IDEAS home Printed from https://ideas.repec.org/p/usg/econwp/201109.html
   My bibliography  Save this paper

Quantile Regression in the Presence of Sample Selection

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://ux-tauri.unisg.ch/RePEc/usg/econwp/EWP-1109.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Angrist, Joshua D., 1997. "Conditional independence in sample selection models," Economics Letters, Elsevier, vol. 54(2), pages 103-112, February.
    2. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
    3. 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.
    4. 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.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, vol. 65(2), pages 347-380, February.
    7. 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.
    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. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    10. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    11. 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.
    12. 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.
    13. Michael Lechner & Blaise Melly, 2010. "Partial Idendification of Wage Effects of Training Programs," Working Papers 2010-8, Brown University, Department of Economics.
    14. 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.
    15. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-1575, September.
    16. Lee, Sokbae, 2007. "Endogeneity in quantile regression models: A control function approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 1131-1158, December.
    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. 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.
    19. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, December.
    20. 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.
    21. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    22. 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.
    23. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    24. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    25. 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.
    26. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
    27. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    28. 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.
    29. Powell, James L., 1987. "Semiparametric Estimation Of Bivariate Latent Variable Models," SSRI Workshop Series 292689, University of Wisconsin-Madison, Social Systems Research Institute.
    30. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ekaterina Selezneva & Philippe Van Kerm, 2013. "Inequality-adjusted gender wage differentials in Germany," Working Papers 334, Leibniz Institut für Ost- und Südosteuropaforschung (Institute for East and Southeast European Studies).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Philippe Van Kerm, 2013. "Generalized measures of wage differentials," Empirical Economics, Springer, vol. 45(1), pages 465-482, August.
    10. 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).
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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, LISER.

    More about this item

    Keywords

    Sample selection; quantile regression; independence; test;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:usg:econwp:2011:09. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Martina Flockerzi). General contact details of provider: http://edirc.repec.org/data/vwasgch.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.