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Unconditional Quantile Regressions

  • Sergio Firpo
  • Nicole M. Fortin
  • Thomas Lemieux

We propose a new regression method to evaluate the impact of changes in the distribution of the explanatory variables on quantiles of the unconditional (marginal) 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, a widely used tool in robust estimation, is easily computed for quantiles, as well as for other distributional statistics. Our approach, thus, can be readily generalized to other distributional statistics. Copyright 2009 The Econometric Society.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 77 (2009)
Issue (Month): 3 (05)
Pages: 953-973

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Handle: RePEc:ecm:emetrp:v:77:y:2009:i:3:p:953-973
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  1. 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.
  2. Jean-Pierre Florens & James Heckman & Costas Meghir & Edward Vytlacil, 2002. "Instrumental variables, local instrumental variables and control functions," CeMMAP working papers CWP15/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Fortin, N.M. & Lemieux, T., 1996. "Rank Regressions, Wage Distributions and the Gender Gap," Cahiers de recherche 9607, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, 09.
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  6. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-60, September.
  7. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November.
  8. 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.
  9. Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers 1166, Econometric Society.
  10. SErgio Firpo & Nicole M. Fortin & Thomas Lemieux, 2006. "Unconditional Quantile Regressions," Textos para discussão 533, Department of Economics PUC-Rio (Brazil).
  11. Melly, Blaise, 2005. "Decomposition of differences in distribution using quantile regression," Labour Economics, Elsevier, vol. 12(4), pages 577-590, August.
  12. Albrecht, James & Björklund, Anders & Vroman, Susan, 2001. "Is There a Glass Ceiling in Sweden?," IZA Discussion Papers 282, Institute for the Study of Labor (IZA).
  13. Thomas Lemieux, 2007. "The Changing Nature of Wage Inequality," NBER Working Papers 13523, National Bureau of Economic Research, Inc.
  14. Javier Gardeazabal & Arantza Ugidos, 2005. "Gender wage discrimination at quantiles," Journal of Population Economics, Springer, vol. 18(1), pages 165-179, 07.
  15. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, 09.
  16. 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.
  17. 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.
  18. 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.
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  20. 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.
  21. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
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  23. 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.
  24. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  25. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
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