Sheepskin effects - signals without signaling

Bryan Caplan is one of the most enthusiastic proponents of the signaling theory of education, and this theory plays an important role in his new book, "The Case Against Education". But I've always had a number of problems with this theory, and also with its application to the education policy issues. Recently, I wrote a Bloomberg View post in response to an essay Bryan wrote in The Atlantic that was adapted from his book. Now, Bryan has responded to my post. He makes many interesting points, but here I'd just like to deal with one issue - the issue of sheepskin effects, and which model they support.

Sheepskin effects

Sheepskin effects are central to my debate with Bryan. In brief, the sheepskin effect is the fact that most of the college wage premium vanishes if you drop out right before finishing (e.g. in the final semester). Bryan, and many proponents of the signaling model, believe that sheepskin effects are solid evidence that college is mostly about signaling. On the other hand, I believe that sheepskin effects are strong evidence against the signaling model, and are consistent with the human capital model of education. 

Why sheepskin effects are evidence against the signaling model

First, why are sheepskin effects evidence against the signaling model? Simple: In the signaling model, the signal must be costly. If signals are not costly, there can be no separating or hybrid equilibrium. Without a separating (or hybrid) equilibrium, there is no return to sending the signal. In the model, low-type agents choose not to send the signal because doing so doesn't pass a cost-benefit test.

In other words, if completing the last semester of college is very hard, it can serve as the type of costly signal that could explain the college wage premium in the signaling model. But if completing one more semester of college isn't very hard, then the signaling model can't describe what's going on.

How hard is it to finish the last semester of college? For some people it would be very very hard - but these people are unlikely to have completed all the other semesters of college prior to the last one. For someone who just finished 7 or more semesters, one more semester probably is not that hard.

Also, if agents are even close to rational - as the signaling model assumes them to be - then they wouldn't complete 7 semesters of college only to balk at the finish line. That would be very very suboptimal behavior - a waste of years of effort and years of foregone earnings, not to mention tuition. 

Caplan writes:

Noah fail[s] to look at school from the point of view of a weak student.  One more semester may seem like nothing to those of us who readily finish.  But for students who find classes boring and baffling, even the thought of enduring even one more semester of academics is agonizing.  

Agonizing, perhaps, but much more agonizing than the last 7 semesters? It seems highly unlikely. And why would a rational agent endure 7 semesters of agony (and foregone earnings and sky-high tuition) for practically no payoff?

Therefore, sheepskin effects are not consistent with the signaling model.

Why sheepskin effects are consistent with the human capital model

How could the last semester of college be so much more important for the building of human capital than the other 7 semesters combined? It cannot. So how can sheepskin effects be consistent with the human capital model of education? Here's how.

Education, in empirical research jargon, is a "treatment." In the human capital model of college, that treatment has different effects on different people - some study diligently and expand their perspectives greatly and build their networks and learn with an open mind, while others party and slack off and waste time on Twitter and fail to learn. 

Employers try to tell whether the treatment worked. They look at GPA, for example. But if many of the human capital benefits of college don't come from grades, but from social networks, personal growth, etc., GPA doesn't tell you all you need to know about whether the treatment worked. So as an employer, you'd try to look for other clues as to whether college improved a student or not. 

Dropping out of school is one such clue. It could mean that you didn't build human networks valuable enough to keep you hanging around. It could mean that you have some emotional problem, and that college therefore didn't give you the emotional maturity that it tends to give most people. In other words, even if the treatment typically works, dropping out - including dropping out right before the finish line - could indicate that the treatment didn't work for you.

Bryan didn't like the analogy I used to explain this idea in my Bloomberg View post, so here's a better (and more fun) one. Suppose a bunch of people are applying to be S.H.I.E.L.D. agents. To be a S.H.I.E.L.D. agent you have to take a serum that makes you a superhero. But the serum doesn't work on everyone - some people it dramatically weakens due to an allergic reaction. So 20 people take the serum. Nick Fury inspects them, and they all seem fine...until 2 of them fall unconscious. These two, obviously, are not hired as S.H.I.E.L.D. agents, while the other 18 are hired.

In this example, the serum DOES build human capital, and falling unconscious in the inspection line is like dropping out just before finishing college.

Sloppy use of the word "signaling"

"But wait, Noah," you may ask. "Aren't 'clue' and 'sign' just synonyms for 'signal'? Didn't you just describe signaling?"

The confusion here is due to sloppy use of the word "signaling." Are we talking about the Spence signaling model, or are we using "signal" to mean "any piece of information"? I believe that if you want to use the fame and the imprimatur of the Spence signaling model to support your view of college, you should stick to that model. 

Also, the kind of "signal" I described in the previous section is 100% compatible with college's value being 100% human capital. Caplan and other detractors of the college system treat "signaling" and "human capital" as mutually exclusive - if dropping out is a (costless) signal of whether you derived human capital from college, then the human capital model is right. 

Simply saying "well it's SOME kind of signal", and relying on the multiple uses of that English word to avoid careful consideration of how the models work, is not good economics! Sheepskin effects look much more like a truth-telling equilibrium in a model where students receive private stochastic shocks to their utility functions.

Sheepskin effects and the consumption/sorting model of college

I do not believe that 100% of the college wage premium reflects the return to college - I believe some fraction of it represents ability sorting. Nor do I believe that 100% of the price students pay to go to college represents investment - I believe some fraction of it represents consumption. College is fun. I believe that college does build some human capital, but part of the institution represents super-smart kids paying to party with each other at Harvard while pretty-smart kids pay to party with each other at Ohio State.

This is a third model of college - the consumption/sorting model of college. I believe that together, the human capital model and the consumption/sorting model explain most of both the price of college and the college wage premium.

Sheepskin effects are consistent with the consumption/sorting model. Employers use your college as a proxy for your ability. But if you drop out right before the finish line, that provides employers with additional, more detailed information about your ability. It might indicate that you're a smart person with emotional problems, motivational problems, or trouble with the law. In other words, it's a way that employers can improve the precision of their information about your ability, beyond relying only on the noisy proxies of alma mater and GPA.

Again, this explanation relies on sheepskin effects being a "signal" in the general, English sense, but not in the specific Spence model sense.

In conclusion, sheepskin effects are consistent with the human capital and consumption/sorting models of college, but not consistent with the signaling model.


Update

Bryan responds. He writes:

Plenty of kids slog through two or three years of college, then get so distracted or disgruntled they fail to finish.  Their exasperated parents could reasonably say, "How hard can it possibly be to finish?!"  But social scientists should just work our way backwards from their failure to finish to the subjective difficulty of doing so.

No doubt. Kids often discover their own ability/motivation level by trying college. That process of self-discovery isn't signaling, but it is important for labor markets. The onus is on college's detractors to prove that this is an inefficient mechanism.

Bryan:

Noah's right that conventional signaling models assume everyone's rational.  But they don't need to.  As long as employers are roughly rational, students can act impulsively without changing the main lesson of the model: Education pays you for what you reveal about yourself, rather than what you actually learn along the way.

Obviously, college has an ability-sorting component. But it isn't very costly, and the cost (taking SATs and AP tests and such) is paid in high school when you apply.

We all know that some part of the college wage premium is not a return to college - it's a return to ability, which is indicated by test scores and grades and such. The ability premium is present whether you finish or drop out - "I dropped out from MIT" implies "I got into MIT". That's on top of the return to college (human capital) and the penalty for observable negative characteristics (early dropout).

Signaling just isn't necessary here. Nor does any of this imply that college is economically inefficient.

Bryan:

Forget models and look at actual human beings.  Plenty of people will put up with something unpleasant for years, then snap.  This is especially true for people who are relatively non-conformist.  And as I've repeatedly said, conformity to social norms is one of the main things employers are looking for.

"Forget models and look at actual human beings" is a phrase I expect to hear from anthropologists, not economics professors! But OK. When I forget models and look at human beings, I see college giving people invaluable life perspective and emotional maturity. When I apply formal models - the signaling model that Bryan invokes again and again to support his case - I find that it doesn't make sense as a major reason for the college wage premium. What's left?

Bryan:

There's no confusion on my part.  Yes, you can equate "signaling" with a literal interpretation of Spence's model.  But it's far more enlightening to treat the Spence model as a mathematical parable - then see how much of the real world the parable illuminates.  Anything that raises the conditional probability of X signals X.  If the world happens to reward X, this spurs people who lack X to send misleading signals of X in order to receive those rewards.  These are the Spencean insights that matter - not the details of any specific model.  

I just can't agree here. If a signal isn't costly, the Spence model isn't a good parable for it, because the Spence model crucially relies on the cost of a signal (really, the cost difference between types) to produce a separating equilibrium. Otherwise everyone lies.

Bryan appears to be taking any observation that employers make about prospective employees during their college years and labeling that "signaling", then concluding that college is waste. That is pretty obviously an incorrect inference.