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Sharp Bounds and Testability of a Roy Model of STEM Major Choices

Author

Listed:
  • Ismael Mourifié

    () (University of Toronto)

  • Marc Henry

    () (Pennsylvania State University)

  • Romuald Méango

    () (Munich Center for the Economics of Agin)

Abstract

We analyze the empirical content of the Roy model, stripped down to its essential features, namely sector specific unobserved heterogeneity and self-selection on the basis of potential outcomes. We characterize sharp bounds on the joint distribution of potential outcomes and testable implications of the Roy self-selection model under an instrumental constraint on the joint distribution of potential outcomes we call stochastically monotone instrumental variable (SMIV). We show that testing the Roy model selection is equivalent to testing stochastic monotonicity of observed outcomes relative to the instrument. We apply our sharp bounds to the derivation of a measure of departure from Roy self-selection to identify values of observable characteristics that induce the most costly misallocation of talent and sector and are therefore prime targets for intervention. Special emphasis is put on the case of binary outcomes, which has received little attention in the literature to date. For richer sets of outcomes, we emphasize the distinction between point-wise sharp bounds and functional sharp bounds, and its importance, when constructing sharp bounds on functional features, such as inequality measures. We analyze a Roy model of college major choice in Canada and Germany within this framework, and we take a new look at the under-representation of women in STEM.

Suggested Citation

  • Ismael Mourifié & Marc Henry & Romuald Méango, 2018. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Working Papers 2018-084, Human Capital and Economic Opportunity Working Group.
  • Handle: RePEc:hka:wpaper:2018-084
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    References listed on IDEAS

    as
    1. Amitabh Chandra & Douglas O. Staiger, 2007. "Productivity Spillovers in Health Care: Evidence from the Treatment of Heart Attacks," Journal of Political Economy, University of Chicago Press, vol. 115, pages 103-140.
    2. James J. Heckman, 2010. "Building Bridges between Structural and Program Evaluation Approaches to Evaluating Policy," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 356-398, June.
    3. 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.
    4. Matthias Parey & Jens Ruhose & Fabian Waldinger & Nicolai Netz, 2017. "The Selection of High-Skilled Emigrants," The Review of Economics and Statistics, MIT Press, vol. 99(5), pages 776-792, December.
    5. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2002. "Removing the Veil of Ignorance in Assessing the Distributional Impacts of Social Policies," NBER Working Papers 8840, National Bureau of Economic Research, Inc.
    6. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6b, January.
    7. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 487-535.
    8. Kenny, Lawrence W, et al, 1979. "Returns to College Education: An Investigation of Self-Selection Bias Based on the Project Talent Data," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(3), pages 775-789, October.
    9. Joseph G. Altonji & Erica Blom & Costas Meghir, 2012. "Heterogeneity in Human Capital Investments: High School Curriculum, College Major, and Careers," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 185-223, July.
    10. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
    11. Basu, A. P. & Ghosh, J. K., 1978. "Identifiability of the multinormal and other distributions under competing risks model," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 413-429, September.
    12. Magali Beffy & Denis Fougère & Arnaud Maurel, 2012. "Choosing the Field of Study in Postsecondary Education: Do Expected Earnings Matter?," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 334-347, February.
    13. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    14. Jörg Stoye, 2010. "Partial identification of spread parameters," Quantitative Economics, Econometric Society, vol. 1(2), pages 323-357, November.
    15. Arcidiacono, Peter, 2004. "Ability sorting and the returns to college major," Journal of Econometrics, Elsevier, vol. 121(1-2), pages 343-375.
    16. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(03), pages 931-951, June.
    17. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    18. James, Estelle, et al, 1989. "College Quality and Future Earnings: Where Should You Send Your Child to College?," American Economic Review, American Economic Association, vol. 79(2), pages 247-252, May.
    19. Lemieux, Thomas, 1998. "Estimating the Effects of Unions on Wage Inequality in a Panel Data Model with Comparative Advantage and Nonrandom Selection," Journal of Labor Economics, University of Chicago Press, vol. 16(2), pages 261-291, April.
    20. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    21. James J. Heckman, 2001. "Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 673-748, August.
    22. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6a, January.
    23. Boudarbat, Brahim & Montmarquette, Claude, 2007. "Choice of Fields of Study of Canadian University Graduates: The Role of Gender and their Parents’ Education," IZA Discussion Papers 2552, Institute of Labor Economics (IZA).
    24. D’Haultfoeuille, Xavier & Maurel, Arnaud, 2013. "Another Look At The Identification At Infinity Of Sample Selection Models," Econometric Theory, Cambridge University Press, vol. 29(01), pages 213-224, February.
    25. Azeem Shaikh & Edward Vytlacil, 2005. "Threshold Crossing Models and Bounds on Treatment Effects: A Nonparametric Analysis," NBER Technical Working Papers 0307, National Bureau of Economic Research, Inc.
    26. Aakvik, Arild & Heckman, James J. & Vytlacil, Edward J., 2005. "Estimating treatment effects for discrete outcomes when responses to treatment vary: an application to Norwegian vocational rehabilitation programs," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 15-51.
    27. Thomas N. Daymonti & Paul J. Andrisani, 1984. "Job Preferences, College Major, and the Gender Gap in Earnings," Journal of Human Resources, University of Wisconsin Press, vol. 19(3), pages 408-428.
    28. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-1160, September.
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    Cited by:

    1. Vitor Possebom, 2019. "Sharp Bounds for the Marginal Treatment Effect with Sample Selection," Papers 1904.08522, arXiv.org.

    More about this item

    Keywords

    Roy model; sectorial choice; partial identification; stochastic monotonicity; intersection bounds; functional sharp bounds; Inequality; optimal transport; returns to education; college major; gender profiling; STEM; SMIV;

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity

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