WPS8309


Policy Research Working Paper                  8309




              A Primer on Human Capital
                                Luca Flabbi
                               Roberta Gatti




Human Development Global Practice Group
January 2018
Policy Research Working Paper 8309


  Abstract
 This note summarizes some of the key contributions in the                          human capital affects growth at the aggregate level (sections
 macro- and micro- economic literature on the pathways                              2, 3 and 4). The note then reviews the micro empirical
 linking human capital and income growth. Rather than                               literature estimating labor income returns of human cap-
 completeness, the objective of this work is to distill some                        ital investments (sections 5 and 6). The conclusion draws
 of the most relevant threads in the evolution of these liter-                      comparisons between the two empirical approaches and
 atures using a human capital lens, with a view to provide                          provides a brief critical assessment on how to interpret the
 a useful yet parsimonious conceptual framework and an                              empirical results. Investing in human capital is a promising
 update on empirical results. The note first describes the                          strategy to attain stable and positive growth. The magni-
 human capital model (section 1). It then outlines the                              tude of the effects is country-specific and varies depending
 main theoretical elements of growth theory and presents                            on the population of interest, the policy under consid-
 empirical results from the cross-country regressions and                           eration, and the human capital component considered.
 development accounting literature to gauge to what extent




  This paper is a product of the Human Development Global Practice Group. 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://econ.worldbank.org. The authors may be contacted
  at rgatti@worldbank.org.




         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
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         its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.


                                                       Produced by the Research Support Team
                              A Primer on Human Capital*



                                           Luca Flabbi
                                         UNC-Chapel Hill

                                         Roberta Gatti
                                        World Bank Group




      JEL Codes: O15, O47, J24
      Keywords: Human Capital, Growth, Returns to Education, Development Accounting.




*
  Luca Flabbi: Department of Economics, University of North Carolina -- Chapel Hill, 107 Gardner Hall,
CB 3305, Chapel Hill, NC 27599-3305, luca.flabbi@unc.edu. Roberta Gatti: Human Development Practice
Group, The World Bank Group, 1818 H Street, NW,Washington, DC 20433, rgatti@worldbank.org. We
thank Aart Kraay for thoughtful conversations and Kathleen Beegle and Tito Cordella for very useful
comments. All errors are our own.
1. Introduction

Human capital and growth are linked by numerous pathways and threads. Investing in
human capital affects productivity, productivity affects growth and growth feeds back to
human capital opportunities. Moreover, human capital is a broad concept, which includes
not only education and training but also many other aspects of individual human
development such as medical care, early childhood interventions, intergenerational
mobility.

A complete review of all the relevant literatures and of all the important policy implications
in this area is a daunting task. Instead, this note distills some of the most relevant threads
in the evolution of these literatures using a human capital lens. It provides two main
contributions: a parsimonious conceptual framework that summarizes the theoretical
contributions and a review of the empirical results that integrate macro and micro literature.
The conceptual framework is used to integrate the two strands of the empirical literature,
to provide an interpretation of the results and to guide the policy implications.

The note is organized as follows. The next Section provides a definition of human capital
and a description of the standard human capital model. Section 3 presents the conceptual
framework, first describing a general model of output growth and then adding human
capital. Section 4 reviews the empirical literature, presenting results from both the macro
and micro literature. The first set of results covers cross-country regressions and
development accounting; the second reports evidence following the life-cycle of individual
agents. The section also draws comparisons between the macro and micro empirical
approaches and provides a brief critical assessment on how to interpret the empirical
results.

The last Section contains the main lessons learned from this review: Investing in human
capital is a promising strategy to attain stable and positive growth but the magnitude of the
effects is country-specific and varies depending on the population of interest, the policy
under consideration, and the human capital component considered. The use of micro data
tailored to evaluate the specific policy of interest in the country under consideration, in
conjunction with economic models able to aggregate the micro-level effects is suggested
as the best methodology to inform policy action.


2. What is Human Capital?

2.1 Definition

Human capital includes education, training, medical care, and other additions to
knowledge and health […] accumulated work and other habits, even including harmful
addictions such as smoking and drug use
(Gary Becker, Nobel Prize Lecture: “The Economic Way of Looking at Life”, 1992)




                                              2
As such, investing in human capital is akin to investing in physical capital: one can invest
in the human factor of production with the expectation of economic returns just as one can
invest in the factor of production physical capital.1 Moreover, since human capital includes
“education, training, medical care, and other additions to knowledge and health”, any
policy affecting these areas affects human capital and, ultimately, growth.

The empirical literature, both at the micro and macro level, has measured different aspects
of human capital, mainly focusing on education and years of schooling as the main
component of general human capital and on on-the-job training as the main component of
specific human capital. More recently, there has been a recognition of the importance of
health in affecting general human capital and of the effectiveness of early childhood
investments.2 General human capital is valued at all firms and jobs and it is therefore
portable across all potential employers. Specific human capital, instead, is not valued at all
firms and jobs since it involves skills and knowledge that have productive value only in a
specific job or firm. As a result, it is not portable across all potential employers. Given
these crucial differences, the incentive to acquire the two types of human capital and the
externalities they may generate are significantly different. Broadly speaking, both the
individual worker and the economy as a whole have an incentive to acquire general human
capital (for example, schooling), while only the firm interested in a specific production
process has an incentive to invest in specific human capital (for example, on-the-job
training about a firm-specific software).3

A different but related question is whether human capital is the same as knowledge.
Romer’s recent contributions [Jones and Romer (2010); Romer (2015)] highlight the
important difference between human capital and knowledge where the first - which is
stored in neural connection in the brain - is a rival and excludable good; while the second
(to be understood as codified knowledge, for example knowledge stored in a document or
a book) is a non-rival and partially excludable good.

2.2 The Human Capital Model

The key intuition behind the human capital model [Becker (1962), Becker (1993)] is that
individuals decide on the "additions to knowledge" that constitute human capital. Decisions
are taken in order to maximize a payoff which includes not only earnings and labor market
performance but also cultural and other nonmonetary gains. Knowledge additions has both
direct and opportunity costs. Direct cost are the actual expenses incurred in the investment
activity such as school tuition or health costs. Opportunity costs are the forgone benefits

1
  This view is now shared by most economists and many other social scientists and policy makers but it was
quite controversial at the time (the first influential papers by Becker and his first book on human capital are
from the early 1960's: see Becker (1962) and Becker (1993 3ed, 1ed 1964)). Famously, Schultz in his
presidential address to the American Economic Association meeting in 1961 said that “free people should
not be equated with property and marketable assets.”
2
  See Section 4 for empirical evidence on education, health and early childhood. Section 4.1 focuses on
evidence at the macro level and Section 4.2 on evidence at the micro level.
3
  This difference was already emphasized in the early work by Becker (1962). More recent work has tried to
empirically disentangle the importance of general and specific human capital. See Sanders and Taber (2012)
for a review.


                                                      3
that could have been obtained in the time that was instead invested in schooling. For
example, full time college participation prevents students from earning a wage for full-time
work in the labor market.

Human capital investment decisions have an intertemporal nature, i.e. they typically
involve an investment today in order to obtain a payoff in the future. These decisions,
therefore, involve quite complex expectations about the future and may introduce
inefficiencies through hold-up problems, any time frictions or market failures are present.
For example, schooling investment are typically made before a worker enters the labor
market and is matched with a specific firm. If all the firms pay marginal productivity, then
the only uncertainty is about aggregate changes in labor market conditions. But if firms
retain some rents because markets are not perfectly competitive - for example due to search
frictions - then agents are also uncertain about the employer they are going to meet. As a
result, they are uncertain about how much of the increase in productivity due to their human
capital investment they can obtain through wages. This in turn affects their decision of how
much education to obtain [Acemoglu and Shimer (1999); Flinn and Mullins (2015)].

The inherent dynamic of human capital investment decisions also generates interactions
between different types of human capital. Dynamic complementarities imply that a given
investment in human capital today not only affects future payoffs but also subsequent
accumulation of human capital [Cunha, Heckman and Schennach (2010); Manuelli and
Seshadri (2014)]. For example, investments in the health and nutrition of children in the
early years of life have a large impact on how effective schooling will be in increasing their
future cognitive skills and knowledge. Dynamic complementarities may be so strong, that
early investments may not be productive at all if they are not followed by later investments
[Cunha et al. (2006)].

Dynamic interactions extend also beyond the life of the individual, involving the
intergenerational transmission of human capital and the importance of family backgrounds
in affecting human capital investments [Becker and Tomes (1986)]. There are two major
sources of individual heterogeneity which may lead agents to make different human capital
investment choices: personal attitudes and talents (ability) and costs involved in investing
today in order to obtain a future benefit (intertemporal discount rate). Both characteristics
are significantly affected by family backgrounds. For example, good child-rearing parental
practices can help a child to reach her full potential in terms of cognitive and non-cognitive
abilities and thus affect ability. Conversely, imperfect capital markets may make the
opportunity cost of giving up current wages in order to study simply too high for low
income families. As stressed early on by Becker [Becker (1993 3ed, 1ed 1964)], if the
returns to human capital exhibit decreasing marginal returns, this type of dynamics may be
a powerful explanation for persistent inequality. For example, consider the investment in
years of schooling. A simplified version of the human capital model implies that a given
agent will invest in schooling in order to maximize the present value of lifetime earnings.
Since in the simplified model the only cost is the opportunity cost, the agent goes to school
until the marginal rate of return to schooling equals the intertemporal discount rate. Since
the returns to schooling are decreasing, individuals from disadvantaged families will stop
accumulating schooling earlier because, with imperfect capital markets, they face higher



                                              4
discount rates. By accumulating less schooling, they will earn lower wages and provide
lower family background to their offspring, thus perpetuating inequality.

Human capital theory models individual agents' behavior, but the impact on aggregate
outcomes and growth has been an early concern [Schultz (1963)]. The key distinction here
is between private and social rate of return to human capital investments [Becker (1993);
Heckman et al. (2006); Krueger and Lindahl (2001)]. The private rate of returns is the
return enjoyed by the individual agent taking the decision. Typically, it does only include
monetary benefits and, as implied by the example above, is the return obtained by equating
the (net) present value of life-time earnings to the net present value of the human capital
investment cost. However, this return not only ignores cultural and other non-monetary
gains at the individual level but also ignores aggregate gains or loss that may be generated
by the investment's positive or negative externalities (the social return). The sources of
externalities are numerous and intuitive. For example, a health initiative introducing mass
vaccinations not only has health benefit for vaccinated individuals but also for those who
are not. Similarly, good schools in crime-prone areas not only improve the lifetime
opportunities of the students attending them but also reduce crime rates improving society
as a whole.


3. Conceptual Framework.

3.1 Where does output growth come from?

The Basic Framework. The basic building block of growth theory is a production function
where output (or GDP, usually denoted by Y) is a function of technology (A), physical
capital (K) and labor (L).

                                 Y = A F(K, L)          [1]

The most common functional form for the production function is the Cobb-Douglas
constant returns to scale formulation:

                                 Y = A Kα Lß            [2]

If α<1 and ß<1, there are marginal decreasing returns to each factor. In competitive
markets, ß is the (constant) share of output that goes to labor.

In equation 1, there are three sources of growth in aggregate output: technological
innovation affecting A, capital accumulation increasing K, and population growth or
changes in the participation rate of the population increasing L. Population growth may be
achieved both by increasing fertility and by increasing life expectancy. Therefore, in this
setting, the role of human development policies is limited to health and fertility
interventions. In this basic framework, L is the stock of labor used in production, often
normalized for some labor supply intensity (participation rate, part-time or full-time work).
However, each unit of L is essential a body, without much consideration for the fact that


                                               5
different individuals may have different skills and productivities or that the same individual
may acquire additional skills and therefore change her productivity over her life-time.

Adding Human Capital. A more general formulation of the previous production function
which takes the role of acquiring skills into account is the following:

                                   Y = A F(K, H)       [3]

where output (Y) is a function of technology (A), physical capital (K) and human capital
(H). In this world, there still are three ways to increase income but the third one is much
richer. Increases in the factor of production labor (H) are not only determined by
demographic changes but also (and in many contexts, mainly) by human capital
investments. Here investment in human capital allow for per-capita growth without
necessarily resorting to technological innovation or physical capital accumulation.

3.2 How does Human Capital affect Growth?

The Direct Channel. The first impact of human capital on growth is the direct impact
implied by its accumulation. This is an impact analogous to physical capital accumulation.
Following Lucas (1988), we can rewrite the production function as:

                                 Y = A F(K, vH)          [4]

where v denotes the portion of the current stock of human capital devoted to production
and (1-v) the portion devoted to skill acquisition. We can think v and (1-v) as proportion
of each unit of time that the representative agent devotes to the two activities. As a result,
the optimal decision of the agent is characterized by the same trade-off of the original
Becker model. Investing in human capital (skill acquisition) comes at the opportunity cost
of not using the time in production. The implication is a law of motion of human capital
that parallels the law of motion of investment in physical capital. Just as the output that is
not consumed (net of depreciation) increases the capital stock, so the human capital that is
not consumed in production increases the human capital stock. Empirically, this means that
we expect GDP growth to be a function of the growth of human capital.

In addition to quantity, also the quality of human capital matters. A simple way to allow
for heterogeneous human capital is by introducing the distinction between skilled (S) and
unskilled (U) workers. Then, the production function assumes the following more general
formulation:
                                   Y=A F(K, vSHS, vUHU)

where the investment decisions vS and vU are now skill-specific. Human capital
accumulation laws of motion will then also be skill-specific.

The Impact on A. The second impact of human capital on growth is through its influence
on technological progress, as represented by the stock of knowledge A. In the long run,
economic growth depends on A’s growth. In Solow’s model, this process is exogenous to



                                              6
the economic forces described in the model. In endogenous growth models, long-run
economic growth (A’s growth) is endogenously determined, including as a function of
human capital. As a result, growth goes on indefinitely because the returns to a broad class
of capital goods do not diminish as the economy develops [see Barro and Sala-i-Martin,
1998, page 12 and Howitt (1998)].

This endogenous growth process, can be described by the following production function:

                                 Y = AF (K, φH)         [6]

                                A = G[(1-φ)H]           [7]

where [7] defines the knowledge component as a function of human capital. In other words,
human capital is an input that can be used to produce new knowledge A, which then
increases Y. In this notation, a proportion of human capital φ is invested in production and
(1- φ) in knowledge generation.

Broadly speaking there are two classes of endogenous growth models: 1) “AK” models
where human and physical capital are not explicitly distinguished and K exhibits constant
marginal product, driving long run growth [Frankel (1962); Romer (1986)]; 2) models
where endogenous growth is innovation-based, i.e. where intellectual capital is distinct
from human and physical capital. The literature identifies various channels through which
innovation generates productivity growth: by increasing the variety of intermediate
products [Romer (1990)]; and by rendering products obsolete through a Schumpeterian
process of creative destruction where the probability of innovation depends on R&D
expenditure [Aghion and Howitt (1992)]. In these models, human capital is an input to
produce knowledge A. Therefore, an important question is “what type of human capital” is
necessary to develop this type of growth. The literature stresses different element as key -
literacy, secondary, or tertiary education, specialization. Romer (1990) and then Mokyr
(2005) identify in research engineer and engineering-minded technicians, respectively, the
key to innovation. In a recent paper, Maloney and Valencia Caicedo (2016) argue that the
density of engineers in 1880 captures well historical differences in innovative capacity,
which in turn explain a significant fraction of the Great Divergence in the Americas.

Recently, Jones and Romer (2010) and Romer (2015) emphasized that the direction of the
impact may also go the other way, from A to H. For example, the education process can be
seen as a form of increasing the human capital stock H by leveraging the accumulated
knowledge A. A similar direction of causation can result from technological innovations
rewarding differently different qualities of human capital. Consider for example the
heterogeneous human capital model in which labor can be broadly divided in skilled and
unskilled. The so-called skill-biased technical change [see Acemoglu (2002) and Violante
(2009) for a review] is an innovation in the production technology that increases the
relative productivity of skilled labor with respect to unskilled labor. The consequence is a
change in relative demand and therefore relative prices between the two types of labor,
which in turn changes the human capital accumulation process. Hsieh and Klenow (2010)
take this reasoning further and add to heterogeneous human capital the presence of different



                                             7
sectors. They document the presence of different levels of A over these different sectors
and argue that these differences can influence the incentive to accumulate physical and
human capital because they affect the price of capital and schooling relative to the price of
output.

The Interaction of H and K. The main interaction between human and physical capital is
the impact of the quantity of physical capital on labor productivity. Equation [3] shows that
the productivity of a human capital investment depends on the level of physical capital
used in the production process. Formally, this means that the first derivative of output with
respect to human capital is, itself, a function of K.

The interaction between human and physical capital also extend to the type of capital used
in production on top of its quantity. Krusell et al. (2000) argue that the substantial
cheapening of equipment capital (notably, computers and information technologies) that
occurred in the 80s has led to an increase in the stock of capital. Since skilled labor is
relatively more complementary to equipment capital than unskilled labor, this process is
also one of the sources of the skilled-biased technical change described in section 3.2.
There is now a large literature on capital-skill complementarity and on its impact on
inequality, productivity and, ultimately, growth.4 Recently, Duffy et al. (2004) has found
support for capital-skill complementarity on a large sample of developed and developing
countries. This interaction may also lead to changes in the share of labor and capital in
production. For example, Kouraboubanis and Neiman (2014) document a decline in the
labor share in the last thirty years and they attribute it to the decrease in relative prices of
investment goods.


4. The empirical Evidence

4.1 The Macro evidence

The macroeconomic literature has used two main methodologies to assess the relationship
between human capital and growth: cross-country regressions and development
accounting.

4.1.1 Cross-country regressions

This literature flourished in the 1990s and was initially motivated by testing the
implications of growth convergence models. Growth convergence predicts that countries
starting at lower income levels should converge to income levels of richer countries in
some version of the Solow–Swan model (1956) augmented with human capital. In the
conditional convergence literature, a country would grow faster the further away it is from
its own steady state level of income. The earlier literature focused on physical capital while
the following and more recent literature also includes a more complete set of state variables

4
  Griliches (1969) is the classic reference; Goldin and Katz (1998) and Katz and Krueger (1998) provide
empirical support of capital-skill complementarity using technological change over time as identification
strategy; Acemoglu (1998) provides theoretical support focusing on technology upgrading.


                                                   8
such as population growth and human capital accumulation. The next frontier is the
inclusion of two additional variables: ideas and institutions [Jones and Romer (2010)].

A typical empirical contribution in this area estimates the correlation between different
measures of human capital (such as years of schooling and life expectancy) and GDP per
capita growth. The question they try to answer is: If a country were to increase investment
in a given human capital component, by how much would income growth change?

Early findings. Barro and Sala-i-Martin’s book summarizes some of the key results of
these estimations. They report that educational attainment is positively correlated with
growth across countries: 1 standard deviation increase in male secondary schooling
(equivalent to 0.68 years of schooling) is associated with an increase in the growth rate by
1.1 percentage points per year. When education is decomposed in primary, secondary and
higher, it is secondary and higher education that are responsible for the positive impact on
growth (Barro and Sala-i-Martin (1995), chapter 12, page 431.) Subsequent work has not
always confirmed these results. For example, Pritchett (2001) uses data on 91 countries
and does not find a significant association between a rise in educational attainment and the
rate of growth of output per worker.

Increases in life expectancy are also found to be positively correlated with growth: 1
standard deviation increase in in life expectancy (13 years) is associated with an increase
in the growth rate of GDP by 1.4 percentage points (Barro and Sala-i-Martin (1995),
chapter 12, page 432). More recently, Barro (2015) reports that growth is positively
associated with lower mortality rate, lower fertility and higher female relative to male
school attainment for those aged 15+, while he finds that the impact of a general increase
in attainment is not significantly different from zero. Zaman and Tiwari (2017) find that an
increase in social protection spending is positively correlated with growth: Moving from 0
to 2% of GDP spending on SP increases growth by 0.1‐0.4 percentage points.

Identification, measurement, and reverse causation. There are many interpretation on
the estimates of a coefficient of GDP growth when regressed on the level of education and
change in education. As discussed in Benhabib and Spiegel (1994) and Krueger and
Lindhal (2001), level of schooling could be a proxy for steady state income, or could
change the steady state growth rate by enabling the work force to develop and adopt new
technologies (as in Nelson and Phelps, 1966 and Romer, 1990), or reflect an exogenous
change in returns to education, or could reflect reverse causality of increased education in
anticipation of future growth.

Importantly, a consensus around this literature is that obtaining unbiased estimated
coefficients in cross-country setups has proven problematic due to potential omitted
variables issues; reverse causality; heterogeneous effects, and measurement error.
Acemoglu and Johnson (2007) use instrumental variables to address some of the
identification problems in these types of regressions. They exploit international health
improvements from the 1940s to estimate the effect of life expectancy on economic
performance. They find that longer life expectancy increases population. It also increases
GDP, but not enough to compensate the population effect so there is no impact on GDP



                                             9
per capita growth. However, finding valid instruments is difficult, see for example the
discussion of Acemoglu and Johnson (2007) in Bloom et al. (2014).

Many have also argued that measurement error may plague the estimation results (Kruger
and Lindhal, 2001). A recent contribution by Barro and Lee (2013) overcomes some of
the limitations of the original perpetual inventory-based education dataset (Barro and Lee,
1993) and improves data accuracy by using information from consistent census data,
disaggregated by age group, along with new estimates of mortality rates and completion
rates by age and education level. A related question is whether using average years of
schooling is the right measure for human capital. Recent work by Hanushek and Woessman
(2015) shows that using school attainment as proxy for human capital fails to account for
differences in quality of education across countries and thus is unlikely to provide a
reasonable estimate of the role of human capital. They thus propose the use of scores from
international tests of mathematics, science and reading achievement.5 Based on an
aggregate value of skills for about fifty countries, they concludes that it is learning – rather
than schooling –that matters.

A further concern with cross country regressions is that causality might run both ways,
from human capital to growth and back. Weil (2013) explicitly discusses this with
reference to health and reviews different mechanisms through which income - or economic
dynamics associated with income growth - might affect health. These include improved
sanitation, which is associated with better health (though with a lag); and higher
urbanization, which is often associated with a negative impact on health.

4.1.2 Development accounting

Growth accounting - i.e. the decomposition of income growth rates into the contribution of
different factors - was first applied to the growth time series of the US by Solow in the
fifties. Later, a similar methodology has been applied on cross-sections of countries,
leading to the development accounting literature. This methodology decomposes income
differences across countries into their measurable components: physical capital (K), human
capital (H), and a residual which is interpreted as Total Factor Productivity (A or TFP).
This work tries to answer the question: What share of aggregate income differences can be
attributed to variation in K and H and how much can be attributed to the efficiency with
which these two factors are used (TFP)?

Accurately measuring income and factors and properly choosing the production function’s
functional form are the two key steps of development accounting. Efficiency is obtained as
a residual. Traditionally, large part of this literature is dedicated to understanding this
residual, which is often referred to as the “measure of our ignorance” [Abramovitz (1957),
cited in Caselli (2005)].



5
 Barro and Lee (2013) show a high correlation between their measure of school attainment and Hanushek
and Woessman (2009)’s measure of human capital quality, though they note that human capital quality is
quite diverse for countries with similar levels of educational attainment.


                                                 10
In the past two decades, the literature has obtained mixed results. Mankiw et al. (1992) use
secondary school enrolment to proxy for the investment rate in human capital and attribute
50% of income differences in their sample of 98 non-oil countries to differences in human
capital. Klenow and Rodriguez-Clare (1997) use years of schooling attainment as inputs to
a human capital aggregator and find instead that human capital accounts for 10 to 30
percent of income differences. When taking into account various measures of school
quality, Caselli (2005) concludes that improving measurement of human capital by
including school quality changes only slightly the conclusion that human capital explains
a small share of income differences. Caselli and Ciccone (2013) compute the maximum
impact that can be obtained by giving to the country under examination the same level of
schooling as the US and they find similar results as Caselli (2005). For example, if Brazil,
India, and Mexico were to move to the same education attainment of the US, the output
gap that would be covered would only be equal to, respectively, 22.4%, 5.4% and 20.1%.6
These are estimated as upper bounds, resting on the assumption of perfect substitutability
of skilled and unskilled labor.

Contributions removing the perfect substitutability assumption arrive at different
conclusions. Jones (2014) advocates the use of more general form of human capital
aggregators than those used in the previous development accounting literature. Human
capital aggregators are those functions that aggregate the heterogeneous human capital in
the economy in one factor of production to be inserted in the production functions
described by equation [1] and [2]. He proposes aggregators taking into account the different
returns of the different types of human capital as a function of: (i) their relative scarcity,
and (ii) the possible complementarities between them. Using the same data used by Caselli
(2005), Jones (2014) estimates that physical and human capital variations can fully explain
output differences between countries. Malmberg (2016) follows a similar approach by
removing other restrictions from the standard development accounting model and by using
different functional forms inspired by theory. Specifically, he allows for imperfect
substitutability between skilled and unskilled labor and uses a broader definition of skills
which is not simply based on education levels but also on the skill contents of specific
occupations as described in the Occupational Employment Statistics (OES) survey
maintained by the US Bureau of Labor Statistics (BLS). 7 He concludes that the human
capital accounts for the majority of income differences across countries.

Development accounting has also been used to study the impact of other human capital
components in addition to education and schooling. Health is an area of recent interest. For
example, Galasso and Wagstaff (2016) compute that the per capita income penalty a
country incurs for not having eliminated stunting when today’s workers were children is,
on average, 6% of GDP per capita. Weill (2013) uses a decomposition à la Caselli (2005)
and estimates that the cross-section income variance explained by health is about 10%.


6
    All data refer to the year 2000.
7
 Sasso and Ritzen (2016) use cognitive skills data from the Programme for the International Assessment of
Adult Competences (PIAAC) and confirm the importance of a definition of skills that goes beyond the simple
education level when performing developing or growth accounting exercises.


                                                   11
4.2 The Micro evidence

4.2.1 Introduction

The most popular micro-level approach uses observations at the individual level - typically
at the level of the worker, the student or the household - to run regressions of individual
wages or earnings on individual levels of human capital plus some additional controls. The
human capital returns obtained in this way are returns for a given individual as a result of
human capital investment on herself. The impact on overall growth is therefore generated
through the impact on wages and labor market performance. The standard specification is
log linear:

                                                          ′                [7]

where a measure of labor income (wi) is regressed on the human capital variable of interest
(hci) and a set of controls (xi). The relative return to the human capital investment, the
coefficient of interest in the regression, is .

Empirically, there are advantages of using this micro-level approach. First, micro-level
regressions use variation at the level of the individual workers instead of aggregating at the
country level. Second, they can estimate more flexible specifications because each country
(sometime different groups of workers within a country, such as men and women) is
allowed to have a different return to the specific human capital component under study.
Third, the range of additional controls that can be added to the specification is larger thanks
to the richer amount of information included in the survey data used in this context. Fourth,
they may take into account the individual heterogeneity which is an integral part of the
original human capital model. The original human capital model posits an investment
decision in human capital made by the individual agent. If individuals are different, they
may make different decisions. Estimates based on micro-evidence allows to take into
account at least some of these individual-agent level differences while the macro evidence
has to aggregate over them.

The main disadvantage of using the micro-level approach is that the link to the variable of
interest, growth, is less direct. The issue is sometime referred to as the difference between
private returns and social returns. The macro-evidence presented in Section 4.1 uses as
dependent variable a measure of GDP either in levels or growth rates. This measure is a
direct proxy for the total output variable considered in all growth models. Assessing
impacts of human capital investments on GDP is assessing the overall aggregate impact of
the investment: the social return. The micro-evidence presented in this Section uses as
dependent variable a measure of individual labor income which is the payoff based on
which the individual agent is making the choice: the private return.8

8
  In both cases, there can be non-pecuniary returns that are not captured either by GDP or by labor income
measures. Some of these returns may be captured by taking into account the externalities we discuss in the
rest of the paper. Other returns go beyond growth rates and while very important will not be discussed in the
paper.


                                                    12
The wedge between private and social returns may be significant. The first reason is that
labor income is only one component of GDP, even if a relevant one. The second, most
important reason is that human capital investment generate externalities. For example, as
seen in Section 3, human capital investments may generate technological progress which
in turn increases productivity of any production inputs. Other examples of typical positive
externalities are: education investments reducing aggregate crime rates or health
investments in mothers making their children healthier [Kruger and Lindhal (2001);
Glewwe (2000)]. The presence of positive externalities does not necessarily mean that the
social return of a given human capital investment is always higher than the private return.
In many countries investment in education is highly subsidized: if the subsidy is too high,
the private return may exceed the social return and lead to overinvestment in education
[Heckman and Klenow (1997)]. What it means, though, is that looking at wages instead of
GDP may under- or over-estimate the overall impact of human capital investments on
growth. The micro-evidence is well equipped to estimate private returns to human capital
investments. How these private returns exactly relate to the social returns at the center of
the growth literature depends on the human capital investment under consideration, the
specific country, the specific time period, the growth model assumptions used to interpret
the results. Still, impacts on wages are relevant since they are systematically correlated
with growth in GDP.

The second issue with the micro level evidence concerns the identification of the effects of
interest. Both econometric issues related to the quality of the estimates and modeling issues
related to the interpretation of the results are as important in the micro evidence as in the
macro evidence. Both concerns are discussed in Section 4.2.3.

The third and final issue concerns measurement errors. In Section 4.1 we already pointed
out the importance of a correct measure of human capital variables. In the empirical micro
literature, measurement errors issues also involve the outcome variables: wages and
earnings. Validation studies have shown the presence of measurement errors in self-
reported wages in economies with well-developed labor markets [Bollinger (1998); Bound
et al. (2001)]. The problem is only amplified in less developed labor markets where the
informal sector is large or the agricultural sector employs a large proportion of the labor
force [Jacoby and Skoufias (1997)]. Possible solutions to measurement errors issues are
the implementation of validation studies able to cross-check different data sources and the
use of administrative data. In economies with large agricultural sectors, proposed solutions
include changing the outcome variable by using consumption data or production data
instead of labor income data.


4.2.2 Review of Empirical Results

Human Capital investment is a dynamic process, involving a variety of decisions covering
the entire life cycle. The following section presents empirical evidence on some of the most
popular human capital investments involved in this process. It starts with early childhood




                                             13
investments and continues with education decisions, skills acquisition, on-the-job
components. It closes with investments in health.

Returns to Early Childhood Development Investments. Recognizing the major dynamic
complementarities discussed in Section 2.2 has led to a renewed interest in early childhood
investments.9 A given investment in human capital today not only affects future payoffs
but also influences subsequent accumulation of human capital. The result is that human
capital accumulation and skill formation should really be seen as a life-cycle, life-long
process where returns on early investments are high while remediation later in life is
difficult [Cunha et al. (2006)]. Such dynamic complementarity is so strong that early
human capital investments and early accumulation of both cognitive and noncognitive
skills seem to sort individuals into different paths of lifetime outcomes [Doyle et al.
(2009)].

Interventions in this area are varied: they range from childcare programs to nutrition
programs, from programs targeting children to programs targeting mothers. They also vary
in quality with success crucially dependent on implementation. García et al. (2016)
estimate a rate of return of 13% per year for a high-quality early childhood program in the
US.10 Bernal and Fernandez (2013) study the impact of a subsidized community-based
childcare program in Colombia11 finding positive impacts on cognitive development and
socioemotional skill (about 0.2 of a standard deviation) but no impact on nutrition. Elango
et al. (2016) revisits the evidence on early childhood education concluding that the quality
of the service provided is crucial. They estimate that only high-quality means-tested
programs are socially efficient (i.e. generates positive net returns at the aggregate level).
Berlinski and Schady (2016) provide a review and an interpretation of the evidence in Latin
America, confirming the importance of quality. Focusing on two types of programs - home
visits and daycare programs - they report positive effects on cognitive skills for all home
visit interventions (ranging from 0.2 to 1.2 standard deviations) while both positive and
negative effects for day care programs (ranging from –0.2 to 0.2 standard deviations).

While the quality of the intervention matters and the benefit-cost ratios vary for different
program, the consensus in the literature is that investing in comprehensive birth-to-five
early childhood programs leads to significant returns in the accumulation of subsequent
human capital, in labor market outcomes, in health outcomes and in positive social
behavior. [Elango et al. (2016); Berlinski and Schady (2016); Heckman and Mosso (2014).]

Returns to Education Investments. Returns to education are one of the most estimated
coefficient in empirical microeconomics. They have been estimated on a large number of



9
   Elango et al. (2016) survey early childhood education; Berlinski and Shady (2016) interpret early years
interventions in Latin America; Heckman and Mosso (2014) focuses on the economics of human
development and social mobility emphasizing the importance of early life conditions; Cunha et al. (2010)
provide methods to estimate skill formation starting from early childhood; and Cunha et al. (2006) review
and interpret the empirical evidence.
10
   The Carolina Abecedarian Project (ABC) and the Carolina Approach to Responsive Education (CARE).
11
   Hogares Comunitarios de Bienestar (HCB).


                                                   14
countries and over long time periods.12 In a typical specification, the human capital
investment of interest is represented by the number of years of schooling completed. Other
specifications look at the highest degree completed, occasionally at the type of degree
within the same level. Typical controls include a quadratic term in labor market experience
(generating the so called mincerian regression, from Mincer (1974)) and demographic
variables such as marital status and gender. For case studies on specific countries the set
of controls may become particularly large, including measure of individual ability (such as
test scores) or family background variables (such as parents' education).

Particularly relevant for the growth literature are papers estimating returns to education on
a large number of countries using comparable data.13 Working with micro data from 149
countries, Montenegro and Patrinos (2014) estimate that, on average, one additional year
of schooling is associate with a 9.7% increase in earnings; with higher increases for women
than men (11.4% with respect to 9.1%). However, they find wide variations between
countries and over time: returns range from more than 25% to less than 1%. Similar results
are found by Caselli (2015) which collects estimation results from different authors on 87
countries in the mid-1990s and 91 countries in the mid-2000s. Regional patterns by world
regions over time show stable returns in Europe and Central Asia (about 7%) and in Africa
and the Middle East (about 8%); a decrease in returns in Latin America and the Caribbean
(from more than 10% in the 1990s to about 8% in the 2000s); and an increase in returns in
South-East Asia and the Pacific (from about 8% in the 1990s to more than 10% in the
2000s.) Again, country variation within world regions is substantial. A different way to
summarize estimates extracted from a large set of different papers is proposed by
Ashenfelter et al. (2001). They acknowledge the importance of potential bias in returns to
schooling estimates, collecting works using different samples and estimation method. They
then conduct a meta-analysis based on about a hundred estimates on nine different
countries. The meta-analysis aggregates the estimation results using different weight based
on estimation method and publication bias. The average returned obtained is comparable
to those reported above: about 7% from estimates based on ordinary least squares (OLS)
and about 9% from estimates attempting to reduce estimation bias (instrumental variable
estimators (IV) and estimators based on sample of twins).

Given the importance accorded to education in building human capital, the empirical
literature has also attempted to estimate the interaction between education and other human
capital components. Heckman, Humphries, and Veramendi (2016) estimate causal
consequences of schooling decisions on health status and smoking behavior using a
dynamic model of investment in schooling. Two main results emerge from their work.
First, returns to schooling investments are very heterogeneous in the population. For high-
ability individuals, completing High School or College has not only high direct returns but
also improves the option of acquiring additional valuable schooling. For low-ability

12
   A partial list of important contributions include: Griliches (1977); Mincer (1974); Card (2001); Heckman,
Lochner, and Todd (2006); Goldin and Katz (2008).
13
   Recent examples presenting estimates for a variety of world regions include Caselli (2015), Montenegro
and Patrinos (2014) and World Bank (2012). Peet, Fink and Fawzi (2015) present results on 25 developing
countries. Flabbi, Paternostro, and Tiongson (2008) focus on 8 ECA countries and estimate returns over two
decades.


                                                    15
individuals, a significant direct effect is still present but the positive impact on future
options is negligible. Second, returns to schooling on health outcomes are significant:
Completing College with respect to dropping out from High School reduces the probability
of smoking by more than 17%. Lochner (2011) is a complete review of empirical works in
economics attempting to estimate what are labeled as the non-production benefits of
education. They include impacts on crime, health, and good citizenship. Some of the results
report very large effects. For example, Lochner and Moretti (2004) propose both an OLS
and IV estimation strategy concluding that an extra year of completed schooling is
associated with a 10-15% reduction in incarceration rates. Brunello et al. (2013) estimate
that years of schooling have a causal effect on the body mass index (BMI) of women living
in nine European countries: one additional year of schooling reduces the BMI by 1.84%.

Finally, a last important interaction between education and human capital concerns the
transmission of the accumulated human capital to the next generation. The empirical
literature has found strong correlations between income and human capital of parents and
children.14 The theoretical literature has pointed out the importance of the intergenerational
transmission of human capital and the role that family backgrounds play in affecting human
capital investments [Becker and Tomes (1986)]. The literature on education mobility is
vast and finds positive and significant impact of mother's education on children outcomes.
The evidence on father's education is more mixed. The impact of policy interventions
aiming at reducing the importance of family background in favor of equality of
opportunities in education is also very well developed.15 Family backgrounds and policy
interventions may also play a role in explaining the persistence of human capital over time.
Rocha, Ferraz, and Soares (2017) is a particularly relevant contribution in this literature
because it is able to link individual-level human capital investment with regional-level
long-term development.

Despite the large variation in estimated returns and the problems in identifying causal
impacts, returns to schooling estimated on micro data provide some valuable lessons:
   1. Returns are different in magnitude but they are positive in virtually all countries
        and periods;
   2. Returns are systematically different not only by country and region but also by
        demographic groups (notably, gender, cohort of birth and ethnic groups);
   3. Returns are different over time within the same country. High income countries
        exhibit more stable returns than developing countries;
   4. Returns to education decisions are not limited to income but include non-
        production benefits, such as impacts on health, crime and political participation.
        These returns are estimated to be positive and significant.




14
   A classic references on the intergenerational transmission of income is Solon (1992); a recent contribution
is Lefgren et al. (2012). On human capital intergeneration transmission, see Black, Devereux, and Salvanes
(2005). International comparisons are provided in Chevalier, Denny, and McMahon (2003) and Hertz et al.
(2007).
15
   For a review on Europe, see Dolton, Asplund, and Barth (2009). For the impact of school tracking and
intergenerational mobility in education, see Dustmann (2004) and Checchi and Flabbi (2007).


                                                     16
Returns to Skills. Human capital investments produce returns only if they generate
valuable skills. Unpacking the process moving from investments to skills formation to
returns implies measuring these skills at different points of the accumulation process.

Many empirical works in this area use the Programme for the International Assessment of
Adult Competences (PIAAC) survey to measure adult skills. PIAAC is developed by the
OECD to measure cognitive skills that are considered necessary to be a productive worker
and a participating member of society. PIAAC also provides measures that are comparable
internationally. Hanusheck et al. (2016) perform cross-country regressions on 31 countries.
They estimate increases in gross hourly wages as a result of a standard deviation increase
in the numeracy score. The estimated returns range from 9.4% (with full controls) to 19.9%
(with only country fixed effects controls). OECD (2016) uses the same survey on all 33
participant countries in 2014-2015 concluding that one standard deviation more on the
literacy scale increase the probability to be employed by 0.8 percentage point and is
associated with a 6% increase in wages.

However, cognitive skills are just one of the possible skills relevant in the human capital
accumulation process. Recently, economists have followed other social scientists in
recognizing the importance of personality traits, or non-cognitive skills, as important
components of human capital and, ultimately, labor productivity.16 Non-cognitive skills
can be defined as components of human behavior, including thoughts and feelings, which
are important in inter-personal and social interactions. A typical taxonomy adopted from
Psychologists includes the Big Five of personality traits: openness, conscientiousness,
extraversion, agreeableness, and neuroticism (emotional stability). Specific traits that have
proved to be particular important for labor productivity are self-esteem and locus of
control, which are strongly associated with conscientiousness and emotional stability
[Almlund et al. (2011)]. Glewwe et al. (2016) is one of the first contribution considering
both cognitive and non-cognitive skills measured in the early years as predictors of
outcomes in a developing country. They focus on China's poorest provinces estimating that
both types of skills are important to predict education attainment. When education
attainment is controlled for, however, they are not strong predictors of early labor market
outcomes.

Returns to Experience and Seniority. Human capital accumulation continues once
individuals transit from schooling to the labor market since working at a given job involves
important learning processes. A standard proxy used to capture the overall return of this
human capital accumulation is the years of work experience accumulated by a given
worker. A typical specification is the so called Mincerian regressions [Mincer (1971)]
where log wages are regressed on years of schooling si and years of work experience ei,
linear and squared:

                                                                              [8]


16
   For a review, see Almlund et al. (2011). For an early example applied to labor productivity, see Heckman
et al. (2006). For an important data collection initiative focusing on middle- and low-income countries see
the World Bank's STEP Skills Measurement Program (STEP) [Pierre et al. (2014)].


                                                    17
Years of work experience enter the specification in a quadratic form to allow for the return
to be decreasing for high values of experience. This is one of the important empirical
regularities originally found by Mincer. The human capital model may explain this
regularity. Over their career, individuals are subject to two processes: accumulation of new
human capital through learning on the job but also depreciation of the human capital
previously acquired. Eventually, the second process dominates leading to a reduction and
possibly a reversal of returns to experience.17 Returns to experience estimates are almost
as common as returns to years of schooling estimates since they are frequently jointly
estimated in a specification similar to equation [8]. In Montenegro and Patrinos (2014) the
estimate for potential experience is centered around 3.1% a year in a large sample of
countries. Potential experience is positively correlated with returns to schooling and its
variation across countries is large, with some countries registering returns twice as large
while others almost zero. The recent literature has also focused on the evolution of returns
to experience over time. Kambourov and Manovskii (2008) focus on the US showing a
flattening of experience profiles over the birth cohorts 1950-1970. Returns to experience
may also change together with other human capital characteristics, such as education [Card
and Lemieux (2001)].

An important characteristic of at least some of the human capital accumulation on-the-job
is being specific to that job, becoming not easily portable to another job. The first original
contributions by Becker, see for example Becker (1962), were emphasizing this argument
by distinguishing between general and specific human capital. In this terminology, years
of schooling are an example of general human capital while years of experience in a given
firm (tenure or seniority) are an example of specific human capital. Typical estimates for a
high-income country such as the U.S. are about 11% wage increase for ten additional years
of seniority at a given firm [Flabbi and Ichino (2001)]. Between the overall experience
accumulated in the labor market and the more specific experience accumulate in a given
firms, recent literature has shown the importance of intermediate categories. Kambourov
and Manovskii (2009) emphasizes the importance of experience accumulated in a specific
occupation or industry. They estimate on US data that 5 years of experience in the same 3-
digit occupation increase wages 12% to 20% a year. Sanders and Taber (2012) provide a
review of the contributions trying to empirically disentangle the importance of general and
specific human capital. They conclude that no human capital accumulation on the job can
be fully described as general or specific. Rather, the empirical evidence fits better a model
of task-specific human capital which is not fully industry-specific nor occupation-specific.
Autor and Handel (2013) estimate that one standard deviation increase in abstract task
content within the same occupation leads to a 7% increase in wages.

There is also a large literature claiming that returns to seniority are not related to
productivity increases.18 These contributions challenge the human capital interpretation of
the positive coefficients estimated on measures of experience and seniority in equations

17
   Mincer, however, did not share this human capital interpration of his results: see Heckman et al. (2006) for
a recent reconsideration of his arguments.
18
   The literature started with Medoff and Abraham (1980) who had the idea of using supervisors' evaluations
to control for productivity differences in wage equations and continued with Altonji and Shakotko (1987).
More recent contributions are Flabbi and Ichino (2001); Dohmen (2004): Buchinsky et al. (2010).


                                                     18
similar to [8]. They propose explanations based on deferred compensation, match-specific
productivity in presence of search frictions, personnel networks within the firm.

Returns to Health Investments. Individual health status is an important component of
human capital but it is more difficult to measure at the micro level than schooling or labor
market experience. This section reviews some of the variables that have been used in the
literature to proxy individual health and discusses their estimated returns.

An important component of individual health which is frequently collected in household
surveys is disability status. Disability is typically defined as "a physical, mental, or other
health condition that limits the kind or amount of work" an individual can perform.19
Gilleskie and Hoffman (2014) use this measure to estimate the impact of health capital on
wages. To reduce endogeneity, they develop a model of joint health and labor market
decisions. Their estimates on U.S. data show that the direct effect of moderate disability
on wages is significant but relatively small (about $0.30 per hour).20 However, they find
strong impacts on labor market transitions: moderately disabled workers are 23% more
likely to make an occupation or employment transition than nondisabled workers. Since
the returns to these transitions are estimated to be lower for individuals affected by
disability and since the disability induces more of them, the overall impact of disability
accrues over time, generating much larger impact on wages in the medium-long run.
Campolieti and Krashinsky (2006) use Canadian data to study the impact of accidents on
the job. They similarly show the important interaction between disability and job mobility.
Their estimates suggest larger wage losses for disabled workers who did not return to work
with their time-of-accident employer than for those who did return, with the latter earning
27% more.

Another component related to health status that is receiving increasing attention is body
mass. Thomas and Strauss (1997) is one of the first contribution studying the impact of
health on wages in Brazil. They estimate a significant association between Body Mass
Index (BMI) and wages of males, in particular among the less-educated. Harris (2014)
estimates the full labor market impact of BMI by allowing long-run effects to take place.
He uses a life-cycle model similar to Gilleskie and Hoffman (2014) estimating that a
reduction in an individual's initial body mass by 10% leads to a 4% increase in wages after
age 30. Brunello et al. (2009) focus on obesity confirming the significant negative
correlation between obesity and wages in a review of a large number of European countries.

Finally, stunting is an important marker of health and cognitive status for children. A child
is affected by stunting when she is being excessively short for her age (2 standard
deviations below the median of a healthy reference population). The review presented by
Hoddinott et al. (2013a) looks at the impact of stunting in the 1000 days after conception
throughout the life cycle. Using a range of estimates for a variety of countries, they
conclude that the prevention of one fifth of stunting would increase income by 11%.
Victora et al. (2008) use a long cohort study on Brazil estimating that a one standard

19
   This is the definition used by one of the most important survey used in the U.S. literature, the Survey of
Income and Program Participation (SIPP) conducted by the United States Census Bureau.
20
   They use the 1996 SIPP which covers individuals up to the year 2000.


                                                    19
deviation increase in the height-for-age score at age 2 increases annual income by 8% for
both men and women. Hoddinott et al. (2013b) use data for Guatemala. They estimate that
being stunted at age 2 decreases wages by 16% for men and 14% for women. When using
an IV strategy to reduce endogeneity bias the impact becomes much larger for men (65%)
and slightly larger for women (18%) but it is less precisely estimated. Finally, the
comprehensive review provided by Galasso and Wagstaff (2016) confirms the large impact
of stunting on income by performing a meta-analysis on program evaluations of nutrition
interventions.

Despite the difficulty in measuring health investments and the problems in identifying
causal impacts, returns to health are potentially a large component of individual human
capital. If some of the earlier literature focused on dramatic impacts on health, such as
disability, the most recent literature is working on outcome variables more susceptible to
marginal changes, such as body mass indexes.

4.2.3 Interpretation of the results

Does the estimated 9.7% return in earnings for one additional year of schooling mean that
if a policy manages to increase education by one year for the entire population the overall
income will increase by 9.7%? Based on the estimate that a reduction in an individual's
initial body mass by 10% leads to a 4% increase in wages, is it possible to conclude that a
national nutrition policy able to achieve that objective for the entire population will lead to
a 4% increase in overall wages? The answer is generally no due to two main reasons: biased
estimates and equilibrium effects. The first relates to the possible bias affecting the
estimates of the parameters of interest. The second relates to the difficulty of building
counterfactual policy experiments able to take into account behavioral responses.

Biased Estimates. In virtually all the settings described in the previous review of the
empirical results the parameters of interest are at risk of estimation bias. In a regression
context, the issue is frequently framed as lack of identification: the estimates of the
parameters of interest are not really causal but may simply represent a conditional
correlation or a potentially spurious empirical association. The two main sources of bias
are unobserved individual heterogeneity and reverse causation.

Unobserved individual heterogeneity refers to relevant individual-level variables affecting
the relation of interest but not available in the data used in estimation. This omission
generates endogeneity either directly as a standard omitted variables bias or indirectly by
implying not-random sample selection. Unobserved individual heterogeneity may also
mask important heterogeneous effects, i.e. the fact that the relation of interest is very
different between individuals in the population. If this is the case, the estimated parameters
may only be reporting a distorted average of them.

Consider once again equation [7] presented at the beginning of this section. Assume that
the human capital variable of interest is the years of schooling completed si:

                                                   ′             [9]



                                              20
The parameter of interest is which could be interpreted as the return (in term of wages
wi) of an additional year of schooling. Now assume the presence of unobserved individual
heterogeneity. For example, that individuals are heterogeneous in their level of ability ai.
Higher ability makes individuals more productive on the job increasing their wages. Since
ability is not observed, will enter the wage equation through the error term which becomes
equal to:



where ui is the usual uncorrelated random error. If one additionally assumes, as in the
original model by Becker, that higher ability also induces higher schooling levels then
ability will also be correlated with the years of schooling completed si. As a result, a simple
regression of log wages lnwi on schooling si and controls xi generates biased estimates. The
intuition is straightforward: the higher wages observed for individuals with higher
schooling may be due both to their higher level of schooling and to their higher level of
ability but it is not possible to disentangle the two separate effects. Formally, the variable
of interest is correlated with the error term:

                                              ,        0

and therefore schooling is endogenous and the OLS estimator is biased.
When this is the case, it becomes difficult to derive sensible policy implications. Consider
a simple version of individual heterogeneity where the population is composed of only two
types of individuals: High ability and Low ability individuals. High ability individuals
complete College earning a wage wHigh; low ability individuals complete only High School
earning a wage wLow. Suppose a policy is implemented in order to increase education at the
level of College for all the individuals with only High School. Based on OLS estimates,
one would expect a return equal to (wHigh - wLow) for each individual. However, the actual
return would be much lower because wHigh is the wage earned by individuals completing
college and endowed with High ability. From the estimates, we cannot predict what the
wage of individuals completing college and endowed with Low ability is and therefore we
cannot evaluate the impact of the policy.

Reverse causation refers to situations in which the direction of the causation is ambiguous.
Again, consider the log wage regression equation presented earlier. Assume that the human
capital variable of interest is a measure of individual health hi:

                                                   ′             [10]

The parameter        can be considered the wage return of health investments. A positive
estimated coefficient suggests that a healthier individual is a more productive worker,
therefore earning a higher wage. However, the opposite direction of causation may also be
true. If health, productivity and returns are jointly determined one cannot exclude the fact
that it is the higher wage the cause of the higher health index. Since higher wages are
associated with the possibility of buying healthier, more nutritious food and with the


                                              21
availability of better health services, there is a genuine causal channel from higher wages
to better health. This may well be the true reason behind the positive estimated coefficient.

Solutions. Both sources of biased estimates have been acknowledged by the literature early
on.21 The two main econometric solutions are the use of exogenous variation in order to
eliminate the source of endogeneity and the use of economic modeling in order to explicitly
trace the channels of the endogeneity. The two methods are almost always used in
combination but specific applications emphasize one or the other. Contributions
emphasizing economic modeling are presented in the next section, when they will be
combined with a discussion of equilibrium effects. What follows is a brief discussion of
contributions emphasizing exogenous variation in a setting very similar to the one just
described in equation [7] to [10]. The approach is the following. Since the source of bias
is the correlation between the human capital variable of interest (hci) and the error term:

                                                       ,       0

it is important to isolate variation in hci which is not correlated with the error term. A
common way to implement this is finding a variable zi (called instrumental variable) which
is correlated with the variable of interest but not with the error term:

                                          ,            0              [11]

                                          ,        0                  [12]

The fact that the variable is correlated with the variable of interest (condition [11]) allows
for the identification of the effect of the interest. The fact that the variable is not correlated
with the variable of interest (condition [12]) is the exogeneity condition necessary to solve
the bias. The returns to schooling literature is particularly rich with examples of
instrumental variable. Starting from the 1990s, these instrumental variables have been
inspired by so called natural experiment, i.e. institutional changes or similar events able to
mimic a quasi-random assignment to a different level of schooling or human capital. A
classic example from the labor literature is the Viet Nam era draft lottery [Angrist and
Krueger (1992).] A classic example from the development literature is the roll out of school
construction in Indonesia [Duflo (2001).] A recent example using a reform of wage setting
in Israeli kibbutzim is able to estimate directly the responsiveness of schooling investment
to changes in their returns [Abramitzky and Lavy (2015)] The last fifteen years have also
seen a flourishing of Randomized Control Trials (RCT) where the exogeneity of the source
of variation is assured by construction by randomly assigning individuals (or household or
villages) to a treatment or to a control group. A recent application randomly assigns women
in rural India to three years of recruiting services providing information about requirements
and remunerations of relatively skilled jobs [Jensen (2012).] Estimation results show that
schooling acquisition increased when women were informed about the labor market
opportunities available with those skills.


21
   See for example the classic Griliches (1977) applied to returns to schooling. A more recent review is Card
(1999) and a simple interpretative framework is provided in Card (2001).


                                                       22
Equilibrium Effects. Even in the presence of unbiased estimated parameters, one
additional problem remains. The parameters are estimated on data extracted from a given
economy, with given prices and policy parameters. Evaluating a policy, or even simply
trying to give an interpretation to a given return, requires imagining or simulating a
counterfactual environment where some of these fundamentals change. For example,
suppose to have estimated returns to schooling in a country with 12 years of average
completed schooling. A relevant policy question may be asking what the average wage or
the overall wage distribution in the country would be when the average years of schooling
completed in the population is increased to 16. The answer is not obvious since it cannot
simply use the wage regression parameters estimated in the pre-policy environment. If
more people complete more education, the supply of skilled workers in the labor market
increases. But if the supply increases, the wages for skilled workers will fall. As a result,
the pre-policy returns cannot be simply transferred to the post-policy environment.

These general equilibrium effects are difficult to fully incorporate in empirical micro-
model while they are more common in many macro-models performing quantitative
exercises using calibrated or estimated parameters.22 Still, interesting examples exist.
Kahanna (2016) uses a large expansion of the public-school system together with a model
of human capital accumulation. Both elements are embedded in a model of the labor market
for skills in order to study returns to schooling once general equilibrium effects are taken
into account. The estimated returns are in the usual range (13.4% return for an additional
year of education) but the equilibrium impact of adding more educated work force to the
labor market is shown to depress the returns to skill reducing the economic benefit of the
human capital investment.

If general equilibrium effects are important when considering large scale policies, they may
be less crucial when the policy intervention is more limited. But even if this is the case,
there can still be partial equilibrium effects due to changes in workers' behavior. Two
examples from the literature on search models of the labor market23 estimated on micro
data [Eckstein and Wolpin (1995); Flinn and Mullins (2015)] illustrate this point. They
assume that that markets are not completely competitive so that it requires time and effort
to meet a firm offering a job.

Eckstein and Wolpin (1995) study returns to schooling in the US. They make the point that
accepted wages may be different from wages offered to the agents during the search
process. Returns estimated from wage regressions such as equation [8] use observed wages,
i.e. wages at which agents have accepted to work. However, each agent may have received
and rejected many wage offers before the one observed in the data. Agents reject wage
offers in the hope of receiving a better offer at the next meeting with an employer. How
selective workers are in accepting a wage offer depends on the schooling level but also on

22
   The debate dates back at least to the so called Lucas critique [Lucas (1976)]. Recent examples include
Dynamic Stochastic General Equilibrium (DSGE) models (see Sbordone et al. (2010) for a review aimed at
policy makers) and macro search model of the labor market incorporating endogenous job creation (see
Rogerson et al. (2005) for a review.)
23
   See for example the reviews by Rogerson et al. (2005) focusing on macro search and by Eckstein and van
den Berg (2007) focusing on empirical micro search.


                                                   23
other factors. Consider a simplified economy where there are just two types of job searcher:
a College educated agent assumed to receive high utility from leisure and a High School
educated agent assumed to receive low utility from leisure. The High School agent will
receive lower job offers because she has completed less schooling. Despite this, she will
be likely to accept them because she does not value leisure very much. The College agent
will receive higher job offers because she has completed more schooling. On top of that
she will be very picky before accepting them because working will force her to give up at
least a portion of the leisure she so much values. The differential in accepted wages
between the two workers will then be driven by two different forces: the difference in
schooling level, which is a genuine return to schooling, and the difference in preferences
for leisure, which should not be factored in as return. Genuine returns to schooling should
be computed based on wage offers not accepted wages. Recovering the wage offer
distribution becomes necessary in order to evaluate the actual returns to schooling. Eckstein
and Wolpin (1995) estimate the differences between returns estimated on accepted wages
and returns estimated on wage offers to be significant. Using NLSY79 data on men, they
estimate the internal annual rate of return for completing College relative to only
completing High School to be 31.5% for blacks and 17.0% for whites. The same returns
would be much lower if only accepted wages were considered: respectively, 9.4% for
blacks and 11.9% for whites.

Flinn and Mullins (2015) show how the previous considerations are also important when
building counterfactuals to evaluate policy experiments. They study school subsidies
taking into account that any change in them, even if small scale, will have an impact on the
reservation wage of all the individuals participating in the market. But if reservation wages
change, then it is not enough to know the current accepted wages: the evaluation of the
policy requires predicting the accepted wages in the new policy environment. In order to
predict the new accepted wages the primitive wage offers need to be recovered. They
accomplish this thanks to the structure of the search model together with some parametric
assumptions. They conclude that a schooling subsidy financed by a lump-sum tax improves
overall welfare, reduces aggregate unemployment, and increases production in the
economy. A school subsidy covering about 10% of the cost of schooling will increase
output by about 4.6%.


5. Conclusion

Human capital is a broad concept including "education, training, medical care, and other
additions to knowledge and health" [Becker (1992)] but also neural connections in the
brain [Romer (2015)]. The importance of human capital in affecting growth has long been
recognized by the literature [Lucas (1988); Romer (1990).] The paper summarizes it by
describing three main pathways:
    1. The direct impact, responsible for increasing the stock and accumulation of the
        factor of production labor;
    2. The impact on technological progress, able to increase the productivity of all the
        factors of production.




                                             24
    3. The interaction between physical and human capital, affecting the returns of a
        given mix of the two main production factors.
As a result of this framework, any policy related to education, job training, health but also
early childhood development and other areas influencing the productivity of an individual
in the economy affects human capital accumulation and, ultimately, growth.

If the direction of the impact is unambiguously positive - the accumulation of human
capital is associated with positive growth - the magnitude of the impact - what is the return
of a given human capital investment - is much more difficult to evaluate. Two strands of
the literature attempt to provide an answer. The empirical macro literature takes a direct
approach, considering output (GDP) as the dependent variable of interest and using
aggregate measures of human capital investments as inputs. The typical example are cross-
country regressions where GDP is the dependent variable. Observed measures of human
capital investments (such as years of schooling and life expectancy) are the regressors of
interest [Barro and Sala-i-Martin (1995).] Equally relevant is the literature on development
accounting where output growth is decomposed into the growth of its measurable
components (physical capital and human capital) with the residual interpreted as TFP
[Caselli (2005).] The empirical micro literature takes a more indirect route because the
dependent variable is typically a measure of labor income observed at the level of the
individual agent. If the impact on growth is more indirect (wages or labor income are only
one component of overall GDP) there are numerous advantages of using this approach.
First, since they do not need to aggregate at the country level, micro-level estimates use all
the information available in the data. Second, they can estimate more flexible
specifications. For example, each country is allowed to have different returns to human
capital investments. Third, the range of additional controls that can be added to the
specification is larger because survey data typically include more detailed information than
aggregate level data. Fourth, micro level estimates may better incorporate the individual
heterogeneity which is an integral part of the original human capital model.

The paper provides a survey of quantitative results in both the empirical macro and micro
literature, considering human capital components ranging from years of schooling to
disability indexes, from early childhood development indicators to multidimensional
measures of skills.

Both theory and evidence show that investing in human capital is a promising strategy to
attain stable positive growth. But the magnitude of the effects remains country-specific,
varying based on the population of interest, the policy under consideration, and the human
capital component considered. As a result, the paper suggests the use of micro data tailored
to evaluate the specific policy of interest in the country under consideration, in conjunction
with economic models able to aggregate the micro-level effects.




                                             25
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