Inferring Trade-Offs in University Admissions: Evidence from Cambridge

Abstract

How do elite universities balance diversity and academics during admissions, anddo they face a trade-off in doing so? We develop a theory-based empirical framework to identify and quantify this potential trade-off ex-post, using post-entry outcomes. We apply our framework to admission and exam-performance data from Cambridge University. Comparing directly admitted students and second-round admits from different demographic groups yields bounds on the magnitude of trade-off, which (A) hold irrespective of whether we observe all applicant characteristics, and (B) require no information on rejected applicants. We find robust evidence of a trade-off between gender balance and performance in math-intensive subjects. It implies a weight of at least 20% on gender-diversity and at most 80% on academics in the university objective. Such trade-offs are not identified for state vis-a-vis privately-funded school students, nor for gender in equally competitive non-mathematical disciplines.