On the Measurement of Human Capital

It can explain somewhere between 0 and 100 percent of income differences between countries

Human capital is the accumulated skills of a people. Like physical capital, we can invest in it and save it, and it will eventually depreciate with senescence and death. As we gain more of it, we are able to produce more, but there are declining returns – eventually we will have spent so much time in training that we never get around to producing.

Like physical capital, it is quite difficult to measure, especially in a way which will allow us to make arguments about what its effects actually are. Suppose we want to know how much a country should invest into education. To answer this, we might start by trying to find how well human capital predicts higher incomes in a country. This is the contribution of Mankiw-Romer-Weil (1992), which really set off the modern literature on human capital in explaining differences in country growth.

They start with the Solow Model, where a country’s GDP is a function of capital and labor, times the residual A, which represents efficiency. Capital and labor are raised to the exponents alpha and 1 minus alpha, which makes this Cobb-Douglas form (having the exponents sum to one gives us constant returns to scale). Capital per person is a function of however much is saved out of total output, reduced by population growth and depreciation. They plug in the estimated capital per person for different countries, and estimate how strongly it predicts country performance. It does fairly well, explaining about 65% of a country’s income.

They then augment the Solow Model with human capital, which they think of as a part of A multiplying labor. Again, all the exponents sum to one, so you have constant returns, and the sum of the exponents of capital and human capital are kept less than one, so that there is a steady state. (Suppose that there were no share going to labor. Then the income of countries would grow without bound, and there would be no convergence.) They use “years of education” as their measure of human capital, and find that it and physical capital explain 82% of differences in income across the world.

Their conclusion is that, while modeling investment into and the discovery of new technology is plausibly important, it isn’t necessary to explain most of the differences in wealth and income between countries. Countries are poor both because they lack physical capital, and because they lack human capital, and accumulating both will plausibly lead to higher income. Interventions which seek to raise the level of education in a country would be extremely beneficial. It also suggests that immigration would have little effect on wages, because income is determined by the skills of a country.

There are a few problems with this approach. First, it is not well-identified if education is actually leading to higher wages, or if countries invest in more education as they get richer. It is possible that the actual contribution of education is minimal, and that people would be accumulating skills outside of school on their own. Second, their measure of human capital is not necessarily measuring human capital at all, or measuring it in the same way across countries. This relates back to the issue of identification, because we can’t even take the estimate of private returns to education as representative of the social return. Education could simply signal higher capabilities, or it may be a licensing scheme for government jobs. Third, the regressions in MRW imply very different factor shares from what is implied by microestimates.

Pete Klenow and Andres Rodriguez-Clare’s 1997 “The Neo-Classical Revival in Growth Economics: Has It Gone Too Far?” is the most famous paper to question this. Human capital accumulation could spuriously explain economic growth if the policies which encourage greater productivity also encourage greater human capital accumulation. They instead pin down the coefficients first, which they do by estimating the returns to an additional year of education, and only then see how much human capital accumulation can explain. They find a much larger residual, because each year of education is associated with a much higher national income gain than an individual income gain. (These results were anticipated in Mankiw-Romer-Weil though, who note that their regression results imply a much different value of alpha than what microeconomic evidence suggested.)

So what gives? It is perfectly plausible for human capital to have positive spillovers, such that the individual returns are smaller than the social returns. A simple example of when this might occur can be taken from Michael Kremer’s “The O-Ring Theory of Economic Development”, when production depends upon multiple links in a chain. An investment in improving the quality of one person may be worthwhile only if everyone else is also investing in improving their quality. This is referred to as “complementarities” – concretely, the returns to learning how to be a software engineer are going to be much larger if other people are learning how to design computers, manufacture computers, repair computers, make an operating system, and so on.

Workers might come in different types, and there is limited substitutability from one role to another. The prior work is assuming that everything can be divided into equivalent units of unskilled labor, such that one skilled person might be substituted for by some number of unskilled workers. If you break this, and make worker productivity depend upon other workers productivity, then human capital can explain a very large portion of income again. The key paper to read here is Ben Jones’s “The Human Capital Stock: A Generalized Approach”, with Chad Jones’s 2011 paper “Intermediate Goods and Weak Links in the Theory of Economic Development” being recommended reading as well. Even here though, identification is poor. Ciccone and Caselli point out that (Ben) Jones’ arguments are dependent on assuming individual wage premiums are solely due to the attributes of individual workers. With changes in assumptions, differences in human capital are now able to explain somewhere between 0 and 100 percent of income differences between countries.

Interestingly, if you allow for workers to be non-substitutable, then immigration can substantially increase output, in spite of the fact that human capital accumulation can explain more of growth between countries. The latter is because it increases the effective variance between countries, and the former because immigration frees up high-skilled workers to best use their skills. A low-skilled worker working as a nanny might allow someone to work a very high-paying job, where otherwise they would have been raising their kid directly.

Now onto some various and sundry issues. It is also worth pointing out here that measures of human capital do not exhibit random error. Years of education is a fuzzy proxy for skills gained at best, and students in developing countries learn less per year of education than those in the developing world. This is extremely well-supported, so I will only give a brief overview, but take for example Justin Sandefur and Dev Patel, who combine standardized tests from around the world in order to make them comparable to each other in “A Rosetta Stone For Human Capital”. Even when people have the same total income, not merely relative income, people in richer nations score higher. This is the consensus; it is extremely common to see noted in RCTs on education in the developing world the very poor performance of students relative to their years of education.

A round-about way of measuring this would be the gains to immigrants from wages, and their effects on local labor market conditions. Note that this method is extremely imperfect, of course – if the reason why higher human capital leads to higher income is through effects on national politics, then we would of course be totally unable to pick up on this. If it doesn’t affect local wages one way or the other, but does increase immigrant wages and increase output, then allowing the immigration is obviously good. Michael Clemens (2013) uses winning the lottery for an H-1B visa to measure the effect of location on wages. Otherwise identical workers in the software industry, despite the good being perfectly tradeable and (I cannot emphasize this enough) working for the same companies either way, earn substantially more. Hendricks and Schoellman (2018) compare the differences in migrants personal wage gains with the difference in incomes between countries, and attribute 40% of the wage gains to differences in institutions.

We can also try to use the literature of the spillovers from education. However, this literature is largely bad. This is not the fault of the researchers – it is an important but difficult to answer question, and so our best shot will likely involve somewhat implausible instruments – but we really shouldn’t be confident in our answer here. The spillovers of an additional year of average education range between nothing (Acemoglu and Angrist, 2000) and 25% (Moretti, 2004). They aren’t even directly comparable estimates, because Acemoglu and Angrist are using changes in high school drop out ages, and Moretti is using the presence of a land-grant college as an instrument for college educated population. I am absolutely inclined to believe that there are positive spillovers from education, although I am not inclined to believe that they are of such nature that adding lower-skilled workers to an area would lower wages.

My takeaway from this is that there is a considerable muddle. This isn’t necessarily surprising, because it is a question for which it is hard to identify a clean answer, but there is enough for someone of essentially any view to make a reasonable argument. There is one thing, however, which I can say with certainty. There is no solid argument against allowing high-skilled immigration. They have spillovers onto other workers, are more likely to gain from close collaboration, and won’t plausibly affect institutions for the worse.