Type
Article
Titre
Quantile and Probability Curves without Crossing
Dans
Econometrica
Auteur(s)
CHERNOZHUKOV Victor - MIT Department of Economics (Auteur)
FERNANDEZ-VAL Ivan - Department of Economics (Boston Univ.) (Auteur)
GALICHON Alfred - Department of Economics, Ecole Polytechnique (Auteur)
Éditeur
US
Volume
78
Numéro
3
Pages
1093 - 1125 p.
ISSN
00129682
Mots clés
Conditional quantiles, structural quantiles, monotonicity problem, rearrangement, isotonic regression, functional delta method
Résumé
EN
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. 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 in finite samples than the original curve, 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 the entire rearranged curve and its functionals. Our limit results are generic in that they apply to every estimator of a monotone econometric 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 quantile functions using data on Vietnam veteran status and earnings.

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