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Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research

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  • Moshe Buchinsky

Abstract

This paper provides a guideline for the practical use of the semi-parametric technique of quantile regression, concentrating on cross-section applications. It summarizes the most important issues in quantile regression applications and fills some gaps in the literature. The paper (a) presents several alternative estimators for the covariance matrix of the quantile regression estimates; (b) reviews the results for a sequence of quantile regression estimates; and (c) discusses testing procedures for homoskedasticity and symmetry of the error distribution. The various results in the literature are incorporated into the generalized method of moments frame-work. The paper also provides an empirical example using data from the Current Population Survey, raising several important issues relevant to empirical applications of quantile regression. The paper concludes with an extension to the censored quantile regression model.

Suggested Citation

  • Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
  • Handle: RePEc:uwp:jhriss:v:33:y:1998:i:1:p:88-126
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    1. Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 6(03), pages 295-317, September.
    2. Jacob A. Mincer, 1974. "Introduction to "Schooling, Experience, and Earnings"," NBER Chapters,in: Schooling, Experience, and Earnings, pages 1-4 National Bureau of Economic Research, Inc.
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    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. James M. Poterba & Kim S. Rueben, 1994. "The Distribution of Public Sector Wage Premia: New Evidence Using Quantile Regression Methods," NBER Working Papers 4734, National Bureau of Economic Research, Inc.
    7. Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, vol. 7(01), pages 46-68, March.
    8. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    9. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    10. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(03), pages 403-436, June.
    11. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    12. 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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