education signaling

How much of education is signaling? — yet again

The social and the private returns to education differ when education can increase productivity and also be used to signal productivity. We show how instrumental variables can be used to separately identify and estimate the social and private returns to education within the employer learning framework of Farber and Gibbons (1996) and Altonji and Pierret (2001). What an instrumental variable identifies depends crucially on whether the instrument is hidden from or observed by the employers. If the instrument is hidden, it identifies the private returns to education, but if the instrument is observed by employers, it identifies the social returns to education. Interestingly, however, among experienced workers the instrument identifies the social returns to education, regardless of whether or not it is hidden. We operationalize this approach using local variation in compulsory schooling laws across multiple cohorts in Norway. Our preferred estimates indicate that the social return to an additional year of education is 5%, and the private internal rate of return, aggregating the returns over the life-cycle, is 7.2%. Thus, 70% of the private returns to education can be attributed to education raising productivity and 30% to education signaling workers’ ability.

That is from a new NBER Working Paper by Gaurab Aryal, Manudeep Bhuller, and Fabian Lange.  You can enter “education signaling” into the MR search function for much more on this ongoing debate.

A simple question about the signaling model of education

Let’s say, for purposes of argument, that education is 100% signaling, and furthermore let’s assume that the underlying traits of IQ, conscientiousness, and so on are not changing in the population over the relevant period of time.

Now consider a situation where income inequality is rising, at least in the early years of jobs.  Since employers cannot discern worker quality — other than by observing the signal that is — this should imply that getting an education is “more separating” than it used to be.

That in turn has to mean that an education is more rigorous than it used to be.  No, not “getting in” (employers could hire their own admissions officers), I mean getting through.  Finishing successfully is more of a mark of quality than it used to be, because finishing is harder.  Finishing is harder because there is more rigor.

Is this true?

How much of Chinese education is about signaling?

Alex Eble and Feng Hu have a new and interesting paper (pdf) on this topic:

Wages are positively correlated with years of schooling. This correlation is largely driven by two mechanisms: signaling and skill acquisition. We exploit a policy change in China to evaluate their relative importance. The policy, rolled out from 1980 to 2005, extended primary school by one year. Affected individuals must then complete more schooling to obtain their highest credential, the main signal of interest. If the primary mechanism behind schooling returns is signaling, we would expect little change in the distribution of credentials in the population, but a large increase in schooling. If skill acquisition dominates, we should see no change in length of schooling but a change in credentials. Our results are consistent with the signaling story. Further consistent with such a story, we estimate that the labor market return to another year of schooling is very small, though greater for the less-educated. We estimate that this policy, while redistributive, likely generates a net loss of at least tens of billions of dollars, reallocating nearly one trillion person-hours from the labor market to schooling with meager overall returns.

In a nutshell, that’s lots of signaling.  Might the pointer there have been from Ben Southwood?  I am no longer sure.  Via Nathaniel Bechhofer, here is a recent study of education and earnings from U.S. data.

Does subsidizing higher education increase or decrease signaling costs?

As of 2004, only 16.7% of the cost of Korean higher education was picked up by government, as opposed to an OECD average of about 77% (see this paper).  That’s a relatively low level of subsidy.  And yet Korea has one of the highest degree-granting rates in the world, the status of the school you go to is all-important, tiers of quality are fairly rigid, admission is closely linked to exam performance, and doubts have been raised about how much people actually learn in those schools.  At least when it comes to surface phenomena, it appears Korean higher education has a lot to do with signaling.

In Germany they just made the universities completely free, and in the past they were quite cheap, which of course means subsidized.  Germany also sends a relatively high percentage of its population to vocational training, where presumably the students learn some concrete skills.  Could it be there is too much slacking in German universities (which I have interacted with twice, both as student and as professor) for attendance to serve as a very effective signal?

Can it be the case that a government subsidy, by limiting privately-perceived quality and returns, can lower private signaling costs?  Should advocates of the signaling model therefore be more favorably inclined toward subsidies?

Score one for the signaling model of education

In the new AER there is a paper by Melvin Stephens Jr. and Dou-Yan Yang, the abstract is this:

Causal estimates of the benefits of increased schooling using US state schooling laws as instruments typically rely on specifications which assume common trends across states in the factors affecting different birth cohorts. Differential changes across states during this period, such as relative school quality improvements, suggest that this assumption may fail to hold. Across a number of outcomes including wages, unemployment, and divorce, we find that statistically significant causal estimates become insignificant and, in many instances, wrong-signed when allowing year of birth effects to vary across regions.

In other words, those semi-natural experiments for the return to education, when some regions move with extra doses of compulsory schooling before others and we estimate differential wage effects, maybe don’t show as much as we used to think.  As I’ve remarked to Bryan Caplan, if there is a criticism of a famous or politically correct result (or better yet both) getting published in the AER, you can up your Bayesian priors on that criticism being on the mark.

There are ungated copies of the paper here.

Bryan Caplan’s signaling model and on-line education

The very useful model is here, and there is further commentary from Bryan here.  My question is this: does the model imply that on-line education should succeed, or not?

Let’s say that education signals conscientiousness.  A purely on-line class, with no ogre standing over your shoulder to discipline you, should be blown off by those who are not conscientiousness.  The on-line class would seem to offer a better signal and a cleaner separation of types.

Alternatively, let’s say education signals IQ or some other notion of “smarts.”  On-line education would seem to offer less opportunity to get through by buttering up the teacher, spouting mumbo-jumbo in basket-weaving classes, and so on.  For better or worse, a lot of on-line education seems to be based on relatively objective tests.  Then on-line education would seem to offer a better signal of smarts.

One possible application of Bryan’s model might be this.  Income inequality is rising, so there is greater care to get the signal, selection, and screening right for top jobs.  Relatively high levels of education should be all the more discriminatory, and that may mean more on-line education.  In fact, in normative terms that might well be a problem with on-line education, namely its inegalitarian nature with regard to curiosity and effort and smarts.

Oddly, the signaling model could be true, but through an invisible hand mechanism — schools competing to separate quality in the most effective ways — you can end up with a state of affairs where upfront signaling costs are fairly low.  Imagine a chess school, needing to sort talent, and unable to teach its students very much, but setting up a quite cheap on-line tournament and declaring some winners.  Aren’t the Khan Academy users some really talented people?

Alternatively, through an invisible hand mechanism, if the learning model is correct, you could end up with an equilibrium in which upfront signaling costs appear to be relatively high, namely that you impose “taxes” to make sure people end up learning what they need to know.  Think Paris Island or KIPP schools.

It is important not to confuse “seeing high upfront signaling costs” with “the signaling model of education is essentially correct.”  They sound like they should go together, but quite possibly they don’t.

Can “education as signaling” models explain recent changes in labor markets?

Acemoglu and Autor present a few non-controversial stylized facts about labor markets, including falling wages of low-skill workers, flattening of the wage premium for workers with less education than college completion, non-monotone shifts in inequality, polarization of employment in advanced economies, and skill-replacing technologies (and don’t forget the new Brynjolfsson and MacAfee book; it is important).

The simplest model is that, because of information technology, employers demand more skills.  The job market responds accordingly, and eventually the education system responds too.  The major shifts are driven by changing productivities of human capital, and that is one reason why the human capital model of labor markets has proven so robust.  It accounts (mostly) for the big changes in labor market returns.

What would a signalling model predict as the results of skill-biased technical change?  I am never sure.  Those models are tricky with comparative statics predictions for at least three reasons:

1. Multiple equilibria are common and arguably essential,

2. It is assumed that employers cannot in the short run (medium run?) observe the marginal products of workers, and

3. The (supposed) relevant factor for employers, the degree, is past history and, if not quite carved in stone, credentialed retraining remains the exception in many market segments.   It hardly drives wage outcomes or observed changes in wages.

The simplest (non-signaling) model is that wages follow MP, albeit with some lag, and adjusting for a suitably sophisticated notion of marginal revenue product, including morale effects on other workers.

Again, how should skill-based technical change matter in a signaling model?  In the model, no employer observes (across what time horizon?) that the MPs of some workers have gone up and that other workers’ MPs have gone down.  Yet it seems that changing MPs matter at margins.  And if employers can sniff out changing MPs, this implies they can sniff out large MP differences more generally, which limits the scope of educational signaling.

It is a strong result these days that occupation and also job tasks predict earnings better than before (see pp.26-27 in the first link), including relative to level of education.  That also seems to run counter to what signaling theories predict.  Most likely we are now better at measuring the quality of workers and their educational signals don’t matter as much as they used to.  The higher returns to post-secondary education, which account for most of the recent growth in the returns to college degrees (p.145 and thereabouts), are skill-based and they are tightly connected to occupation and job tasks.

These are all reasons why the signaling model for education is not growing in popularity, namely that  it does not speak well to current comparative statics and to the current big stories in labor markets.

It is an embarrassing question for signaling models to ask: with what lag do employers get a good estimate of a worker’s marginal product?  If you say “it takes 37 years” it is hard to account for all the recent changes in wage rates in response to technology, as discussed above.

Alternatively, let’s say the lag is two years.  There are several RCT estimates of the return to education, based on earnings profiles measured over twenty or thirty year periods.  The estimated returns to education are high, and if those returns were just signaling-based you would expect the IV-elevated individuals to show up as underskilled and for the credentials-based wage gains to fall away with a few years’ time.  That doesn’t happen (if you are wondering, the IV-elevated individuals are those who for essentially random reasons end up getting more education, or an instrumental variable proxies as such, without the elevation being correlated with their underlying quality as workers,).

In other words, the signaling model is caught between two core results — high long-term measured returns to the education of IV-elevated individuals, and technology drives wage changes in the medium-term.  It is hard for a signaling model to explain both of those changes at the same time.

There is a way to nest signaling models within human capital models, rather than viewing them as competing hypotheses.  Using matching theories, let’s say employers learn the quality of workers they have, but find it hard to estimate the quality of workers they don’t have.  IV-elevated workers can’t fool the market/the employer for very long, and so their high pecuniary returns from education really do measure productivity gains.  Nonetheless there can be undervalued “diamonds in the rough.”  Think of them as geniuses, or at least good workers, who hate getting the education.

From the point of view of these students (or dropouts, as the case may be), the signaling model will appear to be true.  They will resent the education and they won’t need the education.  If it is costly enough to sample worker quality from the “outsiders bin,” it will remain an equilibrium that a degree is required to get the job, at least provided workers of this kind are not too numerous.  If there were “lots and lots” of such workers, more employers would scrounge around in the outsider’s bin.  In other words, the anecdotal evidence for signaling fits into a broader model precisely because such cases aren’t too common.

Further papers on signaling and education

Pursuing this topic, here are some of the good or interesting papers I discovered:

This UK piece reframes the David Card IV literature in terms of signaling and with UK data estimates that signaling accounts for one-third of the educational wage premium.  It uses a “compulsory” instrumental variable from earlier UK schooling reforms.

Here is the Hanming Fang paper (IER): “…productivity enhancement accounts for close to two-thirds of the college wage
premium.”  It uses very different techniques, based on simulations, not IV and the like.

This paper shows that rank measure in class doesn’t affect earnings, contrary to what signaling theories should predict.  This may be a puzzle for learning theories as well.

Here is a good piece (it ended up in the JPE) which shows signaling must have some import; it does not attempt to estimate how much of the educational wage premium is due to signaling.

This paper suggests that signaling may be especially important for MBAs.

German education helped drive their Industrial Revolution.

This Carneiro, Heckman, and Vytlacil paper I found impressive.  It redoes much of the IV Angrist and Card work with greater emphasis on heterogeneous agents and also heterogeneous margins.  It seems to be the current peak of the IV approach and finds rates of return in the 15-20 percent range and that is for college.  It also finds that lower ability individuals are harder to educate and therefore reap lower (though still high) marginal rates of return, contra some of the simpler IV papers.

This very interesting Kevin Lang paper argues that signaling theories do not diminish the case for education and also that they do not create particular problems for measuring the social rate of return on education.

When are signaling and human capital theories of education observationally equivalent?

Going as far back as Andrew Weiss’s survey paper, there are various attempts to argue that the two theories make the same predictions about earnings and education.  A randomly elevated individual will earn more money but is this from having learned more or from being pooled with a more productive set of peers?

To explore this, let’s pursue the very good question asked by Bryan Caplan:

Our story begins with a 22-year-old high school graduate with a B average.  He knows an unscrupulous nerd who can hack into Harvard’s central computer and give him a fake diploma, complete with transcript.  In the U.S. labor market, what is the present discounted value of that fake diploma?

If he can fake a good interview (a big if, but let’s say), and if certification from recommenders is not important in the chosen sector (another big if), he may get a Harvard-quality job for his first placement.  If you believe in the signaling theory, however, his marginal product is fairly low, much lower than the wage he will be paid.  They will fire him.  He’ll come out a bit ahead, if he is not too demoralized, but within a few years he will be paid his marginal product.

In most jobs they figure out your productivity within two or three months after training, if not sooner.

In a one-shot static setting, signaling and human capital theories might have the same empirical implications because the learning and pooling effects can produce similar links between education and wages (again assuming someone can fake an interview).  But not over time and of course the wage dispersion for an educational cohort does very much increase with time.  The workers don’t keep on receiving their “average marginal product” for very long.

Do not be tricked by those who serve up one-period examples to establish the empirical equivalence of signaling and human capital theories!

To tie this back to the academic literature, if IV-elevated workers enjoy an enduring wage effect comparable to that of the other degreed workers, you should conclude they learned something comparable at school unless you wish to spin an elaborate and enduring W > MP story.

Addendum: There is a less drastic scenario than the one outlined by Bryan.  Let’s say there are fourteen classes of workers and a class nine worker is randomly elevated to class seven credentials.  He might use that momentary good fortune to learn from smarter peers, work hard to establish a foothold, and so on.  His lifetime earnings might end up as roughly those of other class seven workers, despite being of initial type nine.  The higher earnings are still based on learning effects (not mainly pooling), though pooling gave that worker temporary access to some new learning and advancement opportunities.  In most regards this works like the learning model, not the pooling model, although the period of learning extends beyond schooling narrowly construed.

And Arnold Kling comments.

Does the returns to education literature really test the signaling model?

Here is a comment by Matt, and also by ArnoldBryan’s response argues that the returns to education tests consider “ability bias” but not “signaling.”  For a lot of the tests that is a distinction without a difference, and indeed you can see this on the first two pages of Angrist and Krueger, which discuss “omitted variables that are correlated with educational attainment and with earnings capacity.”  The tests still discriminate against the signaling model, even if signaling and ability bias differ in other regards.  In a nutshell, artificially or randomly elevated workers fare better in the longer run than the signaling model predicts.

Here’s a parable to illustrate.  Imagine a market situation with wages and different education levels observed for two classes of workers — call the locale Honduras.  Now compare that to another setting — Nicaragua — where education is handed out on some subsidized, randomized basis.  In the latter case some of the low ability group will be induced to get more schooling, and the pool of the educated will contain more low ability individuals in Nicaragua, compared to Honduras.

Now measure the long term earnings and compare.

If the signaling model is correct, the average long-term wage rates of return for the subsidized/elevated group in Nicaragua will be noticeably below the average wage rates of return of the educated group from the separating equilibrium in Honduras.  After all, the subsidy-elevated group adds many more “low ability individuals” to the Nicaraguan mix of the educated than one would find in Honduras.  According to the signaling model, in Nicaragua eventually the lower skill level of the elevated group will be discovered and their wage rates of return won’t stay so high forever.

But the wage rates of return for the elevated groups do not plummet back to earth and generally they are robust over time.  That measures the real learning which went on in school, or so it would seem.  Education is good for more than getting a good first job offer right off the bat.

The modern liberal interpretation (which may or may not be true) is that these poor people were waiting for a helping hand up the ladder, and then they took good advantage of it when it came.  And if the elevated group in Nicaragua has higher long-term wage rates of return than the educated Hondurans (a result which does sometimes pop up in the data), that is because their lower initial margin of education made them an especially potent investment.

The actual tests are more complicated than this, and I use the country names to make the example easy to follow, not out of verisimilitude.  But this example is one way to see some of the intuitions behind why the data do not treat the signaling model so kindly.

One empirical implication is that crude OLS measures of the return to education are much better than they may at first appear.  These results are also one reason why most modern labor economists might object to the arguments of Charles Murray.

Here is a recent Brookings piece on the return to education, I have not had time to go through it.

Signaling vs. certification at Harvard

Harvard will be teaching solely on-line this fall (with some students in residence), yet charging full tuition rates.  Many commentators are thus suggesting this supplies evidence for the signaling theory of education.

But not exactly.  The signaling theory, taken quite literally, is that education is a very difficult set of hurdles to surmount, and if you can get through Harvard you must be really really smart and hard-working.  Caltech maybe, but Harvard like Stanford and many other top schools makes it pretty easy to get through with OK enough grades.

The hard part about Harvard is getting in.  By selecting you, Harvard certifies you (as long as you are not part of “the 43% percent,” legacy, athletes, etc…but wait that counts too!).

Why isn’t there a service that just certifies you directly?  Surely you could run a clone of the Harvard admissions department pretty cheaply.

Perhaps the logical conclusion is that both the “social connections/dating” services of Harvard and the certification services of Harvard are strong complements.  If you are certified by Harvard, but live on a desert island, or carry a contagious disease, that certification is worth much less.  So it is hard to unbundle the services and sell the certification on its own, without the associated social networks.  Nor is it so worthwhile to sell the social connections on their own.  Harvard grads are socially connected to their dry cleaning workers as it stands, but that does not do those workers much good.

It takes a good deal more work to get signaling to enter this story.  In the signaling story, you can’t tell who is high quality without actually running the tournament, and that is more or less the opposite of the certification story.

Keep also in mind that the restricted Harvard services are probably only for one year (or less), so most students will still get three years or more of “the real Harvard,” if that is what they value.  And they can use intertemporal substitution to do more networking in the remaining three years.  It’s like being told you don’t get to watch the first quarter of a really great NBA game.  That is a value diminution to be sure, but there will still be enough people willing to buy the fancy seats.  Most viewers in the arena don’t watch more than three quarters of the game to begin with.

Extending the Race between Education and Technology

There is a new and updated take on this topic by Autor, Goldin, amd Katz:

The race between education and technology provides a canonical framework that does an excellent job of explaining U.S. wage structure changes across the twentieth century. The framework involves secular increases in the demand for more-educated workers from skill-biased technological change, combined with variations in the supply of skills from changes in educational access. We expand the analysis backwards and forwards. The framework helps explain rising skill differentials in the nineteenth and twenty-first centuries, but needs to be augmented to illuminate the recent convexification of education returns and implied slowdown in the growth of the relative demand for college workers. Increased educational wage differentials explain 75 percent of the rise of U.S. wage inequality from 1980 to 2000 as compared to 38 percent for 2000 to 2017.

Emphasis added, here is the full NBER working paper.  For background, here is my old NYT column on their earlier work on this topic.

Note that for the most recent rise in inequality across 2000-2017, most of it has happened within educational groups.  The less polite way of putting that — my words not those of the authors — is that the real marginal product of education is explaining less of the variation in earnings, or in other words the higher earners are drawing upon something they are not getting at school.

Students of the “education as signaling” debate also should note that, due to these results, now a) signaling is more relevant for your early wage offer, and b) signaling is less relevant for your eventual wage profile, which in fact is now more determined by your personal level of skill.

Bryan Caplan’s stance on higher education policy

In my Warren post I wrote:

7. College free for all: Would wreck the relatively high quality of America’s state-run colleges and universities, which cover about 78 percent of all U.S. students and are the envy of other countries worldwide and furthermore a major source of American soft power.  Makes sense only if you are a Caplanian on higher ed., and furthermore like student debt forgiveness this plan isn’t that egalitarian, as many of the neediest don’t finish high school, do not wish to start college, cannot finish college, or already reject near-free local options for higher education, typically involving community colleges.

Bryan wishes me to point out that he does not favor “free tuition for all,” and indeed that is true, as I can verify from years of discussion with him.  Nonetheless I still believe such a policy would come closer to limiting educational signaling (by making so many schools worse and lowering the value of the signal) than would Bryan’s preferred policies toward higher ed.

Educating animals (not just signaling)

Formal training programs, which can be called education, enhance cognition in human and nonhuman animals alike. However, even informal exposure to human contact in human environments can enhance cognition. We review selected literature to compare animals’ behavior with objects among keas and great apes, the taxa that best allow systematic comparison of the behavior of wild animals with that of those in human environments such as homes, zoos, and rehabilitation centers. In all cases, we find that animals in human environments do much more with objects. Following and expanding on the explanations of several previous authors, we propose that living in human environments and the opportunities to observe and manipulate human-made objects help to develop motor skills, embodied cognition, and the use of objects to extend cognition in the animals. Living in a human world also furnishes the animals with more time for such activities, in that the time needed for foraging for food is reduced, and furnishes opportunities for social learning, including emulation, an attempt to achieve the goals of a model, and program-level imitation, in which the imitator reproduces the organizational structure of goal-directed actions without necessarily copying all the details. All these factors let these animals learn about the affordances of many objects and make them better able to come up with solutions to physical problems.

The paper is by Ken Cheng and Richard W. Byrne, via the excellent Kevin Lewis.