Nonparametric estimation and inference under shape restrictions

Joel L. Horowitz () and Sokbae (Simon) Lee
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Joel L. Horowitz: Institute for Fiscal Studies and Northwestern University

No CWP67/15, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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.

Date: 2015-10-19
New Economics Papers: this item is included in nep-ecm
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Related works:
Journal Article: Nonparametric estimation and inference under shape restrictions (2017)
Working Paper: Nonparametric estimation and inference under shape restrictions (2016)
Working Paper: Nonparametric estimation and inference under shape restrictions (2016)
Working Paper: Nonparametric estimation and inference under shape restrictions (2015)
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