Sharp bounds and testability of a Roy model of STEM major choices

TL;DR

This paper derives sharp bounds and testable implications for the Roy model of sector selection, focusing on potential outcomes, instrumental variables, and applications to STEM major choices and gender disparities.

Contribution

It provides a novel characterization of sharp bounds and testability conditions for the Roy model with unobserved heterogeneity and introduces the SMIV constraint for empirical testing.

Findings

Testability of Roy model via stochastic monotonicity

Identification of costly misallocations of talent

Application to gender disparities in STEM

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.