Questioning the Signaling Model of Education

I was an early adopter of the Higher Ed Bubble thesis. Like all early adopters, I’ve gotten skeptical now that it’s popular. I recently attended a talk by Bryan Caplan where he discussed his thesis that higher education is about signaling good qualities, not about attaining them. This explains lots of puzzles in the education market, from “will this be on the final exam?” to choosing English Lit over Computer Science to 40% absentee rate in typical college classrooms. One of the most compelling pieces of evidence for the signaling model: on average, one more year of education predicts 10% higher income for an individual. But it predicts 2% higher GDP for a country. [Citation needed: Caplan mentions it in his talk, but it is surprisingly hard to Google for.]

The trouble with signaling is that it’s too good. Signaling is always a possible explanation for phenomena that are visible but don’t have an obvious cause, but like lots of other powerful explanations (“market price” or “survival of the fittest”) it’s also strong enough to explain counterfactuals. It’s still valid and meaningful, but signaling is not necessarily a comprehensive model. And in this case there’s another model that can explain some of the gains: accumulating lots of knowledge is disproportionately useful in fields where a) winners win big, and b) growth in that field is has an unusually small impact on GDP growth.

One sensible critique of higher ed is that even in STEM fields, people don’t actually use a ton of the knowledge they accumulate. If you’re really good at esoteric calculus tricks, you are probably going to do a great job teaching calculus to undergrads, but you’re not going to be that much better at, say, building a bridge or a bomb.

Okay, actually, you will be better at building a bomb: in Surely You’re Joking, Mr. Feynman, Richard Feynman notes that he learned One Weird Trick for fiddling with integrals:

That book also showed how to differentiate parameters under the integral sign – it’s a certain operation. It turns out that’s not taught very much in the universities; they don’t emphasize it. But I caught on how to use that method, and I used that one damn tool again and again. So because I was self-taught using that book, I had peculiar methods of doing integrals.

The result was, when guys at MIT or Princeton had trouble doing a certain integral, it was because they couldn’t do it with the standard methods they had learned in school. If it was contour integration, they would have found it; if it was a simple series expansion, they would have found it. Then I come along and try differentiating under the integral sign, and often it worked. So I got a great reputation for doing integrals, only because my box of tools was different from everybody else’s, and they had tried all their tools on it before giving the problem to me.

Then, a few years later, working on the Manhattan Project:

I was sent to Chicago with the instructions to go to each group, tell them I was going to work with them, and have them tell me about a problem in enough detail that I could actually sit down and start to work on it. As soon as I got that far, I was to go to another guy and ask for another problem. That way I would understand the details of everything.

It was a very good idea, but my conscience bothered me a little bit because they would all work so hard to explain things to me, and I’d go away without helping them. But I was very lucky. When one of the guys was explaining a problem, I said, “Why don’t you do it by differentiating under the integral sign?” In half an hour he had it solved, and they’d been working on it for three months.

A little knowledge is a dangerous thing. A lot more knowledge is an incredibly dangerous thing, if the other guy has the knowledge and you’re standing within the blast radius.

“We’re not all Richard Feynman!” you can object. That’s true. Two good reasons for that: one, none of us are that smart. Two: none of us have insisted on accumulating a giant library of techniques-that-might-come-in-handy. One of those is fixable.

(Incidentally, I’m spending some of my between jobs-time reading Apostol’s Calculus. It’s a pain, and will have few practical applications. But one practical application is that math-heavy work is vastly less intimidating. Fluency with calc makes it easier to achieve fluency with stats, and fluency with stats is absolutely essential in finance, even if you’re not a quant.)

An early Facebook growth hacker used the term “surface area” to describe one of Facebook’s valuable assets: the fact that a lot of people are bumping into the site at any given time, and any small change Facebook makes to optimize their experience is going to have a disproportionate impact. Learning more problem-solving techniques is a good way to expand your problem-solving surface area.

And, actually, wait a second: if you weren’t used to thinking geometrically, would the concept of “surface area” pop into your head? People think about that idea generally all the time, but it’s tough to find a peg to hang the idea on. And then you hear “surface area” and suddenly stuff as disparate as “read more” and “meet more people” all pop into place—they’re all hacks to increase your surface area so you bump into more solvable problems.

Charlie Munger has a lot to say about this:

You’ve got to have models in your head. And you’ve got to array your experience—both vicarious and direct—on this latticework of models. You may have noticed students who just try to remember and pound back what is remembered. Well, they fail in school and in life. You’ve got to hang experience on a latticework of models in your head.

What are the models? Well, the first rule is that you’ve got to have multiple models—because if you just have one or two that you’re using, the nature of human psychology is such that you’ll torture reality so that it fits your models, or at least you’ll think it does. You become the equivalent of a chiropractor who, of course, is the great boob in medicine.

It’s like the old saying, “To the man with only a hammer, every problem looks like a nail.” And of course, that’s the way the chiropractor goes about practicing medicine. But that’s a perfectly disastrous way to think and a perfectly disastrous way to operate in the world. So you’ve got to have multiple models.

And the models have to come from multiple disciplines—because all the wisdom of the world is not to be found in one little academic department. That’s why poetry professors, by and large, are so unwise in a worldly sense. They don’t have enough models in their heads. So you’ve got to have models across a fair array of disciplines.

You may say, “My God, this is already getting way too tough.” But, fortunately, it isn’t that tough—because 80 or 90 important models will carry about 90% of the freight in making you a worldly-wise person. And, of those, only a mere handful really carry very heavy freight.

It’s not an accident that all of the people I’m citing are in either tech or finance. These are two fields where a) constantly accumulating knowledge is hugely valuable, and b) the very biggest winners win quite disproportionately.

And what’s startling is that more education as a way to perform better in tournaments like finance and tech, it would explain both the high individual benefits to more schooling and the low collective benefits. Facebook has made a lot of Facebook employees rich, but that increased net worth produces proportionately little increased GDP. At least, little compared to the net worth vs GDP impact of, say, running a successful retailer.

A similar dynamic applies in finance. Good fundamental stock pickers are constantly implicitly managing their surface area—learning a couple adjacent industries really well so that when Company A’s announcement implies bad news for supplier B who reports earnings right before B’s competitor C, being able to trace the impact of that new bit of information fast is a competitive advantage. And it’s a competitive advantage in a field where really successful people achieve extraordinary levels of net worth while directly creating maybe a couple dozen jobs.

This is not at all a nail in the coffin for the signaling theory. Caplan is broadly correct that we likely overinvest and malinvest in education. But it’s too easy to overfit: at least some of that education pays off in a big way, and in a way that doesn’t contradict the raw stats about the median student benefiting little from education, and the aggregate impact of education being low.

I would go on, but I have a calc problem set to get to.

| November 12th, 2014 | Posted in economics |

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