The Bennett Hypothesis – the notion that federal financial aid enables colleges to increase tuition – has undergone a remarkable revival in the past couple of years. In policy circles, the idea went from being publicly mocked to pretty widespread agreement that it is a valid concern for at least some aid programs and some institutions. I’m excited by the 180-degree shift because it’s something my research and writing have been urging. (Note that the Quick and the Ed blog is currently misdirecting incoming links – I’m assuming this is temporary).

But the transformation among policy wonks pales in comparison to the revival of the Bennett Hypothesis among academics. Two fascinating working papers by Lesley Turner and Nicholas Turner prominently feature findings consistent with a version of the Bennett Hypothesis, as did Stephanie Cellini and Claudia Goldin’s 2012 paper.

To this fast growing literature, we can add *The U.S. Market for Higher Education: A General Equilibrium Analysis of State and Private Colleges and Public Funding Policies* by Dennis Epple, Richard Romano, Sinan Sarpça, and Holger Sieg. Their headline finding (regarding the Bennett Hypothesis) is that,

“Private colleges game the federal financial aid system, strategically increasing tuition to increase student aid, and using the proceeds to spend more on educational resources and to compete for high-ability students.”

I know not many people prefer arguments in mathematical form, but their setup illuminates a number of issues that are almost impossible to see with prose alone, so stick with it even if you’re typically a mathophobe – I’ll walk you through it and the payoff is substantial. The groundwork is laid in Epple et. al.’s equations 26 and 27:

In the equations (you can ignore the subscripts):

- A is the amount of financial aid a student is eligible for;
- Ᾱ (A with a bar above it) is the maximum federal student aid award;
- p is the price of the college. For readability, I’ll just call this tuition, but it is technically a college’s “Cost of Attendance” (CoA), which includes tuition, room and board, and other educational expenses. See here for more details on what is and is not included in CoA;
- y is the student’s and family’s income;
- EFC(y) is the student’s expected family contribution, as a function of student characteristics including income.

Equation 26 lays out a simplified formula for determining how much aid a student will receive, and is equal to tuition minus expected family contribution [ p-EFC(y) ] unless that value is higher than the maximum award ( Ᾱ ) or lower than zero. Equation 26 captures the general essence of how the federal government determines a student’s aid eligibility (though some federal financial aid programs – such as the campus-based aid programs – have different rules and methods).

Equation 27 then asks how the student’s aid eligibility changes as tuition increases. There are two situations in which, when tuition is rising, a student does not qualify for additional financial aid. The first of these occurs when the college’s tuition is less than the student’s expected family contribution ( p < EFC ). In this case, an increase in tuition does not increase aid eligibility because the student does not qualify for aid at all. Similarly, when the student’s combined expected family contribution and aid package are already less than tuition [ EFC + Ᾱ < p ], an increase in tuition would qualify the student for more aid *except* the student is already receiving the maximum amount of aid, so the student does not receive any additional aid. Thus, in the first and third cases of equation 27, an increase in tuition does not affect the amount of aid a student receives (∂A/∂p = 0).

But the second case of equation 27 is quite interesting. For these students, tuition is greater than their expected family contribution but less than the combined expected family contribution and maximum aid [ EFC < p < EFC + Ᾱ ]. **This means that when tuition increases by $1, the aid the student is eligible for increases by $1 as well** (∂A/∂p = 1).

To this point, these equations are just a straightforward description of how aid eligibility changes when tuition changes – essentially a statutory relationship dictated by the federal laws and rules governing the financial aid programs. The Bennett Hypothesis emerges when we think about how colleges respond to this statutory relationship. As Epple et al. note, from the college’s perspective

Translated into English, this means that colleges will not set their tuition at a level between the expected family contribution and the expected family contribution plus maximum aid. The reason is that within that range, these colleges can increase tuition, which benefits the college, without harming the student since the student automatically gets $1 more in aid for every $1 increase in tuition (for simplicity, we’ll assume this is all grant aid). This is a “free lunch” from the college’s perspective – more revenue for the college without hurting the student (since aid increases) — and when they exploit it by raising tuition, we get the Bennett Hypothesis.

For policy makers, this mathematical framework helps us see a few things more clearly than we likely could from verbal explanations alone. For starters, the Bennett Hypothesis is only a danger when higher tuition can lead to more aid. If higher tuition doesn’t lead to higher aid (if ∂A/∂p = 0, such as in the first and third cases of equation 27), then the college can’t get the “free lunch” by raising tuition. This observation leads to a distressing conclusion, but also points to a way forward.

The distressing conclusion is that (given the current structure of higher education) **we cannot hope to make college more affordable for the middle class through universally available financial aid.** To see why, note that expected family contribution (EFC) increases as income increases, so for any given level of tuition, the three different possibilities in equation 27 loosely correspond to student income. “High Income” students are generally going to be in the first category ( p < EFC ) as their EFC will be high enough to afford tuition without aid. “Low Income” students are generally going to be in the third category ( EFC + Ᾱ < p ) as even with the maximum aid, they may still not be able to afford tuition. Lastly, “Middle Income” students will be in the second category ( EFC < p < EFC + Ᾱ) since they can generally afford tuition with some aid. Yet this is the only category where the Bennett Hypothesis is a danger, so when these students are given aid, the colleges can respond by raising their tuition. The implication is that universal financial aid programs can only reliably help low income students pay for college. When made available to middle or upper income students, these programs likely enable colleges to raise tuition.

But sensible policy responses to the Bennett Hypothesis are also evident. In particular, since **the Bennett Hypothesis is a behavioral response on the part of colleges to a statutory relationship between tuition and aid eligibility**, we can fight against the Bennett Hypothesis on two fronts: the behavioral response and the statutory relationship.

On the behavioral front, public shaming or calls for new leadership may help a little, but will not accomplish much. The Bennett Hypothesis arises because some colleges respond rationally to the incentives they face to spend as much as possible, in part by raising tuition:

“In higher education, colleges essentially compete in a zero-sum game for relative standing. Due to the lack of measures of output and outcomes, colleges cannot compete on quality, and instead compete based on reputation/prestige/excellence. Essentially, they use high quality inputs as proxies for quality because there is no way to demonstrate high quality directly. Since high quality inputs are costly, and colleges are playing a zero-sum game of relative position, there is no limit to what college[s] will spend in the pursuit of excellence. Thus, they will spend as much as they can…”

So to end the Bennett Hypothesis from the behavioral side of things, we need to change colleges’ incentives.

“The clearest way to escape [the Bennett Hypothesis] is to change the nature of competition. Colleges compete in a zero-sum game based on prestige because they cannot compete based on value, and they cannot compete based on value because measures of both quality and price (net tuition) are obscured. If information on those two were available, the pursuit of excellence would be replaced by the pursuit of value… and [the Bennett Hypothesis] would no longer be a concern.”

Changing the nature of competition in higher education is obviously a difficult and long term undertaking, so in the meantime, what can be done about the statutory relationship between tuition and aid eligibility to combat the Bennett Hypothesis?

Recalling equation 27 gives us some indications of what can be done.

We saw that the Bennett Hypothesis is not a danger in the first and third cases of equation 27, since higher tuition would not lead to higher aid for those students (∂A/∂p = 0). But since higher tuition leads to equivalently higher aid in the second case (∂A/∂p = 1), colleges have an incentive to raise tuition which gives us the Bennett Hypothesis.

I see four options for attacking the Bennett Hypothesis from the statutory relationship side.

First, modify the EFC calculation to reduce the number of students falling into the middle category. There is some low hanging fruit here (e.g., reducing aid for students from families making over $100,000 that receive Pell grants), but we can’t expect too much from this reform as any reasonable determination of what a family can afford to pay (what EFC is designed to measure) will still result in many students in the middle category of equation 27.

Second, ensure that all aid programs have sensible maximum awards. If there is no maximum award (no Ᾱ), then the third case in equation 27 disappears. Those students end up in the second category, and the second category is the only one where the Bennett Hypothesis is a danger. The key point is that **the lack of a maximum award for aid programs massively increases the danger of the Bennett Hypothesis**, so we should ensure that all aid programs have reasonable maximum awards (loan programs like Parent PLUS and GRAD PLUS do not currently have maximum awards [the maximum is capped by a college’s Cost of Attendance (CoA), but CoA does not have a cap], and other programs’ maximums may be too high).

Third, phase out the higher education tax credits and deductions. In addition to a host of other problems, these programs are predominantly used by students from high income families, which in effect move these students from the first case of equation 27 to the second. In other words, the tax credits and deductions take a subset of the population for which the Bennett Hypothesis was not a concern, and, by giving them aid, ensures that the Bennett Hypothesis applies for them too (though colleges may not have enough information to fully exploit this since unlike other aid, this aid is disbursed through the tax system). The remedy is to phase out the higher education tax credits and deductions.

These three approaches can be thought of as reducing the danger of the Bennett Hypothesis. The fourth, and most important idea, would eliminate the danger once and for all. This would entail changing the aid eligibility formula to use the median cost of college rather than a college’s cost of attendance. Currently, each college sets its own cost of attendance (the p in the formulas). If the student’s expected family contribution cannot cover this cost, the student is eligible for aid. This gives rise to the Bennett Hypothesis since for some students, an increase in tuition will increase the aid they are eligible for (∂A/∂p > 0). But if the aid formula ignored each college’s specific price, and instead used the median cost of college for all colleges, then there would be no relationship at all between a college’s tuition/CoA and the aid its students received (∂A/∂p = 0). (Note that the median cost of college could be defined for categories of institutions). Since higher tuition would not lead to more aid, colleges would not have an incentive to raise tuition for the sole purpose of harvesting federal financial aid, which would eliminate concerns about the Bennett Hypothesis (at the level of individual colleges at least).

To illustrate the effects of the change to a median cost of college method, consider two cases. The first is a college that was charging low tuition. Under the old method (college specific CoA), their students were not eligible for much aid. Under the new method, their students are eligible for more aid. Wouldn’t this college simply raise tuition to exploit the greater aid their students are receiving? I would argue no, since the college’s available choices do not change. The college could have raised tuition under the old system but chose not to, so whatever was keeping them from raising tuition before (a strong commitment to access, political pressure, economic considerations, etc.) would presumably still keep them from raising tuition under the new system. Thus, the most likely effect of switching to a median cost of college method for colleges below the median is to help make college more affordable for their students.

Now consider a college that was charging high tuition. Under the old method, their students received a considerable amount of federal financial aid, and partly as a result, these institutions devoted much of their own financial aid budget to merit-based rather than need-based aid to poach desirable students from other schools. But under the new method, their students will not receive as much aid. As students become more price conscious, the college would face increased pressure to lower tuition and to shift their own financial aid offerings away from merit-based and towards need-based aid (reversing the latest trend). Thus, the main impact of the switching to a median cost of college method for colleges above the median would be price containment and equity enhancement.

To sum up, everyone likes a free lunch, and colleges sometimes get one when federal financial aid policy allows them to raise tuition at virtually no cost to students. To fix the problem, we should change either institutions’ behavior or federal law (or both). Changing behavior depends on shifting the way we judge colleges from prestige/reputation to the value they provide students (that is, quality – measured by learning and/or labor market outcomes – compared to price). To undermine the statutory roots of the Bennett Hypothesis, Congress could undertake several actions, including imposing maximum awards on all federal aid programs, phasing out certain tax credits and deductions, and replacing the Cost of Attendance (CoA) with the median cost of college (among similarly situated schools) when determining each students’ aid eligibility. It’s time for institutions’ free lunch to end. Let’s take charging students ever-higher tuition just for the sake of enhancing reputation off the menu.