IDEAS home Printed from https://ideas.repec.org/p/iza/izadps/dp8256.html
   My bibliography  Save this paper

Extremal Quantile Regressions for Selection Models and the Black-White Wage Gap

Author

Listed:
  • D'Haultfoeuille, Xavier

    (CREST)

  • Maurel, Arnaud

    (Duke University)

  • Zhang, Yichong

    (Singapore Management University)

Abstract

We consider the estimation of a semiparametric location-scale model subject to endogenous selection, in the absence of an instrument or a large support regressor. Identification relies on the independence between the covariates and selection, for arbitrarily large values of the outcome. In this context, we propose a simple estimator, which combines extremal quantile regressions with minimum distance. We establish the asymptotic normality of this estimator by extending previous results on extremal quantile regressions to allow for selection. Finally, we apply our method to estimate the black-white wage gap among males from the NLSY79 and NLSY97. We find that premarket factors such as AFQT and family background characteristics play a key role in explaining the level and evolution of the black-white wage gap.

Suggested Citation

  • D'Haultfoeuille, Xavier & Maurel, Arnaud & Zhang, Yichong, 2014. "Extremal Quantile Regressions for Selection Models and the Black-White Wage Gap," IZA Discussion Papers 8256, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp8256
    as

    Download full text from publisher

    File URL: http://ftp.iza.org/dp8256.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Victor Chernozhukov & Iv'an Fern'andez-Val & Tetsuya Kaji, 2016. "Extremal Quantile Regression: An Overview," Papers 1612.06850, arXiv.org, revised Feb 2017.
    2. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    3. Charles Brown, 1984. "Black-White Earnings Ratios Since the Civil Rights Act of 1964: The Importance of Labor Market Dropouts," The Quarterly Journal of Economics, Oxford University Press, vol. 99(1), pages 31-44.
    4. Paul Beaudry & David A. Green & Benjamin M. Sand, 2016. "The Great Reversal in the Demand for Skill and Cognitive Tasks," Journal of Labor Economics, University of Chicago Press, vol. 34(S1), pages 199-247.
    5. 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.
    6. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    7. Joseph G. Altonji & Prashant Bharadwaj & Fabian Lange, 2012. "Changes in the Characteristics of American Youth: Implications for Adult Outcomes," Journal of Labor Economics, University of Chicago Press, vol. 30(4), pages 783-828.
    8. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College," NBER Working Papers 9546, National Bureau of Economic Research, Inc.
    9. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, vol. 65(2), pages 347-380, February.
    10. D’Haultfœuille, Xavier & Maurel, Arnaud, 2013. "Inference on an extended Roy model, with an application to schooling decisions in France," Journal of Econometrics, Elsevier, vol. 174(2), pages 95-106.
    11. Victor Chernozhukov & Iván Fernández-Val, 2011. "Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 559-589.
    12. 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.
    13. Carneiro, Pedro & Heckman, James J & Masterov, Dimitriy V, 2005. "Labor Market Discrimination and Racial Differences in Premarket Factors," Journal of Law and Economics, University of Chicago Press, vol. 48(1), pages 1-39, April.
    14. Altonji, Joseph G. & Blank, Rebecca M., 1999. "Race and gender in the labor market," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 48, pages 3143-3259, Elsevier.
    15. Schafgans, Marcia M.A. & Zinde-Walsh, Victoria, 2002. "On Intercept Estimation In The Sample Selection Model," Econometric Theory, Cambridge University Press, vol. 18(1), pages 40-50, February.
    16. Neal, Derek, 2006. "Why Has Black-White Skill Convergence Stopped?," Handbook of the Economics of Education, in: Erik Hanushek & F. Welch (ed.), Handbook of the Economics of Education, edition 1, volume 1, chapter 9, pages 511-576, Elsevier.
    17. Gonzalo Castex & Evgenia Kogan Dechter, 2014. "The Changing Roles of Education and Ability in Wage Determination," Journal of Labor Economics, University of Chicago Press, vol. 32(4), pages 685-710.
    18. Carneiro, Pedro & Hansen, Karsten T. & Heckman, James J., 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," IZA Discussion Papers 767, Institute of Labor Economics (IZA).
    19. 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.
    20. Cunha, Flavio & Heckman, James J., 2007. "Identifying and Estimating the Distributions of Ex Post and Ex Ante Returns to Schooling," Labour Economics, Elsevier, vol. 14(6), pages 870-893, December.
    21. repec:eee:labchp:v:3:y:1999:i:pc:p:3143-3259 is not listed on IDEAS
    22. D’Haultfoeuille, Xavier & Maurel, Arnaud, 2013. "Another Look At The Identification At Infinity Of Sample Selection Models," Econometric Theory, Cambridge University Press, vol. 29(1), pages 213-224, February.
    23. Derek Neal, 2004. "The Measured Black-White Wage Gap among Women Is Too Small," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 1-28, February.
    24. Richard Butler & James J. Heckman, 1977. "The Government's Impact on the Labor Market Status of Black Americans: A Critical Review," NBER Working Papers 0183, National Bureau of Economic Research, Inc.
    25. Donald W. K. Andrews & Marcia M. A. Schafgans, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 497-517.
    26. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    27. Donald W. K. Andrews, 1999. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 67(3), pages 543-564, May.
    28. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "2001 Lawrence R. Klein Lecture Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 361-422, May.
    29. José A. F. Machado & Paulo Parente, 2005. "Bootstrap estimation of covariance matrices via the percentile method," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 70-78, March.
    30. D’Haultfœuille, Xavier & Maurel, Arnaud & Zhang, Yichong, 2018. "Extremal quantile regressions for selection models and the black–white wage gap," Journal of Econometrics, Elsevier, vol. 203(1), pages 129-142.
    31. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    32. Chinhui Juhn, 2003. "Labor Market Dropouts and Trends in the Wages of Black and White Men," ILR Review, Cornell University, ILR School, vol. 56(4), pages 643-662, July.
    33. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    34. Falk, Michael, 1991. "A note on the inverse bootstrap process for large quantiles," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 359-363, August.
    35. Songnian Chen & Gordon B. Dahl & Shakeeb Khan, 2005. "Nonparametric Identification and Estimation of a Censored Location-Scale Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 212-221, March.
    36. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    37. Derek Neal & Armin Rick, 2014. "The Prison Boom and the Lack of Black Progress after Smith and Welch," NBER Working Papers 20283, National Bureau of Economic Research, Inc.
    38. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    39. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    40. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
    41. Neal, Derek A & Johnson, William R, 1996. "The Role of Premarket Factors in Black-White Wage Differences," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 869-895, October.
    42. 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.
    43. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    44. Yuichi Kitamura & William Johnson & Derek Neal, 2000. "Evaluating a Simple Method for Estimating Black-White Gaps in Median Wages," American Economic Review, American Economic Association, vol. 90(2), pages 339-343, May.
    45. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    46. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    47. Smith, James P & Welch, Finis R, 1989. "Black Economic Progress after Myrdal," Journal of Economic Literature, American Economic Association, vol. 27(2), pages 519-564, June.
    48. 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.
    49. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    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. Paul Demeré & Michael P. Donohoe & Petro Lisowsky, 2020. "The Economic Effects of Special Purpose Entities on Corporate Tax Avoidance," Contemporary Accounting Research, John Wiley & Sons, vol. 37(3), pages 1562-1597, September.
    2. Yashiv, Eran, 2020. "Moving from a Poor Economy to a Rich One: The Contradictory Roles of Technology and Job Tasks," IZA Discussion Papers 13131, Institute of Labor Economics (IZA).
    3. Daniel S. Hamermesh & Katie R. Genadek & Michael C. Burda, 2021. "Racial/Ethnic Differences in Non-Work at Work," ILR Review, Cornell University, ILR School, vol. 74(2), pages 272-292, March.
    4. D’Haultfœuille, Xavier & Maurel, Arnaud & Zhang, Yichong, 2018. "Extremal quantile regressions for selection models and the black–white wage gap," Journal of Econometrics, Elsevier, vol. 203(1), pages 129-142.
    5. Burda, Michael, 2017. "Racial/Ethnic Differences in Non-Work at Work," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168183, Verein für Socialpolitik / German Economic Association.
    6. Xavier D’Haultfoeuille & Arnaud Maurel & Xiaoyun Qiu & Yichong Zhang, 2020. "Estimating selection models without an instrument with Stata," Stata Journal, StataCorp LP, vol. 20(2), pages 297-308, June.
    7. Biewen, Martin & Fitzenberger, Bernd & Seckler, Matthias, 2020. "Counterfactual quantile decompositions with selection correction taking into account Huber/Melly (2015): An application to the German gender wage gap," Labour Economics, Elsevier, vol. 67(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xavier D’Haultfoeuille & Arnaud Maurel & Xiaoyun Qiu & Yichong Zhang, 2020. "Estimating selection models without an instrument with Stata," Stata Journal, StataCorp LP, vol. 20(2), pages 297-308, June.
    2. D’Haultfœuille, Xavier & Maurel, Arnaud, 2013. "Inference on an extended Roy model, with an application to schooling decisions in France," Journal of Econometrics, Elsevier, vol. 174(2), pages 95-106.
    3. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    4. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, March.
    5. Martin Huber, 2014. "Treatment Evaluation in the Presence of Sample Selection," Econometric Reviews, Taylor & Francis Journals, vol. 33(8), pages 869-905, November.
    6. Chen, Songnian & Zhou, Yahong, 2010. "Semiparametric and nonparametric estimation of sample selection models under symmetry," Journal of Econometrics, Elsevier, vol. 157(1), pages 143-150, July.
    7. Claudia Olivetti & Barbara Petrongolo, 2008. "Unequal Pay or Unequal Employment? A Cross-Country Analysis of Gender Gaps," Journal of Labor Economics, University of Chicago Press, vol. 26(4), pages 621-654, October.
    8. D’Haultfoeuille, Xavier & Maurel, Arnaud, 2013. "Another Look At The Identification At Infinity Of Sample Selection Models," Econometric Theory, Cambridge University Press, vol. 29(1), pages 213-224, February.
    9. 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.
    10. Klein, Roger & Shen, Chan & Vella, Francis, 2015. "Estimation of marginal effects in semiparametric selection models with binary outcomes," Journal of Econometrics, Elsevier, vol. 185(1), pages 82-94.
    11. Valentina Corradi & Daniel Gutknecht, 2019. "Testing for Quantile Sample Selection," Papers 1907.07412, arXiv.org, revised Jan 2021.
    12. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    13. Casey B. Mulligan & Yona Rubinstein, 2004. "The Closing of the Gender Gap as a Roy Model Illusion," NBER Working Papers 10892, National Bureau of Economic Research, Inc.
    14. Seneviratne, Prathi, 2020. "Gender wage inequality during Sri Lanka’s post-reform growth: A distributional analysis," World Development, Elsevier, vol. 129(C).
    15. Evgeniy M. Ozhegov, 2014. "The Underwriting, Choice And Performance Of Government-Insured Mortgages In Russia," HSE Working papers WP BRP 31/FE/2014, National Research University Higher School of Economics.
    16. Fortin, Nicole & Lemieux, Thomas & Firpo, Sergio, 2011. "Decomposition Methods in Economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 1, pages 1-102, Elsevier.
    17. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355, April.
    18. David S. Lee, 2002. "Trimming for Bounds on Treatment Effects with Missing Outcomes," NBER Technical Working Papers 0277, National Bureau of Economic Research, Inc.
    19. Jochmans, Koen, 2015. "Multiplicative-error models with sample selection," Journal of Econometrics, Elsevier, vol. 184(2), pages 315-327.
    20. McGovern, Mark E. & Canning, David & Bärnighausen, Till, 2018. "Accounting for non-response bias using participation incentives and survey design: An application using gift vouchers," Economics Letters, Elsevier, vol. 171(C), pages 239-244.

    More about this item

    Keywords

    sample selection models; extremal quantile regressions; black-white wage gap;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

    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:iza:izadps:dp8256. 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: . General contact details of provider: http://www.iza.org .

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Holger Hinte (email available below). General contact details of provider: http://www.iza.org .

    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.