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Two-stage quantile regression when the first stage is based on quantile regression

  • Tae-Hwan Kim
  • Christophe Muller

We present the asymptotic properties of double-stage quantile regression estimators with random regressors, where the first stage is based on quantile regressions with the same quantile as in the second stage, which ensures robustness of the estimation procedure. We derive invariance properties with respect to the reformulation of the dependent variable. We propose a consistent estimator of the variance--covariance matrix of the new estimator. Finally, we investigate finite sample properties of this estimator by using Monte Carlo simulations. Copyright Royal Economic Socciety 2004

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Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 7 (2004)
Issue (Month): 1 (06)
Pages: 218-231

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Handle: RePEc:ect:emjrnl:v:7:y:2004:i:1:p:218-231
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  1. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
  2. José Ferreira Machado & José Mata, 1998. "Earning Functions in Portugal 1982-1994: Evidence From Quantile Regressions," Working Papers w199802, Banco de Portugal, Economics and Research Department.
  3. Jaume Garcia & Pedro J. Hernández & Ángel López Nicolás, 1998. "How wide is the gap? An investigation of gender wage differences using quantile regression," Economics Working Papers 287, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Frank Cowell & Emmanuel Flachaire, 2002. "Sensitivity of inequality measures to extreme values," LSE Research Online Documents on Economics 2213, London School of Economics and Political Science, LSE Library.
  5. Christophe Muller & Tae-Hwan Kim, 2004. "Two-Stage Quantile Regression When The First Stage Is Based On Quantile Regression," Working Papers. Serie AD 2004-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. Buchinsky, Moshe, 1995. "Quantile regression, Box-Cox transformation model, and the U.S. wage structure, 1963-1987," Journal of Econometrics, Elsevier, vol. 65(1), pages 109-154, January.
  7. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
  8. Alberto Abadie & Joshua Angrist & Guido Imbens, 1999. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Working papers 99-16, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Omar Arias & Walter Sosa-Escudero & Kevin F. Hallock, 2001. "Individual heterogeneity in the returns to schooling: instrumental variables quantile regression using twins data," Empirical Economics, Springer, vol. 26(1), pages 7-40.
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