I am going to treat his post as a challenge. Romer wrote
1) There is a crucial distinction between human capital (stored in neurons), and codified information (stored in some external form, such as printed text or bits on a hard drive.) 2) Anything stored in neurons is a rival good. 3) A person’s human capital is fully excludable as long as people have legal control over their own bodies. So there are no human capital “spillovers” and no human capital “externalities.”
His discussion goes on, but I want to challenge the third claim.
For one thing, I think the post is, for the purposes of growth theory, just like a human capital spillover. I learned from the post. I didn't pay for it (nore did Romer expect any payment). The fact that something is excludeable doesn't mean that others are, in fact, excluded. People voluntarily share knowledge as Romer did in his post including the claim that there are no human capital spillovers.
I agree with Romer that ESP doesn't exist, so we can't steal knowledge from each other's brains. We don't learn just by being around someone who knows something. But I think there are human capital spillovers and externalities.
The reason is that we can learn by watching someone use their human capital (I really mean watch with our eyes).
This is a very inefficient way to learn. It is much more efficient for the knowledgeable person to explain things, sometimes it is necessary for the learner to attempt a task and be critiqued by the teacher or coach. But "no" is a strong word.
Someone who wants to prevent this can use knowledge only in private and prevent others from watching (as someone can lock up a document). But someone who is indifferent about the knowledge of others will use skills when being watched and the others will learn (slightly) more than nothing.
Human capital is invisible when it just sits there, but more than exactly none of it can be inferred by watching someone use it.
I think there are much more important processes which aren't true spillovers but which can be usefully modeled as if they were spillovers.
1) altruism. In standard models agents are selfish but actual people aren't. People teach other people without demanding payment or negotiating. The effect on the spread of information is like a spillover. Pretending it just happens while using standard utility functions is an almost harmless shortcut.
2) Gift exchange. People can have a norm or custom that they teach each other (so long as it isn't too hard). This is an exchange not a spillover. However, I think in the real world there is a lot of this going on without cash payment, negotiation or checking how much each is teaching and how much each is learning. The macro effects are similar to those of a spillover and quite different from purchasing of education. This is not a spillover, but modeling it as a spillover is a more useful approximation than modeling it as a market exchange.
3) people with complementary skills work together in teams. In the process, with the sole aim of getting the task done, they explain what they are doing. This is learning and teaching by doing. The fact that both end up learning from the others is a by product of the effort to perform a task together.
4) some people enjoy teaching. I had a lot of knowledge pretty much forced on me by people I knew in college. This is a case of how you can get models to do anything by playing with utility functions. But it is reality. Consider blogging. Some people do it without expecting any reward. Romer is very clear that he expects costs not benefits from his posts on mathiness. This is not at all like market exchange of education services. The post on how human capital doesn't spill over is a human capital spillover.
5) When learning it is best to expose ones imperfect knowledge to criticism. One kind of non spillover teaching is the lecture where someone knowledgeable talks and learners listen. Another is the presentation with criticism, the problem set with correction etc where someone who is learning talks or writes and someone knowlegeable comments critiques and corrects. In the real world, the roles are not always clear. If I think I understand something but am not sure, it is useful to me to try to explain it to a critical listener who doesn't know about it already. Who is the teacher and who is the student? This isn't a spillover (we are both expending effort) but it is better modeled as a spillover than as a market exchange.
So I think there are minor unimportant human capital spillovers and also extremely important social interactions which spread knowledge which aren't spillovers but which have similar implications for the spread of knowledge and economic growth and all that, while they don't have anything like the same implications as the purchase of teaching services with tuition.
So I think models with human capital spillovers are useful even if actual human capital spillovers are unimportant.