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Implementing Box-Cox Quantile Regression


  • Bernd Fitzenberger
  • Ralf A. Wilke
  • Xuan Zhang


The Box-Cox quantile regression model introduced by Powell (1991) is a flexible and numerically attractive extension of linear quantile regression techniques. Chamberlain (1994) and Buchinsky (1995) suggest a two stage estimator for this model but the objective function in stage two of their method may not be defined in an application. We suggest a modification of the estimator which is easy to implement. A simulation study demonstrates that the modified estimator works well in situations, where the original estimator is not well defined.

Suggested Citation

  • Bernd Fitzenberger & Ralf A. Wilke & Xuan Zhang, 2010. "Implementing Box-Cox Quantile Regression," Econometric Reviews, Taylor & Francis Journals, vol. 29(2), pages 158-181, April.
  • Handle: RePEc:taf:emetrv:v:29:y:2010:i:2:p:158-181 DOI: 10.1080/07474930903382166

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    References listed on IDEAS

    1. Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, vol. 82(2), pages 235-287, February.
    2. Elke Lüdemann & Ralf Wilke & Xuan Zhang, 2006. "Censored quantile regressions and the length of unemployment periods in West Germany," Empirical Economics, Springer, vol. 31(4), pages 1003-1024, November.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, March.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Jose A. F. Machado & Jose Mata, 2000. "Box-Cox quantile regression and the distribution of firm sizes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(3), pages 253-274.
    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. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
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    Cited by:

    1. Polpo, A. & de Campos, C.P. & Sinha, D. & Lipsitz, S. & Lin, J., 2014. "Transform both sides model: A parametric approach," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 903-913.
    2. Ghosh, Pallab Kumar, 2014. "The contribution of human capital variables to changes in the wage distribution function," Labour Economics, Elsevier, vol. 28(C), pages 58-69.
    3. Benjamin Colling & Cédric Heuchenne & Rawane Samb & Ingrid Van Keilegom, 2015. "Estimation of the error density in a semiparametric transformation model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 1-18, February.
    4. Bernd Fitzenberger & Ralf A. Wilke, 2010. "New Insights into Unemployment Duration and Post Unemployment Earnings in Germany," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(6), pages 794-826, December.

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