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Comparing Distribution and Quantile Regression

Listed author(s):
  • Samantha Leorato

    (University of Rome Tor Vergata)

  • Franco Peracchi

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

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.

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Paper provided by Einaudi Institute for Economics and Finance (EIEF) in its series EIEF Working Papers Series with number 1511.

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Length: 35
Date of creation: 2015
Date of revision: Oct 2015
Handle: RePEc:eie:wpaper:1511
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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, 09.
  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. 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, 05.
  5. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, October.
  6. Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 433-447, February.
  7. 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.
  8. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
  9. 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.
  10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  11. 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.
  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, 03.
  13. 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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