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.