The Cost of Crafting a Class: (In)Efficient Financial Aid Allocation at Two Private Colleges

In order to meet two key objectives, enrollment managers at colleges and universities make extensive use of single equation probability models. The first objective is to generate sufficient financial resources to educate the students enrolled. The more dependent the institution is on tuition revenues, the more important is this objective. The second objective is to distribute and monitor student subsidies according to need, merit, and the institution's diversity goals. This paper reviews the existing theoretical literature on the allocation of financial aid and proposes a more complete method of analyzing the matriculation process. Using proprietary data from two representative small colleges, we demonstrate that single equation estimates of enrollment probabilities can suffer from an endogeneity bias. We propose a simultaneous probit-tobit system that corrects for this bias. Our two major findings are: (1) contrary to the predictions of the theoretical model, institutions of higher education make larger financial aid awards to students with high enrollment propensities and (2) traditional single equation models therefore systematically overstate the true impact of financial aid on enrollment probabilities.