Quantile and Probability Curves Without Crossing

Victor Chernozhukov, Iv·n Fern·ndez-Val and Alfred Galichon

Econometrica, 2010, vol. 78, issue 3, 1093-1125

Abstract: This paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions, also known as the quantile crossing problem (Bassett and Koenker (1982)). The method consists in sorting or monotone rearranging the original estimated non-monotone curve into a monotone rearranged curve. We show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples, establish a functional delta method for rearrangement-related operators, and derive functional limit theory for the entire rearranged curve and its functionals. We also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals. Our limit results are generic in that they apply to every estimator of a monotone function, provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions. Consequently, our results apply to estimation of other econometric functions with monotonicity restrictions, such as demand, production, distribution, and structural distribution functions. We illustrate the results with an application to estimation of structural distribution and quantile functions using data on Vietnam veteran status and earnings. Copyright 2010 The Econometric Society.

Date: 2010
References: Add references at CitEc
Citations: View citations in EconPapers (259)

Downloads: (external link)
http://hdl.handle.net/10.3982/ECTA7880 link to full text (text/html)
Access to full text is restricted to subscribers.

Related works:
Working Paper: Quantile and Probability Curves Without Crossing (2014)
Working Paper: Quantile and Probability Curves without Crossing (2010)
Working Paper: Quantile and Probability Curves without Crossing (2010)
Working Paper: QUANTILE AND PROBABILITY CURVES WITHOUT CROSSING (2007)
Working Paper: Quantile and probability curves without crossing (2007)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ecm:emetrp:v:78:y:2010:i:3:p:1093-1125

Ordering information: This journal article can be ordered from
https://www.economet ... ordering-back-issues

Access Statistics for this article

Econometrica is currently edited by Guido Imbens

More articles in Econometrica from Econometric Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().