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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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    1. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
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    8. Holger Dette & Stanislav Volgushev, 2008. "Non-crossing non-parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627.
    9. 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.
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    Cited by:

    1. 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.
    2. Richey, Jeremiah & Rosburg, Alicia, 2016. "Understanding intergenerational economic mobility by decomposing joint distributions," MPRA Paper 72665, University Library of Munich, Germany.
    3. Richey, Jeremiah & Rosburg, Alicia, 2015. "Decomposing economic mobility transition matrices," MPRA Paper 66485, University Library of Munich, Germany.
    4. repec:gam:jeners:v:10:y:2017:i:9:p:1402-:d:111989 is not listed on IDEAS
    5. Franco Peracchi & Samantha Leorato, 2015. "Shape Regressions," Working Papers gueconwpa~15-15-06, Georgetown University, Department of Economics.
    6. 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 for the Study of Labor (IZA).
    7. García, A., 2016. "Oaxaca-Blinder Type Counterfactual Decomposition Methods for Duration Outcomes," DOCUMENTOS DE TRABAJO 014186, UNIVERSIDAD DEL ROSARIO.
    8. 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.
    9. 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.
    10. Ying-Ying Lee, 2015. "Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification," Econometrics, MDPI, Open Access Journal, vol. 4(1), pages 1-14, December.
    11. Kaspar Wüthrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.

    More about this item

    Keywords

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

    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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