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Comparing Distribution and Quantile Regression

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  • Samantha Leorato

    (University of Rome Tor Vergata)

  • Franco Peracchi

    (Georgetown University, University of Rome Tor Vergata and EIEF)

Abstract

We study the sampling properties of two alternative approaches to estimating the conditional distribution of a continuous outcome Y given a vector X of regressors. One approach – distribution regression – is based on direct estimation of the conditional distribution function; the other approach – quantile regression – 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 or, to guarantee monotonicity, their rearranged versions. We provide a systematic comparison of the asymptotic and finite sample performance of monotonic estimators obtained from the two approaches, considering both cases when the underlying linear-in-parameter models are correctly specified and several types of model misspecification of considerable practical relevance.

Suggested Citation

  • 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.
    • Handle: RePEc:eie:wpaper:1511
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    References listed on IDEAS

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    1. Samantha Leorato & Franco Peracchi, 2015. "Shape Regressions," EIEF Working Papers Series 1506, Einaudi Institute for Economics and Finance (EIEF), revised Jul 2015.
    2. Christoph Rothe, 2012. "Partial Distributional Policy Effects," Econometrica, Econometric Society, vol. 80(5), pages 2269-2301, September.
    3. Roger Koenker & Samantha Leorato & Franco Peracchi, 2013. "Distributional vs. Quantile Regression," CEIS Research Paper 300, Tor Vergata University, CEIS, revised 17 Dec 2013.
    4. Fortin, Nicole & Lemieux, Thomas & Firpo, Sergio, 2011. "Decomposition Methods in Economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 1, pages 1-102, Elsevier.
    5. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    6. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    7. Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 433-447, February.
    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, July.
    9. Hall, Peter & Muller, Hans-Georg, 2003. "Order-Preserving Nonparametric Regression, With Applications to Conditional Distribution and Quantile Function Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 598-608, January.
    10. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    12. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    13. Torsten Hothorn & Thomas Kneib & Peter Bühlmann, 2014. "Conditional transformation models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 3-27, January.
    14. 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.
    15. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    16. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
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    Cited by:

    1. Franco Peracchi & Samantha Leorato, 2015. "Shape Regressions," Working Papers gueconwpa~15-15-06, Georgetown University, Department of Economics.
    2. Anatolyev, Stanislav & Baruník, Jozef, 2019. "Forecasting dynamic return distributions based on ordered binary choice," International Journal of Forecasting, Elsevier, vol. 35(3), pages 823-835.
    3. Wüthrich, Kaspar, 2019. "A closed-form estimator for quantile treatment effects with endogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 219-235.
    4. Jozef Barunik & Lubos Hanus, 2022. "Learning Probability Distributions in Macroeconomics and Finance," Papers 2204.06848, arXiv.org.
    5. Rothe, Christoph & Wied, Dominik, 2020. "Estimating derivatives of function-valued parameters in a class of moment condition models," Journal of Econometrics, Elsevier, vol. 217(1), pages 1-19.

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