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

Abstract

We analyze the empirical content of the Roy model, stripped down to 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 model. We apply these bounds to derive a measure of departure from Roy self-selection, so as to identify prime targets for intervention. Special emphasis is put on the case of binary outcomes. We analyze a Roy model of college major choice in Canada and Germany and take a new look at the underrepresentation of women in science, technology, engineering, and mathematics.