Wednesday, May 31, 2017

Economics of College Cost

This post builds on two prior posts. However, this post can be read standalone, especially if you're more interested in the conclusions than in the data. Quick recap:
  • The question is why the cost of college has risen much faster than inflation for almost 40 years, with relatively little increase in quality.
  • There’s really two questions in there. First, there’s an accounting question: where is all the extra money going? Second, there’s an economics question: knowing where the extra money is going, why is it going there?
  • The first post addressed the accounting part, mainly using data on 4-year private nonprofit colleges from the Digest of Education Statistics, running from 1999-2013.
  • A large mismatch between sticker-price tuition and tuition revenue confirms what private college students know: sticker price isn’t what’s actually charged. Real tuition charges have grown at about half the rate of sticker price, although that’s still after adjusting for inflation.
  • All the extra tuition money has gone to paying faculty and staff. The growth in per-student expenditure is mostly driven by decreasing student/faculty (and probably student/staff) ratio. Faculty salary has also increased a bit faster than inflation.
  • Based on some quick statistics on Berkeley’s old course catalogues, the extra faculty per student are fueling a cambrian explosion in academic courses.
So we have a pretty good idea of where all the extra money is going: students today face a much wider buffet of course options, which requires more faculty per student. That’s the “what?” part. This post tackles the “why?” part, moving our view from trees to forest.

Our main driving question is this: why doesn’t somebody just set up a college that teaches roughly the same courses as back in the 70’s, with roughly the same student/faculty ratio, and charge half as much as the rest of today’s colleges?

There’s a few pieces to the puzzle.

We’ll start with the low-hanging fruit. College education is the textbook example of signalling - the game theory text at the foot of my bed spends the first half of the signalling chapter just on that. The standard education signalling game won’t provide all the pieces we need, but it will provide the main framework for reasoning about the problem.

Here’s the usual setup: we have two players, an employer and a prospective worker. For simplicity, there are two types of workers: high value workers (more intelligent, more diligent, follow directions, whatever) and low value workers (opposite of all that). All else equal, the employer would rather hire a high value worker than a low value worker, but it’s hard to tell them apart in interviews. It’s not like the employer can just ask “hey, are you smart and diligent?” because everybody will just say yes.

What the high value workers really want is some way to signal to the employer that they’re high value. That’s where college comes in: obtaining a degree is a lot easier for people who are more intelligent, more diligent, follow directions, etc. So the high value workers go get a degree, and now the employer can tell high value workers apart from low value workers by asking whether they have a degree. Since the employer wants high value workers more, they get offered more money.

Of course, this is the dramatically over-simplified version. Pick up a game theory textbook if you want to build up a more realistic model.

The signalling model of education quickly leads into a general framework.

From an economic standpoint, the primary function of post-secondary education is filtration. Ever wondered why so many people pay so much money for a college education, when the vast majority of the material they learn is never used in the workplace? Well, there’s your answer: the things learned aren’t relevant. The main economic purpose of higher education is not to acquire knowledge, but to signal intelligence/diligence/direction-following/etc.

This is hardly novel; it’s the default assumption among the small portion of education researchers who actually bother with statistics. Researchers tend to focus more on high school than college, but the same idea applies: education isn’t about learning, it’s about filtering.

There’s an endless stream of idiots in education research saying things like “hey look, top-scoring schools all have lots of trees!”. Then the people who bother with statistics say “yes, but if you account for top-scoring schools having higher-scoring students coming in, then the trees don’t have any significant effect.”. Then the idiots ignore them, and go on a big political campaign to spend hundreds of millions of dollars planting more trees at low-scoring schools. Ten years later, lots of low-scoring schools have more trees, and their scores haven’t improved at all.

Anyway, I digress. If you want more details, here’s an entire blog to check out. For our purposes, the takeaway is this: in and of itself, education has very little effect on the sorts of things employers care about. The vast majority of what people learn in college goes unused at work. The economic role of education is not to acquire knowledge, but to filter higher-value workers from lower-value workers.

Furthermore, the difference between “better” and “worse” schools is mainly filtration. Harvard teaches roughly the same material as any state school, but employers pay a premium for Harvard grads because Harvard is pickier in its admissions. This will turn out to be a key piece of the puzzle.

Back to our main problem: why doesn’t someone start a college which teaches roughly the same subjects as the late 1970’s, at half the cost of other colleges today?

One obvious guess is “well, maybe all those new subjects teach new skills which are needed in our ever-diversifying economy”. The signalling framework disagrees, and offers two sanity checks: employers don’t care exactly what you studied, and most of what was covered won’t be used anyway.

But this raises a question. Clearly, academic courses and content have little to do with employer needs. So what does drive courses and content? Why are students so interested in a wild variety of courses that they’re willing to pay double for it?

What do colleges want?
Now for the last key piece: what do colleges want? We’re talking mainly about private nonprofits here, so it’s not like they’re out to make money. College administrators give lip service to all sorts of ideals, but what objectives actually drive their spending?

Well, we mentioned earlier that from an employer’s point of view, the difference between Harvard and a state school is that Harvard graduates higher-quality students on average, mainly by bringing in higher-quality students in the first place. So… what if that’s the main goal driving college behavior? What if colleges are mainly competing to attract and retain the best students?

Intuitively, that makes a lot of sense.

How do colleges attract and retain the best students? Generous scholarships for top students are one obvious approach. The difference between sticker price and actual tuition paid for college isn’t the main focus of this post, but competition for top students explains it neatly.

But what about the cambrian explosion of courses? My guess is that top students are much more likely than average to have specific academic interests. A college which can provide courses tailored to a student’s particular interests will have a major advantage over a college with a few generic courses.

A college adds a handful of courses in a hot new field, and they attract some excited top students. Other colleges catch on, and begin to offer courses in the hot new thing themselves. The cycle repeats. It’s an arms race to attract the best and brightest by offering courses in the hottest new fields.

Finally, we have a coherent picture. From an economic standpoint, college is about signalling, as we’d expect. Individual colleges are economically incentivized to recruit the best and brightest students they can. Thus the key insight: college is optimized, not for the average students, but for the top students.

And then it makes all sorts of sense.

What do the top students want? Courses tailored to their interests, and a free ride. What do the top students get? Courses tailored to their interests, and a free ride. The economic weirdness of college cost growth - the cambrian explosion in courses, the divergence between actual cost and sticker price - is a result of competition for top students.

Zooming out, why is attracting top students the main de-facto goal of most colleges? The signalling model provides an economic answer. The higher the quality of the students a college attracts, the more employers will eventually pay for those students, and the more the college’s degree is worth.

In short: colleges are economically incentivized to optimize for top students, not average students.

The real point of this whole exercise is not to better understand college cost growth. The real point is that, since we didn’t understand college cost growth, there was probably some key principle missing. By looking at college costs, we hope to dredge up that missing principle, and then generalize it to other domains.

So let’s formulate the key principle more generally.

Suppose there’s some class of signalling goods whose main role is to signal X. Maybe X is wealth, maybe X is virtue, maybe X is intelligence, maybe X is hipness, maybe X is membership in some group. The general principle is: under competition, goods used to signal X will be optimized for people with the highest X, not for their average consumer.

Why? Well, it’s fashion 101. If the cool people do it, everyone else will follow. If the cool people don’t do it, nobody else will either. So, the successful products will be those which optimize for the cool people.

As applied to college, the logic goes like this: colleges which optimize for top students will get the top students. If a college tries to break out and optimize for average students, then they won’t get any top students. Employers will realize this, and will not be very interested in their graduates. Since employers won’t be interested in their graduates, even average students won’t want to attend.


  1. I found your earlier posts on college costs very strong but count me a little unconvinced on this one. Is it really true that the top students drive the curriculum? I'm sure that's true in some cases but is it really driving the Cambrian Explosion (nice phrase by the way)?

    So the number of different courses on offers have increased, but is this the same for different colleges, different disciplines?

    1. FWIW, I'm not entirely convinced myself.

      The signalling framework is definitely strong - there's a reason it's so widely accepted, it's very hard to explain why people spend so much effort learning things they won't ever use without signalling.

      The bit at the end, that goods for signalling X will optimize for people with high X, is also strong. It's a theorem, even if I haven't bothered to cast it in the formal language of game theory.

      I'm not convinced that those pieces fully explain the Cambrian Explosion. I think it's plausible, and it's a good default theory, since it does not require any new hypotheses - it uses only the standard signalling framework. But I don't have the data to properly verify it. I would view it as a strong hypothesis at this point, but certainly not a closed case.