Imperfect substitution and development accounting


Published 12.07.18
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Newhouse School of Public Communications

Technological and institutional environments, rather than differences in human capital, are behind variations in skill premia across countries

Low output per worker goes together with low levels of schooling, cognitive test results, and health indicators, naturally leading to the conjecture that low levels of human capital are responsible for low levels of income. This conjecture has contributed to motivating several decades of international focus on policies aimed at increasing the quantity and quality of schooling, as well as improving overall health, in low-income countries.1

The advent of development accounting

Over the last 20 years, several researchers have developed and refined a set of tools, now known as development accounting, that has allowed – among other things – a quantitative evaluation of the hypothesis that human capital is a major driver of the large gaps in income we observe around the world. Time and again contributions in this line of research find a relatively modest role for human capital (e.g. Klenow and Rodriguez-Clare 1997, Hall and Jones 1999, Caselli 2005).

To get a glimpse of why development accounting studies find a small role for human capital, consider the case of schooling differences. Labour economists estimate that an extra year of schooling delivers an increase in wages of about 10%. Under fairly standard ‘neoclassical’ conditions, this is also the increase in human capital associated with an extra year of schooling. Assuming that the aggregate production function has a weight of 2/3 on human capital (as is usually assumed), this means that a country’s income increases by approximately 2/3*0.10=0.066 if its workforce’s schooling increases by one year. Since the income of the richest countries in the world exceeds the income of the poorest by a factor of 100, it is clear that any reasonable increase in years of schooling can make only a relatively small dent in that gap. The model can be enriched by accounting for differences in cognitive skills and health, but the unexplained income gap remains huge (e.g. Weil 2007, Hanushek and Woessmann 2012).

But most development accounting calculations are based on a counterfactual model of aggregate human capital where skilled and unskilled workers are perfect substitutes. So, if some workers become skilled, this has no impact on the marginal productivity of other participants in the labour force. A long labour economics tradition, however, shows convincingly that workers with different skills are imperfect substitutes (Hamermesh 1993, Katz and Autor 1999, Ciccone and Peri 2005). Hence, if a group of workers becomes skilled, this has implications for the marginal productivity of workers who remain unskilled as well as workers who were already skilled. The measurement of aggregate human capital should take this into account.

The implications of imperfect substitutability among workers with different educational attainment

The implications for development accounting of imperfect substitutability among workers with different educational attainment have been considered by Caselli and Coleman (2006), Caselli and Ciccone (2013), Jones (2014), and Caselli and Ciccone (2018). In this column, which is based in particular on Caselli and Ciccone (2018), we attempt to distil the lessons from these studies.

When workers with different educational attainment are imperfect substitutes, we expect the relative wage between workers with different skills to vary across countries in a manner that depends systematically on the relative supplies of such skills. In particular, if there are two skill types – college workers and workers with at most high-school education – we expect the wage premium earned by college workers to be high in countries with relative few college-educated workers and low in countries with an abundance of such workers. Given that the relatively supply of skills varies enormously between rich and poor countries, for plausible values of the elasticity of substitution between skilled and unskilled workers we would expect to observe college premia that are much higher in poor countries than in rich ones. Empirically, however, as originally observed by Caselli and Coleman (2006), the gradient in the cross-country relationship between relative skill supplies and college premia is almost flat, and certainly much flatter than expected based on the reasoning above.

Why are college premia not much higher in (skill-)poor countries? Caselli and Coleman reasoned that there must be some other factor that keeps the relative marginal productivity of skilled workers from declining as the relative skill supply increases. They also noticed that a similar – or indeed an even more pronounced – version of the same phenomenon appeared to be present in the time series for many countries. Since the mid-1980s, college premia have been growing despite a contemporaneous increase in the relative supply of college-educated workers. As there is a broad consensus that the time-series evidence is well explained by skill-biased technical change, Caselli and Coleman posited that the cross-sectional evidence was also likely due to skill-biased differences in technology across countries. A simple model of appropriate technology choice did indeed fit the data well.

In interpreting the force that increases the relative productivity of skilled workers in skill-abundant countries as skill-biased technology, Caselli and Coleman focus on a feature of the economic environment, and not on workers’ characteristics. Jones (2014) reinterprets the evidence in Caselli and Coleman (2006) and ascribes it to traits of the workers. In particular, he reasons that if college premia are as high where skilled workers are abundant as where they are scarce, it must mean that skilled workers have more human capital in skill-abundant countries than in skill-poor countries. In other words, he turns the cross-country variation in wages not explained by the relative supply of workers with different skills into an estimate of the human capital embodied in skilled workers. This allows him to construct a new measure of human capital that takes into account both the quantity of schooling (a relative supply effect) and the efficiency embodied in skilled workers, as retrieved from the unexplained variation in college premia (a relative efficiency effect). Jones finds that defined like this, human capital has the potential to explain the totality of the variation in income across countries.2

Jones’s finding is clearly very striking in light of the previous consensus of a relatively modest role for human capital in accounting for international income gaps. In Caselli and Ciccone (2018), we explain how the result comes about. As just mentioned, Jones’s measure of human capital is driven by variation in both the relative supply of skills and in the relative efficiency of skilled workers. Hence, Jones’s striking success in accounting for underdevelopment with human capital could be because imperfect substitution between skilled and unskilled workers magnifies the role of cross-country differences in the relative supply of skills, or because it magnifies the role of cross-country differences in relative efficiency. 

The effect of cross-country differences in the relative supply of skills in development accounting with imperfect substitution between skilled and unskilled workers is the focus of an earlier paper of ours (Caselli and Ciccone 2013). There, we show that the impact on income of changes in the relative supply of skills is maximal when skilled and unskilled workers are perfect substitutes. In other words, the relative supply effect leads to less – not more – variation in human capital across countries under imperfect substitution than under perfect substitution. Hence, it cannot be the relative-supply effect that boosts human-capital differences when skilled and unskilled workers are imperfect substitutes. Jones's result must therefore be driven by the relative-efficiency effect which, as Caselli and Coleman show, is large for plausible values of the elasticity of substitution between different skills.

The upshot is that when workers with different educational attainment are imperfect substitutes, cross-country differences in skilled-bias efficiency are large for plausible values for the elasticity of substitution. The role of human capital for cross-country income differences varies enormously with the interpretation of these differences in skilled-bias efficiency. In particular, if one is willing to assume that all of the skill bias of efficiency reflects the human capital of more educated workers, then one can convince oneself that underdevelopment is entirely a human capital issue.

On the other hand, the role of human capital for cross-country income differences is diminished to the extent that skill-biased efficiency also reflects technology, institutions, and other features of the economic environment. In the limit, if all of the cross-country variation in the skill bias of efficiency is due to the economic environment, then allowing for imperfect substitution implies that human capital explains even less of the variation in income than was originally thought in the development accounting literature.

So which interpretation of the residual variation in wages is more plausible – skill-biased technological and institutional differences, or human capital? In Caselli and Ciccone (2018), we point to a limit in how far one can go in explaining cross-country differences in income with human capital quality when different types of human capital are imperfect substitutes. Imperfect substitution implies that, other things equal, skilled workers are more productive where there are more unskilled workers. As a result, skilled workers in rich countries could realise large gains in earnings by working in poor countries (with a very abundant supply of unskilled workers) if their human capital quality truly was much greater than that of skilled workers in poor countries. This contrasts with the virtual absence of skilled migration from rich to poor countries. We illustrate this point quantitatively in the context of Jones’s analysis. In particular, we show that for plausible values of the elasticity of substitution between workers with different educational attainment levels, some types of skilled US workers could multiply their earnings by more than tenfold by moving to Jamaica. We also show that this is true no matter what the pattern of complementarity/substitutability among different types of skilled workers may be.

Another contribution that casts doubts on the interpretation of relative efficiency as human capital is Rossi (2018). He estimates country of origin-specific skill premia for immigrants in the US. Crucially, he focuses only on immigrants who were educated in their country of origin. If, conditional on the supply of workers with different educational attainment, wage premia reflect mainly human-capital characteristics, then country of origin-specific skill premia in the US should vary as much as skill premia vary across countries. But Rossi finds that skill premia in the US vary relatively little across countries of origin – an order of magnitude less than they vary across countries. He concludes that residual variation in wages across countries is much more likely to reflect technological/institutional differences than differences in the human capital of skilled workers.


In conclusion, both our back-of-the-envelope calculations in Caselli and Ciccone (2018) and the systematic empirical work of Rossi strongly suggest that differences in skill premia across countries (after controlling for the relative supply of skills) are not due to differences in human capital embodied in skilled workers. Rather, they are more likely to be due to differences in country-specific technological and institutional environments. In turn, this means that the consideration of imperfect substitutability per se does not weaken (indeed, probably strengthens) the conclusions from the existing body of development accounting research, namely, that human capital appears to be a comparatively minor contributing factor to cross-country differences in income.3

Editors' note: This column first appeared on on 9 June 2018.


Caselli, F (2005), “Accounting for Cross-Country Income Differences”, in P Aghion and S Durlauf (eds.), Handbook of Economic Growth, vol. 1A, Elsevier.

Caselli, F, and A Ciccone (2013), “The Contribution of Schooling in Development Accounting: Results from a Nonparametric Upper Bound”, Journal of Development Economics, 104 (1), 199-211.

Caselli, F, and A Ciccone (2018), “The Human Capital Stock: A Generalized Approach Comment”, American Economic Review, forthcoming.

Caselli, F, and J Coleman (2006), “The World Technology Frontier”, American Economic Review 96 (3), 499-522.

Ciccone, A, and G Peri (2005), “Long-Run Substitutability between More and Less Educated Workers: Evidence from U.S. States 1950-1990”, Review of Economics and Statistics,87 (4), 652-663.

Ek, A (2018). “Cultural Values and Productivity”, unpublished, LSE.

Hamermesh, D (1993), Labor Demand, Princeton University Press.

Hanushek, E, and L Woessman (2012), “Schooling, Educational Achievement, and the Latin American Growth Puzzle”, Journal of Development Economics 99(2), 497-512.

Hall, R, and C Jones (1999), “Why Do Some Countries Produce So Much More Output Per Worker Than Others?”, Quarterly Journal of Economics, 114, 83-116.

Hendricks,L, and T Schoellman (2018), “Human Capital and Development Accounting: New Evidence from Wage Gains at Migration”, The Quarterly Journal of Economics, 133 (2), 665–700.

Ilzetzki, E, and S Simonelli (2018). “Measuring Productivity Dispersion: Lessons from Counting One-Hundred Million Ballots”, unpublished, LSE.

Jones, B (2014), “The Human Capital Stock: A Generalized Approach”, American Economic Review 104 (11), 3752-3777.

Katz, L, and D Autor (1999), “Changes in the Wage Structure and Earnings Inequality”, in Ashenfelter and Card (eds.) Handbook of Labor Economics,vol. 3, Elsevier.

Rossi, F (2018), “The Relative Efficiency of Skilled Labor Across Countries: Measurement and Interpretation”, unpublished, Johns Hopkins University. 

Weil, D (2007), “Accounting for the Effect of Health on Economic Growth”, Quarterly Journal of Economics 122, 1265-1306.


[1] Needless to say improvements education and health are desirable in their own right, quite apart from their impact on income per capita.

[2] Caselli and Coleman (2006) discuss the possibility that residual variation in wage premia reflects workers’ quality, or human capital, but find it implausible.

[3] Of course, this still leaves entirely open the question whether there are other approaches to human-capital measurement, other than introducing imperfect substitution, which can boost the contribution of human capital. Recent papers by Hendricks and Schoellman (2018), Ek (2018), and Ilzetzki and Simonelli (2018) use very different strategies to identify significant differences in human capital across countries (or across regions), after controlling for years of schooling. This evidence does not contradict the evidence in Rossi, or our more general discussion. The quality differences identified by these authors appear to affect all skill groups similarly, and so they would not be expected to induce differences in skill premia across countries.