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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 108-126 |
| Number of pages | 19 |
| Journal | Journal of Econometrics |
| Volume | 201 |
| Issue number | 1 |
| DOIs | |
| State | Published - Nov 2017 |
Funding
Research wassupported in part by European Research Council Grant ERC-2014-CoG-646917-ROMIA. We thank David Jacho-Chávez for providing the data used in this paper and two anonymous referees for useful comments. Part of this research was carried out while Joel L. Horowitz was a visitor at the Department of Economics, University College London, and the Centre for Microdata Methods and Practice.
Keywords
- Conditional mean function
- Constrained estimation
- Convex
- Monotonic
- Slutsky condition
ASJC Scopus subject areas
- Economics and Econometrics
