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Sharp Bounds And Testability Of A Roy Model Of Stem Major Choices

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  • Ismael Mourifie
  • Marc Henry
  • Romuald Meango

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.

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  • Ismael Mourifie & Marc Henry & Romuald Meango, 2018. "Sharp Bounds And Testability Of A Roy Model Of Stem Major Choices," Working Papers tecipa-624, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-624
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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.
    2. Casey B. Mulligan, 2018. "Quantifier Elimination for Deduction in Econometrics," NBER Working Papers 24601, National Bureau of Economic Research, Inc.
    3. Kamat, Vishal, 2019. "Identification with Latent Choice Sets," TSE Working Papers 19-1031, Toulouse School of Economics (TSE).
    4. Vishal Kamat, 2017. "Identification of Program Access Effects with an Application to Head Start," Papers 1711.02048, arXiv.org, revised Oct 2020.
    5. Vishal Kamat, 2018. "On the Identifying Content of Instrument Monotonicity," Papers 1807.01661, arXiv.org, revised Oct 2019.
    6. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Marc Henry & Ivan Sidorov, 2020. "Occupational segregation in a Roy model with composition preferences," Papers 2012.04485, arXiv.org.
    8. Hiroaki Kaido & Yi Zhang, 2019. "Robust likelihood ratio tests for incomplete economic models," CeMMAP working papers CWP68/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Ban, Kyunghoon & Kedagni, Desire, 2020. "Nonparametric Bounds on Treatment Effects with Imperfect Instruments," ISU General Staff Papers 202010120700001113, Iowa State University, Department of Economics.
    10. Hiroaki Kaido & Yi Zhang, 2019. "Robust likelihood ratio tests for incomplete economic models," CeMMAP working papers CWP68/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.

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    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.;
    All these keywords.

    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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