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Unconditional Quantile Regressions

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  • SErgio Firpo

    ()
    (Department of Economics PUC-Rio)

  • Nicole M. Fortin

    (University of British Columbia)

  • Thomas Lemieux

    (University of British Columbia)

Abstract

We propose a new regression method to estimate the impact of explanatory variables on quantiles of the unconditional distribution of an outcome variable. The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explanatory variables. The influence function is a widely used tool in robust estimation that can easily be computed for each quantile of interest. We show how standard partial effects, as well as policy effects, can be estimated using our regression approach. We propose three different regression estimators based on a standard OLS regression (RIFOLS), a Logit regression (RIF-Logit), and a nonparametric Logit regression (RIFNP). We also discuss how our approach can be generalized to other distributional statistics besides quantiles.

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Bibliographic Info

Paper provided by Department of Economics PUC-Rio (Brazil) in its series Textos para discussão with number 533.

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Length: 54p
Date of creation: Nov 2006
Date of revision:
Handle: RePEc:rio:texdis:533

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Keywords: Influence Functions; Unconditional Quantile; Quantile Regressions.;

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References

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  1. Melly, Blaise, 2005. "Decomposition of differences in distribution using quantile regression," Labour Economics, Elsevier, vol. 12(4), pages 577-590, August.
  2. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
  3. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November.
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  5. J.P. Florensy & J. J. Heckmanz & C. Meghirx & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous Treatment and Heterogeneous Effects," Working Papers 200832, Geary Institute, University College Dublin.
  6. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  7. David Card & Thomas Lemieux & W. Craig Riddell, 2004. "Unions and Wage Inequality," Journal of Labor Research, Transaction Publishers, vol. 25(4), pages 519-562, October.
  8. Javier Gardeazabal & Arantza Ugidos, 2005. "Gender wage discrimination at quantiles," Journal of Population Economics, Springer, vol. 18(1), pages 165-179, 07.
  9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  10. Thomas Lemieux, 2007. "The Changing Nature of Wage Inequality," NBER Working Papers 13523, National Bureau of Economic Research, Inc.
  11. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
  12. Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
  13. SErgio Firpo & Nicole M. Fortin & Thomas Lemieux, 2006. "Unconditional Quantile Regressions," Textos para discussão 533, Department of Economics PUC-Rio (Brazil).
  14. José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
  15. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-60, September.
  16. Jeffrey M. Wooldridge, 2004. "Estimating average partial effects under conditional moment independence assumptions," CeMMAP working papers CWP03/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  17. Thomas Lemieux, 2006. "Increasing Residual Wage Inequality: Composition Effects, Noisy Data, or Rising Demand for Skill?," American Economic Review, American Economic Association, vol. 96(3), pages 461-498, June.
  18. James Albrecht & Anders Bjorklund & Susan Vroman, 2003. "Is There a Glass Ceiling in Sweden?," Journal of Labor Economics, University of Chicago Press, vol. 21(1), pages 145-177, January.
  19. Nicole M. Fortin & Thomas Lemieux, 1998. "Rank Regressions, Wage Distributions, and the Gender Gap," Journal of Human Resources, University of Wisconsin Press, vol. 33(3), pages 610-643.
  20. Card, David, 1996. "The Effect of Unions on the Structure of Wages: A Longitudinal Analysis," Econometrica, Econometric Society, vol. 64(4), pages 957-79, July.
  21. David H. Autor & Lawrence F. Katz & Melissa S. Kearney, 2008. "Trends in U.S. Wage Inequality: Revising the Revisionists," The Review of Economics and Statistics, MIT Press, vol. 90(2), pages 300-323, May.
  22. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, vol. 61(5), pages 1199-223, September.
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