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.
Authors
Research Fellow Columbia University
Sokbae is an IFS Research Fellow and a Professor at Columbia University, with an interest in Econometrics, Applied Microeconomics and Statistics.
Northwestern University
Journal article details
- DOI
- 10.1016/j.jeconom.2017.06.019
- Publisher
- Elsevier
- Issue
- Volume 201, Issue 1, August 2017, pages 108-126
Suggested citation
Horowitz, J and Lee, S. (2017). 'Nonparametric estimation and inference under shape restrictions' 201(1/2017), pp.108–126.
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