Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes

Quantile and quantile effect (QE) functions are important tools for descriptive and causal analysis due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This article offers a simple, practical construction of sim...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2020-01, Vol.115 (529), p.123-137
Main Authors: Chernozhukov, Victor, Fernández-Val, Iván, Melly, Blaise, Wüthrich, Kaspar
Format: Article
Language:English
Subjects:
Clinical outcomes
Counterfactual distribution
Decomposition analysis
Distribution functions
Distribution regression
Economic factors
Health care
Health insurance
Health services utilization
Inference
Insurance
Insurance coverage
Quantile treatment effect
Random variables
Regression analysis
Sampling
Social factors
Socioeconomic factors
Statistical methods
Statistics
Transformation
Uniform inference
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Summary:Quantile and quantile effect (QE) functions are important tools for descriptive and causal analysis due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This article offers a simple, practical construction of simultaneous confidence bands for quantile and QE functions of possibly discrete random variables. It is based on a natural transformation of simultaneous confidence bands for distribution functions, which are readily available for many problems. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparametric, and nonparametric modeling methods for observed and counterfactual distributions, and does not depend on the sampling scheme. We apply our method to characterize the distributional impact of insurance coverage on health care utilization and obtain the distributional decomposition of the racial test score gap. We find that universal insurance coverage increases the number of doctor visits across the entire distribution, and that the racial test score gap is small at early ages but grows with age due to socio-economic factors especially at the top of the distribution. Supplementary materials (additional results, R package, replication files) for this article are available online.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2019.1611581