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Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks

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  • Victor Chernozhukov
  • Ivan Fernandez-Val

Abstract

Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many economic and financial applications, such as conditional value-at-risk, production efficiency, and adjustment bands in (S,s) models. In this paper we provide feasible inference tools for extremal conditional quantile models that rely upon extreme value approximations to the distribution of self-normalized quantile regression statistics. The methods are simple to implement and can be of independent interest even in the non-regression case. We illustrate the results with two empirical examples analyzing extreme fluctuations of a stock return and extremely low percentiles of live infants' birthweights in the range between 250 and 1500 grams.

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File URL: http://arxiv.org/pdf/0912.5013
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Paper provided by arXiv.org in its series Papers with number 0912.5013.

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Date of creation: Dec 2009
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Publication status: Published in Review of Economic Studies (2011) 78 (2): 559-589
Handle: RePEc:arx:papers:0912.5013

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  1. James J. Heckman & Christopher J. Flinn, 1982. "New Methods for Analyzing Structural Models of Labor Force Dynamics," NBER Working Papers 0856, National Bureau of Economic Research, Inc.
  2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, Fall.
  3. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931, Octomber.
  4. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
  5. Donald, Stephen G. & Paarsch, Harry J., 2002. "Superconsistent estimation and inference in structural econometric models using extreme order statistics," Journal of Econometrics, Elsevier, vol. 109(2), pages 305-340, August.
  6. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers 1832, Iowa State University, Department of Economics.
  7. Patrice Bertail & Christian Haefke & Dimitris N. Politis & Halbert White, 2001. "A subsampling approach to estimating the distribution of diversing statistics with application to assessing financial market risks," Economics Working Papers 599, Department of Economics and Business, Universitat Pompeu Fabra.
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Cited by:
  1. Florens, Jean-Pierre & Simar, Léopold & Van Keilegom, Ingrid, 2014. "Frontier estimation in nonparametric location-scale models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 456-470.
  2. Sascha O. Becker & Hans K. Hvide, 2013. "Do Entrepreneurs Matter?," CESifo Working Paper Series 4088, CESifo Group Munich.
  3. repec:cge:warwcg:108 is not listed on IDEAS
  4. d'Haultfoeuille, Xavier & Maurel, Arnaud & Zhang, Yichong, 2014. "Extremal Quantile Regressions for Selection Models and the Black-White Wage Gap," IZA Discussion Papers 8256, Institute for the Study of Labor (IZA).

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