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Distributional vs. Quantile Regression

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Abstract
Given a scalar random variable Y and a random vector X defined on the same probability space, the conditional distribution of Y given X can be represented by either the conditional distribution function or the conditional quantile function. To these equivalent representations correspond two alternative approaches to estimation. One approach, distributional regression (DR), is based on direct estimation of the conditional distribution function; the other approach, quantile regression (QR), is instead based on direct estimation of the conditional quantile function. Indirect estimates of the conditional quantile function and the conditional distribution function may then be obtained by inverting the direct estimates obtained from either approach. Despite the growing attention to the DR approach, and the vast literature on the QR approach, the link between the two approaches has not been explored in detail. The aim of this paper is to fill-in this gap by providing a better understanding of the relative performance of the two approaches, both asymptotically and in finite samples, under the linear location model and certain types of heteroskedastic location-scale models.

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  • Roger Koenker & Samantha Leorato & Franco Peracchi, 2013. "Distributional vs. Quantile Regression," CEIS Research Paper 300, Tor Vergata University, CEIS, revised 17 Dec 2013.
    • Handle: RePEc:rtv:ceisrp:300
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    Cited by:

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    3. Samantha Leorato & Franco Peracchi, 2015. "Comparing Distribution and Quantile Regression," EIEF Working Papers Series 1511, Einaudi Institute for Economics and Finance (EIEF), revised Oct 2015.
    4. Richey, Jeremiah & Rosburg, Alicia, 2016. "Understanding intergenerational economic mobility by decomposing joint distributions," MPRA Paper 72665, University Library of Munich, Germany.
    5. Ricardo J. Bessa & Corinna Möhrlen & Vanessa Fundel & Malte Siefert & Jethro Browell & Sebastian Haglund El Gaidi & Bri-Mathias Hodge & Umit Cali & George Kariniotakis, 2017. "Towards Improved Understanding of the Applicability of Uncertainty Forecasts in the Electric Power Industry," Energies, MDPI, vol. 10(9), pages 1-48, September.
    6. Franco Peracchi & Samantha Leorato, 2015. "Shape Regressions," Working Papers gueconwpa~15-15-06, Georgetown University, Department of Economics.
    7. Ferreira, Francisco H. G. & Firpo, Sergio & Galvao, Antonio F., 2017. "Estimation and Inference for Actual and Counterfactual Growth Incidence Curves," IZA Discussion Papers 10473, Institute of Labor Economics (IZA).
    8. García, A., 2016. "Oaxaca-Blinder Type Counterfactual Decomposition Methods for Duration Outcomes," Documentos de Trabajo 14186, Universidad del Rosario.
    9. Philippe Van Kerm & Seunghee Yu & Chung Choe, 2016. "Decomposing quantile wage gaps: a conditional likelihood approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(4), pages 507-527, August.
    10. Kolodziej, Ingo W.K. & García-Gómez, Pilar, 2017. "The causal effects of retirement on mental health: Looking beyond the mean effects," Ruhr Economic Papers 668, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    11. Paul Redmond & Karina Doorley & Seamus McGuinness, 2021. "The impact of a minimum wage change on the distribution of wages and household income," Oxford Economic Papers, Oxford University Press, vol. 73(3), pages 1034-1056.
    12. Ying-Ying Lee, 2015. "Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification," Econometrics, MDPI, vol. 4(1), pages 1-14, December.
    13. Wang, Yunyun & Oka, Tatsushi & Zhu, Dan, 2023. "Bivariate distribution regression with application to insurance data," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 215-232.
    14. Jeremiah Richey & Alicia Rosburg, 2018. "Decomposing economic mobility transition matrices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 91-108, January.
    15. Bargain, Olivier B. & Doorley, Karina & Van Kerm, Philippe, 2018. "Minimum Wages and the Gender Gap in Pay: New Evidence from the UK and Ireland," IZA Discussion Papers 11502, Institute of Labor Economics (IZA).
    16. Redmond, Paul & Doorley, Karina & McGuinness, Seamus, 2019. "The impact of a change in the National Minimum Wage on the distribution of hourly wages and household income in Ireland," Research Series, Economic and Social Research Institute (ESRI), number RS86.
    17. Doorley, Karina & Privalko, Ivan & Russell, Helen & Tuda, Dora, 2021. "The Gender Pay Gap in Ireland from Austerity through Recovery," IZA Discussion Papers 14441, Institute of Labor Economics (IZA).
    18. Wied, Dominik, 2024. "Semiparametric distribution regression with instruments and monotonicity," Labour Economics, Elsevier, vol. 90(C).
    19. Xu Chen & Surya T. Tokdar, 2021. "Joint quantile regression for spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 826-852, September.
    20. Kaspar W thrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    21. Yuanhua Feng & Wolfgang Karl Härdle, 2021. "Uni- and multivariate extensions of the sinh-arcsinh normal distribution applied to distributional regression," Working Papers CIE 142, Paderborn University, CIE Center for International Economics.
    22. Ricardo Masini, 2022. "Distributional Counterfactual Analysis in High-Dimensional Setup," Papers 2202.11671, arXiv.org, revised Sep 2023.

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    More about this item

    Keywords

    Quantile regression; distributional regression; functional Delta-method; asymptotic relative efficiency; linear location model; location-scale models.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: 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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