College Expenditures and Federal Aid Policy in the Market for Higher Education

This paper draws very heavily from the work of Dennis Epple, Richard Romano, Sinan Sarpça, and Holger Sieg (2017), and I am extremely grateful to each of them for their kindness not only in allowing me to use their work but also in helping me to understand it. Not only were they supportive of my attempt to extend their model of higher education, but they even went as far as to send me their code, which greatly improved my paper and saved me an enormous amount of time. I am particularly grateful to Sinan Sarpça who, when I struggled to understand some of the mathematics of their model, immediately sent me detailed notes explaining how to work it out. The work I present in this paper is only a tiny addition to their previous work, and the little amount I have managed to contribute was only made possible by their immense kindness and generosity.

The Bennett Hypothesis posits that increases in federal student aid lead colleges to invest in frivolous luxury items in order to extract higher tuition prices, turning college campuses into luxury resorts with little focus on education. To explore this theory, I extend the model of the market for higher education developed by Epple, Romano, Sarpça, and Sieg (2017) to include college expenditure choices and student preferences for quality of life on campus. Public schools (which are assumed to seek to maximize the total achievement of in-state students) and private schools (which are assumed to seek to maximize their academic quality) choose between two types of expenditures: (i) educational expenditures, which improve the school's academic quality and provide students with higher achievement, and (ii) noneducational or luxury expenditures, which improve the school's quality of life and provide students with greater enjoyment. Students are assumed to vary by income, ability, and their affinity for luxury, and their utility functions are assumed to be increasing in both their level of achievement as well as their enjoyment.

A parameterized version of the model is then calibrated to capture key characteristics of the market for higher education. The calibrated model does a very good job of matching aggregate characteristics of the U.S. market for higher education, including per-student educational and noneducational expenditures. Using the calibrated model, an increase in federal student aid funding is simulated.

The simulation results suggest the Bennett Hypothesis may in fact hold to some extent, but they also highlight the complexity of the market for higher education and the inherent difficulties involved in evaluating the effects of a given policy. While the model finds that an increase in federal student aid leads bottom-tier private schools to shift their expenditures toward luxury, it also finds that total enrollment and achievement are increased. Thus, the policy helps to increase access to higher education, particularly among lower income students. The final assessment of the merits of increasing federal student aid will depend on the objective function of the policymaker.

The Bennett Hypothesis posits that increases in federal student aid lead colleges to spend more on luxury items---such as luxurious dormitories, student centers, and rec centers---soaking up aid through higher tuition prices while doing little to increase academic achievement. According to the Bennett Hypothesis, colleges have increasingly become more like luxury resorts, where unserious students go on extended vacations financed by federal student loans. To test the merits of this argument, I use a sophisticated mathematical model of the market for higher education to simulate an increase in federal student aid funding. The model is an extension of the model developed by Dennis Epple, Richard Romano, Sinan Sarpça, and Holger Sieg (2017). It includes public state schools and private schools which compete for students by adjusting the tuition prices they charge students. Each school can also adjust how much it chooses to spend on educational expenses (such as professors, lecture halls, labs, etc.) and noneducational expenses (such as dormitories, student centers, rec centers, etc.).

Students vary by income, academic ability, and their affinity for luxury. Each student decides which school to attend (if any) based on the characteristics of each school, including its academic quality, the quality of its campus, and its tuition price. All else equal, schools prefer to have higher ability students, so they typically offer them lower tuition prices. However, schools will also consider a student's income when deciding what price to charge. While schools know that students prefer more luxurious campuses, they are unable to observe any particular student's affinity for luxury, so they cannot price discriminate based on this characteristic.

Overall, the model is very complicated, and it realistically captures the various objectives of students and schools. This is demonstrated by the model's ability to capture key features of the market for higher education observed in the real world. When the model is run (so that all students decide which school to attend, and each school decides how much to spend on educational and noneducational expenses, which students to offer admission to, and what prices to charge, etc.), the behavior in the model closely matches real-world behavior. For example, comparing the output of the model with the real world: the same percentage of eligible students choose to attend college as in the real world; the same percentage of students choose to attend a state school versus a private school; tuition prices are similar to those in the real world, including the variation in prices observed across schools of different academic quality; educational and noneducational expenditures are similar to those in the real world; the percentage of students receiving federal aid is similar to the real world; etc.

I then use the model to simulate an increase in federal student aid funding. The increase in aid leads to a significant increase in the number of eligible students who choose to attend college, especially among low-income students. And, with the exception of bottom-tier private schools, all of the schools shift their spending toward educational expenditures and away from luxury items. However, consistent with the Bennett Hypothesis, bottom-tier private schools actually shift their spending toward luxury items, placing less of an emphasis on education. Interestingly, this is despite the fact that they are modeled as seeking to maximize their academic quality rather than their profits. Making matters worse, the students enrolled at the bottom-tier private schools are also the largest recipients of federal aid, suggesting that much of the increase in aid does in fact fund increases in the luxuriousness at private schools with the lowest academic quality.