Can cross-country income differences be explained by differences in skills?

An homage to the B+ research designs that help us make progress on big questions

Why are some countries so rich and others so poor? Why do people earn so much more in some countries than in others? Economists like to ask big questions like these. In the old days, we would advance sweeping theories of everything in a single paper (or book). These papers had grand titles like “The Use of Knowledge in Society”, “The Role of Monetary Policy”, or “On the Mechanics of Economic Development”.

Maybe I’ll title my next paper “Das Humankapital”.

Economic science has matured considerably over the last century. This is good overall but has led to a significant scaling back of our ambitions. The latest issue of the Quarterly Journal of Economics includes papers about the impact of deciding not to prosecute misdemeanors in Suffolk County, MA; the impact of vehicle air pollution standards imposed by the Clean Air act of 1967; and the optimal visual presentation of results from regression discontinuity designs (These are all fantastic papers, and I’ve written many papers on specialized topics myself. If you are one of the authors, please don’t get mad at me!).

The classic papers of yore advanced important theories that made us think differently about the world, but the evidence supporting their arguments was often quite speculative. Today, top econ journals like QJE ensure that each of the papers they publish is near-perfectly executed and incredibly convincing. They just answer smaller questions. 

This is overall a good thing for science. No single paper should convince anyone of anything. Rather, we are pointed toward the truth by a cumulative body of work to which many scholars have contributed. Since these scholars have different strengths and various points of view, we can be more confident in their collective wisdom than in any one person’s grand theory.

In economics, the best is sometimes the enemy of the good

Still, there is one thing about modern economics that bothers me. If we accept the premise that most papers should make an incremental contribution to answering a big, important question, there are at least two ways to accomplish the goal. The first way is to lock down some small part of the parameter space with near 100% confidence. For example, suppose I am interested in the big question – “how important is human capital to explaining cross-country income differences?” I can make an incremental but valuable contribution by obtaining a credible causal estimate of the return to education in some country at some point in time. If enough papers do this, we can stitch the evidence together to try and answer the big question.

The second option, less often pursued, is to address bigger questions with a “B+” research design.¹ In my experience this is a hard row to hoe, because readers instinctively want to make an up or down judgment about whether to believe the story told by a paper. There are some questions for which a clean experiment is unlikely to ever be available, so we must do our best with what we have. I worry that professional incentives lead us to underprovide papers that ask important questions with imperfect research designs. I think we learn a lot when many good-but-flawed results points in the same direction.

Today I want to talk about a criminally underrated paper that uses a B+ research design to answer the big question “how important is human capital to explaining cross-country income differences?”. That paper is “Human Capital and Development Accounting: New Evidence from Wage Gains at Migration” by Lutz Hendricks and Todd Schoellman.²

Development Accounting - like nailing Jell-O to the wall

To understand why this paper is so valuable, you first need a little context. There are two approaches to figuring out how much human capital “matters” for cross-country income differences. The first is to estimate cross-country regressions of income growth on schooling and other covariates. The classic reference here is Mankiw, Romer and Weill (1992), who augment a Solow growth model to allow for the accumulation of human capital as well as physical capital. Using data from 98 countries between 1960 and 1985, they estimate strong correlations between average levels of schooling across countries and GDP growth over the 25-year period.³

The obvious problem with cross-country regressions is that differences in schooling probably covary with other determinants of growth such as technology adoption, institutions, and other factors.

The second approach is development accounting, which asks how much of the cross-country variation in income can be statistically explained by human capital. Here the burden is on the data – any income differences that are not explained by schooling get attributed to total factor productivity, sometimes called the “Solow residual” because no one ever actually measures it.

The problem with development accounting is that your results end up being incredibly dependent on measurement and on unverifiable assumptions about the structure of the aggregate production function.⁴ First, you must assume that labor markets are perfectly competitive, despite the raft of recent evidence to the contrary. Second, you must assume something about how workers with different amounts of education substitute for each other in production. Most readers won’t care about these details, but if you do, read the footnote.⁵

What does all this mean for the importance of human capital in development accounting? Jones (2014) and Caselli and Ciccone (2019) debate the credibility of different assumptions about the structure of the aggregate production function. Collectively they conclude that human capital explains somewhere between 0 and 100 percent of cross-country income differences. This is not very helpful.

The larger point is that development accounting demands a lot – perhaps too much – of the data. What one really wants is a natural experiment (or even better, multiple experiments) that identifies one or more parameters of the aggregate production function. An ideal - but unrealistic - experiment would vary a country’s total factor productivity (e.g. the Solow residual) or its human capital stock, holding the other factor constant, and see what happens to cross-country income differences.

The wage gains from migration

Hendricks and Schoellman (2018) provide a very clever approximation by studying the wage gains from migration. If you are willing to assume that skills travel with the individual who migrates, then we are observing a change in the Solow residual holding human capital constant. We can then compare the wage gains for migrants to average income differences across countries and ask how much of the overall difference is “explained” by human capital.

Here is a simple example. Average wages in the United States are about twice as high as in Poland. If this difference is due entirely to average differences in human capital across countries, then a person who migrates from Poland will earn the same amount in the U.S., because they have the same amount of human capital. If income differences are all about productivity or institutions (e.g. U.S. firms are more efficient, or the U.S. labor market is more dynamic), then the incomes of Polish migrants will roughly double when they come to the U.S. Anything in between gives us a sense of how much human capital matters.

Hendricks and Schoellman measure pre- and post-migration wages of U.S. migrants using the New Immigrant Survey (NIS). They find that migrants to the U.S. from poor countries experience wage gains equal to about 40 percent of the total GDP-per-worker gap in each source country, implying that the remaining 60 percent is accounted for by human capital.⁶

Now, the caveats. What if skills don’t fully transfer across countries? They look at a subset of immigrants who come to the U.S. on employment visas, have job offers in hand, and work in the same occupation as they did in their origin countries. Even in these cases, they estimate that human capital accounts for 50 percent of cross-country income differences. The decision to migrate is hardly random. People may choose to migrate precisely because they have high expected earnings gains. This would tend to understate the importance of human capital. Finally, one could be concerned about data issues like the short amount of time pre- and post-migration over which wages are observed in the NIS, truthful reporting of pay, and differences in purchasing power.

And yet, it’s hard to see how we are going to do better! We can’t randomly assign countries to different levels of technology, nor can we force people to migrate en masse to satisfy the whims of social scientists. Studying the wage gains from migration introduces a lot of issues and is hardly a clean experiment. The research design might get a B+ by the standards of applied microeconomics, but Hendricks and Schoellman (2018) get an A+ in my book for pushing the scientific frontier forward.

Notably, their approach gives us an omnibus measure of the importance of human capital. By contrast, standard development accounting models ask how much of cross-country income differences can be explained by proxies for human capital like years of completed schooling. Migrants don’t just bring their schooling with them, but also everything else they’ve learned outside of school, including on-the-job training, social learning, and everything else that is hard to measure. Thus, it’s not surprising that Hendricks and Schoellman find larger estimates of the importance of human capital than other work. They are capturing all aspects of human capital that affect earnings, not just schooling.

1. To be clear, the B+ grade is relative to modern empirical standards. I’m not suggesting that we go back to running two million regressions.

2. Is the paper really underrated if it was published in the QJE, the top journal in economics? The paper was published in 2018, yet it’s *only* been cited 149 times. In my opinion, it’s the most credible validation of the importance of human capital for explaining income differences across countries. Considering that multiple scholars have won Nobel Prizes for trying to answer questions like this one, I think the paper should probably receive more attention.

3. Given the positive relationship between schooling, institutions and technology adoption, the omission of good measures of each is likely to bias upward the impact of schooling on growth – see Klenow and Rodriguez-Clare (1997) and Hall and Jones (1999) for details.

4. Rossi (2020) finds that cross-country differences in schooling and academic achievement can explain between 7 and 20 percent of earnings differences between the U.S. and poor countries and 20-40 percent between the U.S. and richer countries. Adding differential returns to work experience greatly increases the contribution of human capital, sometimes fully explaining cross-country income differences.

5. Most papers in the development accounting literature assume that workers with different amounts of education are perfect substitutes for each other, which allows one to equate marginal products with wages and to “add up” a country’s human capital stock using aggregate data. While perfect substitution is a convenient modeling assumption, it is at odds with the evidence. A well-established literature in labor economics shows that the ratio of wages between skilled and unskilled workers (often called the skill premium) has responded to shifts in the relative supply of skilled workers over time. The Katz-Murphy “education race” model I discussed two weeks ago estimates an elasticity of substitution of around 1.5. Other studies estimate long-run elasticities of substitution of around 4.

6. Previous papers by the authors compared post-migration wages of immigrants from poor vs. rich countries but did not use pre-migration earnings data. This turns out to be important because immigrants are overall highly selected on education and wages, and the degree of selection is much greater for immigrants from poorer countries. The most sampled poorer countries were India, the Philippines, China, Ethiopia, Nigeria, and Vietnam. In a 2021 follow-up paper, the authors use the wage gains from migration to calibrate development accounting models with different degrees of substitution. They estimate that human capital explains between 50 and 75 percent of cross-country income differences, depending on model assumptions.