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Quantile Regression in the Presence of Sample Selection

  • Huber, Martin


  • Melly, Blaise


Most sample selection models assume that the errors are independent of the regressors. Under this assumption, all quantile and mean functions are parallel, which implies that quantile estimators cannot reveal any (per definition non-existing) heterogeneity. However, quantile estimators are useful for testing the independence assumption, because they are consistent under the null hypothesis. We propose tests for this crucial restriction that are based on the entire conditional quantile regression process after correcting for sample selection bias. Monte Carlo simulations demonstrate that they are powerful and two empirical illustrations indicate that violations of this assumption are likely to be ubiquitous in labor economics.

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Paper provided by University of St. Gallen, School of Economics and Political Science in its series Economics Working Paper Series with number 1109.

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Length: 33 pages
Date of creation: Mar 2011
Date of revision:
Handle: RePEc:usg:econwp:2011:09
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  1. Michael Lechner & Blaise Melly, 2010. "Partial Idendification of Wage Effects of Training Programs," Working Papers 2010-8, Brown University, Department of Economics.
  2. Chaudhuri, Probal, 1991. "Global nonparametric estimation of conditional quantile functions and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 246-269, November.
  3. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers 70, Bell Communications - Economic Research Group.
  4. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
  5. Moshe Buchinsky, 1998. "The dynamics of changes in the female wage distribution in the USA: a quantile regression approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 1-30.
  6. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-75, September.
  7. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
  8. Blundell, Richard & Powell, James L., 2007. "Censored regression quantiles with endogenous regressors," Journal of Econometrics, Elsevier, vol. 141(1), pages 65-83, November.
  9. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  10. Pedro Carneiro & Sokbae (Simon) Lee, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," CeMMAP working papers CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Martin Huber & Giovanni Mellace, 2015. "Sharp Bounds on Causal Effects under Sample Selection," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 129-151, 02.
  12. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, vol. 47(1), pages 153-61, January.
  13. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
  14. Whitney Newey, 1999. "Two Step Series Estimation of Sample Selection Models," Working papers 99-04, Massachusetts Institute of Technology (MIT), Department of Economics.
  15. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  16. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-43, Nov.-Dec..
  17. Matzkin, Rosa L., 2007. "Nonparametric identification," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 73 Elsevier.
  18. Sokbae Lee, 2004. "Endogeneity in Quantile Regression Models: A Control Function Approach," Econometric Society 2004 North American Summer Meetings 521, Econometric Society.
  19. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  20. Angrist, J.D., 1996. "Conditional Independance in Sample Selection Models," Working papers 96-27, Massachusetts Institute of Technology (MIT), Department of Economics.
  21. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
  22. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 33-58.
  23. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
  24. Chen, Songnian & Khan, Shakeeb, 2003. "Semiparametric Estimation Of A Heteroskedastic Sample Selection Model," Econometric Theory, Cambridge University Press, vol. 19(06), pages 1040-1064, December.
  25. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  26. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, vol. 65(2), pages 347-380, February.
  27. 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.
  28. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
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