The Large Core of College Admission Markets: Theory and Evidence

TL;DR

This paper analyzes stable college admission allocations considering financial terms, showing how heterogeneity among applicants influences the size and composition of stable matches in large markets.

Contribution

It introduces the impact of financial heterogeneity on stable allocations, contrasting with traditional matching models that ignore financial terms.

Findings

Non-merit-based stable allocations can increase assigned students by 1.9%.

Heterogeneity affects 8.3% of applicants in large markets.

Results differ from matching without contracts literature.

Abstract

We study stable allocations in college admissions markets where students can attend the same college under different financial terms. The deferred acceptance algorithm identifies a stable allocation where funding is allocated based on merit. While merit-based stable allocations assign the same students to college, non-merit-based stable allocations may differ in the number of students assigned to college. In large markets, this possibility requires heterogeneity in applicants' sensitivity to financial terms. In Hungary, where such heterogeneity is present, a non-merit-based stable allocation would increase the number of assigned applicants by 1.9%, and affect 8.3% of the applicants relative to any merit-based stable allocation. These findings contrast sharply with findings from the matching (without contracts) literature.