To me, one of the ways in which my 1990 paper, Endogenous Technological Change, was a step forward relative to the first round models of endogenous growth was the explicit distinction that it allowed between the stock of human capital H and the stock of knowledge A. To be sure, this was a very small step. In the model, they interacted the simplest possible way. Human capital H was an input that could be used to produce new knowledge A.

Stated in words, this sounds trivially obvious. But with mathematical theory, you have to think carefully to say even things that are trivial and obvious. Things such as what, precisely, do we mean by human capital?

I am a big fan of micro-foundations; provided, that is, that they are true. What has given a reliance on micro-foundations a bad name is letting people get away with using ones that are false and claiming that this has anything to do with science.

Here is the true micro-foundation that I used to think about human capital. Human capital is stored as neural connections in a brain. For example, when a person reads from a book how to use a 3-4-5 triangle to construct a right angle using only a measuring rod, this information is stored in a set of neural connections in his/her brain. These neural connections increase the productivity of this person as a carpenter. To get empirical proxies for human capital, we measure the time someone spends reading or this increase in productivity, as reflected in the carpenter’s higher wage.

Once you have this micro-foundation in hand, it is crystal clear that human capital is a rival good and that even without any legal protection, human capital is almost perfectly excludable. Short of torturing me, there is no way for you to get information out of my neurons that I do not want to give to you. When I give someone information, for example by answering a question, I’m engaging in voluntary exchange in exactly the same way as when I hand this person some object that is in my possession.

Now, here is an alternative micro-foundation for human capital. There is a little homunculus inside each person’s head who knows everything the person knows and who has his own low-powered ham radio station. When two people come into proximity, neither of them can prevent the homunculus in each head from broadcasting over the ham radio to the other homunculus, all the things it knows. So the mere fact of close proximity causes valuable bits of knowledge, such as how to make a right angle using only a measuring rod, to flow from one person’s head to the other person’s head, which then raises the productivity of the other person as a carpenter.

This micro-foundation justifies the idea that human capital is not fully excludable. In less precise language, it justifies human capital externalities or spillovers. As you may have noticed, this micro-foundation is also false.

If you accept micro-foundations that are false, you can reach all kinds of incorrect conclusions. (Sprinkle around the phrase “as if” and they will still be incorrect.) But if you stick to micro-foundations that are true,  human capital is perfectly excludable. There are no human capital externalities. Zero. Nada. Zilch.

So how can we tease out the meaning we can extract from the inchoate sense many people seem to have that there are human capital externalities? The key is to look at the production process I mentioned in the beginning: Someone with H can use it to produce some A.

Again, it helps to be precise by invoking a (true) micro-foundation. Suppose that someone with some H that encodes knowledge of the Pythagorean theorem and 3-4-5 triangles writes this down in words and symbols that go into a book. This means that he/she has used H to produce some codified knowledge A. Suppose also that it is costless to copy books. (This simplifies the argument presented here, but the argument is little changed if it is expensive to copy the book. I’ll come back to this point in a subsequent post.) This codified knowledge is a nonrival good. The pages of the book can be copied many times. Then many people can use the information in the text at the same time. And what might they do with it? They will go through the reverse transformation, one that I did not try to capture in my model. They will use A to produce H so they can be better carpenters. Or better mathematicians.

If there is no legal protection that prevents copying of books, then A is nonexcludable. Having something like copyright protection for books might or might not be a good thing. This is what makes it intellectually interesting to consider changing the rules that determine the degree of excludability for A. But to be precise, the fact that H can produce something that might be nonexcludable does not mean that H itself is nonexcludable.

People make the claim that there are human capital externalities because they have not figured out how to reason separately about H and the A that it can produce. If you lump them together and pretend you can’t tell the difference between text on the page and the neural connections in someone’s brain tissue, you can sorta convince yourself that when one person knows the Pythagorean Theorem, this knowledge just sorta gets spread around by the these overactive homunculi.

But this kind of sloppy thinking closes off another intellectually interesting opportunity, looking in more detail at how H in neurons gets translated into a codified form A and then, typically, back into H in someone else’s head. Of course, this is not the only way for A to produce value. For example, a new piece of A might take the form of computer code that runs on a machine that produces some value. But most of the A produced by the H in one brain, creates value when it is used as an input in the production of new H in another brain.

There is a lot that goes on in this round trip. Think of early attempts at creating expert systems that were supposed to codify all the H of some expert. When people working on AI first tried to develop these systems, they discovered that producing A was a lot more difficult than they imagined. And going the other way, from A to H? This is what education is all about. So both of the steps in the chain H → A → H are complex and costly.

In the 25 years since I took the first small step by suggesting that it would be useful to think carefully about the difference between H and A, the biggest surprise for me is how little attention this H → A → H roundtrip has attracted among economists interested in the theory of growth.

Speech. Printing. Digital communications. There is a lot of human history tied up in our successful efforts at scaling up the H → A → H round trip.

This is #2 in a collection of posts on the 25th anniversary of the publication of my 1990 JPE paper.

#1: Nonrival Goods After 25 Years