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

63 Pages Posted: 21 Apr 2012 Last revised: 4 Apr 2019

See all articles by Ismael Mourifie

Ismael Mourifie

University of Toronto - Department of Economics

Marc Henry

Pennsylvania State University

Romuald Meango

Max Planck Society for the Advancement of the Sciences - Munich Center for the Economics of Aging (MEA)

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Date Written: November 2, 2018

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 pointwise 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.

Keywords: Roy model, sectorial choice, partial identification, stochastic monotonicity, intersection bounds, functional sharp bounds, inequality, optimal transport, college major, gender profiling, STEM

JEL Classification: C31, C34, C35, I21, J24

Suggested Citation

Mourifie, Ismael and Henry, Marc and Meango, Romuald, Sharp Bounds and Testability of a Roy Model of STEM Major Choices (November 2, 2018). Available at SSRN: https://ssrn.com/abstract=2043117 or http://dx.doi.org/10.2139/ssrn.2043117

Ismael Mourifie

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S3G7
Canada

Marc Henry (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

Romuald Meango

Max Planck Society for the Advancement of the Sciences - Munich Center for the Economics of Aging (MEA) ( email )

Amalienstrasse 33
Munich, 80799
Germany

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