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Extremal quantile regression: an overview

Author

Listed:
  • Victor Chernozhukov
  • Ivan Fernandez-Val
  • Tetsuya Kaji
Abstract
Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants of low infant birth weights, and auction models. This chapter provides an overview of recent developments in the theory and empirics of extremal quantile regression. The advances in the theory have relied on the use of extreme value approximations to the law of the Koenker and Bassett (1978) quantile regression estimator. Extreme value laws not only have been shown to provide more accurate approximations than Gaussian laws at the tails, but also have served as the basis to develop bias corrected estimators and inference methods using simulation and suitable variations of bootstrap and subsampling. The applicability of these methods is illustrated with two empirical examples on conditional value-at-risk and financial contagion.

Suggested Citation

  • Victor Chernozhukov & Ivan Fernandez-Val & Tetsuya Kaji, 2017. "Extremal quantile regression: an overview," CeMMAP working papers 65/17, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:65/17
    DOI: 10.1920/wp.cem.2017.6517
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    References listed on IDEAS

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    1. Aigner, D J & Amemiya, Takeshi & Poirier, Dale J, 1976. "On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 377-396, June.
    2. Jason Abrevaya, 2001. "The effects of demographics and maternal behavior on the distribution of birth outcomes," Empirical Economics, Springer, vol. 26(1), pages 247-257.
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    Cited by:

    1. Chao, Shih-Kang & Härdle, Wolfgang K. & Yuan, Ming, 2021. "Factorisable Multitask Quantile Regression," Econometric Theory, Cambridge University Press, vol. 37(4), pages 794-816, August.
    2. Xavier D’Haultfoeuille & Arnaud Maurel & Xiaoyun Qiu & Yichong Zhang, 2020. "Estimating selection models without an instrument with Stata," Stata Journal, StataCorp LP, vol. 20(2), pages 297-308, June.
    3. Yuya Sasaki & Yulong Wang, 2022. "Fixed-k Inference for Conditional Extremal Quantiles," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 829-837, April.
    4. Matthew A. Masten & Alexandre Poirier & Linqi Zhang, 2024. "Assessing Sensitivity to Unconfoundedness: Estimation and Inference," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(1), pages 1-13, January.
    5. Firpo, Sergio & Galvao, Antonio F. & Pinto, Cristine & Poirier, Alexandre & Sanroman, Graciela, 2022. "GMM quantile regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 432-452.
    6. Matthew A Masten & Alexandre Poirier, 2023. "Choosing exogeneity assumptions in potential outcome models," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 327-349.
    7. Marian Vavra, 2023. "Bias-Correction in Time Series Quantile Regression Models," Working and Discussion Papers WP 3/2023, Research Department, National Bank of Slovakia.
    8. D’Haultfœuille, Xavier & Maurel, Arnaud & Zhang, Yichong, 2018. "Extremal quantile regressions for selection models and the black–white wage gap," Journal of Econometrics, Elsevier, vol. 203(1), pages 129-142.
    9. Matthias Fischer & Daniel Kraus & Marius Pfeuffer & Claudia Czado, 2017. "Stress Testing German Industry Sectors: Results from a Vine Copula Based Quantile Regression," Risks, MDPI, vol. 5(3), pages 1-13, July.

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