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Quantile Regression under Misspecification

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  • I. Fernandez-Val
  • J. Angrist
  • V. Chernozhukov

Abstract

Quantile regression (QR) methods fit a linear model for conditional quantiles, just as ordinary least squares (OLS) regression estimates a linear model for conditional means. An attractive feature of the OLS estimator is that it gives a minimum mean square error approximation to the conditional expectation function even when the linear model is mis-specified. Empirical research on quantile regression with discrete covariates suggests that QR has a similar property, but the exact nature of the linear approximation has remained elusive. In this paper, we show that QR can be interpreted as minimizing a weighted mean-squared error loss function for the specification error. We derive the weighting function and show that it is approximately equal to the conditional density of QR residuals. The paper goes on to derive the limiting distribution of QR estimators under very general conditions allowing for mis-specification of the conditional quantile function. Finally, we develop methods for the use of QR as a modelling tool for the entire conditional distribution of a random variable. Testable hypotheses include location-scale models, proportional heteroscedasticity, and stochastic dominance. These ideas are illustrated with a human capital earnings function

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 198.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:198

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Keywords: Quantile Regression; Misspecification;

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Cited by:
  1. repec:ese:iserwp:2004-01 is not listed on IDEAS
  2. Wiji Arulampalam & Alison Booth & Mark Bryan, 2010. "Are there asymmetries in the effects of training on the conditional male wage distribution?," Journal of Population Economics, Springer, Springer, vol. 23(1), pages 251-272, January.
  3. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, Elsevier, vol. 142(1), pages 379-398, January.
  4. Kees Bouwman & Richard Jong-A-Pin & Jakob de Haan, 2005. "On the relationship between central bank independence and inflation: some more bad news," Applied Financial Economics Letters, Taylor and Francis Journals, Taylor and Francis Journals, vol. 1(6), pages 381-385, November.
  5. Taisuke Otsu, 2009. "RESET for quantile regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 18(2), pages 381-391, August.

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