Are University Admissions Academically Fair?

High-profile universities often face public criticism for undermining academic merit and promoting social elitism through their admissions-process. In this paper, we develop an empirical test for whether access to selective universities is meritocratic. If so, then the academic potential of marginal candidates -- the admission-threshold -- would be equated across demographic groups. But these thresholds are difficult to identify when admission-decisions are based on more characteristics than observed by the analyst. We assume that applicants who are better-qualified on standard observable indicators should on average, but not necessarily with certainty, appear academically stronger to admission-tutors based on characteristics observable to them but not us. This assumption can be used to reveal information about the sign and magnitude of differences in admission thresholds across demographic groups which are robust to omitted characteristics, thus enabling one to test whether different demographic groups face different academic standards for admission. An application to admissions-data at a highly selective British university shows that males and private school applicants face significantly higher admission-thresholds, although application success-rates are equal across gender and school-type. Our methods are potentially useful for testing outcomebased fairness of other binary treatment decisions, where eventual outcomes are observed for those who were treated.