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

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  • Xavier D'Haultfoeuille
  • Arnaud Maurel
  • Yichong Zhang
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.

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  • Xavier D'Haultfoeuille & Arnaud Maurel & Yichong Zhang, 2014. "Extremal Quantile Regressions for Selection Models and the Black-White Wage Gap," NBER Working Papers 20257, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:20257
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    1. 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.
    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. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    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. 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.
    6. Victor Chernozhukov & Iván Fernández-Val, 2011. "Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 559-589.
    7. 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.
    8. 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.
    9. 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.
    10. 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).
    11. 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.
    12. 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.
    13. 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.
    14. Erik Hanushek & F. Welch (ed.), 2006. "Handbook of the Economics of Education," Handbook of the Economics of Education, Elsevier, edition 1, volume 1, number 1, June.
    15. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    16. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
    17. 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.
    18. 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.
    19. 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.
    20. Racine, Jeffrey & Su, Liangjun & Ullah, Aman, 2014. "The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics," OUP Catalogue, Oxford University Press, number 9780199857944.
    21. 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.
    22. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    23. 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, President and Fellows of Harvard College, vol. 99(1), pages 31-44.
    24. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, vol. 65(2), pages 347-380, February.
    25. 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.
    26. 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.
    27. 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.
    28. 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.
    29. Donald W. K. Andrews & Marcia M. A. Schafgans, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 497-517.
    30. Erik Hanushek & F. Welch (ed.), 2006. "Handbook of the Economics of Education," Handbook of the Economics of Education, Elsevier, edition 1, volume 2, number 2, June.
    31. 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.
    32. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    33. repec:eee:labchp:v:3:y:1999:i:pc:p:3143-3259 is not listed on IDEAS
    34. Victor Chernozhukov & Iv'an Fern'andez-Val & Tetsuya Kaji, 2016. "Extremal Quantile Regression: An Overview," Papers 1612.06850, arXiv.org, revised Feb 2017.
    35. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    36. 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.
    37. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    38. 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.
    39. 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.
    40. 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.
    41. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    42. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    43. 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.
    44. 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.
    45. 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.
    46. 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.
    47. 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.
    48. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    49. 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.
    50. 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.
    51. 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.
    52. 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.
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    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

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