19 October 2015
Type: cemmap Working Paper, CWP67/15
DOI: 10.1920/wp.cem.2015.6715

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.

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Joel L. Horowitz and Sokbae (Simon) Lee July 2016, Nonparametric estimation and inference under shape restrictions, cemmap Working Paper, CWP29/16, IFS

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