# Inequality and Stochastic Human Capital

### I have been pondering the interaction between inequality and the return to human capital. I haven’t fully figured out what I think about the issue, but I thought blog readers might enjoy seeing some initial ruminations, presented in the form of a numerical example.

There are three people, which I will call P, M, and R. P has no human capital and an income that I will normalize to one. M and R each have 10 years of human capital. Human capital is risky. Initially, human capital has an average return of 7.5 percent per year, but M gets a return of 5 percent and R gets a return of 10 percent. So M has an income of (1+0.05)^10=1.63, and R has an income of. (1+0.1)^10=2.59. P is poor, M is middle-class, and R is rich.Now suppose that the rate of return to human capital doubles for every individual, and nothing else happens in the economy. P’s income stays the same at 1. M’s income rises to (1+0.1)^10=2.59, which is an increase of 59 percent. R’s income rises to (1+0.2)^10=6.19, which is an increase of 139 percent.

Not surprisingly, inequality has increased. Perhaps more surprisingly, inequality within education groups has increased. R and M have the same amount of human capital, but R is gaining more than M. The rich are getting richer, while the middle-class are getting richer at a slower rate. The poor are being left behind.

Some economists might look at this situation and say, “See, the return to human capital has increased.” Indeed, by construction, the only change is a doubling in the rate of return to education. Yet other economists might say, “The increase in equality cannot be fully explained by the increased education premium, because there is increased inequality within groups. The rich have no more human capital than the middle class, and they getting the biggest gains.”

A key feature of this example is that the increase in the rate of return is proportionate, so those with an initially higher return get a larger increase. The results would be very different if the increase were additive, so that each person’s rate of return rose by, say, 5 percentage points. There are a couple ways to justify the assumption of a proportionate increase.

One way is measurement error in the amount of human capital. Those with high apparent return may actually have more human capital. They might have attended better schools. Or they might have taken courses with low consumption value and high investment value (accounting rather than modern cinema). In this case, even if the return to human capital is the same across people, the apparent return will differ, and it will differ more when the return rises.

A second, more intriguing justification is to draw an analogy to the Capital Asset Pricing Model. Like physical capital, human capital differs in riskiness. Some human capital has a high beta (such as an MBA), and some has a low beta (such as an MD). When the market return to human capital increases, the impact is larger for high-beta capital.

Is the phenomenon illustrated with this example representative of what is happening with the recent increase in inequality in the U.S. economy? I don’t know. In this example, inequality increases more for those with human capital than for those without. That is, the change in inequality is a positive function of human capital. I don’t know if this is also occurring in the U.S. economy, but I will bet a nickel it is. If any reader knows the answer, please let me know.

Here is one reason I am intrigued by this hypothesis. According to the Piketty-Saez data, inequality was particularly low in the early 1970s. That was the time when my Harvard colleague Richard Freeman was writing his book “The Overeducated American,” arguing that the return to human capital had fallen so low that we should reconsider its value. Maybe that period was the flip side of the recent phenomenon of increasing inequality and an increasing skill premium.

written by Gregory Mankiw