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Unconditional Quantile Regressions

  • Sergio Firpo
  • Nicole M. Fortin
  • Thomas Lemieux

We propose a new regression method to estimate the impact of 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 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 (RIF-OLS), a logit regression (RIF-Logit), and a nonparametric logit regression (RIF-OLS). We also discuss how our approach can be generalized to other distributional statistics besides quantiles.

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File URL: http://www.nber.org/papers/t0339.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0339.

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Date of creation: Jul 2007
Date of revision:
Publication status: published as Econometrica Volume 77, Issue 3, pages 953–973, May 2009
Handle: RePEc:nbr:nberte:0339
Note: LS TWP
Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
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  1. 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).
  2. 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.
  3. 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.
  4. 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.
  5. Fortin, N.M. & Lemieux, T., 1996. "Rank Regressions, Wage Distributions and the Gender Gap," Cahiers de recherche 9607, Universite de Montreal, Departement de sciences economiques.
  6. 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.
  7. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, 09.
  8. Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. 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.
  10. Thomas Lemieux, 2008. "The changing nature of wage inequality," Journal of Population Economics, Springer, vol. 21(1), pages 21-48, January.
  11. Melly, Blaise, 2005. "Decomposition of differences in distribution using quantile regression," Labour Economics, Elsevier, vol. 12(4), pages 577-590, August.
  12. David Card, 2000. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," NBER Working Papers 7769, National Bureau of Economic Research, Inc.
  13. Javier Gardeazabal & Arantza Ugidos, 2005. "Gender wage discrimination at quantiles," Journal of Population Economics, Springer, vol. 18(1), pages 165-179, 07.
  14. repec:cup:cbooks:9780521608275 is not listed on IDEAS
  15. Sergio Firpo & Nicole M. Fortin & Thomas Lemieux, 2009. "Unconditional Quantile Regressions," Econometrica, Econometric Society, vol. 77(3), pages 953-973, 05.
  16. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  17. repec:cup:cbooks:9780521845731 is not listed on IDEAS
  18. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  19. 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.
  20. 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.
  21. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
  22. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
  23. 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.
  24. 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.
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