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.

Signalling

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.

Framework

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.

Decoupling

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.

Summary

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.

Epilogue

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.

User Adoption Energetics

I’m pretty sure this idea isn’t new, but I can’t find another source talking about it directly. I think I got it from a Yudkowsky essay talking about venture investing.

There’s a strong analogy between the rate of a chemical reaction, and the rate at which new users adopt an app.

Chemistry

In chemistry, there’s a standard picture of the energy in a reaction:

Here’s the idea in english. Imagine the chemicals in the reaction as a bunch of balls sitting on the flat part of the curve pictured, right above “reactants”. The big hill, called the energy barrier, keeps them in place. If the big hill were removed, the balls would all roll down to the right, where it says “products”. In physical terms, when a ball crosses the hill and rolls down the other side, it represents a few reactant molecules turning into product molecules.

But the balls don’t just sit there. In real life, there’s heat! It’s like we’re shaking the balls around. Shake hard enough, and they’ll start to bounce up over the hill; the reactants will turn into products. The harder we shake (i.e. the more heat we add), the faster balls will bounce over the hill, and the faster the reactants will turn into products.

But shaking doesn’t just turn reactants into products. Shake enough and, every once in a while, a ball from the product side will bounce back to the reactant side. This is a reverse reaction - products turning back into reactants. If the reactants are much higher in energy than the products, then balls will bounce forward much more than backward. But if the two sides are about even - if reactants and products have about the same energy - then the balls will bounce backward just as often as forward.

Product and UI

We can use exactly the same model for user adoption of a product, e.g. an app.

Now, the balls represent potential users. People on the “reactants” side are not yet users; people on the “products” side have fully adopted the product. In between, there’s a hump - the energy barrier which a potential new user must cross.

Generally, we want to get everyone to adopt our product. In order to make that happen, we need two things.

First, we want to make the energy barrier as low as possible. In other words, make it easy for new users to adopt the product. Things like a steep learning curve or long onboarding flow or upfront cost make the energy barrier higher. A lot of UI design, especially for onboarding, is focused on making that barrier lower.

But the energy barrier is only half the equation. We also need the “products” to have much lower energy than the “reactants”. In other words, our users need to get lots of value out of the product once they’ve adopted it. If the users are about equally happy between using the product or not, or if they’re happier without the product, then they’ll just bounce back to the other side. We’ll see high “churn”, with lots of users leaving.

In chemistry, a strong reaction requires two pieces: low activation energy and a big energy drop. A successful product requires the same two pieces: low activation energy (easy acquisition/onboarding) a big energy drop (value for the user). If either one of those is missing, then the product will not see much use.

Thoughts From China

I recently returned from my third trip to Shanghai, so I wrote up a post with a bunch of idle thoughts from the trips - with photos!

Shanghai Startup Scene - The Tank Problem

This picture isn’t mine, but during my previous trip to Shanghai (September 2016), these orange bikes were everywhere. They’re owned by Mobike, a bike rental startup. You walk down the sidewalk until you find one of their bikes sitting around, scan the QR code on the bike to pay, the bike unlocks, and you ride off. When you get where you’re going, just re-lock the wheel and leave the bike.

Anyway, note the prominent serial number by the back wheel - the bike pictured is number 10748. So naturally, my idle thoughts drifted to the tank problem.

As the story goes, the tank problem arose in WWII. The allies wanted to estimate how many tanks the Germans had available, so they looked at serial numbers on captured tanks. So, for instance, if they saw a serial number of 10748, then they knew that there were at least 10748 tanks out there. With a little Bayesian stats magic, they were able to get much more precise estimates - so precise that, after the war, it turned out the statistical estimates based on serial numbers were more accurate than the estimates from spies!

Back to Shanghai. I kept an eye on serial numbers of the orange bikes, and came up with a rough estimate of 42,000 bikes.

Shanghai Startup Scene - Defensible Differentiation

When something works, people copy it. Sure enough, in the roughly 8 months between my 2016 trip to Shanghai and my most recent trip, Mobike had sprouted a competitor - at least four competitors, in fact, each with a different bike color. Judging by number of bikes, the competition was mostly between first mover Mobike (orange) and newcomer Ofo (yellow).

My guess is that both companies are burning cash like crazy. With competition this stiff, they can’t both expect to stay in business. Assuming most customers have both apps and grab whichever bike is closest, this is a battle of who can put the most bikes on the street without going bankrupt. Heck, if these two companies can raise enough capital, Shanghai may soon have more bikes than people - it’s in both their best interest to keep putting bikes on the road until the other folds, even past the point where each bike is profitable.

But the real game here is product differentiation - if one company can present an easier lock or a better bike, then people will choose their bike rather than grabbing whatever’s closest, and that company will not need to compete for most bikes on the road. Indeed, at least one company has taken this route: another company offers green bikes, not pictured here, with a small electric motor on them. Of course, their product differentiation isn’t defensible either - someone else could come along and offer electric bikes too.

Real Interest Rates

Among the interesting sights in China were stores like this - less than a hundred square meters of floor space, with backpacks covering all the wall surface and piled ten deep on the floor. That’s right, those stacks you see on the floor? More backpacks. We were in a whole building like this. The floorplan was like a four-story self-storage place, but rather than storage units, there were tiny stores. Every single store was piled from floor to ceiling with some very specific good - this one had backpacks, others had umbrellas, pantyhose, stickers, stationary… one was even filled with tubs of plushies.

But what makes this place strange is the foot traffic - or lack thereof. Even at peak hours, the building had more store owners than customers. For units with that much inventory crammed in, they weren’t moving much volume. What gives?

My guess is that this was caused by negative real interest rates. Here’s how that works. Normally, store owners pay for their inventory with credit, so the cost of holding inventory comes from the interest rate paid on it. Looking at these little units, crammed with inventory but lacking customers, it seems like they’d have trouble selling enough to make up for the interest cost. But there’s a catch - inflation. With positive inflation, prices go up - including prices of all those goods. If the rate of inflation is greater than interest rates - a situation called “negative real interest” - then gains from rising prices on the inventory outpace the expense of interest. In other words, when real rates are negative, you can make money by taking out a loan, filling a warehouse with inventory, and then just sitting there.

During the past decade, negative real rates have been quite common worldwide, especially for short-term borrowing. Given that China goes to extra lengths to devalue its currency, their real rates should be even lower than most countries. I suspect that’s what drives these little “shops” - at the moment, they’re not really shops so much as warehouses with a little side business selling direct to consumers. Most of the inventory will eventually be sold in bulk, hopefully at a profit.

Trade Theory of Tasty Food

This dish is fried spiced naan bread, with some lamb skewers behind it. The restaurant advertises itself as “silk road” style cuisine, a cross between Chinese, Indian and Persian foods.

This gave rise to my trade theory of tasty food: the better access an area had to historic trade routes, the better their ethnic food. Thus the best ethnic food comes from places like India and the Middle East, where trade routes granted access to lots of spices and allowed ideas from many corners of the world to pass through. On the other hand, remote places like Britain or Japan are characterized by bland food with relatively little variety.

Chinese Food

One pattern in real Chinese dishes is a big pile of vegetables with little pieces of meat hiding in it. Older Chinese people, who grew up in the early communist era, are extremely talented at racing to find the little bits of meat hiding under the vegetables.

Based on the stories, this sort of dish was probably a by-product of the communist famines. I suspect that the “Chinese food” we see in the U.S. today is probably more similar to historic Chinese food than the dishes of modern-day China, since pre-Mao Chinese immigrants never had to adopt their dishes to the constraints of famine the same way people in China did.

Today, though, meat is back with a vengeance. Having grown up with relatively limited meat, older Chinese people today think meat=value when it comes to food.

College Costs, Part II

Turns out the previous post on college costs omitted some important accounting. This (shorter) post will fill that hole, and then we’ll finally be ready to talk economics. This post will start off right where the previous post left off: decreasing student/faculty ratios.

Decreasing student/faculty ratios mean at least one of three things:

• Individual faculty are teaching fewer classes
• Individual students are taking more classes
• Classes are smaller

In principle, any of these scenarios could be identified with the right data. In practice, data on e.g. class size in college is hard to come by, but many answers can be found just from historical course catalogues. Berkeley is particularly helpful; their course catalogues are available online going back to 1870.

If I really wanted my data to be perfect, I’d go through the course catalogues and count the number of classes (or hire someone else to do so). But for now, I’m just looking for a rough estimate, so I’ll use the number of pages in the course catalogue as a stand-in for the number of classes. Berkeley’s catalogue has kept a pretty consistent three-column format since the mid-70’s, so hopefully this estimate won’t be too far off the mark.

Anyway, looking at the number of pages in Berkeley’s course catalogue by year gives a very satisfying graph:

These numbers line up neatly with the numbers from the previous post. From 2003-2012, the length of the course catalogue increased by 11.0%; last post mentioned that faculty per student increased by 12% from 2003-2013. Similarly, over this whole period, the length of the course catalogue almost doubled; a chart from the previous post suggests that the number of faculty per student has almost doubled over roughly the same period (at least for law schools).

The course catalogue also lists all of Berkeley’s professors. Again, I didn’t count them all, but I searched for “Ph.D.” and counted the hits. This is definitely a noisy measure, since “Ph.D.” doesn’t just appear after professors’ names in the catalogue, but it should suffice for a quick-and-dirty check. In the 1980-81 catalogue, there were 2139 hits for “Ph.D.” and the catalogue was 239 pages, a ratio of 8.9. In the 2011-2013 catalogue, there were 4132 hits and the catalogue was 414 pages, a ratio of 10.0. So if anything, there are fewer professors per class - professors are teaching slightly more courses on average. But the main takeaway is that the number of courses taught per professor has remained roughly constant even though the number of faculty per student has roughly doubled.

Going back to our original list of possibilities:

• Individual faculty are teaching fewer classes -> nope.
• Individual students are taking more classes
• Classes are smaller

I doubt there’s any statistics on how many classes students take, but… sanity check. Are students today taking twice as many courses as students thirty years ago? No way. Maybe there’s been some change, but there’s no way it’s the lion’s share of the effect.

That just leaves one possibility: classes are smaller.

Great! So, colleges could cut their costs in half by trading small sections for large lecture halls, right?

Not really.

If the number of classes offered at a typical college has roughly doubled - as seems to be the case for Berkeley - then it’s not just twice as many sections of Math 101. After all, we measured the growth in courses offered by looking at number of pages in the course catalogue… and multiple sections of the same course usually go under a single entry in the catalogue.

Classes aren’t just half the size; there are twice as many different classes now compared to thirty years ago. If the data and assumptions here generalize, then there’s been a cambrian explosion in diversity of academic subjects, creating a proliferation of new courses and specialties. Anyone who’s been in academia should be able to confirm that this matches experience. At Harvey Mudd, for instance, this period saw two new departments created (biology and computer science), along with more specialties within the existing departments.

This finally gives us a satisfying answer to our original accounting question: where does all the money go? As the previous post showed, growth in college cost has practically all gone to more faculty and staff per student. But more qualitatively, the growth in faculty and staff per student has fed a cambrian explosion in academic specialties, as shown by a proliferation of new courses.

That tells us what all the extra money has been spent on, but we still don’t know why so much money has been spent. Why aren’t most colleges offering a narrower selection of courses for half the price? With that question, we’re finally ready to talk economics. That will be the subject of the next post.