Some dangers in estimating signaling and human capital premia

by on July 19, 2013 at 4:16 am in Economics, Education, Uncategorized | Permalink

Let’s say you signal your way into a first job, then learn a lot from holding that perch, and enjoy a persistently higher income for the rest of your life.  Is that a return to signaling or a return to learning?  Or both?

Maybe it matters that “the signaling came first.”  Well, try this thought experiment.

Let’s say you have to learn to read and write to signal effectively.  Can we run a causal analysis on “learning how to read and write”?  Take away that learning and you take away the return to signaling.  Should we thus conclude that the return to signaling is zero, once we take learning into account?  After all, the learning came first.  No, not really.

The trick is this: when there are non-additive, value-enhancing relationships across inputs, single-cause causal experiments can serve up misleading results.  In fact, by cherry-picking your counterfactual you can get the return to signaling, or to human capital, to be much higher or lower.  Usually one is working in a model where the implicit marginal causal returns to learning, IQ, signaling, and so on sum up to much more than 100%, at least if you measure them in this “naive” fashion.  If you think of a career in narrative terms, IQ, learning, and signaling are boosting each others’ value with positive and often non-linear feedback.  And insofar as these labor market processes have “gatekeepers,” it is easy for the marginal product of any one of these to run very high, again if you set up the right thought experiment.

Along related lines, many people use hypothetical examples to back out the return to signaling, learning, IQ, or whatever.  “Let’s say they make you drop out of Harvard and finish at Podunk U.”  “Let’s say you forge a degree.”  “Let’s say you are suddenly a genius but living in the backwoods.”  And so on.  These are fun to talk and think about, but like the above constructions they will give you a wide range of answers for marginal returns, again depending which counterfactual you choose.  A separate point is that many of these are non-representative examples, or they involve out of equilibrium behavior.

I call the methods discussed in the above few paragraphs the single-cause causal measures, because we are trying to estimate the causal impact of but a single cause in a broader non-additive, multi-causal process.

There is another way to analyze the return to signaling, and that is to leave historical causal chains intact and ask what if a degree is removed.  Let’s say I’ve held a job for ten years and my team is very productive.  But the boss can’t figure out who is the real contributor.  I get an especially large share of the pay because, from my undergraduate basket weaving major, the boss figures I am smarter than those team members who did not finish college at all.  If I didn’t have the degree, I would receive $1000  less.  So that year the return to signaling is $1000.  I call this the modal measure.  It is modal rather than causal because we take my degree away in an imaginary sense, without taking away my job (which perhaps I would not have, earlier on, received without the degree).

There are also the measures (not easy to do) based in notions from bargaining theory.  Consider IQ, learning, and signaling as coming together to form “coalitions.”  One-by-one, remove different marginal elements of the coalition in thought experiments, estimate the various marginal products, and then average up those marginal products as suggested by various bargaining axioms.  You could call those the multi-cause causal measures.  They are more theoretically correct than the single-cause causal measures, but difficult to do and also less fun to talk about.

Yet another method is to pick out a single counterfactual on the basis of which policy change is being proposed.  I’ll call these the policy measures.  Let’s say the proposal is to subsidize student transfer from community colleges to four-year institutions.  You can then ask causal questions about the group likely to be affected by this.  (It is possible to estimate the private return to education for this kind of policy, but hard to break that down into signaling and learning components.)  In any case the answers to these questions will not resolve broader debates about the relative importance of signaling, learning, IQ, and so on and how we should understand education more generally.

Usually when people argue about the return to signaling, they are conflating the single-cause causal measures, the modal measures, the bargaining theory measures, and the policy measures.  The single-cause causal measures are actually the least justified of this lot, but they exercise the most powerful sway over most of our imaginations.

The single-cause causal measures are especially influential in the blogosphere, where they make for snappy posts with vivid narrative examples and counterexamples.  But they are misleading, so do not be led astray by them.

1 mw July 19, 2013 at 5:11 am

Just as important as the nonlinearity involved in combining factors is the much more simple, easy to understand, and yet just as poorly appreciated nonlinearity of each *individual* factor. Despite the paucity of evidence for steep nonlinearity in the learning outcomes going from next-to-top-tier to top-tier university in the same majors, the income outcomes are nonetheless steeply nonlinear, because the latter get you the interview with goldman sachs. Or on the bottom end, there is increasing evidence for just as steep a “desperation” nonlinearity. (Related, I suggest you consider the general implications of your post for the bottom end of outcomes. I fear you might not like it as much).

Of course it’s in the best interests of social cohesion for everyone to maintain the fiction that such nonlinearities don’t exist, so we can pretend all outcomes are “deserved” in some pointless moralizing sense.

2 prior_approval July 19, 2013 at 5:42 am

‘Let’s say you have to learn to read and write to signal effectively.’

Or let’s say, you need to learn to read and write to be able to function as an engineer or programmer, where dealing with quantitative matters involving correct and incorrect answers has nothing to do with signalling. The people who manufacture such things as can openers are under no illusions about the impossibility of wishing something into existence.

Well, actually, in today’s U.S., such concerns are not really that important, are they? Which just might be why the Dreamliner, to give an ongoing example of a prestige project from one of America’s premier manufacturing companies, is more about the well reasearched marketing requirements than actually building a product that does not catch on fire, in flight or on the ground.

In comparison, Airbus seems to be less concerned about signalling, and more concerned about building high technology products that remain more advanced than Boeing’s still not quite available Dreamliner. Because for companies that require paying customers, the signalling involved by flying a Boeing state of the art airliner remains negative.

3 prior_approval July 19, 2013 at 3:05 pm

Will somebody please respond to my post? I’m seeking attention.

4 Josh July 19, 2013 at 6:17 am

The policy questions are particularly difficult once you consider general equilibrium effects. If you send many new people to college through subsidies, then the former college graduates may be more likely to go to graduate school to signal.

To estimate the effect of sending those new people to college, we can’t use current returns to college even if we assume all people have equal learning abilities, etc. The policy-relevant return is the return to learning because, by the time the new people graduate from college, a college degree will have lost its signal value.

5 Steven Kopits July 19, 2013 at 6:20 am

It’s seem to me that really bright, extremely well-educated people are the primary believers in signaling.

6 Andrew' July 19, 2013 at 6:24 am

By “well-educated” I assume you mean well-credentialed?

7 de Broglie July 19, 2013 at 2:01 pm

That seems like a safe assumption in this context.

8 Rich Berger July 19, 2013 at 10:24 am

I wonder how the recipients of the signal feel? I know from anecdotes that graduates of big signal colleges often have an inflated sense of their own worth.

It also seems to me that Tyler took a lot of words to express his view. I don’t have time now, but I believe the essential argument could be condensed to a paragraph.

9 The Original D July 19, 2013 at 7:49 pm

Q: Know how to tell someone went to Harvard?
A: They’ll tell you.

10 Bender Bending Rodriguez July 20, 2013 at 4:41 am


11 Silas Barta July 19, 2013 at 10:43 pm

Why would he want to make his arguments easier to follow? That just makes it easier to pin him down.

12 crs July 19, 2013 at 6:38 am

neat post. here’s an applied micro translation (leaving GE effects aside): run a horse race regression (include IQ, human capital, and signaling together as explanatory variables), nonparametric specification best … lacking power, at least put in the interaction terms. And from earlier posts, look at different outcome variables: wages at first hire, wages over first 10 years, lifetime earnings, (life satisfaction, health,) etc.

I like the point about interaction terms very much and I think it’s even more complicated over time. For a portion of my job (the part that will consume the rest of my day), we hire no one out of grad school who knows how to do it. (I was surprised when I got picked, given the job description.) The trick is to make sure they have the requisite building blocks (human capital) AND that they signal a capacity to learn the rest (and to be, on net, happy about it). So in hiring deliberations we do talk about signals a fair bit, but they are not hot air signals…we are trying to get a sense of the future human capital (and how they will grow into and add to our team).

Of course, one can tell lots of different stories, so let the data sort it out but be mindful of the specification (that is how you frame the question).

13 Andrew' July 19, 2013 at 7:00 am

Surely there is a huge literature on a process we have decided is right for every single person that is run by the people who produce the literature.

To me it’s less about being precise than just recognizing the obvious and then making sure the signaling is fast and cheap, the teaching is distinct and the value-added measured properly, the credentialing separate, etc.

14 MD July 19, 2013 at 12:19 pm

Maybe the signaling can’t be fast and cheap, though. Maybe one of the important things that college signals is that you follow through on long term projects, aren’t completely lazy, and have experienced a situation where you had a lot of freedom and didn’t flame out on drugs, alcohol, crime, etc. So you put people in a dorm, give them some classes that they have to put at least a little effort into, and wait four years.

15 Andrew' July 19, 2013 at 2:12 pm

I would counter that so many people leave college because of personal finances and logistics (e.g. mom gets sick, etc.) not to mention that jobs now last an average of what, on the order of 3 years? So the need to signal the ability to stick out 4+ years is a stretch in my mind.

16 MD July 19, 2013 at 2:44 pm

Anybody that would drop out of Flagship University of State in the Midwest to take care of a sick parent probably isn’t the sort of person we’d want to hire here. Lacks the proper priorities.

17 Handle July 19, 2013 at 7:01 am

Let’s focus. The point of the signalling discussion is to make a criticism of our notions of pedagogy, the education market, and the interaction between higher education credentials and the labor market. There are large anomalies and mysteries – with enormous quantities of resources at stake – which cry out for explanation but which seem to be met with either dismissiveness or befuddlement.

Specifically, the main criticism revolves around the notion that we are wasting a lot of people’s time (maybe the vast majority of the population) in a very expensive way. Top-quintile folks are the ones analyzing this, and yet, they are like the infovores that can derive disproportionate consumer surplus from things like the internet. Even from that class, my anecdotal polling leads to me to believe that most of them thought most of their education experience was a costly, counterproductive waste, useful only for the degree they received and can put on their resume. That should be big, important news; a problem we should be trying to diagnose and cure, neh?

Yes, there are lots of other goals to education (primary, secondary, and higher), but in terms of ‘long-term retention of knowledge presented’ my guess is that 80% of people couldn’t answer 80% of the questions of the basics in any class they took over a year ago. Cowen’s Law – there’s a literature on that, and from Caplan’s presentation, it’s ugly. Hanson, “School isn’t about learning.” Ok, so why are we doing things they way we are?

There are a lot of reasons for that waste, for example, the strong demand to have a quick, easy, and widely accepted credential of ability, status, class, and other positive-valence notion we associate with ‘college’. If that credential is strongly correlated with talent, class, and character, all the better. Except, if we could make it much cheaper and use the time much more effectively than we are and avoid the enormous waste and debt. There’s more than mere inertia at work here as MOOC’s try to break into the market and supply an alternative for that credential. There’s a lot of resistance to changing the way we do things, and that also demands explanation.

If degree+institution is tightly correlated with ‘future productivity’, but there is another test we can use that is just as tightly correlated but orders of magnitude less expensive, (Caplan argues that there is), then why aren’t we using it?

But people have known all this and discussed it for decades, and yet from the perspective of this waste being a problem, then the situation has clearly gotten much, much worse.

So, how else to discuss the question honestly and open up a space where what would amount to very radical change is possible? At some point, you can to accuse the system of being a scam, of perpetrating some kind of gigantic fraud, or having a kind of successful monopoly or rent-seeking operation where it grants itself the ability to give quality credentials regardless of what actually happens in four years or how much knowledge people retain. So we say, “Signalling,” to try and restart an unjustly dead conversation.

18 Andrew' July 19, 2013 at 8:03 am

Here’s my thing, maybe it’s a feature considering how rudderless (and dangerous) 16-25 year olds are. Thus education makes a virtue out of necessity, but the risk is that they don’t adjust, the gap becomes so wide that it has a catastrophe and we end up with something even worse.

19 Brian Donohue July 19, 2013 at 10:52 am

Speaking personally, my 20-year old is home for the summer from State U (price- expensive but not absurd).

When he came home last summer, it was clear that he was only about one-quarter ‘done’. Now, he looks and acts about half ‘done’. He still needs a couple years to marinate. He’s not a rocket scientist, but I think he works reasonably hard at school.

I went to Fancy U 30 years ago (price: way less than today.) Contrary to the general view, I thought it was challenging in a lot of ways, if not directly relevant to my life afterwards. But I needed somewhere to cook for a few years too.

There seems to be a logic to college in the rhythm of modern life. Nowadays, of course, I think it’s hard for most people to justify Fancy U on other than status grounds.

20 Andrew' July 19, 2013 at 2:16 pm

We now know that the frontal lobe keeps developing until (at least?) 25.

So, maybe the kiddo needs a master’s too 😉

21 Nathanael July 20, 2013 at 7:13 pm

I actually got a lot out of my education, but then (1) I went to a small liberal arts college and was taught by professors, rather than going to a garbage factory-schools like Harvard and being taught by grad students, and (2) I pursued an ideosyncratic and self-directed curriculum, which is uncommon even at small liberal arts schools.

I still doubt that the learning was worth the $120K I paid for it, though; I could have learned all that stuff extramurally. The main value I got out of college was not that, and it wasn’t signalling either (since I’m independently wealthy). It was the social network. I met lots of awesome people. If you think about the etymology of “college”, you’ll begin to realize that that’s what it’s actually for — social networking among intellectuals.

22 Andy July 19, 2013 at 9:03 am

Partial derivatives are not total derivatives. I don’t understand why this is so complicated.

23 mpowell July 19, 2013 at 2:44 pm

It is not a partial versus full derivative issue (is full what you mean by total?) The issue is that if you have f(x,y) and you find the full derivative of f with respect to each, that does not mean f=x*df/dx+y*df/dy. But that’s what the single-cause measures are trying to do. It doesn’t work very well.

24 Andy July 19, 2013 at 4:55 pm

It appears full and total derivatives are synonyms:

We have a LOT of information on partial derivatives. Almost all empirical studies are explicitly after them. Ceteris paribus, etc. But if there are any complementarities then partial derivatives are insufficient for a decomposition exercise. I think we’re on the same page.

25 steve July 19, 2013 at 9:29 am

Let us say GMU suddenly has the top rated undergrad economics department. You will then have (numbers made up) 1000 applicants for 100 positions. Of that 1000, the top 300 have essentially identical SAT scores and grades. How do you choose? Probably through signaling, or at least that is what I think you can infer from the work by Unz. If you can do a good job of signaling that you are similar to the interviewer, or to some image set by the interviewer, you get in. I suspect the same holds true at the grad level and for that first job.

If GMU increases its class size to 500, remains number 1, and retains roughly the same size and quality of application pool, then signaling becomes less important than learning, IQ or whatever.


26 Nathanael July 20, 2013 at 7:15 pm

“How do you choose?”
There are so many choices.

Choice by persistence is perhaps the best — pick the people who come in and bang on your door trying to get in.

If that isn’t sufficient, choose by lottery.

27 Rick July 19, 2013 at 9:34 am

There is a strong parallel to the assessment of damages in patent infringement cases. The plaintiff will argue that “you couldn’t have made that mobile phone without my technology,” so the value of the patent is a large part of the value of the phone. Of course, there are thousands of patented technologies in a phone, so under this reasoning, the sum of the marginal returns to each would be much greater than the value of the phone.

28 Steven July 22, 2013 at 11:50 pm

very very good argument

29 Uninformed Observer July 19, 2013 at 9:45 am

But the whole point of signalling is that it’s differential signalling. Having a nondescript bachelor’s degree is of little signal worth, except in the company of others who lack the credential. That’s the point that policy-makers always miss. They think that the value of the signal is absolute, and that, why, if everyone had a degree, then everyone could make an extra $1000!

30 albatross July 19, 2013 at 10:45 am

I wonder how much the signaling in these cases is not between the employer and employee, but rather between the employer and third parties.

a. If I hire only Ivy Leaguers, I’m signaling to others outside the company: “I get my pick of employees, I can hire the very best.” I am also signaling to prospective and current employees, to regulators, etc.

b. It’s common to see organizations brag about the fraction of their employees with PhDs or MSNs or whatever, and I’ve heard stories of older people being pushed to go back to school or encouraged to retire because the management wanted to have 100% impressive credentials.

31 mike July 19, 2013 at 2:53 pm

Most importantly, at least in certain fields, you’re signaling to customers. A single customer can’t really tell whether you’re a good doctor, or a good lawyer, or whatever, as long as you look and act the part. So instead they rely on the degree. I’ve had employers tell me that they’d rather have someone who was in the top 10% of their class in a Directional State professional school than someone from the bottom 50% at a top school, but customers want to see degrees from schools they recognize.

32 Nathanael July 20, 2013 at 7:18 pm

Unfortunately, places like Harvard are giving false signalling. At this point, a Harvard degree proves… that you were able to get into Harvard, either by doing well in high school or by having lots of money and a Harvard parent. It doesn’t prove that you learned a damn thing while you were there.

I wonder how long it’s going to take before people notice that a number of elite institutions are providing false signalling. This usually heralds the decline of such institutions into obscurity, although they remain rich — look at all the religious schools of the Middle Ages. Mostly they’re *still around* and *still have lots of money* but nobody respects them any more. We respect the schools which made the transition during the Enlightenment to teaching science.

33 Sebastian H July 19, 2013 at 12:41 pm

“Let’s say you have to learn to read and write to signal effectively.”

Or let’s say the signal means you are already a scion of the 1%.

The problem is distinguishing between when the signal shows useful skills, and when the signal shows non-useful other particulars.

The problem is further compounded by what we want to count as useful skills. In a very corrupt nation, kissing up to functionaries is a much more useful skill than being an excellent medical doctor, a researcher who can cure a disease, or someone who can produce food with twice the effectiveness of his nearest competitor. Much of this discussion is a back door way to avoid discussing what the value of ‘connections’ actually consists of in the United States.

The law school at the University of California at Berkley is one of the best in the nation (ranked between 6-9th depending on the year). Stanford is almost always 3rd. But if you go to either of those schools and fail to attend Harvard or Yale, you definitely won’t be a Supreme Court justice. And if you go to Berkley instead of Harvard or Yale, your expected lifetime income is dramatically lower. Yet no one seriously argues that Harvard or Yale are better at training in the law. What they are better at is signalling that you either come from a family rich with both tangible wealth and connections, or you hang out with such families.

I don’t think that even serious signalling adherents claim that the signal is useless in the sense that it fails to correlate to income. The question is whether or not it fails to correlate to income in a fashion which is reflected in a way that is generally socially productive rather than generally socially wasteful. I have no idea what the economically correct term for it is, but it is clear that if your economy spends lots of its energy and money on bribe taking and bribe seeking, that is worse than an economy that focuses much more on food production, machines and art. Similarly the returns to ‘connections’ can be high without that meaning that returns to ‘education’ as more commonly understood are high in our society as currently functioning.

34 Nathanael July 20, 2013 at 7:19 pm

That’s the most important comment on this blog entry. Thanks.

35 Ryan July 19, 2013 at 12:59 pm
36 Philo July 19, 2013 at 3:09 pm

Of course, we distinguish between *education* per se and *obtaining an educational credential*. The former makes one a more competent person, the latter signals one’s diligence and conformism, as well as one’s competence (since it is a sign of actual education). It is not clear that the general question, “How much does actual education contribute to one’s greater income, and how much does the signal provided by an educational credential contribute?” is worth worrying over, since the answers for each instance in which a particular morsel of education is received or a particular credential is bestowed will vary so much.

37 ladderff July 19, 2013 at 4:52 pm

Can we cut the bullshit, please?

Let’s say you signal your way into a first job, then learn a lot from holding that perch, and enjoy a persistently higher income for the rest of your life. Is that a return to signaling or a return to learning? Or both?

As far as the higher-ed discussion goes, that’s a return to signaling, because the return accrued to you instead of the next guy because of your signal, not because of the human capital you were supposed to have gotten at school. Are there any hard questions you want to raise? Is the best defense you can muster for all this education that the winners get to learn something on the job? Then leave it to the employers to figure out who should get it!

Andrew Prime is dead right about this and many other issues.

And to repeat my own self: this issue is best decided by using your own eyes and brain to observe what happens on campus. Or I can save you a trip: nonsense.

38 crs July 19, 2013 at 11:20 pm

yep, nonsense (what you said).

I am not a fan of the signaling framework (as a content-free differentiator) and I think the value of human capital at any one point in time is oversold (or at least too generic). for most people, jobs / careers are massive matching problem. and the more latent ability or even general skills a person has the trickier the sorting. higher education gives young adults a chance to sample different fields and think about where they later want to specialize. many jobs have a high ratio of job-specific skills to general-field skills.

at my work we rarely hire research assistants with masters degrees … they have too many specialized skills/interests already (some which don’t need), we want people ready to start specializing … but who have shown in course work that they want to and have some capacity to specialize in our work. I “signaled” my way into such a job out of college by having a 4.0 from a non-Ivy (supposedly signaling I would be a hardworking RA, but not think I needed my own RA). Colleges could do a better job with the sorting problem and career/lifetime learning preparation, but it’s not nonsense what happens on campus.

39 Jacob A. Geller July 20, 2013 at 9:53 am

This reminds me of an old George Carlin joke: “Every heroin addict started with baby milk.”

40 Jacob A. Geller July 20, 2013 at 9:54 am

…or is it breast milk? (Sorry, not a father…)

41 weareastrangemonkey July 20, 2013 at 10:45 am

It is breast milk. You can’t milk babies.

42 FC July 21, 2013 at 1:55 am

Sure you can. The same procedure is used to make almond milk.

43 allan July 20, 2013 at 4:53 pm

Unbelievable….paragraph after paragraph of utter non-sense.

I defy any of the comment writers to give a plain, understandable explanation of these phrases, especially the second one:

“Let’s say you signal your way into a first job…”

“The trick is this: when there are non-additive, value-enhancing relationships across inputs, single-cause causal experiments can serve up misleading results.”

44 allan July 20, 2013 at 5:55 pm

1. You get a Ph.D. in economics from Harvard. Your dissertation advisers are Rogoff and Reinhardt.

2. You get a job at the Federal Reserve. You advise that debt and deficits must be reduced, especially in a severe recession. You advise that all public spending, especially on poor people, must be drastically reduced. Except that spending on defense contracts must be increased.

3. Then you see that the Rogoff-Reinhardt austerity “model” has been completely destroyed.

4. You keep advising austerity, except, of course, for the Pentagon and giant agri-business.

5. You therefore have learned nothing.

So what’s more important? A Ph.D. in economics from Harvard or the inability to learn?

This would be easy to check. Just see how many austerity economists with Ivy League degrees have lost their jobs in the last six months.

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