Journal
ECONOMETRICA
Volume 78, Issue 3, Pages 1093-1125Publisher
WILEY-BLACKWELL
DOI: 10.3982/ECTA7880
Keywords
Conditional quantiles; structural quantiles; monotonicity problem; rearrangement; isotonic regression; functional delta method
Categories
Funding
- National Science Foundation
- Chaire X-Dauphine Finance et Developpement Durable.
- Economic and Social Research Council [ES/F015879/1] Funding Source: researchfish
- Direct For Social, Behav & Economic Scie
- Divn Of Social and Economic Sciences [0752823, 0752266] Funding Source: National Science Foundation
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available