Bryan Caplan  

What Arrow Said About Education in 1973

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In the early 90s, I saw Ken Arrow informally debate Murray Rothbard.  Arrow was not impressive; all he did was repeat tired textbook arguments about market failure.  My subsequent encounters with Arrow's thought were no better.  Early this year, however, I read Arrow's 1973 "Higher Education as a Filter," and decided I was completely wrong about the man.  He wasn't just a pioneer of the mathematics of the signaling model; he foresaw and answered many misinterpretations of the model that still plague us today.

The highlights begin on page one, when Arrow describes the many ways that education could increase productivity - and, by implication, the many traits that education could signal:
From the viewpoint of formal theory, it does not matter how the student's productivity is increased, but implicitly it is assumed that the student receives cognitive skills through his education. Educators on the other hand, have long felt that the activity of education is a process of socialization; the latent content of the process, the acquisition of skills such as the carrying out of assigned tasks, getting along with others, regularity, punctuality, and the like, being at least as important as the manifest objectives of conveying information... [F]rom the viewpoint of economic theory, the socialization hypothesis is just as much a human capital theory as the cognitive skill acquisition hypothesis. Both hypotheses imply that education supplies skills that lead to higher productivity.
Only then does Arrow introduce his alternative:
I would like to present a very different view. Higher education, in this model, contributes in no way to superior economic performance; it increases neither cognition nor socialization. Instead, higher education serves as a screening device, in that it sorts out individuals of differing abilities, thereby conveying information to the purchasers of labor.
On page two, Arrow immediately disavows the silly "100% signaling" story so popular with critics of the model, then acknowledges the consumption benefits of education:
Perhaps I should make clear that I personally do not believe that higher education performs only a screening purpose. Clearly professional schools impart real skills valued in the market and so do undergraduate courses in the sciences. The case is considerably less clear with regard to the bulk of liberal arts courses. But in any case I think it better to make a dramatic and one-sided presentation of the screening model in order to develop it than to produce a premature synthesis. It should also be understood that I am speaking only about the contribution of higher education to production; the consumption aspects are real and important, but they are irrelevant to the points being made here.
On page three, Arrow considers and rejects the "employer learning" critique of the model:
It will probably be argued that this description [that "the buyer has very good statistical information but nothing more"] is valid enough at the time of hiring but that after a period of time the employer will know his workers and their productivities on an individual basis. No doubt there is something to this viewpoint but not as much as may be thought. After all, what is needed for allocative efficiency is the marginal productivity of each individual. But in a complex production process, the employer has simply no way of determining that. All he can do is act like an ideal econometrician, relating his output to the numbers of different kinds of workers (and other inputs, from which I am abstracting in this
paper).
In the conclusion, Arrow specifically rejects the view that IQ tests are a sufficient statistic for the "ability" that educational success supposedly signals to employers.  He admits that this is unsatisfying, but prefers to be vaguely right than clearly wrong:
[T]he model of this paper depends upon an unmeasured and unmeasurable variable, "ability". There may be no way of ever achieving a direct measurement; after all, a premise of the model is that employers cannot measure ability directly, and there is no reason to suppose that the economist is going to do better. It remains to be seen if the theory can be made to yield interesting and testable implications in the absence of direct measurements of ability.
He even anticipates my point that in a signaling model, national educational success remains a symptom - though not a cause - of economic success:
[T]he filter model has some implications for macroeconomic observations. It says that an
increase in the resources devoted to college education will have no positive effect on output in the non-educational sector, if all other variables are controlled for. This is indeed a strong inference, but its usefulness in making intertemporal or international comparisons is limited by the need to hold the statistical distribution of ability constant. If "ability" is influenced by cultural factors, then it will certainly vary internationally and may also be thought to vary over time.
The signaling model of education still needs improvement.  I wouldn't be writing a book about the topic if I thought otherwise.  What "Higher Education as a Signal" shows, however, is that the model hit the ground running.  Almost four decades ago, Ken Arrow foresaw and answered many of the objections that human capital extremists have never stopped repeating.



COMMENTS (12 to date)
Steve Sailer writes:

Signaling theory is pretty obvious.

But it's silly to say that having a population that has had some schooling is not useful. For example, military leaders were a lot more pleased by the literacy levels of draftees in WWII than in WWI.

Michael writes:

Perhaps, he stuck to the basics on TV in order to convince people.

Daniel Kuehn writes:

re: "On page two, Arrow immediately disavows the silly "100% signaling" story so popular with critics of the model"

Bryan, could you lay out very clearly in a post what you think of human capital theory. You talk about it as if people are naive to take it seriously "even as an approximation" (as I believe you've put it in the past).

That would suggest that you have been advocating a 100% signaling story, which I do have a problem with (as I'm sure others do too). My experience is that almost everybody I know thinks signaling is part of the story and human capital is part of the story.

Is that all you think too? I was a little thrown by this sentence. I wouldn't want to criticize your posts on these grounds if you don't actually have a 100% signalling story, but you've been so quick to denounce human capital theory I always got the impression that was the case.

I think a post on what you think the merits of human capital theory are would be interesting.

Keith writes:

Typo: In the last paragraph, you've written the wrong title for Arrow's paper.

KnowPD writes:

What about company sponsored MBA programs? Presumably, employers would be in abetter position to evaluate for job skills than professors. I think the consumption model is undervalued. Employees who see education as a consumption good are better knowledge workers and employers know this. They pay for more education as incentives to retain.

Ted Craig writes:

I thought the man was an idiot until I found he wrote something I agreed with!

English Professor writes:

Arrow writes: "I am speaking only about the contribution of higher education to production; the consumption aspects are real and important, but they are irrelevant to the points being made here."

I'm not sure what he means by "the consumption aspects." Does this mean that a college-educated person is likely to consume more (or different) things than someone with less education? Or does he mean that the benefits one gets from a college education (perhaps a deeper understanding of art, philosophy, and economics) are in themselves a form of consumption?

This distinction, though, between the production and consumption effects is one that I don't recall Bryan making.

Nathan Smith writes:

Concerning the consumption aspects, it seems to me that those might actually explain the statistical correlation between education and income.

Suppose, for the sake of argument, that education has no productive value whatsoever. Suppose, furthermore, that employers can ascertain employees' abilities quite rapidly, either in an interview or shortly after hire. That is, suppose the human capital and signalling theories of education are both false.

But also suppose this: that education is a lot of fun, and that by enriching the mind it enhances our enjoyment of everything else. One who has read Wordsworth, with some coaching by a lit prof to enable full appreciation, gets more beauty from all kinds of natural scenery. Knowing science helps too. One who has studied philosophy gets all sorts of delights from reflection. Operas and great novels become accessible. One can have refined, erudite, subtle conversations. One can write poetry. One can tour Europe and know what the monuments mean. And so forth.

Finally, suppose people know their own ability.

Now, a person who knows himself to be high ability foresees a high lifetime income. He is therefore able to afford the large investment in personal capacity for enjoyment that education represents. Of course, he makes this investment as soon as possible, since every year he spends as a philistine is a year in which he foregoes great cultured enjoyments. Afterwards, he goes to a job interview, where an employer recognizes his ability (which he always had), offers a commensurate salary, and the college grad begins to pay off his debts.

A person who knows himself to be of low ability foresees a lot lifetime income. To divert some of its scarce income into paying off college loans would cause major hardship. He resigns himself to an impoverished, philistine lifestyle, in order at least to be able to keep himself fed and clothed and maybe raise a family.

It's an obvious theory once you think of it. I'm not aware of whether it's been written down anywhere though. I hope your book will take it into account! Of course, I wouldn't claim that it's the full explanation. It did sometimes seem to me that BUSINESS majors in college were of lower ability than humanities majors. The humanities types knew they weren't raising their earning power much, but they were a little more self-confident about their ability to get by, and wanted to expand their minds. The business types sometimes seemed more afraid for their ability to make a living at all. I think this really is PART of the explanation for college.

BZ writes:

English Professor: I read that to refer to the later "the benefits one gets from a college education (perhaps a deeper understanding of art, philosophy, and economics) are in themselves a form of consumption?". As someone who derived great joy from many of my classes, knowing full well they meant nothing to my job prospects, that's how I read it at least.

Willard Moore writes:

It sounds like an interesting paper, but the full text doesn't seem to be available anywhere for less than $30, which is a little much for a 30-year-old paper. Obviously, someone with a real job isn't going to go to the public library to read it. It's interesting that academics like Arrow don't aspire to influence the views of educated econ majors with full-time non-academic jobs, but I guess he has his reward.

Roger Sweeny writes:

English Professor,

When Arrow refers to the "consumption aspects" of higher education, he is using economist shorthand. Economists often divide things into "consumption" and "investment." Investment refers to something that requires sacrifice now but pays off later. Consumption provides present pleasure. Some people like reading and thinking and that sort of thing. Many of them become professors and writers. For them, college is a good time and a good deal. They get "utility" both now and later. They are engaging in both consumption and investment.

Other people don't especially enjoy reading and thinking. They won't enjoy that part of college. But they may well enjoy having thousands of age-mates around, people they can do interesting things with, ranging from playing Dungeons and Dragons to getting wasted and having sex. These are "consumption aspects" for many of the people who attend college. These consumption aspects, and the credential students get at the end, make up (if just barely) for the unpleasantness of reading and thinking.

(And, yes, there are some people who go to college expecting to "invest" in developing a capacity to appreciate high culture and science. My experience, however, is that all too many professors are more interested in what is important to their fellow professors, in narrow and "academic" issues, rather than in helping students enjoy "the best humanity has done and thought.")

Glen S. McGhee writes:

You need to address the problem of "overinvestment in the signal" for its own sake.

That's what's driving the credential inflation spiral now -- but it may have been Spence, not Arrow, that mentioned this problem.

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