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Quantile Regression under Misspecification

Author

Listed:
  • 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

Suggested Citation

  • I. Fernandez-Val & J. Angrist & V. Chernozhukov, 2004. "Quantile Regression under Misspecification," Econometric Society 2004 North American Winter Meetings 198, Econometric Society.
    • Handle: RePEc:ecm:nawm04:198
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    Cited by:

    1. repec:hum:wpaper:sfb649dp2008-41 is not listed on IDEAS
    2. Bernd Fitzenberger & Karsten Kohn & Alexander C. Lembcke, 2013. "Union Density and Varieties of Coverage: The Anatomy of Union Wage Effects in Germany," ILR Review, Cornell University, ILR School, vol. 66(1), pages 169-197, January.
    3. repec:zbw:sfb649:sfb649dp2008-41 is not listed on IDEAS
    4. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
    5. 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;European Society for Population Economics, vol. 23(1), pages 251-272, January.
    6. Taisuke Otsu, 2009. "RESET for quantile regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 381-391, August.
    7. Juergen Jung & Michael Makowsky, 2014. "The determinants of federal and state enforcement of workplace safety regulations: OSHA inspections 1990–2010," Journal of Regulatory Economics, Springer, vol. 45(1), pages 1-33, February.

    More about this item

    Keywords

    Quantile Regression; Misspecification;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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