Category: Education

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.

On Twitter Bryan asks me:

Would you state your human capital/ability bias/signaling point estimates using my typology?

He refers to this blog post of his, though he does not clearly define the denominator there: is it percentage of what you spend on education or explaining what percentage of the variation in lifetime earnings?  I’ll choose the latter and also I’ll focus on signaling rather than trying to separate out which parts of human capital are from birth and which are later learned.  My calculations are thus:

1. I don’t wish to count “credentialed” occupations, where you need a degree and/or license, but you are reaping rents due to monopoly privilege.  It’s neither human capital nor signaling (it’s not about intrinsic talent), though you could argue it is a kind of human capital in rent-seeking.  In any case, let’s focus on private labor markets without such barriers.

2. Most capital and resource income is due to factors better explained by human capital theories or due to inheritance.  That is more than a third of earnings right there.  Note that the higher is inequality, the less the signaling model will end up explaining.  That is one reason why the signaling model has become less relevant.

3. Depending on job and sector, what you’ve signaled, as opposed to what you know, explains a big chunk of wages in the first three to five years of employment.  Within five years (often less), most individuals are earning based on what they can do, setting aside credentialism as discussed under #1.  Here is my earlier post on speed of employer learning.

Keep in mind that everyone’s wages change quite a bit over their lifetime and that is mostly not due to retraining (i.e., changes in the educational signal) in the formal sense, as most people stop formal retraining after some point.  The changes are due to employer estimates of skill, modified by bargaining power.  In this sense all theories are predominantly human capital theories, whether they admit it or not.

To be generous, let’s give Bryan the full first five years of income based on signaling alone, out of a forty year career.  And let’s say that on average wages rise at the rate of time discount (not true as of late, but a simplifying assumption and I think Bryan believes in a claim like this anyway.)

How much of income is explained by signaling?  I’m coming up with “1/8 of 2/3,” the latter fraction referring generously to labor’s share in national income.  That will fall clearly under ten percent, but recall I’ve inserted some generous assumptions here.

Bryan wants to call me “a signaling denialist,” yet I see signaling as still very important for understanding some aspects of the labor market.  But it’s far from the main story for the labor market as a whole, especially as you move into the out years.

That all said, this “decomposition” approach may obscure more than it illuminates.  Let’s consider two parables.

First, imagine a setting where you need the signal to be in the game at all, but after that your ingenuity and your personal connections explain all of the subsequent variation in income.  Depending what margin you choose, the contribution of signaling to later income can be seen as either zero percent or one hundred percent.  Signaling won’t explain any of the variation of income across people with the same signal, yet people will compete intensely to get the signal in the first place.

Second, in a basic signaling model there are two groups and one dimension of signaling.  That’s too simple.  A signaling model implies that a worker is paid some kind of average product throughout many years, but of course the reference class for defining this average product is changing all the time and is not, over time, based on the original reference class of contemporaneous graduating peers.  For the purposes of calculating your wage based on a signal, is your relevant peer group a) all those people who got out of bed this morning, b) all those people in the Yale class of 2012, or c) all those who have been mid-level managers at IBM for twenty years?  This will change as your life passes.

So there’s usually a signaling model nested within a human capital model, with the human capital model determining the broader parameters of pay, especially changes in pay.  The employer’s (reasonably good but not perfect) estimate of your marginal product determines which peer group you get put into, if you choose to invest in additional signals (or not).  The epiphenomena are those of a signaling model, but the peer group reshufflings over time are ruled by something else.  Everything will look like signaling but again over time signaling won’t explain much about the variation or evolution in wages.

Seeing the relevance of those “indeterminacy” and “nested” perspectives is more important than whatever decomposition you might cite to answer Bryan’s query.

Here is one recent report of falling salaries in public institutions, and, on the bright side, universities are having trouble filling some of those slots:

Public university professors don’t enter the profession to get rich. But some faculty are having trouble paying bills, and have even qualified for foods stamps, Olson said. “For somebody to go five to seven years beyond college to obtain a Ph.D. degree and to realize that you are in need of federal assistance to make ends meet — and that’s for a tenure-track position –” is devastating.

Adding what some view as insult to injury, a recently published database of public employee salaries shows that some professors earn less than their colleagues at local high schools without doctorates.

Yet how would they feel about actual poor people?  The article focuses on University of Wisconsin, Stevens Point, and serves up the following numbers:

Faculty salaries averaged $67,000 for full professors; $57,100 for associate professors; and $51,900 for assistant professors during the 2012-13 academic year.