For almost 30 years, the evidence on the Bennett Hypothesis has been all over the place. Given this mixed evidence, I’ve argued elsewhere that “ ‘Is the Bennett Hypothesis true?’ is the wrong question as it has no consistent answer. The better question is, ‘When does the Bennett Hypothesis hold or not hold, and why?’ ” So I am pleased that Archibald and Feldman avoid the common mistake of being Bennett Hypothesis zealots or deniers.

But they do go wrong in their selection of the model to explain the mixed evidence. They follow an “enrollment management model” that builds upon the observation that “unlike most firms, nonprofit colleges and universities often turn away business. They care about who purchases their services.” If these colleges prioritize enrolling the “best-possible incoming class,” it is relatively straightforward to show that these schools will often forgo the opportunity presented by an increase in federal aid to raise tuition because allowing students to keep some of the aid—instead of jacking up tuition to harvest those government dollars—helps in attracting high-quality students.

Their model isn’t necessarily wrong as a description of what colleges try to do in enrolling a class. But that isn’t the issue they are investigating. Rather, they are seeking to explain the empirical evidence on the Bennett Hypothesis, and for that their model isn’t helpful.

Violating an assumption / The first problem with Archibald and Feldman’s argument is that to explain the empirical evidence, their model needs to violate one of its foundational assumptions.

Their model starts with the assumption that “the revenue needs [of the college] are set first … and the tuition-setting and admission decisions are made together afterward.” This is the AT * × E* amount in their Figures 1–3: the product of multiplying a school’s average tuition revenue by its enrollment. Basically, their model assumes that there is a predetermined amount of tuition revenue that schools need to raise from their students. Colleges will then recruit the best students possible subject to the condition that this class of students must, in aggregate, pay this predetermined tuition revenue. As Archibald and Feldman point out, this doesn’t mean that each student pays the exact same amount (AT *). Rather, students whom the college wants to attract (e.g., those with high academic or athletic potential) will often be offered discounts/​scholarships in the hopes of enticing them to enroll. Other, less desirable students will be charged more than average to finance those discounts.

When federal aid is offered, the empirical evidence clearly indicates that colleges have a range of different “tax” rates, Archibald and Feldman explain. By “tax,” they refer to a college decreasing the discounts/​scholarships it gives a student from its own funds when the student gets federal aid. This way, schools can harvest the federal funds without harming their original, intended enrollments.

The problem for Archibald and Feldman is that they misinterpret what their model implies about these “tax” rates. They claim that the “enrollment management model offers no firm prediction about the tax rate an institution might choose.” This is false. The model explicitly assumes that tuition revenue is fixed. The only tax rate that leaves tuition revenue unchanged is 0%. Any tax rate greater than zero will result in an increase in tuition revenue. This oversight appears to be based on confusion between tuition revenue (what the college receives) and net price (what the student pays). They acknowledge that with a hypothetical 100% tax rate (every $1 increase in federal aid leads to a $1 decrease in college aid), “the institution would get a tuition windfall,” but then they change topics to focus on net tuition: “But notice that in neither case would the student see a higher list price or net price.” The “tuition windfall” result violates the assumptions of their model, without which the prediction of no increase in net price has no basis.

In other words, Archibald and Feldman are trying to explain the empirical evidence of greater than zero “tax” rates with a model that is only internally consistent with its own assumptions if the “tax” rate is zero. They need to find a model that can explain the evidence without violating its own assumptions.

For-profits / A number of studies find that the Bennett Hypothesis does hold for for-profit colleges. Archibald and Feldman explain that this isn’t a strike against their model because for-profits do not try to enroll the best possible class, and therefore their “model is not a good description of how for-profit schools operate. These schools maximize revenue in the short run and profits in the long run.” They then note, with more than a touch of irony, the “greedy colleges” that would react to increases in the generosity of federal financial aid by hiking tuition tend to be found in the for-profit sector, which is the most market-oriented segment of the higher education industry.

But step back for a moment and recognize how bizarre the evidence is: the producer is able to capture a large portion of the subsidy. This would be like if the government offered a $1 subsidy per loaf of bread, and the result was that bakeries increased the price of bread by roughly $1. While such a price increase would be possible in the short term if there are capacity constraints (if each bakery is already producing the most bread it can), the extra revenue from higher prices would translate into unusually high profits, which would then attract entrepreneurs to build new bakeries. The competition from these new bakeries would drive down the price of bread until profits were no longer unusually high. In the long run, we would expect for the consumer to pay $1 less for bread, which combined with the $1 subsidy would leave bakery profits unchanged (assuming a perfectly elastic long-run supply curve).

Yet the empirical evidence shows that this doesn’t happen in the for-profit college sector. For-profit colleges are able to raise prices even in the long run. It would be like if the original bakeries were able to raise prices by $1 and keep them there indefinitely. Thus, even though Archibald and Feldman correctly argue that the enrollment management model doesn’t apply to for-profits because for-profits do not seek to enroll the best possible class, they still can’t explain why we see convincing evidence of the Bennett Hypothesis among for-profit colleges. (Elasticity arguments cannot salvage this result either, as supply in the for-profit sector, which uses scalable online courses heavily, is likely to be very elastic in long run).

One possible explanation for the for-profit results that would be consistent with Archibald and Feldman’s argument is the “90/10” rule. This rule dictates that no more than 90% of a college’s revenue can come from federal financial aid programs. But colleges can’t control how much federal aid a student gets (the government determines this), so a good case can be made that these colleges have to set their price above the level of federal aid. For example, if the government is giving each of a college’s students $90 in federal aid, then the college needs to charge tuition of at least $100 to comply with the 90/10 rule. This implies that an increase in federal aid would lead to a corresponding increase in tuition, explaining the evidence showing the Bennett Hypothesis occurs at for-profit colleges. I actually think there is a lot of truth to this story, but if so, then Archibald and Feldman’s schadenfreude about for-profits being “greedy” seems more than a little misplaced as their behavior is driven by compliance with government policies.

A better model? / Archibald and Feldman are on the right track in seeking a “structural model” that accounts for the goals of colleges, but perhaps there is a better model that is more consistent with both the “tax rate” and for-profit evidence. My own research leads me to the conclusion that Howard R. Bowen’s Revenue Theory of Costs, better known as Bowen’s Laws, provides the basis for a better structural model, in part because it doesn’t assume away the revenue goal like the enrollment management model does. Indeed Bowen’s Laws treat the determination of revenue as a central question to be answered by the college. According to Bowen:

• The dominant goals of institutions are educational excellence, prestige, and influence.
• In quest of excellence, prestige, and influence, there is virtually no limit to the amount of money an institution could spend for seemingly fruitful educational needs.
• Each institution raises all the money it can.
• Each institution spends all it raises.
• The cumulative effect of the preceding four laws is toward ever increasing expenditure.

As I detail in “Introducing Bennett Hypothesis 2.0,” a policy paper available from the Center for College Affordability and Productivity, this theory does a good job of explaining the mixed evidence. Colleges want more tuition revenue, so when federal aid is given to their students, they will be tempted to either raise tuition or cut back on their own discounts/​scholarships. But their goal is not revenue maximization; it is prestige maximization, which means that sometimes other considerations (e.g., maintaining selectivity) will preclude the college from choosing to harvest all the federal aid by raising tuition or cutting their own scholarships/​discounts. The mixed evidence that we’ve seen over the past 30 years is therefore exactly what we’d expect.

In summary, Archibald and Feldman are right in seeking a more structural model and in highlighting the importance of changes in college-provided discounts/​scholarships as opposed to only focusing on listed tuition. (This is a great insight that many scholars, including myself, have not adequately appreciated in the past.) But their enrollment management model does not help explain the evidence on the Bennett Hypothesis. Models building off of Bowen’s Laws do a better job of explaining the evidence, and therefore offer a much more promising path for future research.