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Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes

Author

Listed:
  • Victor Chernozhukov
  • Iv'an Fern'andez-Val
  • Blaise Melly
  • Kaspar Wuthrich
Abstract
Quantile and quantile effect functions are important tools for descriptive and causal analyses 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 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 affecting child development especially at the top of the distribution. These are new, interesting empirical findings that complement 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 observed and counterfactual quantile functions and for their difference -- the 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 Aug 2018.
    • Handle: RePEc:arx:papers:1608.05142
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Larocque, Denis & Randles, Ronald H., 2008. "Confidence Intervals for a Discrete Population Median," The American Statistician, American Statistical Association, vol. 62, pages 32-39, February.
    4. 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.
    5. Roland G. Fryer & Steven D. Levitt, 2013. "Testing for Racial Differences in the Mental Ability of Young Children," American Economic Review, American Economic Association, vol. 103(2), pages 981-1005, April.
    6. Christoph Rothe & Dominik Wied, 2013. "Misspecification Testing in a Class of Conditional Distributional Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 314-324, March.
    7. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    8. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    9. Winkelmann, Rainer, 2006. "Reforming health care: Evidence from quantile regressions for counts," Journal of Health Economics, Elsevier, vol. 25(1), pages 131-145, January.
    10. 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.
    11. 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.
    12. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    13. Amy Finkelstein & Sarah Taubman & Bill Wright & Mira Bernstein & Jonathan Gruber & Joseph P. Newhouse & Heidi Allen & Katherine Baicker, 2012. "The Oregon Health Insurance Experiment: Evidence from the First Year," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1057-1106.
    14. Yanyuan Ma & Marc Genton & Emanuel Parzen, 2011. "Asymptotic properties of sample quantiles of discrete distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 227-243, April.
    15. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    16. Cheng, Guang & Yu, Zhuqing & Huang, Jianhua Z., 2013. "The cluster bootstrap consistency in generalized estimating equations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 33-47.
    17. Junni L. Zhang & Donald B. Rubin, 2003. "Estimation of Causal Effects via Principal Stratification When Some Outcomes are Truncated by “Deathâ€," Journal of Educational and Behavioral Statistics, , vol. 28(4), pages 353-368, December.
    18. Joshua Angrist & Eric Bettinger & Michael Kremer, 2006. "Long-Term Educational Consequences of Secondary School Vouchers: Evidence from Administrative Records in Colombia," American Economic Review, American Economic Association, vol. 96(3), pages 847-862, June.
    19. Yu-Chin Hsu & Robert P. Lieli & Tsung-Chih Lai, 2015. "Estimation and Inference for Distribution Functions and Quantile Functions in Endogenous Treatment Effect Models," IEAS Working Paper : academic research 15-A003, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    20. Foresi, S. & Paracchi, F., 1992. "The Conditional Distribution of Excess Returns: An Empirical Analysis," Working Papers 92-49, C.V. Starr Center for Applied Economics, New York University.
    21. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    22. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
    23. Katherine Baicker & Amy Finkelstein & Jae Song & Sarah Taubman, 2014. "The Impact of Medicaid on Labor Market Activity and Program Participation: Evidence from the Oregon Health Insurance Experiment," American Economic Review, American Economic Association, vol. 104(5), pages 322-328, May.
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    Cited by:

    1. Chernozhukov, Victor & Fernández-Val, Iván & Weidner, Martin, 2024. "Network and panel quantile effects via distribution regression," Journal of Econometrics, Elsevier, vol. 240(2).
    2. Ferdi Botha & John P. de New & Sonja C. de New & David C. Ribar & Nicolás Salamanca, 2020. "COVID-19 labour market shocks and their inequality implications for financial wellbeing," Melbourne Institute Working Paper Series wp2020n15, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    3. 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.
    4. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2019. "Distributional conformal prediction," Papers 1909.07889, arXiv.org, revised Aug 2021.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Valentina Corradi & Daniel Gutknecht, 2019. "Testing for Quantile Sample Selection," Papers 1907.07412, arXiv.org, revised Jan 2021.
    11. 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.
    12. Tatsushi Oka & Shota Yasui & Yuta Hayakawa & Undral Byambadalai, 2024. "Regression Adjustment for Estimating Distributional Treatment Effects in Randomized Controlled Trials," Papers 2407.14074, arXiv.org.

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    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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