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Inference on an Extended Roy Model, with an Application to Schooling Decisions in France

Author

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  • Arnaud Maurel
  • Xavier D'Haultfoeuille
Abstract
This paper considers the identification and estimation of an extension of Roy’s model (1951) of sectoral choice, which includes a non-pecuniary component in the selection equation and allows for uncertainty on potential earnings. We focus on the identification of the non-pecuniary component, which is key to disentangle the relative importance of monetary incentives versus preferences in the context of sorting across sectors. By making the most of the structure of the selection equation, we show that this component is point identified from the knowledge of the covariates effects on earnings, as soon as one covariate is continuous. Notably, and in contrast to most results on the identification of Roy models, this implies that identification can be achieved without any exclusion restriction nor large support condition on the covariates. As a byproduct, bounds are obtained on the distribution of the ex ante monetary returns. We also propose a three-stage semiparametric estimation procedure for this model, which yields root-n consistent and asymptotically normal estimators. Finally, we apply our results to the educational context, by providing new evidence from French data that non-pecuniary factors are a key determinant of higher education attendance decisions.

Suggested Citation

  • Arnaud Maurel & Xavier D'Haultfoeuille, 2011. "Inference on an Extended Roy Model, with an Application to Schooling Decisions in France," Working Papers 11-10, Duke University, Department of Economics.
    • Handle: RePEc:duk:dukeec:11-10
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    References listed on IDEAS

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    Cited by:

    1. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    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. Peter Arcidiacono & V. Joseph Hotz & Arnaud Maurel & Teresa Romano, 2014. "Recovering Ex Ante Returns and Preferences for Occupations using Subjective Expectations Data," NBER Working Papers 20626, National Bureau of Economic Research, Inc.
    4. Nicole Maestas & Kathleen J. Mullen & David Powell & Till von Wachter & Jeffrey B. Wenger, 2023. "The Value of Working Conditions in the United States and the Implications for the Structure of Wages," American Economic Review, American Economic Association, vol. 113(7), pages 2007-2047, July.
    5. Ivan A Canay & Magne Mogstad & Jack Mount, 2024. "On the Use of Outcome Tests for Detecting Bias in Decision Making," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(4), pages 2135-2167.
    6. Johannes S. Kunz & Kevin E. Staub, 2016. "Subjective Completion Beliefs and the Demand for Post-Secondary Education," SOEPpapers on Multidisciplinary Panel Data Research 878, DIW Berlin, The German Socio-Economic Panel (SOEP).
    7. 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.
    8. Yifan Gong & Todd Stinebrickner & Ralph Stinebrickner & Yuxi Yao, 2022. "The Role of Non-Pecuniary Considerations: Locations Decisions of College Graduates from Low Income Backgrounds," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20221, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    9. Brian Clark & Clément Joubert & Arnaud Maurel, 2017. "The career prospects of overeducated Americans," IZA Journal of Labor Economics, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 6(1), pages 1-29, December.
    10. Eran Yashiv, 2020. "Moving from a Poor Economy to a Rich One: The Contradictory Roles of Technology and Job Tasks," Discussion Papers 2010, Centre for Macroeconomics (CFM).
    11. Delavande, Adeline & Zafar, Basit, 2014. "University choice: the role of expected earnings, non-pecuniary outcomes and financial constraints," ISER Working Paper Series 2014-38, Institute for Social and Economic Research.
    12. Henry, Marc & Méango, Romuald & Mourifié, Ismaël, 2024. "Role models and revealed gender-specific costs of STEM in an extended Roy model of major choice," Journal of Econometrics, Elsevier, vol. 238(2).
    13. Marc Henry & Romuald Meango & Ismael Mourifié, 2020. "Revealing Gender-Specific Costs of STEM in an Extended Roy Model of Major Choice," Working Papers 2020-035, Human Capital and Economic Opportunity Working Group.
    14. Marc Henry & Ismael Mourifié, 2012. "Sharp Bounds in the Binary Roy Model," CIRJE F-Series CIRJE-F-835, CIRJE, Faculty of Economics, University of Tokyo.
    15. Kunz, Johannes S. & Staub, Kevin E., 2020. "Early subjective completion beliefs and the demand for post-secondary education," Journal of Economic Behavior & Organization, Elsevier, vol. 177(C), pages 34-55.
    16. Philipp Eisenhauer & James J. Heckman & Edward Vytlacil, 2015. "The Generalized Roy Model and the Cost-Benefit Analysis of Social Programs," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 413-443.
    17. Marc Henry & Romuald Meango & Ismael Mourifie, 2020. "Role models and revealed gender-specific costs of STEM in an extended Roy model of major choice," Papers 2005.09095, arXiv.org, revised Aug 2023.
    18. Joseph G. Altonji & Peter Arcidiacono & Arnaud Maurel, 2015. "The Analysis of Field Choice in College and Graduate School: Determinants and Wage Effects," NBER Working Papers 21655, National Bureau of Economic Research, Inc.
    19. Tyler Ransom, 2021. "Selective Migration, Occupational Choice, and the Wage Returns to College Majors," Annals of Economics and Statistics, GENES, issue 142, pages 45-110.
    20. Eran Yashiv, 2021. "Moving from a Poor Economy to a Rich One: A Job Tasks Approach," RF Berlin - CReAM Discussion Paper Series 2119, Rockwool Foundation Berlin (RF Berlin) - Centre for Research and Analysis of Migration (CReAM).
    21. Myoung‐jae Lee & Jin‐young Choi, 2022. "Finding mover–stayer quantile difference due to unobservables using quantile selection corrections," Bulletin of Economic Research, Wiley Blackwell, vol. 74(3), pages 704-721, July.
    22. Yashiv, Eran, 2021. "Moving from a poor economy to a rich one: A job tasks approach," Labour Economics, Elsevier, vol. 72(C).
    23. Oliver Cassagneau-Francis, 2022. "Essays on skills and education [Essais sur les compétences et l'éducation]," SciencePo Working papers Main tel-03857494, HAL.

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    More about this item

    Keywords

    Roy model; nonparametric identification; schooling choices; ex ante returns to schooling;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity

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