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Quantile Regression in the Presence of Sample Selection

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  • Huber, Martin
  • Melly, Blaise

Abstract

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.

Suggested Citation

  • Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series 1109, University of St. Gallen, School of Economics and Political Science.
    • Handle: RePEc:usg:econwp:2011:09
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    1. Angrist, Joshua D., 1997. "Conditional independence in sample selection models," Economics Letters, Elsevier, vol. 54(2), pages 103-112, February.
    2. Chen, Songnian & Khan, Shakeeb, 2003. "Semiparametric Estimation Of A Heteroskedastic Sample Selection Model," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1040-1064, December.
    3. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    4. Blundell, Richard & Powell, James L., 2007. "Censored regression quantiles with endogenous regressors," Journal of Econometrics, Elsevier, vol. 141(1), pages 65-83, November.
    5. 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.
    6. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    7. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    8. 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, February.
    9. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    10. 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.
    11. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, vol. 65(2), pages 347-380, February.
    12. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    13. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    14. Michael Lechner & Blaise Melly, 2010. "Partial Idendification of Wage Effects of Training Programs," Working Papers 2010-8, Brown University, Department of Economics.
    15. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318, December.
    16. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-1575, September.
    17. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    18. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    19. Lee, Sokbae, 2007. "Endogeneity in quantile regression models: A control function approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 1131-1158, December.
    20. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    21. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    22. 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.
    23. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
    24. 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.
    25. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    26. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    27. 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.
    28. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, December.
    29. Maria Fraga O. Martins, 2001. "Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(1), pages 23-39.
    30. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    31. 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.
    32. 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.
    33. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    34. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
    35. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    36. Powell, James L., 1987. "Semiparametric Estimation Of Bivariate Latent Variable Models," SSRI Workshop Series 292689, University of Wisconsin-Madison, Social Systems Research Institute.
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    Cited by:

    1. Tansel, Aysit & Keskin, Halil Ibrahim & Ozdemir, Zeynel Abidin, 2008. "Public versus Private Sector Wage Gap in Egypt: Evidence from Quantile Regression on Panel Data," MPRA Paper 89540, University Library of Munich, Germany.
    2. 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, February.
    3. Olivier Bargain & Prudence Kwenda, 2014. "The Informal Sector Wage Gap: New Evidence Using Quantile Estimations on Panel Data," Economic Development and Cultural Change, University of Chicago Press, vol. 63(1), pages 117-153.
    4. Schwiebert, Jörg, 2012. "Semiparametric Estimation of a Sample Selection Model in the Presence of Endogeneity," Hannover Economic Papers (HEP) dp-504, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    5. Philippe Van Kerm, 2013. "Generalized measures of wage differentials," Empirical Economics, Springer, vol. 45(1), pages 465-482, August.
    6. Rebekka Christopoulou & Vassilis Monastiriotis, 2016. "Public-private wage duality during the Greek crisis," Oxford Economic Papers, Oxford University Press, vol. 68(1), pages 174-196.
    7. Philippe Van Kerm & Seunghee Yu & Chung Choe, 2016. "Decomposing quantile wage gaps: a conditional likelihood approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(4), pages 507-527, August.
    8. Ekaterina Selezneva & Philippe Van Kerm, 2013. "Inequality-Adjusted Gender Wage Differentials in Germany," SOEPpapers on Multidisciplinary Panel Data Research 579, DIW Berlin, The German Socio-Economic Panel (SOEP).
    9. Tansel, Aysit & Keskin, Halil Ibrahim & Ozdemir, Zeynel Abidin, 2008. "Public versus Private Sector Wage Gap in Egypt: Evidence from Quantile Regression on Panel Data," MPRA Paper 89540, University Library of Munich, Germany.
    10. DOORLEY Karina & SIERMINSKA Eva, 2011. "Beauty and the beast in the labor market: Evidence from a distribution regression approach," LISER Working Paper Series 2011-62, Luxembourg Institute of Socio-Economic Research (LISER).
    11. Ekaterina Selezneva & Philippe Van Kerm, 2016. "A distribution-sensitive examination of the gender wage gap in Germany," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 14(1), pages 21-40, March.
    12. Stefan Hoderlein & Bettina Siflinger & Joachim Winter, 2015. "Identification of structural models in the presence of measurement error due to rounding in survey responses," Boston College Working Papers in Economics 869, Boston College Department of Economics.
    13. Christofides, Louis N. & Polycarpou, Alexandros & Vrachimis, Konstantinos, 2013. "Gender wage gaps, ‘sticky floors’ and ‘glass ceilings’ in Europe," Labour Economics, Elsevier, vol. 21(C), pages 86-102.
    14. Bargain, Olivier & Doorley, Karina & Van Kerm, Philippe, 2018. "Minimum Wages and the Gender Gap in Pay: New Evidence from the UK and Ireland," IZA Discussion Papers 11502, Institute of Labor Economics (IZA).
    15. Zheng Fang & Chris Sakellariou, 2015. "Glass Ceilings versus Sticky Floors: Evidence from Southeast Asia and an International Update," Asian Economic Journal, East Asian Economic Association, vol. 29(3), pages 215-242, September.
    16. Martin Huber & Blaise Melly, 2012. "A test of the conditional independence assumption in sample selection models," Working Papers 2012-11, Brown University, Department of Economics.
    17. Rebekka Christopoulou & Vassilis Monastiriotis, 2014. "The Greek Public Sector Wage Premium before the Crisis: Size, Selection and Relative Valuation of Characteristics," British Journal of Industrial Relations, London School of Economics, vol. 52(3), pages 579-602, September.

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    More about this item

    Keywords

    Sample selection; quantile regression; independence; test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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