Continuing our debate, Noah Smith defends on odd view on sheepskin effects.  Here’s my reply.  He’s in blockquotes; I’m not.

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.

If you knew nothing about actual students on actual college campuses, Noah’s argument would be highly plausible.  Since both of us have spent many years on such campuses, however, I’m puzzled.  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.

By analogy, imagine you have a lonely friend.  He desperately wants a girlfriend, but never asks anyone out on a date.  You tell him: “It’s easy.  Just walk up to her and ask her out.  End of story.”  And what does he say?  “Sure, it’s easy for someone like you…”  The difficulty of finishing a degree is much the same.

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.

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.  In fact, rationality is one of the traits students signal with their behavior!  The more rationally you act, the more rational you’re likely to be.  

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, 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?

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.

Therefore, sheepskin effects are not consistent with the signaling model.
I’m surprised by how unempirical Noah is here.  Check out his cv.  He has a B.S. from Stanford and a Ph.D. from the University of Michigan.  If he refused to comply with even one of Stanford’s graduation requirements, U Mich never would have accepted him.  If he refused to show up for his dissertation defense, U Mich never would have given him his Ph.D.  His advisor, Miles Kimball, would undoubtedly have begged him to reconsider.  But if Noah stubbornly stuck to his guns, the labor market would have severely punished him.  Signaling explains all this.  Nothing else does.
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.

A strange motive to impute.  Sure, employers want to know if you have the Right Stuff.  But why should they care whether you acquired it via “treatment,” or just had it all along?

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.
Key question: If Noah’s subpar student make a last-ditch Herculean effort to finish, would he have a good chance of successfully fooling employers about his merits?  If not, why not?  If so, Noah doesn’t really disagree with me. 

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?”
Yes, this is exactly my view.
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.

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. 


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.

Noah overstates.  Sure, college students have fun.  But so do yuppies.  When I searched the research literature, I found little evidence that college students are having more fun than yuppies.  And if college is really so delightful, why are students so eager to move off-campus? 

The main advantage of college partying over yuppie partying is that parents are far more willing to subsidize the former.  Indeed, imagine parents just handed their 18-year-olds four years worth of tuition.  How many would use the money to have great fun off-campus?  Plenty.  Nerds like Noah and myself may find paradise on a college campus, but for most students college is merely the funnest activity their parents will fund.