Robust Counterfactuals in Centralized Schools Choice Systems: Addressing Gender Inequality in STEM Education

TL;DR

This paper introduces a new counterfactual analysis method for Gale-Shapley mechanisms, enabling policy evaluation on gender inequality in STEM education with incomplete preference data.

Contribution

It develops a flexible, less assumption-dependent framework for counterfactual analysis in school choice, providing sharp bounds on outcomes and applying it to gender-focused policies in Chile.

Findings

Efficient computation of bounds on stable matchings.

Policy insights for increasing female STEM enrollment.

Framework applicable under weaker assumptions.

Abstract

Counterfactual analysis is central to education market design and provides a foundation for credible policy recommendations. We develop a novel methodology for counterfactual analysis in Gale-Shapley deferred-acceptance (DA) assignment mechanisms under a weaker set of assumptions than those typically imposed in existing empirical works. Instead of fully specifying utility functions or students' beliefs about admission probabilities, we rely on interpretable restrictions on behavior that yield an incomplete but flexible model of preferences. This framework addresses the challenge of partial identification by delivering sharp bounds on counterfactual stable matching outcomes, which we compute efficiently using a combination of algorithmic techniques and integer programming. We illustrate the methodology by evaluating policies aimed at increasing female enrollment in STEM fields in Chile.