Monday, December 18, 2017

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.


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.

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.

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?

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. 


  1. Doesn't the assumption of (somewhat) rational, forward-looking students make outcome penalties implicit evidence of significant costs for completing the degree? The value of what they give up proxies their minimum subjective cost of completion.

    1. If I leave free money on the table, that's not a cost; that's revealed preference.

  2. I find this entire debate fascinating but I also hate it a little because you keep saying that college is not a waste of time because college has all these characteristics (sheepskin effect, intense socialization, high price) that my particular college doesn't have.

    What am I even doing with my life. I feel like my University is nothing but a cargo cult.

  3. Spence's view of signaling is much broader than what you have in mind, see this passage from the classic paper:

    "We have stipulated that the employer cannot directly observe the marginal product prior to hiring. What he does observe is a plethora of personal data in the form of observable characteristics and attributes of the individual, and it is these that must ultimately determine his assessment of the lottery he is buying. (The image that the individual presents includes education, previous work, race, sex, criminal and service records, and a host of other data.) This essay is about the endogenous market process whereby the employer requires (and the individual transmits) information about the potential employee, which ultimately determines the implicit lottery involved in hiring, the offered wages, and in the end the allocation of jobs to people and people to jobs in the market.

    At this point, it is useful to introduce a distinction, the import of which will be clear shortly. Of those observable, personal attributes that collectively constitute the image the job applicant presents, some are immutably fixed, while others are alterable. For example, education is something that the individual can invest in at some cost in terms of time and money. On the other hand, race and sex are not generally thought to be alterable. I shall refer to observable, unalterable attributes as indices, reserving the term signals for those observable characteristics attached to the individual that are subject to manipulation by him. Some attributes, like age, do change, but not at the discretion of the individual. In my terms, these are indices.

    Sometime after hiring an individual, the employer will learn the individual's productive capabilities. On the basis of previous experience in the market, the employer will have conditional probability assessments over productive capacity given various combinations of signals and indices. At any point of time when confronted with an individual applicant with certain observable attributes, the employer's subjective assessment of the lottery with which he is confronted is defined by these conditional probability distributions over productivity given the new data.
    From one point of view, then, signals and indices are to be regarded as parameters in shifting conditional probability distributions that define an employer's beliefs."

    1. Right on, Spence!!

      I see dropping out just before the finish line of college as more of an "index" than a "signal" here.

    2. I know, because you've been abusing the terminology! ;-)

      Imagine if you had said straight out, "No dropping out is not a signal, because a student has no control over whether they drop out or not."

      Of course, a signal can become an index. You have the choice to commit a crime, but you can't change later that you have a criminal record. It's hard to say that about college, though.

    3. It is not I who have been abusing the terminology; it is those who claim sheepskin effects are "signaling".

  4. Perhaps should be useful to distinguish between two types of signalling:

    a) intentional signaling - where the students choose to go to college too signal that they are more conformist, hard-working, etc. than the average, and employers hire college graduates because think that college graduates are in average more conformist, hard-working, etc.

    b) unintentional signaling - where the students are not intending to show conformism, work ethics, etc. but, in the end, conformists and hard-workers frequent and finish college at a disproportionate rate; and also employers see that college graduates are more conformist and hard working than the general population, but don't give a damn if a college degree only signals conformism and work ethics, or if it is the college that creates conformism and work ethics.

    Can be argued that b) is not really "signalling", but their practical implications are essential the same.

    [A strong argument for b) instead of a) is that the signaling theory is, afaik, very unpopular - to the point that believing in the signaling model could be considered a way of signal non-conformism; but a) requires that students - and perhaps also employers - believe in the signaling model, what means, I think, that can only b true in a society where the signaling model is the conventional wisdom]

    "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."

    And, in the end, Caplan and you are saying almost exactly the same thing - that employers use a finished college degrees as a proxy to conformism, emotional stability, etc (you are saying that college creates conformism, emotional stability, etc, and Caplan that college only signals that, but in the end I don't know if the difference is much, specially with the b) version of the signaling model.

    1. We're really saying a quite different thing. Caplan is arguing that college is wasteful. He's using a model in which the waste is unavoidable, which is one thing I criticize. But I'm proposing alternative models in which there is, in fact, no waste at all.

  5. I understand that as you say, "relying on the multiple uses of that English word to avoid careful consideration of how the models work, is not good economics."

    However, your post very clearly concedes the fact that at least a large portion of why employers want college graduates is not because of knowledge of the material they were taught in their classes. It certainly seems possible for young people to be engage in the human capital "treatment" while also being productive instead of learning material that they will never directly use again. So the direct material you learn is more consumption and you are only really adding human capital by learning how to learn. Once you admit that such a large part of college is consumption, there is a lot of room Caplan's main thesis and policy prescriptions.

    I think it's also important to note that for behavioral reasons some young people are not going to "learn how to learn" very well in a strictly academic environment and might do this better on the job where this ability feels more directly connected to monetary incentives. Hence the meme about frustration with school that is "mitochondria are the powerhouse of the cell"

    1. However, your post very clearly concedes the fact that at least a large portion of why employers want college graduates is not because of knowledge of the material they were taught in their classes. It certainly seems possible for young people to be engage in the human capital "treatment" while also being productive instead of learning material that they will never directly use again. So the direct material you learn is more consumption and you are only really adding human capital by learning how to learn. Once you admit that such a large part of college is consumption, there is a lot of room Caplan's main thesis and policy prescriptions.

      Well, not really "concede", as this is just my prior.

      So, there's human capital outside of class like maturity, perspective, etc. that you might not be able to get outside of college.

      There's human capital that's full of externalities both positive and negative, like human networking.

      And there's consumption, which is worth it if people pay for it, but might not be worth subsidizing via the government.

      So it's a very complex issue.

    2. Thanks for responding, it helped me better understand your argument and be more persuaded.

      Are there papers comparing the impact of a college degree in getting a job in different industries or positions? It seems like some of the skills you argue you can only gain in college should vary in importance across types of jobs. Maybe identifying which industries find it to be more important, controlling for factors such as intelligence or salary, could help us identify why employers in general find college to be important. It might be easier to identify what skills are important to specific jobs that value college education even more than normal than it is to figure out exactly what skills you learn in college.

    3. There is research that breaks out the wage premium by college major, but I don't know of any that breaks it out by industry. It probably does exist.

  6. 100% layman here - I just don't think college offers much human capital at all. When I think about my college days 4 years ago, for myself and most of my peers, studying and learning weren't the focus. Maybe for a small minority, but most of us don't use our degree and even before graduating forgot most of what we learned.

    That's anecdote, not data, but I'd be surprised to find this narrative isn't the same for most students. I'm in the signal camp for now.

    1. I suspect that this intuitive impression is behind the persistent popular appeal of the signaling theory, despite evidence to the contrary.

    2. Anonymous9:38 AM

      I suspect you learned a lot more than you think--socializing (social capital), you have the degree (symbolic capital), along the way you learned how to think more clearly, even if just to bs on papers (human capital). I've watched 30 years of students change drastically, and it's pretty clear those changes and skills owe themselves to the college environment. (Others who did not do so lack many of these skills, especially when it comes to clearer thinking). It's amazing how much you really learn when you have independence with a security blanket (vs going straight into the job market).

    3. "it's pretty clear those changes and skills owe themselves to the college environment. (Others who did not do so lack many of these skills, especially when it comes to clearer thinking). It's amazing how much you really learn when you have independence with a security blanket (vs going straight into the job market)."

      This is a very interesting take, and seems slightly different from Noah's or Caplan's, perhaps offering a middle ground. Caplan thinks college is a waste, Noah thinks it is useful, and Anonymous suggests a way in which it might be useful-but-not-in-the-way-it's supposed-to-be. Seen in this light, Caplan might be partly correct that college is a big waste of money, since "independence with a security blanket" might be achieved at a lower price than fifty grand a year.

  7. I tend to think Bryan is right, that we over subsidise education (my grand parents went to school 1 year and were educated) and spend too much time in school, but I will say one thing in support of Noah, I think that since I took a broad array of science classes and liked the professors I had, I do not fall for common ideas like, eating organic food is more healthy and the professors are all paid of by the chemical companies. Or nuclear power is so dangerous and nuclear engineering professors are paid off by the power companies etc. The press is so yellow and ignorant of science that you would not learn that from them.

    Clearly the professors I had in the 1970's where terribly wrong about impending environmental collapse of the planet but not because they where dishonest and paid off by anyone.

    I tell people to ignore journalists and read the academics but alas.

  8. Noah,

    After graduating (from Stony Brook, actually) I used to (somewhat) joke about there being a hidden, advanced-level but tuition-free independent-study course that needed to be passed before receiving a degree at any SUNY college. I called it Advanced Bureaucracy 401. The hoops that had to be jumped through, and the documentation that needed to be provided - I essentially needed to prove to the administration that yes, I was in fact, entitled to graduate. The default assumption of the bureaucrats certainly seemed to be that I wasn't, and it took nearly a month of work, tracking down professors and filling out forms, to satisfy them.

    Later in my life, as a hiring manager, it occurred to me that the ability to successfully navigate through a bureaucracy, and to put up with completing seemingly meaningless projects, and annoying classmates, etc. was one of the things that a job candidate with a degree proved to me that he or she had.

    I think what I'm saying is that not all human capital is acquired in the classroom -a fair chink of it is learned almost incidentally.

  9. Related to what Jefftopia mentioned, signaling is an interesting concept but how could the sheepskin effect ever be actually tested statistically ??? I'm not an economist but I've noticed that economists like to have long discussions about issues that can't ever be known or even tested. How would one ever know if dropping out of college caused less "utility" in the future. Do we include Bill Gates, Mark Zuckerberg in the treatment group ?. Sometimes I think economists like to bring these discussions up so they can talk about something but the basic assumptions of the discussion can't be answered, atleast not very easily !!!!!

    1. Anonymous9:41 AM

      One test is to compare average wages vs degree earned: no HS diploma, HS diploma, some college, BA/BS. Somewhere I've seen data that there is a significant gap across these boundaries. (And Gates is an outlier. Plenty of college-educated, and MBA-educated, multi-millionaires out there.)

  10. If Caplan were right then why aren't employers paying attention to other strong signals of employability which aren't degrees? For example, I learned that only 5% of all students taking any given MOOC actually finish. If a job applicant has finished several, surely that signals something about how her personal virtues stack up against the mean. If there would be another reliable signal source that she also been appropriately socialized - maybe through Facebook + LinkedIn + FICO - why not hire her? It's a chance to get a quality worker at a bargain wage. I'm no employer, but it seems like a no-brainer that employers in this data-crunching world should be devoting considerable effort into reading the tea leaves for how to identify valuable employees without degrees. We send out huge clouds of signals every day. Getting good at interpreting these would give employers a huge competitive advantage, and it's hard for me to believe that simply for being unanimously lazy and conventional, employers would all leave all this money on the table. Come on HR, Moneyball those non-degree applicants!

    And of course, once firms start doing this, they create a legitimate end-round for college. The signals they would be reading would still be costly in the technical sense, but many would also be free in the "free beer" sense.

    1. What you said is true but companies-people are too scared to go outside the box when it comes to hiring. If they do, and it backfires, then they don't have a scapegoat. going the traditional route ( what college, what's your GPA, what degree etc ) is safer for them.

  11. "Employers use your college as a proxy for your ability"

    Probably not. I recall a study several years ago that found that, once you controlled for IQ, which college you graduated from did not predict differences in earned income.

    Even more dubious is your "learning how to learn" thesis. It has been long accepted in psychology that this is an IQ effect, not an educational effect. Besides, what study or learning skills are picked up in college that you did not already have multiple opportunities to learn during your previous 12 years of universal education?

    Also, consider that typical employers do not even allow persons without a college background even to apply for many positions. This is typically true even when the employer does not require a degree in any particular field for the position in question. So far, Caplan's position looks stronger than yours.

    I suspect that demand for expensive sheepskins would diminish if the US Supreme Court were to reverse its long-standing (and absurd) ruling that general ability (IQ) testing by employers is unconstitutional.

  12. Lenny4:01 PM

    I think one of the important questions to consider here is why it's important to distinguish between "signalling" and "human capital". It seems like Bryan's point is that the details of a college education don't really matter other than the alma mater and the binary fact of graduation (or perhaps he would include the major / double-major / minor, and any other certifications among the signals). Without seeing a lot of comparative data (which I haven't but perhaps he has) this sounds more like a problem with data being to aggregated than a real property of college educations.

    In other words, there are probably all sorts of different college experiences, some of which build more capital than others, and the average premium assigned to them is based on the average amount of capital acquired.

    To really refine the question of drop-outs vs. graduates you would have to look at drop-outs with GPAs that are the same as the graduates, who dropped out by choice (rather than being expelled for some violation). Otherwise you might just be comparing bottom-of-the-bell-curve individuals to middle- or top-of-the-curve ones. Do we know that people in that boat actually see a lower premium than the graduates? If so, does it matter whether the "signal" is a negative one sent by dropping out or a positive one sent by graduating? Either way completing the act of graduating is clearly a low-cost way to send an income-creating signal and if there was no stigma attached to dropping out when you were done / no laurel attached to seeing it through to the "end", then there would be only a small difference between the 7-semester student and the 8-semester one. That difference is arbitrary and unlikely to represent a true sign of major differences in human capital.

    The same can be said of private education vs. public. Do people who go to Ivy league schools actually end up being significantly better workers than those who go to mid-tier schools? If the entirety of the difference in their future output is determined by their qualifications at the end of high school, then the difference in premium (and price) between top schools and other schools is entirely a signalling cost.

    Finally, all this stuff is signalling in the Spence sense (hehe) - scoring highly on a test is a signal that is difficult to fake, completing college courses is a signal that is difficult to fake, writing a thesis that gets accepted, publishing papers, and so on. These are all costly signals that are used as proxies by firms for data they can't otherwise test. Some of them are probably not the most efficient signals possible and therefore require wasted work to produce the signal (a credential of some sort) that would be better spent elsewhere if better data could be acquired. Just as a pure pie-in-the-sky example, if the essential prerequisites for every job could be broken down into an interactive quiz/game that adapted to test the applicant's abilities and knowledge, college GPA, alma mater, degree, etc., would all cease to matter. Instead, potential applicants would simply create an account, play the game, and their scores would determine whether they bubble up for follow-up or get buried under better applicants. This is clearly not how it works now, so there is some amount of signalling involved. The important question is how easy it is to fake the signals.

    Speaking of Moneyball... have Google, Facebook, and Amazon started forming Minor Leagues yet? That is, companies that develop raw talent along the lines the big firms find most valuable with an eye to getting them a job at the parent firm and then hiring the next graduate...

  13. Anonymous8:13 AM

    as someone who took a number of extra years to finish my undergrad from an Ivy-league school, it became a necessity to understand how the system works in order to get a job.

    i learned, from talking to recruiters and my own trials and errors, that applicants can put a college on their resume, but unless the interview team specifically asks if the applicant has graduated, it might not affect the hiring process until after an offer has been accepted and a background check is commencing.

    some companies have a box on their application for graduated? or year graduated, but it's not required to fill in. if you leave the year you graduated off the resume, employers don't really ask. most people who interview don't really care if you finished or not, they're looking for fit and ability mostly.

    of course, if they do ask, you have to explain what's going on, and then it becomes an honest judgement call, especially if you double down in a dumb way.

    if you get the offer and accept it, then the background check is where it becomes relevant. at that point you have to be honest because everything will come out once they contact the university, and getting caught in a lie is far worse than not finishing your degree.