Mini-post on Log Returns to Education

The return to a year of education is conventionally taken in logs. An additional year of education leads to a percentage increase in wages, generally around 8% per year. This is really weird, though — if a year of education is adding skills, and you only have time for a certain number of skills to be instilled, then the percentage gain in wages should be declining.

What it suggests is that the return to education is shaped by market pressures. People will invest in obtaining education up until the point where they would profit more by spending their time doing other things. Grant, in some clarifying assumptions, that everyone is identical, there is only one skill, and everyone is able to linearly increase that skill as a function of time. An increase in the demand for workers will therefore be reflected in the quantity of educated workers, and not in the price of workers. If the returns to education are dependent upon what other people are doing, ala Kremer’s O-ring theory — which seems eminently plausible; for example, it is more profitable to design computers when there are lots of skilled people able to use them — then there’s a knife-edge condition for the economy as a whole. A shift in demand for skilled labor changes the number of people obtaining skills, which in turn increases the demand, and so on.

This doesn’t work if the number of workers is constrained. As they obviously are, income growth is determined by the number of births. It doesn’t seem impossible, though, that AI allows us to make substitutes for humans, and we get takeoff through increasing returns. Jones (1995) shows how, if there are declining marginal returns to research, then growth is determined in the long run by population growth. Even if perfect substitutability means labor income goes to zero, it’s still what we should be hoping for. We’d have to redistribute, but it’d be far better to redistribute infinity, than have labor income be finite.