Pricing Higher Ed

My last post included a link to "Admission, Tuition, and Financial Aid Policies in the Market
for Higher Education" by Epple, Romano, and Sieg from 2003. In the paper, they test economic models against actual data and reach some very interesting conclusions about how pricing works. One of the assumptions is "In our model, colleges seek to maximize the quality of the educational
experience provided to their students."

I thought about this for a while. It's not obviously true, is it? I'm trying to remember how many meetings I've sat in where someone talked about the quality of educational experience. Of course, in many small ways programs, individual instructors, chairs, and so on do bits and pieces that impact this quality. And the SACS Quality Enhancement Plan is supposed to turn this into a visible project.

But by and large, I think most of my meeting time has been spent on solving problems, grinding away at the routine bureaucracy, or (once in a while) trying to make the bureaucracy work better. Of course, outcomes assessment is supposed to lead to continual improvements in the quality of education, but it would be a wonderful thing if board meetings were opened with the sentiment: we're here to improve the quality of educational experience.

As it turns out, I'm in the middle of a project to improve the "experience" part of that by helping organize strategic planning action items along those lines, and I'm going to start using that language.

In the article, the authors give some dependencies for quality:

1. peer ability of the student body
2. a measure of peer-student income diversity
3. instructional expenditures per student
   

Quality is relative, and two of the dependencies listed above are intuitive: students don't want to attend classes populated with students who are all less able than themselves. They also perceive the institution's ability to spend money in the classroom. This one is reflected in college rankings too (see "Zza's Best Liberal Arts Schools"), which probably has some affect on decisions. The second dependency, however, is surprising to me.

They see a distinct stratification that bestows economic benefits to the top schools:

Colleges at low and medium quality level have close substitutes in equilibrium and thus a limited amount of market power. Admission policies are largely driven by the “effective marginal costs” of educating students of differing abilities and incomes.

Colleges with high quality have more market power. These colleges do not face competition from higher-quality colleges. Hence, they can set tuitions above effective marginal costs and generate additional revenues that are used to enhance quality.

This suggests a Darwinian struggle for schools at the low and mid-levels of means and quality. In a catch-22, they lack the pricing power to enhance their position much. But once breaking through a ceiling, it becomes easier. At least that's my interpretation.

On the subject of price, the authors illuminate the second dependency (financial diversity):

We also find that colleges at all levels link tuition to student (household) income. Some of this pricing derives from the market power of each college. This allows colleges to extract additional revenues from students that are inframarginal consumers of a college. However, as noted above, our empirical findings suggest that market power of lower and middle ranked colleges is limited. This suggests that pricing by income may be driven by other causes.

I found an explanation of what an "inframarginal consumer" in another source "The inframarginal consumer is willing to pay more for the good than is the marginal consumer." So, if your college has a good market position, you can charge a premium. But the authors argue that that this isn't the whole story:

In this paper, we then also explore the role that income diversity measures play in determining college quality. Our findings here indicate that colleges and students believe that the quality of a student’s educational experience is enhanced by interacting with peers from diverse socioeconomic backgrounds.

Obviously there are many reasons for wanting a diverse student body, but the authors propose to actually use that as a factor that contributes to the price model. This begins to make more sense in Section 6 of the paper, where they verify empirically that college quality increases with income diversity, stating that "To attract students from lower-income backgrounds, colleges give financial aid that is inversely related to income as detailed below." While this is no doubt true for some institutions, others have a more directly self-interested reason for giving need-based aid: to increase enrollment in those students who couldn't otherwise afford to attend. I talked about the revenue-generating effect of this "gap filling" in "The Power of Discriminant Pricing."

Also in Section 6, they make an observation about college size:

Absent scale economies, peer effects and endowments create a force for colleges to reduce size to increase student quality–in the limit maximizing quality by admitting a handful of brilliant students and lavishing the entire endowment on educating those students. The countervailing effect of scale economies is captured in our cost function primarily by the c3 term in the cost function.

This outlines a good strategy for an elite school: keep it small because it's easier to maintain a high level of average student quality, but not so small that the economies of scale drive up costs unreasonably.

A hundred points of SAT is worth between $4688 and $10363 in merit aid (in 2003), according to the model output. The difference depends on what tier of college the applicant applies to.

Conclusions: First, remember I'm not an economist. But the paper is clearly written, and you can skip the mathy bits easily enough. The model presented has errors, as the authors describe, but the approach seems to lead to some insights, like the relationship between size and quality, the effect of financial diversity on institutional quality, and price sensitivity by student ability and income. I have not delved into all of these in my notes above. I don't know how hard it would be to simulate their model numerically to actually use it to build your policies (e.g. by running scenarios), but it's probably worth showing it to your IR office. And if you have an economics department handy, maybe they can shed some light as well.