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 CWP29/16, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
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: NONPARAMETRIC ESTIMATION; SHAPE RESTRICTIONS (search for similar items in EconPapers)
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Journal Article: Nonparametric estimation and inference under shape restrictions (2017)
Working Paper: Nonparametric estimation and inference under shape restrictions (2015)
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