metadata: authors: 0: author: Rossi,Federico
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docna: 0: docna: Human Capital and Macro-Economic Development
            : A Review of the Evidence
docty: Policy Research Working Paper
subtopic: Health Care Services Industry,Skills Development and Labor Force Training,Labor Markets,Rural Labor Markets
teratopic: Industry,Social Protections and Labor,Rural Development
abstracts: cdata!: This paper reviews the evidence on the
            importance of human capital for macro-economic development.
            Through the lens of a simple aggregate production function,
            human capital might increase output per capita by directly
            entering in the production process, incentivising the
            accumulation of complementary inputs and facilitating the
            adoption of new technologies. The paper discusses the
            advantages and limitations of three methodological
            approaches that have been used to evaluate the importance of
            these channels: cross-country regressions, development
            accounting and quantitative models. The key findings in the
            literature are reviewed, and some of them are replicated
            using updated data. The bulk of the evidence suggests that
            human capital is an important determinant of cross-country
            income gaps, especially when its measurement is broadened to
            go beyond simple proxies of educational attainment. The
            paper concludes by highlighting promising avenues for future work.
repnme: repnme: Human Capital and Macro-Economic
            Development : A Review of the Evidence
display_title: Human Capital and Macro-Economic
            Development : A Review of the Evidence
listing_relative_url: /research/2018/11/30624288/human-capital-macro-economic-development-review-evidence
topicv3: Education, Skills Development and Labor
            Market m1326135 1484,Labor Markets m1326488 855,Unskilled Workers m1504036 2733,Human Capital Accumulation m1504139 2816,Health m1504661 3480
publishtoextweb_dt: 2018-11-19T00:00:00Z
historic_topic: Industry,Social Protections and Labor,Rural Development
no_of_pages: 41
author_keys: 0: author_key: 1631102
model_extractions: WPS8650 Policy Research Working Paper 8650 Human Capital and Macro-Economic Development A Review of the Evidence _Federico Rossi_ Human Development Global Practice November 2018
Policy Research Working Paper 8650

# **Abstract**

This paper reviews the evidence on the importance of human capital for macro-economic development. Through the lens of a simple aggregate production function, human capital might increase output per capita by directly entering in the production process, incentivising the accumulation of complementary inputs and facilitating the adoption of new technologies. The paper discusses the advantages and limitations of three methodological approaches that have been used to evaluate the importance of these channels: cross-country regressions, development accounting and quantitative models. The key findings in the literature are reviewed, and some of them are replicated using updated data. The bulk of the evidence suggests that human capital is an important determinant of cross-country income gaps, especially when its measurement is broadened to go beyond simple proxies of educational attainment. The paper concludes by highlighting promising avenues for future work.

This paper is a product of the Human Development Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The author may be contacted at Federico.Rossi@warwick.ac.uk.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Human Capital and Macro-Economic Development: A Review of the Evidence**<sup>_∗_</sup>

Federico Rossi<sup>_†_</sup>

> _∗_ This paper was written while I was a Short-Term Consultant to the Human Development Practice Group at the World Bank. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The author may be contacted at federico.rossi@warwick.ac.uk. The author is grateful to Ciro Avitabile, Roberta Gatti and Aart Kraay for useful comments and suggestions.

> _†_ University of Warwick and Johns Hopkins University - SAIS. Corresponding address: University of Warwick, Department of Economics, Coventry, CV4 7AL, UK.
# **1 Introduction**

Does human capital contribute to economic development? If so, how much? And through which channels? Different declinations of these questions have played a central role in the macro-development literature of the last few decades.

Credible answers are needed to inform several policy debates. At a broad level, the degree to which gaps in human capital, as opposed to other factors of production and technology, explain cross-country differences in income per capita is informative on the extent to which growth-promoting policies should focus on education and skills formation. Moreover, understanding which dimensions of human capital are particularly lacking in developing countries and why is necessary to guide the formulation of concrete policy interventions.

This paper discusses the academic literature on the links between human capital accumulation and aggregate economic performance. I consider several methodological approaches that have been used to analyse different aspects of this complex relationship: cross-country regressions, development accounting and quantitative models. Rather than offering an exhaustive list of all papers in these areas, I focus on a general discussion of the underlying assumptions, advantages and limitations of these approaches for evaluating the role of human capital, as well as of the broad insights that have emerged in several decades of research.<sup>1</sup> Moreover, I replicate and illustrate some of the key results using recent data.

A significant part of the debate concerns the definition of human capital. Traditionally, economists have concentrated on years of schooling and other measures of educational attainment. However, several pieces of evidence suggest that this focus on schooling quantity misses important dimensions of the variation in human capital, both at the individual and the aggregate levels. As a consequence, recent work gives a more central role to schooling quality on one hand, and human capital accumulated outside of the schooling system on the other.

Across countries, observable proxies for human capital are strongly correlated with measures of aggregate economic performance, explaining the prominence of this theme in the development debate. Figure 1 shows average years of schooling completed in the workingage population against log GDP per worker in 2010. There is a positively sloped relationship, and the cross-country gaps in educational achievement appear large. A similar pattern emerges when focusing on a direct measure of cognitive skills, the average performance in standardized tests (Figure 2), or on a proxy for the health status of the population, the survival rate to age 65 (Figure 3).<sup>2</sup>

> 1Previous reviews on cross-country growth regressions and development accounting include Klenow and Rodr ́ıguez-Clare (1997a) and Caselli (2005), while a related discussion on human capital is Flabbi and Gatti (2018). Compared to these works, the present review focuses in greater detail on recent contributions in the development accounting and quantitative modeling literatures.

> 2The sources and construction of these variables are discussed below.

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While suggestive, these correlations are not necessarily informative on the role of human capital for economic development. On one hand, the relationship might not be causal in nature, as third factors might explain cross-country differences in both human capital and GDP per worker, and the latter might also explain the accumulation of the former. Moreover, several dimensions of human skills are inherently difficult to measure, and the proxies considered here might miss an important part of the picture. Finally, even a positive and causal relationship between average human capital and development would not be fully informative on the potentially complex role of human skills in the production process.

The approaches reviewed in this paper attempt to overcome these problems through different strategies. As a background for the discussion of these methodologies, I start by sketching in Section 2 a simple production function framework which highlights how human capital can affect aggregate economic performance.

Section 3 reviews results from the cross-country regressions approach, which consists of relating measures of economic performance and human capital in a regression model. Section 4 discusses development accounting, a methodology based on the direct calibration of an aggregate production function (rather than its estimation). Here I also replicate some of the key results in this literature using data from 2010. Section 5 reviews some of the key insights from quantitative models on the accumulation and allocation of human capital. Finally, the last Section concludes by drawing general lessons and highlighting avenues for future work.

# **2 A General Framework**

The starting point for most macroeconomic analyses on the effects of human capital is the postulation of an aggregate production function, The aggregate production function relates GDP ( _Y_ ) to the amounts of physical capital ( _K_ ), human capital ( _H_ ) and technology ( _A_ ) available in the economy. In the simplest specification, aggregate human capital is the sum of the human capital of all workers, that is _H_ “ _hL_ where _h_ is the human capital of a representative worker and _L_ is the number of workers. Alternative specifications assume that _H_ is a more complex aggregator of different types of workers.

A common choice for the _F_ aggregator is the Cobb-Douglas function, 3
which is characterized by constant returns to scale. Under competitive markets for factors of production, _α_ is the physical capital share of income, while 1 - _α_ is the human capital share. The fact that these shares are approximately constant both in the US time-series and in the cross-section provides a justification for the Cobb-Douglas assumption. Moreover, estimates of these income shares reprensent useful benchmarks for the estimation or the calibration of the production function.

Cross-country comparisons of standards of living are normally based on differences in GDP per worker, _y_ “ _Y_ { _L_ . Broadly speaking, there are three main ways human capital plays a role in shaping these cross-country differences.

First, there is a direct effect implied by the fact that _H_ is a factor of production. Countries with higher levels of human capital per worker have, mechanically, higher levels of GDP per worker (or, equivalently, growth rates of GDP per worker are positively related to growth rates of human capital). Higher levels of human capital per worker can be achieved through human capital accumulation at the individual level as well as, depending on the specific human capital aggregator, through different combinations of heterogeneous workers.

Second, if human and physical capital are complementary in production, a larger availability of the former encourages the accumulation of the latter. The degree of complementarity might depend on the composition of both _K_ and _H_ . For example, the empirical evidence suggests that computers are more complementary with human capital than other types of equipments (Caselli and Wilson, 2004), and capital equipment appears to complement more college-educated workers than less skilled labor (Krusell et al., 2000).

Third, endogenous growth models emphasize that technological innovations, i.e. changes in _A_ over time, are determined by a number of economic forces, including the availability of human capital. In particular, human capital is seen as instrumental in the development, adoption and operation of new technologies (Nelson and Phelps, 1966). In the context of an aggregate production function like (1), this effect can be captured by assuming that rate of change of _A_ is a function of _H_ . A direct implication is that the level of human capital at a given point in time affects the growth rate of GDP per worker over subsequent periods.

To summarise, a simple aggregate production framework suggests several mechanisms through which human capital can affect aggregate economic performance. Human capital directly enters in the production process, encourages the accumlation of complementary inputs and facilitates the adoption of new technologies. Through these channels, human capital gaps should be reflected in cross-country differences in GDP per worker levels and growth rates. The rest of the paper discusses alternative approaches to investigate the empirical relevance of these predictions.

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# **3 Cross-Country Regressions**

In the growth literature, the earliest studies on the importance of human capital and other factors of production were based on cross-country regressions. This approach was originally motivated by the purpose of testing the predictions of the Solow-Swan model. While the first contributions mostly focused on physical capital, starting from Mankiw et al. (1992) there was a burgeoning of studies examining the importance of human capital.

Broadly speaking, the approach consists of running a regression of GDP per worker on proxies for physical and human capital per worker. This regression is normally run using logs, since the Cobb-Douglas production function implies a linear relationship between the logarithms of output per worker and factors of production. Technology is treated as unobservable, and as such is part of the residual. The main objects of interest of this type of analysis are the coefficients on the proxies for human and physical capital as well as the R squared, which provides an estimate of the share of cross-country variation in GDP per worker “explained” by observable factors of production.

The vast majority of the studies employing this approach have traditionally focused on educational attainment as a measure of human capital. More recently, however, strands of the literature focusing on alternative dimensions of human capital have developed. In the next subsections I consider in turn these lines of work.

## **3.1 Educational Attainment**

Mankiw et al. (1992) is an early implementation of the cross-country regression approach. This paper considers a version of the Solow model augmented with a process of human capital accumulation, and estimates a specification based on the steady state expression for output per worker in that model. In the authors’ preferred specification, GDP per worker is regressed on the fraction of the working age population enrolled in secondary school (a proxy for the rate of human capital accumulation), the saving rate and the rates of capital depreciation, population growth and productivity growth.

The results are supportive of an important role for human capital. The coefficient on the human capital variable is positive and highly significant. When all controls are included, the R squared of the regression is 78%, suggesting that proxies for physical and human capital account for most of the cross-country variation in GDP per worker. Moreover, in a specification based on the transitional dynamics of the Solow model, human capital is positively related to GDP growth between 1960 and 1985 (conditional on the starting level of GDP, as well as on the other determinants of the steady state income per worker).

These conclusions have been disputed in successive work. The identification assumption in Mankiw et al. (1992) is that measures of physical and human capital are uncorrelated 5
with unobservable determinants of cross-country differences in economic performance. As pointed out in Klenow and Rodr ́ıguez-Clare (1997b), countries with policies discouraging capital accumulation are also likely to have in place policies or institutions discouraging technology adoption. This would lead to a violation of identification assumption in Mankiw et al. (1992), where the level of technology is treated as unobservable.

Various approaches have been proposed to overcome these identification challenges. Islam (1995) adopts a panel data approach, where time invariant “country effects” are added to the dynamic specification of Mankiw et al. (1992). To the extent that the common drivers of capital accumulation and technology adoption are indeed fixed over time, they are captured by these country effects and do not spuriously inflate the contribution of physical and human capital to output per worker. In this setting, Islam (1995) finds that proxies for human capital are not strongly related to output per worker, questioning the empirical relevance of the Solow model with human capital accumulation. While levels of school enrollment are positively related to levels of GDP per worker, the relationship is much weaker when introducing the temporal dimension.

This approach is itself subject to a number of issues. First, the least squares estimation of dynamic panel model including fixed effects is generally biased, as showed by Nickell (1981). Second, temporal comparisons are particularly sensitive to problems in the measurement of human capital. Given that average school attainment at the country level changes slowly over time, short-run fluctuations are likely to be mostly driven by measurement error. Indeed, Lindahl and Krueger (2001) argue that commonly used international data on educational attainment are subject to problems of incompleteness, imprecision and lack of consistency across countries. Cohen and Soto (2007) show that when using a more accurate dataset on average years of schooling across countries, increases over time in this measure of human capital are in fact positively related to GDP growth.

Other authors attempted to solve the identification problem through instrumental variables. This approach consists of finding variables (instruments) that are correlated with the variables of interest, but not with the unobservable confounders that bias the regression results to start with. By focusing on variation “induced” by these instruments, in principle one can separate the effect of the variables of interest from the one of unobservable factors.

Unfortunately, finding suitable instruments in the context of cross-country regression is a challenging task. A seminal contribution in this direction is Acemoglu et al. (2001). The paper focuses on political institutions, and proposes to identify the importance of institutional quality for economic development by using the mortality rate among European colonizers as an instrumental variable. The logic is that colonizers created extractive institutions in colonies where they could not easily settle, whereas they attempted to recreate European institutions in environments more favourable to their inhabitancy. The main result of the paper 6
is that the cross-country variation in institutions induced by these historical circumstances has a large effect on income per worker.

Using a similar methodology, Glaeser et al. (2004) questions Acemoglu et al. (2001)’s view on the importance of institutional quality for economic development, and argues for a central role of human capital (as measured by educational attainment). The starting point is the observation that European settlers did not just bring European institutions with themselves, but also their human capital. Indeed, Glaeser et al. (2004) show that the instrument used by Acemoglu et al. (2001) is positively correlated with current educational attainment, and argues that institutional quality is a product as opposed to a cause of the process of economic development. This view is supported by a regression specification where institutional quality and educational attainment are simultaneously instrumented for, from which it emerges that educational attainment has a stronger explanatory power for economic performance. This conclusion has been in turn questioned by Acemoglu et al. (2014), which argues that the instruments used by Glaeser et al. (2004) are not valid sources of exogenous variation.<sup>3</sup> Recent work has shifted the focus from a national to a subnational setting. Gennaioli et al. (2013) use data at the regional level across 110 countries to examine the relative importance of human capital and other possible determinants of local economic performance. Within-country comparisons allow the authors to control for unobservable factors varying at the country-level, such as national institutions, national culture and national language. In this subnational regression specification, educational attainment emerges as the most important predictor of regional economic performance. Moreover, Gennaioli et al. (2013) use firm-level data to document that entrepreneurs’ and managers’ human capital plays a particularly important role in explaining differences in firms’ productivity. However, Acemoglu et al. (2014) argue that country fixed effects are not sufficient to eliminate omitted variable biases, and that the measure of institutions used by Gennaioli et al. (2013) misses meaningful subnational variation in institutional quality.

Another study exploiting within-country heterogeneity is Ciccone and Papaioannou (2009). The paper adopts a sectoral perspective to test whether human capital favours technology adoption and growth. The authors use data for 37 manufacturing industries across 40 countries, and show that countries with higher levels of education in 1980 saw faster growth in human-capital-intensive industries (relative to other industries) in the following decades, a period characterised by the rapid introduction of skilled labor augmenting technologies. They interpret this result as evidence that high educational attainment was instrumental in

> 3The instruments used by Glaeser et al. (2004) are a dummy for French legal origin and either settler mortality or population density in 1500. As pointed out by Acemoglu et al. (2014), the rationale behind this empirical strategy is not clearly discussed, and it is even unclear whether the two instruments have distinct explanatory power when considered jointly.

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the adoption of these technologies.

# **3.2 Other Dimensions of Human Capital**

A recent strand of the cross-country regression literature proposes to go beyond measures of schooling quantity and to focus on direct proxies for knowledge and skills. The rationale for this is twofold. On one hand, if school quality varies across countries, a given level of educational attainment implies different levels of human capital depending on where it is reached. Moreover, by construction measures of schooling quantity do not capture skills acquired outside of the schooling system.

Hanushek and Woessmann (2012a) consider international standardized tests in mathematics and science as proxies for the stock of cognitive skills across countries. The authors document that long-run growth rates (between 1960 and 2000) across countries are positively related to the performance in these tests, and that this relationship is stronger and more robust than the corresponding association between economic growth and traditional measures of school attainment. In the baseline estimates, one standard deviation in test scores is associated with a higher average annual growth rate in GDP per worker of two percentage points.

This result is subject to similar identification concerns to those discussed above for crosscountry regressions including education-based measures of human capital. Countries where students perform well in standardised tests might be inherently different in terms of culture or institutions, and these factors might explain their faster growth. Moreover, country-level economic performance itself might have an impact on school resources and students’ learning, leading to concerns of reverse causality.

Hanushek and Woessmann (2012a) provide several pieces of evidence to alleviate these concerns. The authors show that the results are robust to an instrumental variable strategy based on the use of institutional features of the school system as instruments for test performance, and to a specification relating changes in performance over time to changes in growth rates. Moreover, they show that US immigrants from countries with high average test scores earn higher wages than immigrants from countries with low average test scores, but only if they were educated in their home country (as opposed to being educated in the US). They interpret this as evidence for the fact that the schooling system is the crucial factor setting apart high-scoring and low-scoring countries. While the authors acknowledge that achieving a perfectly credible identification is impossible in a cross-country setting, these different pieces of evidence all point towards an important role of cognitive skills for explaining cross-country differences in economic performance.

Another aspect of human capital that has received attention in the cross-country regression literature is health. Since a large micro literature suggests that improvements in 8
health are associated with higher productivity, a natural hypothesis is that variation in health conditions across countries might be associated with differences in economic performance. However, the fact that causality is likely to run in both directions makes empirical inference complicated in a regression setting. Acemoglu and Johnson (2007) propose to use the change in mortality rate predicted by the effect of international health interventions on specific diseases as an instrument. They find that health improvements lead to increases in population and aggregate GDP, but not in GDP per worker.<sup>4</sup> These results highlight that the effects of health on individual-level productivity are not necessarily accompanied by corresponding effects on income per worker. A similar message emerges from Young (2005), which shows that the decrease in population associated to the HIV/AIDS epidemics in South Africa was accompanied by an increase in consumption per worker, despite the enormous human suffering caused by the disease.

## **3.3 Taking Stock**

What do cross-country regressions teach us on the importance of human capital on a macroeconomic scale? While several results are consistent with human capital playing a role in promoting growth, the evidence is too patchy to allow definite conclusions. The identification challenges associated with cross-country regressions are formidable, and even when progress is made towards alleviating those concerns, strong doubts remain on the reliability of the results from a qualitative and, especially, a quantitative perspective.

# **4 Development Accounting**

In light of the identification problems associated with cross-country regressions, researchers have turned to alternative approaches aimed at addressing the importance of capital accumulation for cross-country differences in economic performance. Development accounting is one of them.

The starting point for this approach is the measurement, for all countries at a given point in time, of the stocks of physical and human capital available in the economy. Then, instead of relying on the statistical association between these measures and GDP per worker, the development accountant uses external evidence to determine the appropriate value of the parameters of the production function. With these at hand, it is possible to compute _F_ p _K, H_ q

> 4Bloom et al. (2014) question the methodology and conclusions of Acemoglu and Johnson (2007). The instrument used in Acemoglu and Johnson (2007) is strongly correlated with health conditions at the start of the sample, which might have impacted economic growth in the following decades. Indeed, when Bloom et al. (2014) introduce the initial level of life expectancy as an additional control, the instrument loses any predictive power for subsequent health improvements.

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in (1), and back out the level of technology _A_ to match _Y_ . This strategy mirrors the one of growth accounting, with a focus on cross-country differences at a given point in time as opposed to cross-time variation within a given country.

The typical questions asked are: how much of the cross-country variation in _Y_ is explained by _A_ as opposed to _F_ p _K, H_ q? Do rich countries have more physical and human capital than poor countries? How would the income distribution look like if all countries had the same level of factors of production?

As in the cross-country regression approach, technology is treated as an unobservable residual. However, development accounting does not involve any estimation, and as such it does not rely on implausible assumptions on the orthogonality between observable and unobservable factors of production. On the contrary, by measuring _F_ p _K, L_ q and _A_ independently, the development accountant can test whether capital abundance is correlated with the level of technology, and the relative role of physical and human capital in explaining this correlation.<sup>5</sup> Development accounting does not come without limitations. This approach strongly relies on the postulation of a given aggregate production function and on the precise measurement of factors of production, and as such it is subject to concerns related to the unavoidable approximations associated with these tasks. Perhaps the most important limitation resides in the “accounting” nature of the exercise. Development accounting quantifies the role of human and physical capital as “proximate” causes of development, but has little to say on what is driving the cross-country variation in these factors of production to start with (the “ultimate” causes of development). Relatedly, factor accumulation and technological innovations are interdependent phenomena, and this approach is not well suited to characterise the links between the two, and therefore to ask counterfactual questions on how, for example, technology would respond to improvements in human capital.

In spite of these limitations, development accounting remains a useful diagnostic tool. If one finds that human capital varies greatly across countries, a natural implication is that policies aimed at stimulating human capital accumulation are a promising avenue to promote economic development. Moreover, by measuring different dimensions of human capital in different ways, one can learn which are particularly important for cross-country gaps in economic performance, therefore further restricting the range of alternative policies under consideration.

I consider implementations of development accounting based on the Cobb-Douglas pro5In the cross-country regression approach, technology is estimated as the residual of the best linear relationship between the logs of GDP per worker and proxies for physical and human capital, so that by construction it is uncorrelated with the latter.

10
duction function in (2), which rewritten in per worker terms becomes where _k_ “ _K_ { _L_ and _h_ “ _H_ { _L_ are physical and human capital per worker. Instead of working with (3) directly, I follow Klenow and Rodr ́ıguez-Clare (1997b) and many papers thereafter in rewriting output per worker as a function of physical capital intensity, human capital and technology The logic of using the formulation in (4) for development accounting is as follows. Stan- <u>1</u> dard models of physical capital accumulation predict that increases in _A_ 1 ́ _α h_ induce a proportional increase in _k_ , so that the capital to output ratio is unaffected. By focusing on the cross-country variation in capital intensity, I give “credit” to technology and human capital for the variation in physical capital induced by these factors.<sup>6</sup> In what follows, I focus on two main measures to summarise the importance of human capital in accounting for cross-country differences in GDP per worker. I take the United States as a benchmark country, and for each country _c_ I compute human capital per worker relative to the United States, _hUS_ { _hc_ , as well as the share of output per worker gaps accounted by human capital gaps, where a value of 1 would imply that, everything else equal, equalizing human capital per worker would close the income gap between country _c_ and the United States.

As an additional summary statistic, I consider the the cross-country variance ratio between the logs of human capital and output per worker which, following the terminology in Caselli (2005), I refer to as the “success” of human capital in explaining cross-country variation in economic performance. A value of 0 would reflect equal endowments of human capital across countries, while a value of 1 would be 6The treatment of physical and human capital is asymmetric here, as human capital differences that arise as responses to pre-existing differences in technology or physical capital are not separately accounted for. Given that in what follows I consider different dimensions of human capital, it is unclear what model of human capital accumulation should be used to assess the strength of these responses. For this reason, I chose to not implement any adjustment in this respect. In Section 5 I discuss how more structural approaches shed light on the link between endogenous human capital accumulation and productivity differences across countries.

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consistent with human capital driving the whole cross-country variation.<sup>7</sup> In the next subsections, I consider different alternatives to measure _h_ . The approach is cumulative: I start from from measures based only on educational attainment, and I gradually introduce additional dimensions of human capital to evaluate their relative importance. I use recent data to replicate the main measurement strategies that have been proposed in the literature, and to illustrate their implications in terms of development accounting results.<sup>8</sup>

# **4.1 Educational Attainment**

The first contributions in the development accounting literature focused on years of schooling as a proxy for human capital. As discussed above, this approach holds some promise as educational attainment is positively correlated in GDP per worker. However, by construction it ignores other potentially important sources of human capital accumulation, such as the quality of schooling, domestic upbringing and on-the-job learning.

I consider the following specification, proposed by Bils and Klenow (2000). Human capital per worker is where _sc_ is the average years of schooling completed in country _c_ . The logarithm of human capital per worker depends linearly on _s_ , with _β_ being the slope of this relationship.<sup>9</sup> The calibration of _β_ is based on micro-economic evidence on returns to education. Under the assumption of perfectly competitive labor markets, (5) implies a log-linear relationship between wages and years of schooling. This equation, often referred to as Mincerian after the seminal work of Mincer (1974), has been widely estimated in the labor economics literature. Reviews of the international evidence (Psacharopoulos, 1994; Psacharopoulos and Patrinos, 2004; Caselli et al., 2016) suggest a Mincerian return of 10%, or _β_ “ 0 _._ 10.

Table 1 illustrates the development accounting results.<sup>10</sup> I display _Share_<sup>_US_</sup> _c_ for countries at the 15<sup>_th_</sup> , 30<sup>_th_</sup> , 45<sup>_th_</sup> , 60<sup>_th_</sup> , 75<sup>_th_</sup> and 90<sup>_th_</sup> percentiles of the income distribution as well as

> 7The cross-country variance of log GDP can be additively decomposed between the variances of log human capital, physical capital and technology, as well as all the covariances. Some authors, including Klenow and Rodr ́ıguez-Clare (1997b), consider measures of success for human capital which include some of the covariance terms. Given that these covariances are positive, this would result in a larger success term for human capital.

> 8To measure _y_ , I use GDP per worker in PPP terms for 2010, which I take from version 9.0 of the Penn World Tables. The baseline sample is made of 130 countries for which the data to conduct exercises on educational attainment, health, migration outcomes and imperfect substitution are available. I consider smaller samples when I look at test scores and returns to experience.

> 9Several authors, including Hall and Jones (1999) and Caselli (2005), consider versions of (5) where years of schooling enter non-linearly in the exponent, to match the fact that returns to schooling are often found to be different across levels of educational attainment. These modifications have limited impact on the development accounting results.

> 10I use average years of schooling for the population above 25 from Barro and Lee (2013).

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its cross-country average, and the _Success_ ratio. The second column shows that human capital per worker as measured by (5) is higher in the United States (which represents the 95<sup>_th_</sup> percentile the income distribution) compared to most other countries. For the poorest countries, however, the human capital gap is substantially smaller than the gap in terms of GDP per worker, reported in the first column. As a consequence, _Share_<sup>_US_</sup> _c_ is relatively low for those countries. The pattern is different for countries above the 60<sup>_th_</sup> percentile, for which human capital can account for the majority of the income gap with respect to the United States.

Overall, the limited variation in human capital between the richest and poorest countries leads to a _Success_ ratio of 8.05%. Indeed, most early contributions to the development accounting literature found a limited role for educational attainment which, combined with similar results for physical capital, lead to the conclusion that Total Factor Productivity, _A_ in equation (4), accounts for most of the cross-country dispersion in economic performance (Hall and Jones, 1999; Caselli, 2005). More recent work has challenged this conclusion by considering broader measures of human capital.

# **4.2 Measure of Cognitive Skills**

In this section I consider extensions of the human capital formulation that include direct measures of cognitive skills. A recent strand of the literature incorporates the average performance in standardized tests of either school-age children (Hanushek and Woessmann, 2012b; Hanushek et al., 2017) or working-age adults (Hidalgo-Cabrillana et al., 2017) in development accounting exercises. This approach partially bypasses the problem of identifying the key _inputs_ for human capital accumulation by measuring directly an _output_ of that process. Differences in cognitive skills, as measured by test scores, reflect a combination of school quality (Hanushek and Woessmann, 2012a), parental influence (De Philippis and Rossi, 2016) and characteristics of the institutional environment (Woessmann, 2016).

I adopt the standard assumption that human capital per worker is given by where _tc_ is an average measure of cognitive skills, while _δ_ is a parameter governing the conversion from this measure to human capital.

For cognitive skills, I use the dataset constructed by Hanushek and Woessmann (2012a), who combine results from various standardized tests and express them on a common metric. I integrate this database with additional test results for Latin American countries that the same authors provide in Hanushek and Woessmann (2012b). This leaves me with a sample of 81 countries. While the tests used for the construction of the dataset were administered 13
across different decades and to school-age children only, cross-country gaps in performance are quite persistent over time, suggesting that these measures of cognitive skills are to a large extent relevant for the current labor force as well.

The calibration of (6) is once again based on micro-economic evidence from log-wage regressions. In particular, _δ_ is the coefficient on test performance in a regression that includes years of schooling as a control. It is important to focus on regressions that include both variables as controls, since cognitive skills and educational attainment are likely to be positively correlated, and omitting one will inflate the contribution of the other. I follow the calibration proposed by Hanushek et al. (2017), based on a comprehensive review of the evidence, according to which _β_ “ 0 _._ 08 and, when test scores are express in terms of individual-level standard deviations, _δ_ “ 0 _._ 17.

Table 2 shows the development accounting results. For comparison purposes, I report the results when using educational attainment only (and _β_ “ 0 _._ 10) on the sample of the 81 countries for which test scores are available. Accounting for cognitive skills increases slightly the human capital gap between the United States and the poorest countries, and decreases the corresponding gap between the United States and the other high-income countries. This reflects the fact that the average test performance students in the United States, while substantially superior to the one of students in many developing countries, puts them only at the 65<sup>_th_</sup> of the international distribution. Indeed, measures of cognitive skills are more effective in explaining income gaps between East Asian countries on one hand, the top performers in standardized tests, and low- to middle-income countries on the other (Hanushek and Woessmann, 2012b). Overall, the result of these patterns is that the _Success_ measures increases by about 5 percentage points compared to the specification including educational attainment only.

# **4.3 Health and Experience**

Other strands of the literature have contributed to the development accounting debate by attempting to measure directly different aspects of human capital. In this subsection I focus on health and experience.

Weil (2007) proposes to use the survival rate to the age of 65 as a proxy for the health status of the population. This is an attractive measure, since it implicitly reflects the incidence of all possible types of sources of mortality, and at the same time is available for a large sample of countries. I follow Weil (2007)’s approach in assuming that human capital per worker takes the form 14
where _rc_ is the average health status as proxied by the afore-mentioned survival rate.<sup>11</sup> Implementing the development accounting exercise requires picking a value for _γ_ . One cannot rely directly on microeconomic evidence in this case, since the survival rate is an aggregate statistics and by definition does not vary within countries. Weil (2007) bypasses this problem by exploiting the fact that, over time, the survival rate is strongly correlated with average height, and that height does vary within countries. Specifically, he postulates a linear cross-country relationship between the survival rate _rc_ and average height _vc_ , _vc_ “ _αr_ ` _γrrc_ , as well as a within-country log-linear relationship between wages and individual height, Since _γr_ and _γv_ can be estimated directly, one can identify _γ_ in (7) as _γ_ “ _γrγv_ . I use the estimates in Weil (2007), which imply _γ_ “ 0 _._ 65. Moreover, I use _β_ “ 0 _._ 10 as before.<sup>12</sup> Table 3 shows the development accounting results. Compared to Table 1, human capital varies more between the United States and poor countries. The measure of _Success_ increases to 11.9%, suggesting that accounting for health differences moderately increases the inferred contribution of human capital.

Another potentially important dimension of human capital is labor market experience. The process of learning does not stop at the end of one’s schooling career, and it is reasonable to think that rich and poor countries might offer differential opportunities for human capital accumulation even at a later age.

Traditionally, the development accounting literature dismissed this dimension of human capital on the ground that the _quantity_ of potential experience is not positively correlated with GDP per worker. While life expectancy is higher in rich countries, longer schooling careers imply that individuals in those countries enter later in the labor market. Klenow and Rodr ́ıguez-Clare (1997b) and Caselli (2005) document that on balance this leads, if anything, to a higher average experience in poorer countries. Since the micro evidence suggests that experience is positively correlated with earnings, adding this component by assuming a common return across countries unavoidably leads to a smaller contribution of human capital to income differences.

Lagakos et al. (2016) argue however that returns to experience do vary across countries. The authors estimate the experience-wage profiles of US immigrants, and show that those

> 11I take the survival rate to 65 by gender from the World Development Indicators, and use the gender composition of the population to compute an average rate. All data refer to 2010.

> 12This is potentially problematic as educational attainment and health (or height) are likely to be positively correlated, and therefore the estimate of _β_ “ 0 _._ 10 from Mincerian regression without health controls might already partially reflect the effect of health. While the estimates Weil (2007) refers to for the calibration of _γ_ are conditional on educational attainment, he does not report the corresponding estimates for the education controls. However, reasonable changes to the value of _β_ do not massively affect the conclusions that follow.

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coming from richer countries have higher returns to both US and foreign experience. In a separate paper, they document that a similar gap exists when looking at non-migrants across a smaller set of rich and poor countries (Lagakos et al., 2018). They interpret these results as evidence for the fact that workers born in rich countries accumulate more human capital over their life-cycle, possibly because of differences in the quantity and quality of their education.

I follow Lagakos et al. (2016) in implementing a development accounting exercise based on their country-specific estimates for the returns to experience. I assume that human capital per worker is where _θc_ is the average experience and _φc_ p _._ q is a country-specific function, reflecting different returns across countries. Since most countries in Lagakos et al. (2016)’s sample have between 15 and 19 years of average experience, I simply use the estimated returns for this category. I focus on returns to foreign experience from their baseline specification.<sup>13</sup> Table 4 shows the result. I report the results for the specification using educational attainment only for the 66 countries for which returns to experience are available. Since the estimates are relative to foreign experience for US immigrants, the sample does not include the United States. I use instead France (90<sup>_th_</sup> percentile of the income distribution) as a benchmark country for the computation of both income and human capital gaps.

Accounting for different returns to experience substantially boosts the contribution of human capital. While human capital in France is 47% larger than in Ghana when measured by educational attainment, the gap is of 366% when experience is taken into account. Overall, the success measure more than triplicates, from 9% to 29%. The accumulation of human capital during workers’ career appears to be an important source of cross-country differences in economic performance.

# **4.4 Development Accounting with Migration Data**

In this section I discuss further recent work using migration data to investigate cross-country differences in human capital. The premise of this approach is that when individuals migrate they bring the human capital accumulated in their country of origin, but then face a common technological and institutional environment in the new host country. Therefore, comparing earnings across migrants’ nationalities is informative on the cross-country variation in human capital, since it allows to keep constant the impact of other factors of production. Of course, these exercises need to take into account that migrants are not randomly selected

> 13Lagakos et al. (2016) emphasize that this approach ignores that life-cycle wage growth also depends on the time allocated to human capital investment. They incorporate this aspect in an alternative exercise, disciplined by a Ben-Porath model of human capital accumulation. They find that the resulting contribution of experience to development accounting is marginally lower.

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from the labor force of their country of origin, and that their labor market outcomes in the new host country do not depend solely on their human capital.

The first implementation of this idea is Hendricks (2002). He documents that gaps in terms of average wages between US natives and immigrants from poor countries to the US are relatively small, and concludes from this that the cross-country variation in human capital must be limited. However, subsequent work points out that Hendricks (2002)’s findings are consistent with some degree of positive selection of immigrants and larger cross-country differences in human capital (Seshadri and Manuelli, 2014).

Here I illustrate two recent extensions of this approach. Schoellman (2012) focuses on returns to schooling for foreign-educated immigrants. He shows that in the United States the wage gain associated with an extra year of schooling is higher for immigrants educated in rich countries compared to those educated in poor countries. He infers from this that educational quality is higher in rich countries. This conclusion does not rely on the migrants being representative of non-migrants from the same country, but on the weaker assumption that there is no differential selection either across levels of educational attainment or on returns to schooling. The author provides several pieces of evidence suggesting that these are not major concerns.

Schoellman (2012) proposes a model of endogenous human capital accumulation to construct a mapping between educational quality, as proxied by the estimated returns to education for immigrants, and human capital per worker. In the model, both years of schooling and the Mincerian return are endogenous objects. In equilibrium, higher educational quality increases the former, because of the complementarity between schooling quantity and quality in the human capital production function, but not the latter. The relationship between human capital per worker and average years of schooling can be written as where _β_ is the Mincerian return for non-migrants (common across countries) and _η_ is a parameter between 0 and 1, in equilibrium positively related to the elasticity of years of schooling with respect to education quality. Equation (9) differs from the standard Mincerian specification in (5) only because of the presence of _η_ in the denominator of the exponent. Intuitively, if individuals go to school for longer when educational quality is higher, for a given gap in years of schooling we can infer a larger gap in human capital than what implied by the Mincerian return alone.

The key step for development accounting is the choice of _η_ . Schoellman (2012) estimates this parameter from the observed cross-country relationship between average years of schooling and educational quality, proxied by immigrants’ returns to education. He finds that _η_ “ 0 _._ 5, which implies that the resulting logarithm of human capital per worker is twice 17
as large compared to when educational quality is not accounted for.

The second and third columns of Table 5 show the corresponding development accounting results. Human capital per worker gaps between the United States and poor countries are substantially higher compared to Table 1. As a result, the _Success_ measure jumps from 8% to 32%.

In a subsequent study, Hendricks and Schoellman (2018) use data on wage gains at migration to provide yet another perspective on cross-country differences in human capital. This approach treats human capital as a residual: wage gains at migration are informative on combined effect of technology and physical capital, and the cross-country dispersion that remains after acocunting for these factors can be attributed to human capital. Formally, from the production function in (4) , the wage of a migrant from country _c_ (and corresponding human capital _hc_ ) when working in the US can be written as while the pre-migration wage of the same worker is (10) with _kUS, yUS_ and _AUS_ replaced by the corresponding quantities for country _c_ . It follows that the wage gain upon migration is so that the relative human capital per worker can be found as This approach is not subject to concerns on migrants’ selection, as wage gains are constructed at the level of individual migrants (therefore keeping constant both observable and unobservable human capital). Moreover, the authors do not need to impose any structure on the human capital production function. Since _hc_ is measured as a residual, its variation across countries might reflect a combination of the quantity and quality of education, as well as of all other country-specific inputs relevant for human capital formation.

Hendricks and Schoellman (2018), for confidentiality restrictions, display only the average wage gains across five groups of countries, corresponding to the five quintiles of the GDP per worker distribution in 2005. To implement my version of their development accounting exercise, I assign to each country in my sample the average wage gain of the relevant group (implictly assuming no change in this quantity between 2005 and 2010). The results are reported in the last two columns of Table 5.

Since wage gains upon migration are small relative to GDP gaps, human capital per 18
worker is inferred to vary substantially across countries. Compared to Table 1, human gaps are noticeably higher for countries in the bottom part of the distribution. The _Success_ ratio increases up to 52.5%.

# **4.5 Imperfect Substitution**

All the approaches reviewed so far treat workers with different levels of human capital as perfect substitutes. This is an extreme assumption, as it implies that high- and low-skill labor supply the same type of inputs in the production process, the difference between the two groups being solely a matter of embedded productivity. Empirical studies (mostly with US data) provide evidence against this assumption, since the relative wage of skilled and unskilled workers appears to react to changes in their relative supply, as predicted by frameworks with imperfect subsitutability between the two (Katz and Murphy, 1992; Ciccone and Peri, 2005).

A recent line of work investigates the implications of relaxing this assumption for development accounting. Caselli and Ciccone (2013) show that allowing for imperfect substitutability between skill types necessarily reduces the contribution of human capital, when measured by educational attainment. Intuitively, under imperfect substitutability increasing the share of skilled (highly educated) workers has two effects: an increase of the share of the most productive workers (which increases output), and a decrease in the relative marginal productivity of skilled and unskilled workers (which decreases output). With perfect substitutability the second effect is not present, and therefore the results in Table 1 can be treated as un upper bound for the contribution of schooling quantity in development accounting.

However, imperfect substitutability has implications for the measurement of other dimensions of human capital (beyond schooling quantity). To illustrate this, I consider the simple case where the aggregate human capital stock is a combination of two types of workers, skilled and unskilled, so that human capital per worker can be written as where _lS,c_ and _lU,c_ are the shares of skilled and unskilled workers in the labor force, and _hS,c_ and _hU,c_ represent the amount of labor services supplied by a given skilled and unskilled worker. The aggregator in (11) features a constant elasticity of substitution equal to _ε_ . Assuming perfectly competitive labor markets, the wage ratio between skilled and unskilled workers (skill premium) is 19
The key observation is that, while _lS,c_ { _lU,c_ is substantially higher in rich countries, _wS,c_ { _wU,c_ is relatively flat across countries (Caselli and Coleman, 2006; Jones, 2014; Rossi, 2017). According to (12), for the range of values for _ε_ estimated in the empirical literature, this implies that _hS,c_ { _hU,c_ is higher in rich countries, i.e. that skilled workers are relatively more “efficient” in those countries. Malmberg (2018) confirms this finding through a different empirical strategy, based on the analysis of trade patterns for skilled- and unskilled-intensive manufacturing goods.

The implications for development accounting depend on how we interpret the crosscountry variation in _hS,c_ { _hU,c_ . Jones (2014) attributes this variation to differences in unmeasured human capital (for given levels of educational attainment), and shows that it can dramatically boost the contribution of human capital in accounting for cross-country income gaps. In contrast, Caselli and Coleman (2006) interpret it as reflecting skill-biased technological differences across countries (i.e. firms in rich countries adopting more skilled labor augmenting technologies compared to poor countries), and Caselli and Ciccone (2017) show that under this interpretation the role of human capital for development accounting is much more limited.

Table 6 illustrates these different results. I construct human capital per worker as in (11), where _hS,c_ { _hU,c_ is backed out from (12) using _ε_ “ 1 _._ 5 as estimated by Ciccone and Peri (2005), and where, following the baseline exercise in Jones (2014), I assume that _hU,c_ does not vary across countries. I start by classifying skilled labor as workers with some secondary education, as in Jones (2014) and Caselli and Ciccone (2017).<sup>14</sup> The second and third column of Table 6 show that the amplification of human capital gaps when incorporating the variation in _hS,c_ { _hU,c_ is dramatic. The cross-country variance in human capital is five times larger than the cross-country variance in GDP per worker. This partially reflect an extremely high value of _hS,c_ { _hU,c_ estimated for the United States, where the share of skilled labor is much higher than in poorer countries, while the skill premium is not dramatically different. However, even when taking France as a benchmark (fourth and fifth columns), human capital accounts for the majority or the entirety of income gaps with respect to other countries.

These results are even larger than those reported in Jones (2014). Given that I am using much more recent data, one valid concern is that considering skilled every worker with at least some secondary education might not be appropriate for my exercise. In 2010, according to this criterion, 97% of the US labor force is high-skilled, and in a few other countries

> 14I also follow Jones (2014)’s approach for the construction of skill premia: I impute the wage for each level of eduational attainment using country-specific Mincerian return, and compute _wS,c_ and _wU,c_ as weighted averages across the educational categories belonging to the skilled and unskilled groups. The share of skilled and unskilled workers in 2010 is computed from Barro and Lee (2013)’s data on educational attainment of the population above 25.

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this share approaches 100%. In the sixth and seventh column of Table 6 I show that, when using the completion of secondary school as the minimum requisite for skilled workers, the inferred human capital gaps are somewhat smaller. Still, the main conclusion stands: human capital can account for most or all the cross-country dispersion in income when incorporating the _hS,c_ { _hU,c_ term.

The last two columns show the results of the alternative exercise proposed in Caselli and Ciccone (2017). Here, it is assumed that the variation in human capital only comes from _lH,c_ and _lU,c_ , while _hH,c_ and _hU,c_ are treated as technology terms. I compute for each country the human capital per worker that would result if the shares of skilled and unskilled labor were equalized with those of the United States, and then compare it in the sixth column to _hc_ as computed above. The results suggest that equalizing educational attainment would actually lower _hc_ in most countries, since having the US share of skilled labor would imply _negative_ skill premia given the technology of those countries.<sup>15</sup> The _Success_ ratio is also substantially lower than what implied by Jones (2014)’s exercise.<sup>16</sup> These results suggest that understanding the cross-country variation in _hS,c_ { _hU,c_ is crucial to evaluate whether imperfect substitutability amplifies the role of human capital in development accounting. Rossi (2017) shows that the patterns of skill premia across US immigrants are not consistent with the variation in _hS,c_ { _hU,c_ being driven to a large extent by differences in educational quality or selection into higher education. His results point towards the importance of country-specific technological and institutional factors in shaping skill premia, consistently with Caselli and Coleman (2006). Whether other forms of human capital might contribute the dispersion in _hS,c_ { _hU,c_ is an open area for future reaserch.

# **4.6 Taking Stock**

Development accounting provides a rich picture of the cross-country variation in human capital and its importance for gaps in economic performance. From the approaches reviewed here, a few messages emerge. First, while educational attainment is higher in rich countries, by itself this contributes relatively little to cross-country differences in income. Second, hu-

> 15This calculation ignores that in practice skilled workers might be able to work in unskilled occupations, which they would find profitable in such a scenario.

> 16When _hH,c_ and _hU,c_ are treated as technology parameters, the logarithm of output per worker is not additively separable in human capital and other factors of production. To calculate _Success_ , I define _h_<sup> ̃</sup> _c_ as the human capital per worker evaluated at the sample average of _hS,c_ { _hU,c_ , and use the variance of log _h_<sup> ̃</sup> _c_ for the numerator.

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man capital gaps are more pronounced when dimensions such as educational quality, health and experience are taken into account. Third, approaches that identify human capital as a residual find even larger cross-country differences, suggesting that some important dimensions of its variation are not captured by the available observable proxies.

# **5 Quantitative Theory**

An alternative approach to the ones described above is to use quantitative models to understand how much and why human capital is associated with economic development. This allows to bypass some of the measurement issues associated with development accounting and cross-country regressions. Moreover, models are more suitable to ask counterfactual questions (such as, how much would income increase if a given human capital policy was implemented?), given that they can incorporate general equilibrium effects and the link between policy interventions and the endogenous responses of economic actors.

In this subsection I review the insights from two broad types of models. First, I consider models where human capital is accumulated endogenously, as a response to various economic fundamentals. Second I discuss models on the allocation, within a given economy, of the human capital of heterogeneous individuals and its consequences in terms of the organization of production.

## **5.1 Models of Endogenous Human Capital Accumulation**

Consider the general production function in (1). The models reviewed in this section treat _H_ as the endogenous outcome of human capital accumulation decision. They can be seen as providing a mapping where the human capital stock depends on total factor productivity _A_ , typically treated as exogenous, and a vector of exogenous economic, institutional and demographic factors, _ξ_ . Different contributions in the literature vary on how broad the notion of _H_ is (i.e. years of schooling vs other dimensions) as well as on the factors considered in _ξ_ and the shape of the _g_ p _._ q function.

This structure can be used to ask two types of (related) questions. First, what explains the dispersion in observable components of _H_ , either across countries and over time? Second, for a given dispersion in _A_ and _ξ_ , how much can we infer _H_ as a whole to be varying across countries? The latter is closely related to the development accounting question, though here the direct measurement of _H_ is replaced by the computation of the equilibrium outcome of a human capital accumulation model.

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A seminal contribution in this literature is Bils and Klenow (2000). This paper focuses on educational attainment as the only source of human capital accumulation, and proposes a model where average years of schooling directly responds to future economic growth. This is because the benefit of more schooling is proportional to future productivity (through its effect on future wages), while the cost is proportional to current productivity (through its effect on the opportunity cost of not working). This result, combined with a relatively limited role of schooling in a growth accounting exercise, leads the authors to conclude the correlation between educational attainment and subsequent economic growth is more the result of reverse causality and omitted factors than a causal effect of the former on the latter.

More recent contributions have considered different determinants of educational choices, as well as richer dimensions of human capital accumulation. As pointed out by Cordoba and Ripoll (2013), the mechanism in Bils and Klenow (2000) can account for a small part of the cross-country dispersion in years of schooling. To improve on this, Cordoba and Ripoll (2013) consider a model of educational investment with credit frictions, and find that crosscountry differences in fertility, mortality and access to public education are the most important drivers of the international dispersion in years of schooling. Moreover, by modelling private and public expenditures on educational services, their approach delivers endogenous cross-country differences in the “quality” of schooling, and gaps in human capital per worker larger than those that can be inferred from years of schooling alone.

Other papers assign a more central role to total factor productivity in driving human capital accumulation. Erosa et al. (2010) consider a model where human capital depends on two inputs: schooling time and goods (such as food, health investments, extracurricular activities, and so on). They show that a higher TFP increases the benefit and the time cost of schooling, but not the cost associated with the expenditures on goods. Since their calibration implies a large role for the latter, the model predicts that individuals in countries with higher levels of TFP endogenously accumulate more human capital, therefore amplifying the effect of TFP on output.

Seshadri and Manuelli (2014) find an even larger amplification of TFP differences due to human capital accumulation. Compared to Erosa et al. (2010) and Cordoba and Ripoll (2013), this paper adds post-schooling human capital accumulation, in the form of on-thejob training, and an explicit role for early childhood investments. The authors find that relatively small differences in TFP are associated with large gaps in human capital per worker, and that these gaps are mostly driven by schooling quality (i.e. the amount of human capital accumulated in a given year of schooling) and pre- and post-school investments as opposed to schooling quantity.

Overall, the following key messages emerge from this literature. Across countries, human capital accumulation responds to economic and institutional characteristics, and am23
plifies the effect of gaps in productivity. The key margin of this response is not schooling quantity, but a combination of investments that determine the productivity of a given time spent in school of out-of-school human capital accumulation. This result resounds well with the conclusions from the development accounting literature discussed above.

# **5.2 Models of Human Capital Allocation**

So far, the discussion has focused on the determinants and the variation of average human capital per worker. Recently, several papers have focused instead on the skill heterogeneity within a given economy, and on the various ways this affects and is affected by the process of economic development. Here, I briefly review contributions on the allocation of different types of human capital in the production process.

One key insight emerging from this literature is that frictions preventing workers from pursuing their comparative advantage are harmful for aggregate economic performance. Hsieh et al. (2013) study the consequences of the discrimination against women and blacks in the United States. They consider a model of human capital accumulation and occupational choice, where individuals have heterogeneous talents for different occupations. Blacks and women face barriers that limit both their educational and occupational choices. The entity of these barriers can be inferred from the equilibrium conditions of the model, allowing the authors to evaluate to what extent these frictions have been changing over time. The key result is that the allocation of talent improved substantially between 1960 and 2008, contributing to aggregate wage and productivity growth.

While these results are relative to the US, the misallocation of human talent likely represents an even larger problem in developing countries. Lagakos and Waugh (2013) show that subsistence requirement lead workers relatively unproductive in agriculture to work in that sector, while Jaimovich (2011) argues that the increase in sectoral variety associated with development improves the allocation of entrepreneurial talent. Other factors that haven been linked to human capital misallocation are financial frictions (Buera et al., 2011) and intergenerational occupational persistence (Sinha, 2016). Overall, this line of work suggests that improving the allocation of existing talent might be as important as encouraging the accumulation of new human capital.

Another strand of this recent literature has focused on understanding how the endogenous allocation of production roles across individuals with different skills is related to the process of economic development. Many of these papers build on the seminal contribution of Lucas (1978), which develops a model where the most talented individuals become managers and leverage their human capital by increasing the size of their firms. Roys and Seshadri (2014) introduce two variations to this framework: endogenous human capital accumulation decisions and imperfect substitutability between the quantity and quality of work24
ers. By varying exogenously aggregate TFP, the model is able to account for many crosscountry patterns on the organization of production, such as lower firm and wage growth and higher dispersion in firm and labor productivity in poor countries.

Porzio (2017) studies the interaction between the allocation of talent and technology adoption. He shows that in poorer countries, where firms have the opportunity to import technologies much more advanced than the locally prevailing vintage, the equilibrium allocation features more concentration of talent and more productivity dispersion across production teams. This prediction is supported by the fact that in developing countries workers with different skills, as proxied by educational attainment, are relatively more segregated across different sectors. The model is also able to account for a sizeable part of the larger productivity dispersion across sectors in poor countries.

This line of research is only in its early stages, and still far from definite conclusions. However, these contribution do suggests that the accumulation and allocation of human capital is a key factor in shaping many features of economic development.

# **6 Conclusions**

Economists have studied the relationship between human capital and economic development through a variety of methodologies. While all the approaches reviewed in this paper come with their own limitations, an overarching consideration of their findings does lead to some general lessons.

Human capital is an important ingredient of economic development. By any metric, rich countries are more abundant in human capital compared to poor countries. The gap is particularly meaningful when the notion of human capital is broadened to go beyond educational attainment, and to incorporate differences in schooling quality and out-of-school investments in skills. Moreover, human capital plays an important role in shaping technology, productivity, wages and the firm size distribution along the process of development.

The cross-country dispersion in these forms of human capital calls for a better understanding of their determinants and implications. Differences in early childhood investments, within-family interactions and institutional features of educational systems might all be important factors behind cross-country gaps in economic performance. Better quantifications and characterizations of their roles are promising avenues for future work.

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