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Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes

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  • Victor Chernozhukov
  • Iv'an Fern'andez-Val
  • Blaise Melly
  • Kaspar Wuthrich

Abstract

Quantile and quantile effect functions are important tools for descriptive and inferential analysis due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This paper offers a simple, practical construction of simultaneous confidence bands for quantile and quantile effect 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 strategies 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. Our analysis generates new, interesting empirical findings, and complements previous analyses that focused on mean effects only. In both applications, the outcomes of interest are discrete rendering existing inference methods invalid for obtaining uniform confidence bands for quantile and quantile effects functions.

Suggested Citation

  • Victor Chernozhukov & Iv'an Fern'andez-Val & Blaise Melly & Kaspar Wuthrich, 2016. "Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes," Papers 1608.05142, arXiv.org, revised Jun 2018.
  • Handle: RePEc:arx:papers:1608.05142
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    References listed on IDEAS

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    1. Machado, Jose A.F. & Silva, J. M. C. Santos, 2005. "Quantiles for Counts," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1226-1237, December.
    2. Frandsen, Brigham R. & Frölich, Markus & Melly, Blaise, 2012. "Quantile treatment effects in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 168(2), pages 382-395.
    3. Donald, Stephen G. & Hsu, Yu-Chin, 2014. "Estimation and inference for distribution functions and quantile functions in treatment effect models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 383-397.
    4. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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    Cited by:

    1. Victor Chernozhukov & Ivan Fernandez-Val & Whitney K. Newey & Sami Stouli & Francis Vella, 2017. "Semiparametric estimation of structural functions in nonseparable triangular models," CeMMAP working papers CWP48/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Victor Chernozhukov & Iv'an Fern'andez-Val & Martin Weidner, 2018. "Network and Panel Quantile Effects Via Distribution Regression," Papers 1803.08154, arXiv.org.

    More about this item

    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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