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Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes

Author

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  • Chernozhukov, Victor
  • Fernández-Val, Iván
  • Melly, Blaise
  • Wüthrich, Kaspar

Abstract

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Chernozhukov, Victor & Fernández-Val, Iván & Melly, Blaise & Wüthrich, Kaspar, 2020. "Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes," University of California at San Diego, Economics Working Paper Series qt5zm6m9rq, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt5zm6m9rq
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    Cited by:

    1. Victor Chernozhukov & Iván Fernández‐Val & Whitney Newey & Sami Stouli & Francis Vella, 2020. "Semiparametric estimation of structural functions in nonseparable triangular models," Quantitative Economics, Econometric Society, vol. 11(2), pages 503-533, May.
    2. Kaspar Wuthrich & Ying Zhu, 2019. "Omitted variable bias of Lasso-based inference methods: A finite sample analysis," Papers 1903.08704, arXiv.org, revised Sep 2021.
    3. Victor Chernozhukov & Iv'an Fern'andez-Val & Siyi Luo, 2018. "Distribution Regression with Sample Selection, with an Application to Wage Decompositions in the UK," Papers 1811.11603, arXiv.org, revised Dec 2023.
    4. Botha, Ferdi & de New, John P. & de New, Sonja C. & Ribar, David C. & Salamanca, Nicolás, 2020. "COVID-19 labour market shocks and their inequality implications for financial wellbeing," GLO Discussion Paper Series 661, Global Labor Organization (GLO).
    5. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    6. Valentina Corradi & Daniel Gutknecht, 2019. "Testing for Quantile Sample Selection," Papers 1907.07412, arXiv.org, revised Jan 2021.
    7. Lamarche, Carlos & Shi, Xuan & Young, Derek S., 2024. "Conditional Quantile Functions for Zero-Inflated Longitudinal Count Data," Econometrics and Statistics, Elsevier, vol. 31(C), pages 49-65.
    8. Tatsushi Oka & Shota Yasui & Yuta Hayakawa & Undral Byambadalai, 2026. "Regression adjustment for estimating distributional treatment effects in randomized controlled trials," Econometric Reviews, Taylor & Francis Journals, vol. 45(1), pages 2-17, January.
    9. Chernozhukov, Victor & Fernández-Val, Iván & Weidner, Martin, 2024. "Network and panel quantile effects via distribution regression," Journal of Econometrics, Elsevier, vol. 240(2).
    10. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2019. "Distributional conformal prediction," Papers 1909.07889, arXiv.org, revised Aug 2021.
    11. Chen, Songnian & Liu, Nianqing & Zhang, Hanghui, 2025. "Distribution regression with censored selection," Journal of Econometrics, Elsevier, vol. 251(C).
    12. Ferdi Botha & John P. de New, 2020. "COVID-19 infections, labour market shocks, and subjective well-being," Melbourne Institute Working Paper Series wp2020n14, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    13. Victor Chernozhukov & Ivan Fernandez-Val & Siyi Luo, 2023. "Distribution regression with sample selection and UK wage decomposition," CeMMAP working papers 09/23, Institute for Fiscal Studies.
    14. Tomu Hirata & Undral Byambadalai & Tatsushi Oka & Shota Yasui & Shingo Uto, 2025. "Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networks," Papers 2507.07738, arXiv.org.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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