Human Capital: How much does it really matter? New Insights on an Old Topic

Human Capital: How much does it really matter?

New Insights on an Old Topic

Thesis for the Research Master in Economics and Business

Supervisors: dr. Robert C. Inklaar and Prof. dr. Marcel P. Timmer

University of Groningen Faculty of Economics and Business

SOM Research Institute

August 27, 2012

Abstract

The effect of increases in education on countries’ GDP per worker constitutes the primary objective of the present study. To this end, the alternative “upper bound” methodology has been employed, alongside the most recent data. Our findings reveal that countries, particularly low-income ones, could greatly benefit from increases in education. On average, a country could raise its output by 67% and, also, halve its output gap to the United States. Cross-country income variation could have been reduced by 37.4%, whereas among the low-income countries this estimate would reach 52.5%. In contrast, conventional techniques estimate the impact of education on cross-country income variation only between 2.2% and 16.6%. Furthermore, since relative wages constitute an inherent component of our “upper bound” calculations, as a secondary objective of our study, we construct relative wages proxies based on a high- versus low-skilled industries approach. These proxies, however, are found to only poorly capture the actual pattern of relative wages, potentially due to the increasingly important phenomenon of offshoring.

Keywords: education, GDP per worker, upper bound, relative wages

1

Introduction

of the Congo), more than half of the population had no schooling. On the contrary, in the United States, the share of the population without schooling was only 0.5% whereas more than 30% of the population had completed college. The following graph also shows how GDP per worker and an indicator of the educational level of a country (the share of hours worked by high-skilled persons engaged, H HS in Timmer (2012)) evolve in the years. For relatively low-income countries, namely Bulgaria (BGR), China (CHN), Indonesia (IDN), India (IND) and Romania (ROM), the two variables are largely moving in the same direction. It seems that GDP per worker goes together with education.

Figure 1: The relationship between output (GDP per worker in logarithms) and an indicator for education (the share of hours worked by high-skilled persons engaged, H HS in Timmer (2012)) for five relatively low-income countries (BGR, CHN, IDN, IND and ROM).

Although education has been found to exert a positive effect on economic growth, a consensus on the magnitude of this effect has not yet been reached in the literature and estimates have varied depending on methodological and data-quality issues1. Re-cent research has suggested that the fraction of the income variance attributed to both physical and human capital centers around 0.40 (Caselli, 2005). Consequently, a large part of cross-country income variation remains unexplained.

In the present study, we explore an alternative methodology to measure how much a country’s GDP would grow, if schooling increased. To this end, we employ the “upper bound” formula of Caselli and Ciccone (2011) which yields the maximum increase in output that could be generated by increasing schooling to a benchmark level. Stated

1

differently, suppose that a country increased its schooling to the US levels. What is the maximum increase that its output could undergo?

For the purposes of our analysis, not only do we explore an alternative method to measure the effect of education on GDP, but we also employ data from three different sources, among which the Socio-Economic Accounts (SEA) of the recently-developed World Input-Output Database (WIOD) (Timmer, 2012) and the latest version of the Barro and Lee (2010) dataset on educational attainment. Our findings are based on the most comprehensive and accurate data in the field and the upper bound methodology we employ overcomes various impediments that conventional approaches have long faced. Previewing our results, we conclude that countries, in particular low-income ones, could greatly benefit by attaining a schooling distribution similar, for example, to that of the Unites States. On average, our estimates suggest that a country could raise its output by 67% and, also, halve its output gap to the United States with increases in education. From these findings it follows that the income variation could have been decreased by up to 37.4%, whereas among the low-income countries this estimate would reach 52.5%. In contrast to conventional approaches which assign to education a very limited part regarding its impact on cross-country income variation, our study illustrates the crucial role it can play for decreases in the gap between the developed and the developing world. In a sample of 27 countries, for example, conventional approaches are found to assign only between 2.2% and 16.6% of cross-country income variation to education.

The secondary objective of our study refers to the construction of relative wages estimates. As will be demonstrated in subsection 3.3, relative wages constitute an in-herent component of our upper bound calculations. The SEA provides us with data on them but we take the analysis a step further by also estimating relative wages on the basis of a high- versus low-skilled industries approach. To this end, data from UNIDO (2006, 2011) are employed. However, as subsection 5.2 will discuss, proxy measures only poorly capture the actual pattern of relative wages. The UNIDO estimates consistently underestimate relative wages, a finding potentially driven by the increasingly important phenomenon of offshoring.

The remaining paper is organized as follows: In the subsequent section, we set the theoretical foundations of the education-income relationship. Section 3 discusses the methods employed in the literature to quantify this relationship and introduces the reader to the alternative “upper bound” approach we are following. Section 4 describes our data and measures and section 5 our findings, whereas section 6 compares our outcomes to the ones already suggested in the literature. Section 7 concludes.

2

Theoretical Foundations

2.1 Private Returns to Education

On the one side of the schooling-income spectrum lies the seminal contribution of Jacob Mincer (1974), who first calculated the returns to schooling and, thereby, implied that the change in a country’s average level of schooling could be a key determinant of income growth. According to the famous Mincerian wage equation, the logarithm of earnings is linearly related to individuals’ years of schooling. The slope of this relationship denotes the average private rate of return to one additional year of education. The equation, augmented with two factors representing working experience, takes the following form:

ln(Wi) = β0+ β1Si+ β2Xi+ β3Xi2+ i (1)

Where ln(Wi) is the natural logarithm of the wage of individual i, Si represents years

of schooling, Xi years of labor market experience and Xi2 the square of labor market

experience. i is the error term.

Equation (1) has been criticized on the basis of omitting individuals’ characteristics, such as inherent ability, which could in turn overstate the rate of return to education (β1) (Barro and Lee, 2001). However, research has concluded that any upward “ability

bias” is offset by a downward bias stemming from measurement error in the years-of-schooling variable (Angrist and Krueger, 1991; Card, 1999, 2001). Furthermore, the micro-economic strand of literature has exploited natural experiments in which variabil-ity in schooling attainment is generated by some exogenous force, such as a change in compulsory schooling laws, the time of the year an individual is born or the proximity to college (Kruger and Lindahl, 2001). All have ruled in favor of a positive link between education and income. In an influential paper, Duflo (2001) has also documented a pos-itive relationship between schools constructed in Indonesia and wages of the country’s workforce.

The Mincerian wage equation has been estimated for numerous countries2and results have revealed that it fits the data rather well, even under very different economic and educational systems (Krueger and Lindahl, 2001). On the whole, compelling evidence suggests that more schooling is associated with higher individual earnings. Simple OLS regressions reveal that the rate of return to education (β1) takes values between 0.05 and

0.153. Typically, each additional year of schooling raises private earnings by about 10% (Psacharopoulos, 1994). At the regional level, the highest average returns to schooling are attained in Sub-Saharan Africa and Latin America and the Caribbean, whereas the lowest in OECD countries (Psacharopoulos and Patrinos, 2004). More specifically, in Sub-Saharan Africa, the return to one extra year of schooling is about 13.4%, whereas the average for OECD countries centers around 6.8% (Psacharopoulos, 1994). The coefficient for Asia is similar in magnitude to the 10% world average (Psacharopoulos and Patrinos, 2004). In sum, returns turn out to be higher for low-income countries, lower levels of schooling and women (Psacharopoulos, 1994; Psacharopoulos and Patrinos, 2004).

2

For an overview, see: Psacharopoulos (1994) and Psacharopoulos and Patrinos (2004).

3_{Instrumental variable techniques suggest that the rate of return to education (β}

1) is slightly higher

2.2 Social Returns to Education

On the other side of the schooling-income spectrum, focus is placed on the social, rather than the private, returns to education. Although research on the private returns has, in general, reached a consensus, the literature regarding social returns has only produced inconclusive outcomes. According to Pritchett (2006), social returns to education may be higher or lower than private ones.

On the one hand, social returns will exceed private ones, if education produces posi-tive externalities that result in technological progress and growth of the economy and/or reduction in crime and inequality, improvements in health and more informed political decisions (Krueger and Lindahl, 2001; Hanushek and Woessmann, 2008). More specif-ically, education increases the innovative capacity of an economy (Romer, 1990) and, according to the seminal contribution of Nelson and Phelps (1966), facilitates the imita-tion and adopimita-tion of new and more productive technologies. An educated labor force is better at creating, implementing and adopting new technologies and, thereby, generating growth. Consequently, economies with more skilled workers have higher labor produc-tivity, generate more ideas and grow faster. Education might as well act as an engine that attracts other factors, such as physical capital, which contribute to income growth (Lucas, 1990). Vandenbussche et al. (2006) also study the contribution of education to economy-wide technological improvements and conclude that skilled labor indeed has a growth-enhancing effect, particularly in countries closer to the technological frontier. Furthermore, recent studies discover evidence of education’s externalities in areas such as reduced crime (Lochner and Moretti, 2004), improved health of children (Currie and Moretti, 2003) and improved civic participation (Milligan et al., 2004). Finally, edu-cation can facilitate inequality reductions. Under the assumption that technology is skill-biased, technological progress widens inequality. Increases in education are, thus, required to counterbalance this effect (Goldin and Katz, 2007).

“knowledge trap” occurs in economies where skilled workers favor broad but shallow knowledge. Rich countries are rich, the author concludes, because they attain deeper knowledge among skilled workers.

From the above-outlined arguments, it becomes apparent that research on social re-turns to education has produced mixed results. In sum, while there is no particular evidence favoring externalities, there is also no compelling evidence against their exis-tence (Pritchett, 2006). Because of this caveat, the literature has largely adopted private returns to education in order to construct measures of human capital and, subsequently, examine its impact on economic growth, implicitly assuming that “the private return to human capital accurately describes its social return” (Caselli, 2005, p.682)4. In the following section, we turn to the techniques that attempt to measure the contribution of human capital on economic growth and review the respective findings of the literature.

3

The Contribution of Human Capital to Economic Growth:

Measuring its Magnitude

As already documented, the Mincerian wage equation implies that schooling positively affects income growth at the country level. Additionally, human capital enters eco-nomic growth theories through various channels and economists have long emphasized its importance, as described by education, to economic development. In the neoclas-sical growth model, for example, no special role is assigned to human capital (Solow, 1956). In endogenous growth models, however, human capital holds a central role that can be divided into two categories: The first broadens the concept of capital to include human capital. In this case, growth is maintained through the accumulation of human capital over time (Lucas, 1988). The second attributes growth to the existing stock of human capital (Nelson and Phelps, 1966; Romer, 1990). From these premises, the macro growth-literature turns to the aggregate, rather than the individual, effect of education on countries’ GDP growth rates. The present section provides a review of the methods hitherto employed to quantify this effect as well as the outcomes reached, and introduces the reader to the alternative “upper bound” approach we are following. Growth regres-sions and development accounting techniques constitute the main tools to estimate the impact of human capital on economic growth and are, in turn, discussed below.

3.1 Empirical Growth Models

Growth regressions have been a useful tool in measuring the effect of human capital on economic growth. On the one hand, a stream of empirical research discovers a positive link between the two. The influential work of Mankiw et al. (1992) follows this tradition. Treating human capital as an input in the production function, the authors conclude that cross-country income disparities are due in large part to differences in human capital, alongside savings and population growth. Benhabib and Spiegel (1994)

4

discover a positive effect of human capital levels, rather than human capital growth, on economic growth. Sala-I-Martin et al. (2004) claim that, among 67 explanatory variables, primary school enrollment is one of the most robust factors affecting GDP growth. On the other hand, however, there is also a stream of research that fails to find a significant impact of human capital on economic growth. Hall and Jones (1999), for example, provide evidence that differences in physical capital and educational attainment can only partially explain the variation in output per worker. In contrast, the authors assert that income differences are mainly driven by, what they call, “social infrastructure”, namely by differences in institutions and government policies. Hendricks (2002) reaches a similar conclusion regarding the effect of human capital by exploiting earnings of US immigrants. He builds on the idea that observing immigrant workers from different countries in the same labor market provides an opportunity to estimate their human capital endowments and suggests that human and physical capital account for only a fraction of cross-country income differences. It, thus, becomes apparent that growth regressions have long produced mixed results regarding the effect of human capital on growth. Below, we briefly review the most recent empirical research on this field which also takes a more firm stand regarding the human capital-growth relationship.

First, Krueger and Lindahl (2001) examine the magnitude of this relationship over varying time intervals (T = 5, 10, 20 years). In its general form, the equation they estimate is the following:

∆ln(yi,(t−1,t))

T = β1Si,(t−1)+ β2

∆Si,(t−1,t)

T + β3ln(yi,(t−1)) + i,t (2) Their dependent variable is the annualized change in a country i’s logarithm of real GDP per capita. For the education variable (Si), they turn to an older version

of the Barro and Lee dataset on educational attainment and employ the measure of average years of schooling (Barro and Lee, 1993). The variables denoting the level of (S_i,(t−1)) and change in (∆S_i,(t−1,t)) education are, first, interchangeably included in the regressions. Subsequently, they enter the equation simultaneously. OLS estimates yield positive and statistically significant coefficients for both levels and changes in education. When Krueger and Lindahl (2001) consider small time intervals (five years), changes in education have only little effect on GDP growth with the coefficient β2taking a maximum

value of 0.039. However, this effect is intensified under larger time intervals resulting in coefficients between 0.086 (ten years) and 0.184 (twenty years). After adjusting for potential measurement error, which could be biasing β2downwards, the authors conclude

that the coefficient describing the returns to investment in education could increase up to 0.30. Furthermore, the share of the variation in economic growth that the model explains, as reflected by the R2 of the regression, reaches 28%. It is, however, noteworthy that when physical capital (its level and/or growth rate) is included among the regressors, Krueger and Lindahl (2001) have difficulties in discovering significance for their schooling variable. The coefficient β2falls by more than 50% when capital growth is included, thus,

Second, in an influential paper, Cohen and Soto (2007) also examine the relationship between human capital and economic growth. The authors further contribute to the literature by constructing a new dataset for years of schooling across countries, intended to reduce the measurement error present in older datasets. Using their own estimates, the authors discover positive and significant coefficients for their schooling variable in both cross-country and panel regressions. The authors first estimate an equation similar to that of Krueger and Lindahl (2001) and conclude that the coefficient describing the returns to investment in education takes values between 0.096 (for the 1960-1990 period) and 0.123 (for the 1970-1990 period) fairly in line with the average findings of labor studies. The inclusion of the initial level of physical capital reduces the magnitude and significance of the schooling variable but, in contrast to Krueger and Lindahl (2001), does not turn it insignificant at conventional levels. In a panel setting, Cohen and Soto (2007) estimate the following equation:

ln(yi,t) = β1Si,t+ β2ln(

ki,t

yi,t

) + βt+ βi+ i,t (3)

Where ki,t

yi,t denotes the capital-output ratio, βi the fixed effects and βt the time

dummy. The coefficient β1 is always positive and statistically significant and is of the

order of 12%, again close to the typical Mincerian return.

Third, following the release of their updated dataset on educational attainment, Barro and Lee (2010) also investigate the relationship between human capital stock and income. Employing the most recent estimates on schooling, the authors discover evidence favoring a positive and statistically significant effect of education on GDP. In its general form, the equation they estimate is the following:

ln(yi,t) = βi,t+ β1Si,t+ β2ln(ki,t) + i,t (4)

Where β1 denotes the marginal rate of return to an additional year of schooling and

β2 the share of capital in total output (α in a Cobb-Douglas production function). A

period dummy variable is also included alongside a dummy for oil exporting countries. Using random and fixed effects panel estimation techniques, as well as instrumental variables’ procedures, Barro and Lee (2010) conclude that the estimated rate of return to an additional year of schooling (β1) varies between 5% and 12% when parents’ education

is used as IV for the current level of education. Without applying the IV methodology, the rate of return to education is around 2% which implies that, ceteris paribus, output for the world economy as a whole would increase by 2% for every additional year of schooling. When the analysis is performed across regional groups, Barro and Lee (2010) discover that advanced countries experience the highest rate of return to education (up to 13.3%), whereas Sub-Saharan Africa and Latin America the lowest (6.6% and 6.5% respectively). Finally, the authors also examine whether the return to schooling varies across levels of education. Indeed, whereas β1 is 0.10 for secondary education, it reaches

of education and countries’ income. This disparity could, however, be an indication for the existence of social returns to education in rich countries. In section 2.2, we presented, for example, Pritchett’s (2006) line of reasoning as to why social returns are below private ones in poor economies, in contrast to rich ones. The findings of Barro and Lee (2010) seem to support this argumentation.

Before we conclude the present subsection, a remark regarding the updated Barro and Lee dataset on educational attainment is warranted. The quality of the Barro and Lee data has often been questioned in the literature. de la Fuente and Dom´enech (2002), as well as Cohen and Soto (2007), to name but a few, emphasize various shortcomings of the Barro and Lee methodology. They claim that the series severely suffer from measurement error and often yield implausible outcomes. For example, according to an earlier version of Barro and Lee (2001), in 1960 Bolivians aged 15 and over were just as educated as the French population and, in 1980, the average Ecuadorian had more years of schooling than the average Italian. Notice, however, that the Barro and Lee (2010) estimates presented above, as well as the data we later use for our analysis, are derived from the updated version of their dataset. Not only have the authors extended their estimates regarding the countries included and the years examined, but they have also improved on the accuracy of their estimates by using more information and better methodology. Measurement error has been reduced and the improvements made address most of the concerns raised by critics (Barro and Lee, 2010). We are, therefore, confident that the findings we present in the subsequent sections are based on the most comprehensive and accurate education data available.

3.2 Development Accounting

Apart from growth regressions, economists have also used development accounting as a tool to quantify the impact of human capital on economic growth. Therefore, in order to answer the question “why are some countries so much richer than others”, emphasis has mainly been placed on differences between countries’ physical and human capital as well as the efficiency with which they are used (Caselli, 2005). More specifically, development accounting usually begins with a standard Cobb-Douglas production function of the following form:

y = Akαh1−α (5)

Where y denotes per capita GDP, k the capital-labor ratio (k = K/L), h the av-erage human capital and A the efficiency with which factors are used. α is a constant symbolizing the capital share.

framework with two factors of production (physical and human capital), a large fraction of the cross-country income variance remains unexplained. To improve on these findings, current research has focused on advancing human capital measurement and/or adopt-ing functional forms that could more accurately capture how it affects income growth (Caselli, 2005; Caselli and Feyrer, 2007).

In an extensive review of the development accounting literature, Caselli (2005) seeks an answer to the question “how much of the variation in per capita income can be explained by the variation in physical and human capital”. The author concludes that the fraction of the income variance attributed to physical and human capital centers around 0.40. Furthermore, Woessmann (2003) specifies that differences in human capital account for 21% of the international variation in output per worker. Consequently, 60% of the income variation is due to residual total factor productivity. Since the variation in income per capita is smaller in homogenous groups of countries, Caselli (2005) also calculates the explanatory power of physical and human capital for countries lying above and below the median of the income distribution, as well as for OECD and non-OECD countries. On the whole, he concludes that it is easier to explain income differences among the rich than among the poor economies. In rich countries, the fraction of the income variance explained by physical and human capital is 0.620 versus 0.407 in poor ones. Similar results are obtained for OECD and non-OECD members. At the continental level, 23% of the income variance in Europe, 30% in Africa, 43% in Asia and Oceania and almost 47% in the Americas can be attributed to physical and human capital variation.

3.3 New Insights on an Old Topic: The “Upper Bound” Approach

In the previous subsections, we outlined the mechanisms through which human capital affects economic growth and discussed the magnitude of this effect as suggested by different strands in the literature. In the present section, we explore an alternative methodology to measure how much would output in a country increase if workers were to have more schooling. This approach, recently introduced by Caselli and Ciccone (2011), constitutes the basis of the remaining analysis.

increase in GDP per worker be, if its high-skilled individuals comprised 53%, instead of 5.3%, of its population? Broadly stated, how much of the output gap with rich countries (e.g. the United States) can developing countries close by increasing their quantity of schooling?

In order to answer this question, Caselli and Ciccone (2011) explore an alternative to the commonly-used parametric production function approach. In contrast to the conventional methods, as outlined in sections 3.1 and 3.2, the upper bound approach is characterized by a non-parametric form. Their analysis is based on two key assumptions: (i) the aggregate production function is weakly concave in inputs and (ii) there is perfect substitutability among different schooling levels. From these premises, they derive the upper bound formula on the increase in output that can be generated by more schooling. The first assumption is commonly made in the development accounting literature. The second one, of perfect substitutability among different schooling levels, has been rejected empirically. However, the assumption remains useful since it produces the upper bound on output increases regardless of the true pattern of substitutability or complementarity among schooling levels. The intuition why perfect substitutability yields this upper bound is explained by Caselli and Ciccone (2011) in a model with two schooling levels, schooled and unschooled. According to the authors, an increase in the share of schooled workers has two types of effects on output. The first is that more schooling increases the share of more productive workers, which, in turn, increases output. The second is that more schooling raises the marginal productivity of unschooled workers and lowers the marginal productivity of schooled workers. Under perfect substitutability between schooling levels, the second effect is ruled out. Increases in marginal productivity are more than offset by decreases in it and, therefore, perfect substitutability yields an upper bound on the increase in output generated by more schooling.

A sequence of formulas yields the upper bound, the basic elements of which are in turn described below. Suppose that output Y is produced with physical capital K and workers Li with different levels of schooling attainment i = 0, . . . , m:

Y = F (K, L0, L1, . . . , Li, . . . , Lm) (6)

The (country-specific) production function F is assumed to be increasing in all ar-guments, subject to constant returns to scale and weakly concave in inputs.

Next, define sias the share of the labor force with schooling attainment i and sCN T =

(s0, s1, . . . , si, . . . sm) as the vector collecting all the shares. The superscript CN T refers

to the country under examination. We wish to measure the increase in output per worker if schooling were to change from the current schooling distribution (sCN T) to the schooling distribution of USA (sU SA) which assigns more weight on higher schooling attainments.

yU SA− yCN T yCN T ≤ m P i=1 (wCN Ti wCN T 0 − 1)(sU SA i − sCN Ti ) 1 + m P i=1 (wiCN T wCN T 0 − 1)sCN T i (7)

Where, as already mentioned, CN T refers to the country we are studying and U SA constitutes our benchmark. The variable y denotes the PPP converted GDP per worker at 2005 constant prices and, in our calculations, is derived from the Penn World Tables 7.0 (rgdpwok in Heston et al. (2011)). Furthermore, the ratio w

CN T i

wCN T 0

refers to the relative wages of workers with schooling attainment i (e.g. high-skilled workers) and workers with the lowest schooling attainment 0 (e.g. low-skilled workers). Finally, the variable sCN T_i measures the share of the labor force with schooling attainment i (e.g. the high-skilled share). Note that in Caselli and Ciccone (2011) inequality (7) is derived based on the assumption that, as the schooling distribution changes from the original (sCN T) to the benchmark one (sU SA), physical capital adjusts to leave the marginal product of capital unchanged, namely M P KU SA _{= M P K}CN T_{. This could be, for example,}

because physical capital is mobile internationally5

In sum, the upper bound formula reveals that the increase in output per worker that can be generated by additional schooling is always below a bound that depends on the wage premia of different schooling groups relative to a schooling baseline. It is exactly the right-hand side of the above inequality that yields the maximum increase in output a country can achieve by increasing its schooling.

The upper bound formula is an important contribution by Caselli and Ciccone (2011) that constitutes an alternative to the conventional methods that measure the effect of human capital on economic growth. A number of advantages emerge from this approach. First, a problem that economists have long faced is how to define and measure human capital. The literature has used literacy rates, school enrollment ratios and average years of schooling as proxies for human capital, the latter being the most commonly used. Still, however, years of schooling are an imperfect measure of human capital (Krueger and Lindahl, 2001; Cohen and Soto, 2007), the choice of which very much de-pends on data availability (Woessmann, 2003). What Caselli and Ciccone (2011) suggest is a more straightforward approach. In order to implement the upper bound calcula-tions, we do not need to argue in favor of a human capital measure but rather only focus on shares of the population by educational level and their wages. Second, growth regressions, an important tool to quantify the relationship between human capital and economic growth, have been criticized on the basis of endogeneity. Omitted variables, such as institutional factors, and/or reverse causality could bias the coefficients in any direction. Woessmann (2003), for example, documents that the relationship between education and growth is sensitive to model specification. It is important to note, how-ever, that, recently, panel data estimations, as well as instrumental variable techniques have improved upon the issues of endogeneity. Still, our methodological set-up does not suffer from these problems. Third, the macro-economic growth regressions impose

the restriction that all countries experience the same relationship between growth and education. Micro-economic evidence indicates, however, a heterogeneous effect of the latter on the former as reflected by the fact that the returns to schooling vary across countries. Furthermore, according to Krueger and Lindahl (2001), education is statisti-cally significant and positively associated with subsequent growth only in countries with low levels of education. The approach of Caselli and Ciccone (2011) allows us to treat each country separately, or at least as part of a homogenous group, and is not subject to the restrictive hypothesis that, for example, increases in schooling in India exert the same effect on growth as increases in schooling in the United States.

4

Data and Measures

In the previous subsection, we presented the upper bound approach, an alternative method that measures how much increases in schooling affect a country’s output, as well as the advantages it entails. It is, thus, warranted at this point of the analysis to discuss the data and measures Caselli and Ciccone (2011) employ to derive the upper bounds, alongside the ones we do. From the upper bound formula (inequality (7)) it becomes apparent that data on two basic variables are required: shares of the population with different educational levels i (sCN T_i ) and their respective relative wages (wCN Ti

wCN T 0

). The following subsections discuss them in turn.

4.1 Data on Educational Shares

Regarding shares of the population with different educational levels i (sCN T_i ), Caselli and Ciccone (2011) either use the IPUMS (Integrated Public Use Micro-data Series) national census data or the latest version of the Barro and Lee (2010) dataset. We, on the other hand, apart from the Barro and Lee (2010) dataset, also turn to the Socio-Economic Accounts (SEA) of the recently-developed World Input-Output Database (WIOD) (Tim-mer, 2012) to find data for the educational-shares variable of the upper bound formula. The SEA database covers 15 years (1995-2009) and 40 countries6 and constitutes an im-portant contribution to the literature. It updates and extends the EUKLEMS dataset (O’Mahony and Timmer, 2009) and is largely based on information from detailed labor force statistics (EUROSTAT’s labor force survey (LFS), in particular). Furthermore, we have already documented the improvements in the quality of the Barro and Lee (2010) data. Consequently, we are confident that our findings rely on the most recent, comprehensive and detailed data available.

For the remaining of our analysis, we distinguish between two groups of skills: high (i) and low (0). Therefore, an important difference between our approach and that of Caselli and Ciccone (2011) is that they construct data for more schooling-attainment

6_{Australia, Austria, Belgium, Brazil, Bulgaria, Canada, China, Cyprus, Czech Republic, Denmark,}

groups than we do. We also performed the upper bound calculations by distinguishing between three skill-groups, namely high, medium and low, and discovered that our results did not vary significantly. More specifically, the correlation between the high-low and the high-medium-low upper bound was around 0.90, statistically significant at the 1% level. Consequently, we consider the distinction between high- and low-skilled groups as a good indicator for the upper bounds and, therefore, we employ it for the remaining of our study.

From the Socio-Economic Accounts, we use the variable that measures the hours worked by (i) high-skilled (H HS), (ii) medium-skilled (H M S) and (iii) low-skilled (H LS) persons engaged, as a share in total hours. It is important to note, however, that, in order for the upper bound formula to hold, education shares should sum up to unity. Therefore, when we distinguish between two skill-groups, the medium-skilled category is added to the high-skilled one. Since, according to the SEA, the medium-skilled group refers to (upper) secondary education and post-secondary non-tertiary education, we believe that it is reasonable to add the medium-skilled group to the high-rather than the low-one.

We next turn to the Barro and Lee dataset on educational attainment (Barro and Lee, 2010), our second data source, and define high- and low-skilled individuals. We do so by drawing an analogy to the classification that the SEA also uses. More specifically, according to the SEA, the high-skilled category refers to first stage of tertiary education and second stage of tertiary education. In Barro and Lee (2010), this corresponds to lh, namely people who enrolled to tertiary schooling (some completed it, some others did not). Again, since we require the education shares to sum up to one, when two skill-groups are used, we augment the high-skilled category with the medium one, which in Barro and Lee (2010) corresponds to lsc, namely people who completed secondary education. The remaining share of the population is classified as low-skilled.

4.2 Data on Relative Wages

Regarding relative wages, Caselli and Ciccone (2011) predict them through Mincerian regressions again based on IPUMS data. The relative-wages data we have at our disposal come from two sources: SEA, as well as the Industrial Statistics of the United Nations Industrial Development Organization (UNIDO, 2006, 2011) and are, in turn, discussed below. Again, we distinguish between two groups of skills: high and low, as described in the previous subsection.

4.2.1 Data on Relative Wages: SEA

As a first step, we extract data on relative wages from the Socio-Economic Accounts (SEA) of WIOD (Timmer, 2012). The wage of each skill-group in SEA is estimated based on the “total industries” category. For the low-skilled group (L), for example, the wage is computed according to the following formula7:

7

w_LCN T = LABLS ∗ LAB

H LS ∗ H EM P (8)

where CN T denotes the country under examination. LABLS is the low-skilled labor compensation as a share in total labor compensation, LAB the labor compensation in millions of national currency and H EM P the total hours worked by persons engaged. Furthermore, H LS denotes the hours worked by low-skilled persons engaged as a share in total hours. Subsequently, the ratio of the high-skilled group’s wage to the low-skilled one’s is computed in order for the relative wage to be derived8.

4.2.2 Data on Relative Wages: UNIDO

So far, we have focused on relative-wages data from the SEA. We, now, turn to a different approach to estimate them. To this end, we employ UNIDO data and attempt a high-versus low-skilled industry level analysis. We use two different versions of the UNIDO database (ISIC Rev.2, 2006 and ISIC Rev.3, 2011) which cover the periods 1963-2003 and 1990-2008 respectively. The databases comprise information at the industry level. We, first, calculate the ratio of the categories (a) wages and salaries and (b) employment and remove all observations for which this ratio equals 0. This is because such observations entail wages and salaries = 0 and employment > 0 which cannot be the case. We, second, classify industries as high- and low-skill intensive. Even though all industries employ both types of workers, high- and low-skilled, this approach is not uncommon in the literature (Keesing, 1971; Peneder, 1999; Woerz, 2005). Finally, we calculate the average wage by skill-group and construct the respective high-to-low ratios.

The hurdle of this approach is to classify industries as low- and high-skill intensive. Various classifications have been proposed and we calculate relative wages according to five of them. We then compare our estimates to the SEA relative wages and choose the classification that produces values as close as possible to SEA, since the latter are generated by labor force statistics and are, thus, more accurate. The criteria we employed in order to compare the classifications are put forward in table 7 of the appendix.

The classification we prefer has its roots on the analysis of Ciccone and Papaioan-nou (2009). The authors propose a ranking of industries according to their knowledge intensity. More specifically, they rank US manufacturing industries according to the average years of schooling of their employees (their reference year is 1980). We identify as high-skilled those industries that lie above the 90% percentile of their “average years of schooling” distribution and as low-skilled those that lie below the 10% percentile. We, therefore, consider as high-skilled the industries 353 (Petroleum refineries), 352 (Chemi-cals, other) and 342 (Printing and publishing), whereas as low-skilled the industries 323 (Leather products), 322 (Wearing apparel, except footwear) and 324 (Footwear, except rubber or plastic). Most importantly, we require all of the above (six) industries to exist

8_{Note at this point that the relative wages for the year 2003 are generated through interpolation due}

in order for a country-year observation to be included in our analysis. Otherwise, the observation is dropped.

We have already stated that we are using two versions of the UNIDO database. Industries are, however, differently classified between the two and, therefore, we have to draw an analogy between the industry classification of the old and the new version of UNIDO. In the latter, high-skilled industries are 2320 (Refined petroleum products), 242 (Other chemicals), 221 (Publishing) and 222 (Printing and related service activities). Accordingly, low-skilled industries are 191 (Tanning, dressing and processing of leather), 1810 (Wearing apparel, except fur apparel) and 1920 (Footwear). Again, we require all of the above industries to exist in order for a country-year observation to be included in the analysis.

A few remarks are in order. First, notice that the Barro and Lee data on educational attainment which we will match to the UNIDO relative wages in order to compute the upper bounds are calculated in five-year intervals. Therefore, and with the aim of using as much information as possible, UNIDO relative wages are calculated as a three-year average. In order, for example, to compute the relative wage for the three-year 1995, information from years 1994 and 1996 is also utilized. Second, observations for which the predicted relative wage was smaller than 1 were dropped from the sample9. Third, relative-wages data from the two UNIDO datasets overlap for the years 1990, 1995 and 200010. Consequently, for the years before 1990, we use the old version of UNIDO (2006), whereas for the years after 2000 the new one (UNIDO, 2011). For the overlapping years, we also prefer the old version of UNIDO since it produces more observations than the new one. Furthermore, there is a very high correlation between relative wages of the old and the new database for the overlapping years (0.9852 and 0.9442 for the years 1995 and 2000 respectively, highly significant at the 1% level11_{) . Because of the very high}

correlation, when an observation was missing from the old UNIDO dataset, estimates from the new one were used instead12.

5

The Upper Bounds: Findings and Insights

Having all data at our disposal, we are now ready to compute the upper bound, as described by the right-hand side of inequality (7), by country and year. This calculation will give us the maximum increase in output that increases in schooling can generate. We have already stated that we employ two measures for relative wages, one stemming from SEA (Timmer, 2012) and the other from UNIDO (2006, 2011), as well as two measures for educational shares, from SEA (Timmer, 2012) and Barro and Lee (2010).

9_{The only country-year observation with a relative wage smaller than 1 that could enter our analysis}

was Algeria in 1975. Notice that focus is only placed on five-year intervals.

10_{Again, the focus is on five-year intervals.} 11

The correlation for the year 1990 was not computed, since for that particular year the new version of UNIDO only had 3 observations.

12

Hence, we compute the upper bound for different combinations of the abovementioned data sources: (i) First, data for both relative wages and educational shares are derived from SEA (Timmer, 2012). We call this method SEA-SEA. (ii) Second, we employ the SEA data for relative wages (Timmer, 2012) and the Barro and Lee (2010) data for educational shares. This is the SEA-Barro-Lee approach. (iii) Third, we combine UNIDO (2006, 2011) relative wages with educational shares from Barro and Lee (2010). We name the latter method UNIDO-Barro-Lee.

5.1 The Upper Bounds across Different Combinations of Data Sources

The upper bounds by country and year have been computed for different combinations of the data sources, as outlined above (SEA-SEA, SEA-Barro-Lee and UNIDO-Barro-Lee). Among them, however, we want to place particular focus on the one that attains the largest explanatory power. To this end, we examine what the three approaches predict regarding the impact of increases in education on cross-country income variation. The upper bound gives us the increase that a country’s output could undergo. Based on it, we calculate the attained output, namely the one that countries could have if the upper bound increases were materialized. Subsequently, we compute the following ratio, which we name income variation:

income variation = var(log(yattained)) var(log(yactual))

(9) Where var(log(yattained)) denotes the cross-country income variation based on the

GDP per worker that countries could have, if the upper bound increases were applied, and var(log(yactual)) denotes the cross-country income variation based on the GDP per

worker that countries actually have. For values smaller than 1, this ratio reveals that the cross-country income variation decreases with increases in education. Values close to 1 indicate that the cross-country income variation largely remains the same, whereas values close to 0 imply that increases in education greatly decrease cross-country income variation. Consequently, the smaller the magnitude of the incomevariation variable, the larger the explanatory power of the approach employed. Another variable that we use in the remaining of our analysis exploits the percentage change in income variation due to increases in education (income variation (%) = income variation − 1). Negative values of this variable reveal that cross-country income variation decreases with increases in education. Consequently, the larger its absolute value, the larger the explanatory power of the approach employed.

Table 1 includes estimates for both income variation and income variation (%) across our three approaches. The smaller-than-one values for income variation, as well as the negative ones for income variation (%) clearly indicate that the cross-country income variation could be to great extent decreased with increases in education.

Relative Wages from: Educational Shares from: income variation income variation (%) 1995 SEA SEA 0.461 -53.9% SEA Barro-Lee 0.444 -55.6% UNIDO Barro-Lee 0.682 -31.8% 2000 SEA SEA 0.615 -38.5% SEA Barro-Lee 0.493 -50.7% UNIDO Barro-Lee 0.733 -26.7% 2005 SEA SEA 0.507 -49.3% SEA Barro-Lee 0.446 -55.4% UNIDO Barro-Lee 0.683 -31.7%

Table 1: Explanatory Power across Different Combinations of Data Sources We observe that, among the three approaches, the SEA-Barro-Lee one entails the largest explanatory power since it produces the smallest values for the income variation variable (and, accordingly, the largest absolute values for the income variation (%) variable). In 1995, for example, cross-country income variation could be by 55.6% de-creased, had countries managed to attain the US educational levels. Consequently, in the remaining of the analysis, we delve into the SEA-Barro-Lee approach. It is also the most intuitive one since it deals with shares of the population with different educational levels, rather than shares of hours worked by persons engaged, as the SEA-SEA approach does.

5.2 A Note on the High- versus Low-Skilled Industries Method

In the previous subsection, we explored three alternative approaches, the SEA-SEA, the SEA-Barro-Lee and the UNIDO-Barro-Lee, and concluded that the second one attains the largest explanatory power. However, as table 1 reveals, under the UNIDO-Barro-Lee approach, we obtain relatively high values for the income variation variable (and, accordingly, relatively low absolute values for the income variation (%) one). As com-pared to the other two approaches, the UNIDO-Barro-Lee one assigns to education the smallest role regarding its impact on cross-country income variation. This remark points our attention to the reliability of the high- versus low-skilled industries method and the relative wages estimates it produces.

leather and footwear). The correlation between the “actual” SEA relative wages and those predicted through the SEA industry-level analysis is 0.4361, higher than the one between the UNIDO and the “actual” SEA relative wages but still not large. It, thus, becomes apparent that the high- versus low-skilled industries approach only modestly approximates the “actual” SEA relative wages. Table 2 below presents the correlations:

SEA (actual) UNIDO SEA (industry-level) SEA (actual) 1.0000 0.3364 0.4361

UNIDO 1.0000 0.2858

SEA (industry-level) 1.0000

Table 2: Correlation Matrix

Consequently, the low explanatory power of the UNIDO-Barro-Lee approach can be attributed to the fact that the high- versus low-skilled industries analysis does not accurately predict relative wages. More specifically, it consistently underestimates them, particularly for the poorest countries of the sample. For India, Indonesia and Mexico, for example, the SEA data source (Timmer, 2012) yields relative wages between two and four times higher than the ones predicted by UNIDO (2006, 2011). According to inequality (7), however, an underestimation of the relative wages results in a lower upper bound and, thus, a smaller increase in a country’s output and a lower explanatory power of the approach.

also face a similar event.

Consequently, the SEA data lead us to conclude that a high-skilled industry in the United States is not necessarily also a high-skilled industry in, for example, Taiwan. All in all, relative wages predicted from industry-level analyses should be treated with caution since, according to our findings, they do not constitute good proxies for relative wages. First, they are likely to underestimate the true pattern of relative wages and, second, a high- versus low-skilled industries classification is difficult to hold for all coun-tries. An explanation for the latter could be the important phenomenon of offshoring which allows foreign labor to substitute for domestic workers’ specific tasks. Economies increasingly participate in global supply chains in which the many tasks required to manufacture complex industrial goods (or to provide services) are performed in several disparate locations at a lower cost than domestically (Grossman and Rossi-Hansberg, 2006). In a globalized world, components and/or unfinished goods can be easily and cheaply transported allowing firms to take advantage of factor cost disparities (Grossman and Rossi-Hansberg, 2008). This process, however, may affect both the relative demand for certain types of labor as well as the structure of wages (Acemoglu and Autor, 2010). More specifically, research has documented that unskilled labor-intensive stages of the production are transferred to unskilled labor-abundant developing countries, whereas the relatively skilled stages remain in the skilled labor-abundant developed world (Fos-ter et al., 2012). Consequently, these offshoring pat(Fos-terns could distort the ranking of industries according to their knowledge intensity and render relative wages estimated through industry-level analyses rough proxies.

5.3 The Upper Bound in Detail: SEA Data for Relative Wages and Barro-Lee for Educational Shares

Across the different combinations of data sources, subsection 5.1 concluded that the SEA-Barro-Lee one entails the largest explanatory power. Therefore, we next delve into this approach and, in detail, present our findings for the upper bound, the maximum increase in output that can be generated by increases in education. Note that our focus is now placed on a larger group of countries, namely all SEA countries, as listed in footnote 5, with the exception of the United States and Luxemburg. The former constitutes our benchmark whereas the latter has in the years 1995, 2000 and 2005 outperformed the US in terms of GDP per worker. The rationale of increasing education with the aim of raising output would not, however, be intuitive if countries richer than the United States were included in the sample.

The figures below show the upper bounds for the three years of our sample, namely 1995, 2000 and 2005. For each country, we plot the upper bound, as described by the right-hand side of inequality (7), against the GDP per worker in that particular year13.

13_{A list of the upper bounds for all three approaches we employed can be found in the appendix. Table}

Figure 2 indicates that the upper bounds vary significantly both across countries and over time. However, in line with Caselli and Ciccone (2011), poorer countries experience larger upper bound increases in output when bringing their education to US levels. India, Indonesia and Mexico experience the largest computed upper bound gains. India in 2000 has an upper bound of the order of 4.332 which largely reflects the huge gap in education between the United States and India in that year. The average years of schooling in India were almost 3.6 versus 13 for the United States. Furthermore, India and the US experienced the largest difference in the share of high-skilled people, indicating that they were characterized by very different educational attainment levels. Brazil also experiences rather large upper bounds (e.g. 1.76 in 1995), in line with what Caselli and Ciccone (2011) also predict. The smallest upper bounds are for the Czech Republic and Russia (3% and 4% respectively) reflecting the fact that these countries had rather similar- in-magnitude educational attainment levels to the US. More specifically, they experienced the smallest difference in the share of high-skilled people as compared to the United States and, additionally, the average years of schooling were almost 13 in the Czech Republic and 11 in Russia.

The average of the computed upper bounds is 0.671. This implies that, on average, a country could increase its output by almost 67% by increasing education to the US levels. This is undoubtedly a significant increase in a country’s GDP. As the summary statistics table below indicates, for the country at the 75th percentile, there could be a sizable increase in output by almost 75%. The median increase is approximately 44%.

Variable Obs Mean Std. Dev. Min Max 25% Prc. 50% Prc. 75% Prc. Upper Bound 114 0.671 0.760 0.031 4.332 0.246 0.438 0.750

Table 3: Summary statistics for the upper bound

Figure 3: Upper bound income increases when moving to US educational attainment against countries’ initial output levels (in logarithms) (all countries and years included)

Another calculation that is interesting to perform is related to the output gap with our benchmark country, namely the United States. More specifically, we would like to explore the relationship between the output gap with the US that countries actually have and the output gap with the US that countries would have, had they managed to increase their education and, consequently, their output. To this end, we compute the ratio of the latter to the former. The table below presents the respective summary statistics14.

Variable Obs Mean Std. Dev. Min Max 25% Prc. 50% Prc. 75% Prc. Output Gap 70 0.458 0.253 0.025 0.948 0.237 0.490 0.633

Table 4: Summary statistics for the output gap ratio

The fact that the values presented in the table are smaller than 1 indicates that the output gap to the United States has decreased. This is also the intuition behind the whole upper bound reasoning. The maximum value of this ratio (0.948) refers to Russia in 2000 (followed by the Czech Republic in 2005 (0.942)) and indicates that its output gap with the United States has largely remained the same. Recall that Russia, alongside the Czech Republic, had the smallest upper bound output increase since its educational attainment levels were very similar-in-magnitude to those of the US. The

14_{Summary statistics are calculated only for positive values of this ratio. Negative estimates indicate}

average country manages to almost halve its output gap to the US with increases in schooling. India’s output gap to the US was in 2005 eight times higher than what it could have been with increases in education. Accordingly, Indonesia’s output gap to the US for that same year was almost four times higher than what it could have been. These estimates largely reflect the crucial role education plays for decreases in the gap between the developed and the developing world.

As a final measure, it is interesting to explore how much the cross-country income variation would decrease if countries managed to attain the US educational levels. This is done through the income variation variable we have already discussed. The difference with subsection 5.1 lies on the fact that we now extend our set of countries to include all SEA economies, with the exception of the United States and Luxemburg. Results are presented in table 5.

1995 2000 2005 income variation 0.740 0.722 0.626 income variation (%) -26% -27.8% -37.4%

Table 5: The impact of increases in education on cross-country income variation

The estimates reveal that the cross-country income variation in 2005 could be by 37.4% decreased if countries managed to attain US educational levels. On average, for the years 1995, 2000, 2005, cross-country income variation could have been lower by almost 30.4%. Notice that the absolute values of the income variation(%) variable are now lower than the ones we predicted in section 5.1. This is, however, expected since we are now dealing with a different and larger group of countries.

It is also noteworthy to explore what happens to the cross-country income variation when we look at specific sub-groups of countries. In Europe, for example, income vari-ation in 2005 could have been decreased by 30%, had countries managed to attain US educational levels. In Asia and the Pacific, cross-country income variation could have been 57% lower, whereas in the Americas 61%. It is also notable that, across low-income economies, income variation decreases to a larger extent. For countries that lie under the median of the GDP per worker distribution, cross-country income variation could be reduced by almost 43%. Furthermore, for those that lie below the 25% percentile, cross-country income variation could be reduced by almost 52.5%. Increases in education are overall beneficial since they trigger increases in output. However, low-income countries, in particular, could greatly converge in output due to increases in schooling.

6

Comparing the Upper Bound to Conventional Methods

in the Literature

an additional test we relax the physical-capital-adjustment assumption based on which inequality (7) is derived. In sum, we end up with a new set of upper bound estimates, as well as four additional approaches that measure the impact of human capital on cross-country income variation. Each of them is, in turn, discussed below and the estimates they produce are, subsequently, contrasted to our original upper bound findings.

First: We want to compare our outcomes regarding the effect of education on cross-country income variation to those of Caselli (2005). Drawing on the seminal contribution of Hall and Jones (1999), the author employs a production function of the following form:

Y = AKα(Lh)1−α (10)

which in per worker terms becomes:

y = Akαh1−α (11)

In equations (10) and (11), Y denotes a country’s GDP, K the aggregate capital stock, L the number of workers, h the average level of human capital and α a constant symbolizing the capital share. Furthermore, A is the efficiency with which factors are used (TFP), y the per capita GDP and k the capital-labor ratio (k = K/L). Subse-quently, we adopt the following expression of human capital:

h = eφ(s) (12)

which turns equation (11) into:

y = Akα(eφ(s))1−α (13)

In equations (12) and (13), s corresponds to average years of schooling. The function φ(s) is piecewise linear with slope 0.134 for s ≤ 4, 0.101 for 4 < s ≤ 8 and 0.068 for s > 8. More specifically, φ(s) = 0.134 ∗ s if s ≤ 4, φ(s) = 0.134 ∗ 4 + 0.101 ∗ (s − 4) if 4 < s ≤ 8 and φ(s) = 0.134 ∗ 4 + 0.101 ∗ 4 + 0.068 ∗ (s − 8) if s > 8. The values for the slope of the φ(s) function are chosen on the basis of Mincerian estimates, as discussed in subsection 2.1. Recall that in Sub-Saharan Africa, which has the lowest levels of education, the return to schooling is 13.4%, whereas in OECD countries, which have the highest levels of education, 6.8%. The world average is 10.1% (Psacharopoulos, 1994). Next, we define:

yAk = Akαand yH = (eφ(s))1−α (14)

which implies that output per worker (y) is described through yH and yAk. From

equation (13), we obtain:

var(log(y)) = var(log(yAk)) + var(log(yH)) + 2cov(log(yAk), log(yH)) (15)

and seek an answer to the following question: If all countries had the same level of yAk, what fraction of income variation could be attributed solely to human capital? The

this fraction. Data for s are derived from the Barro and Lee (2010) dataset, whereas α is set, as commonly in the literature, equal to 1/3:

caselli = var(log(yH))

var(log(y)) (16)

Second: Klenow and Rodriguez-Clare (1997) proposed an alternative method to estimate the fraction of income variation attributed to human capital. This is described by equation (17) where again y denotes the per capita GDP and h the average level of human capital (we name this ratio klenow):

klenow = COV (log(y), log(h))

var(log(y)) (17)

Third: As an additional test, we compute the ratio of equation (16) by using, this time, country-specific returns to education. Psacharopoulos (1994) and Psacharopoulos and Patrinos (2004) provide an overview of the returns to education by country and, employing their estimates, we compute, what we name the psacharopoulos ratio.

Fourth: Focus has recently been placed on the quality of human capital, a field that, due to data limitations, has long remained unexplored. Measures for the education qual-ity have only recently been developed, with the most common one being the test scores. A few studies have already documented a positive relationship between human capital quality and economic growth (Bishop, 1989; Hanushek and Kimko, 2000; Hanushek and Woessmann, 2008, 2009). This is an important consideration since “a year of secondary schooling in the United States cannot be equivalent to a year at the same grade level in Egypt” (Hanushek and Kimko, 2000, p.1185). Woessmann (2003) suggests that a quality-adjusted human capital specification takes the following form:

hQ= (eφ(s))Q= er∗Q∗s (18) where r is the world average rate of return to education and Q Hanushek and Woess-mann’s (2009) educational quality index. The latter is constructed based on international tests of math and science and, according to the authors, provides a measure of cognitive skills across nations. Employing this quality-adjusted measure of human capital, we compute what we name quality ratio, again as in equation (16).

Table 6 presents the fraction of cross-country income variation that different methods in the literature attribute to education. Note that the calculations are performed for the common set of observations across the six methods15. The last row of the table refers to the absolute value of our income variation (%) measure, whereas income variationph.cap.

(%) denotes the absolute value of income variation (%) when the physical-capital-adjustment assumption is relaxed16. All in all, these estimates demonstrate the magni-tude of education’s impact on cross-country income variation.

15

The common set of countries includes: Australia, Austria, Brazil, Canada, China, Cyprus, Den-mark, Estonia, Finland, France, Germany, Greece, Hungary, India, Indonesia, Italy, Japan, Mexico, Netherlands, Poland, Portugal, Russia, South Korea, Spain, Sweden, Taiwan and United Kingdom.

16

physical-capital-1995 2000 2005

caselli 2.4% 2.2% 2.5%

klenow 16.6% 15.7% 15.6%

psacharopoulos 4.7% 5.2% 7.3%

quality 4.6% 4.8% 6.1%

income variationph.cap.(%) 34% 34.2% 41.8%

income variation (%) 37.7% 37.5% 46.6%

Table 6: The impact of education on cross-country income variation across different methods

From table 6, it becomes apparent that our original upper bound estimates (as described through the income variation (%) variable) attribute to education a more important role than conventional techniques do. Evidently, these estimates refer to the maximum increase a country’s output could undergo, but still the disparities to conventional methods in the literature are large. Caselli (2005), for example, would argue that, in 2005, only 2.5% of income variation could be attributed to human capital. We, however, state that increases in education could almost halve income variation. Interestingly, Klenow and Rodriguez-Clare (1997) would also assign a rather important role to education. Their method has, however, often been criticized on the basis of overestimating the role of human capital (Caselli, 2005). Another interesting remark is related to the psacharopoulos as well as the quality ratios. Compared to the caselli method, these two measures attribute to education a larger fraction of cross-country income variation. The importance of using country-specific returns to education and also considering the quality of education, thus, becomes apparent. Finally, relaxing the physical-capital-adjustment assumption reduces our original estimates, but not to a large extent.

In sum, from our analysis we are able to conclude that education can indeed play an important role regarding increases in output. Contrary to what conventional techniques would suggest, there is ample potential for education to trigger convergence between countries. Furthermore, it is important to note that literature should turn its focus to the quality of education, as well as the country-specific returns to it, since they both seem to draw a clearer and more comprehensive picture regarding the impact of human capital on economic development.

7

Conclusion

In the present study, we have followed an alternative approach to measure the effect of education on countries’ output. To this end, we have employed data from three different sources and constructed various measures that our analysis required. Our findings are based on the most recent and comprehensive data and the upper bound methodology we

employ, overcomes various impediments that conventional approaches have long faced. Consequently, we have contributed to the literature that measures the cross-country income variation that can be attributed to education. Our estimates have revealed that countries, in particular low-income ones, could greatly benefit by attaining a schooling distribution similar, for example, to that of the Unites States.

More specifically, we have explored (i) by how much increases in schooling could increase a country’s output, (ii) how much of the output gap with the US could increases in schooling close and, finally, (iii) to what extent would cross-country income variation be reduced if countries managed to attain the US educational levels. On average, our estimates suggest that a country could raise its output by 67% and, also, halve its output gap to the United States with increases in education. Furthermore, cross-country income variation could have been reduced by up to 37.4%, whereas among the low-income countries this estimate would reach 52.5%. These findings clearly demonstrate the key role education can play for decreases in the gap between the developed and the developing world. As a secondary objective, we have constructed relative wages estimates based on a high- versus low-skilled industries approach and concluded that such methods only poorly capture the actual pattern of relative wages, potentially due to the increasingly important phenomenon of offshoring.

A

Appendix

Method 1 Method 2 Method 3 Method 4 Method 5** High-Skilled Industries* 351,352,353, 354,382,383 353,352,342, 351,385 352,353,351, 342,385,383, 384 352 353,352,342 Low-Skilled Industries* 321,322,323, 324 323,322,324, 321,332 323,321,322, 324,332,331, 361,390,311, 314 323,321,322, 324,332,331, 361,390,311, 314 323,322,324 Number of Observations 67 129 110 129 136 Difference (average) 1.1132 0.7369 1.1280 1.1334 0.4317 Percentage of

Ob-servations for which Difference> 1 or < −1 41% 26% 31% 35% 23% Number of Observations smaller than 1 3 4 5 78 8 Correlation 0.4109*** 0.4100*** 0.6718*** 0.4616*** 0.4103*** Spearman Ranking

Cor-relation

0.4049*** 0.5407*** 0.5772*** 0.3961*** 0.5150***

σU N IDO/σSEA 0.4912 0.5118 0.3094 0.3459 0.7370

Table 7: Predicting Relative Wages through Different Classification Methods (comparison be-tween UNIDO and “actual” SEA relative wages)++ _{Note: *For each classification method, we}

require all high- and low-skilled industries to exist. Industry Codes and Names: 311: Food products; 314: Tobacco; 321: Textiles; 322: Wearing apparel, except footwear; 323: Leather products; 324: Footwear, except rubber or plastic; 331: Wood products, except furniture; 332: Furniture, except metal; 361: Pottery, china, earthenware; 390: Other manufactured products; 342: Printing and publishing; 351: Industrial chemicals; 352: Chemicals, other; 353: Petroleum refineries; 354: Misc. petroleum and coal products; 382: Machinery, except electrical; 383: Ma-chinery, electric; 384: Transport equipment; 385: Professional & scientific equipment. **Method 5 is the preferred one since it produces estimates as close as possible to the SEA relative wages. ***Statistically significant at the 1% level.

++_{A Note on the Different Classification Methods:}

From these two variables, we derive three measures which we name (i) high (corresponds to education ≥ 16years), (ii) medium (corresponds to 12years ≤ education < 16years) and (iii) low (corresponds to education < 12years). According to method 3, if an in-dustry experiences values of the variable high larger than the average, it is classified as high-skilled. Accordingly, if it experiences values of the variable low larger than the average, it is classified as low-skilled. Method 4 employs a similar classification pattern but excludes from the high-skilled group all those industries that experience values of the variable medium larger than the average. Finally, method 5 identifies as high-skilled those industries that in the Ciccone and Papaioannou (2009) ranking of industries accord-ing to their knowledge intensity lie above the 90% percentile “average years of schoolaccord-ing” distribution and as low-skilled those that lie below the 10% percentile.

We then compare our estimates to the “actual” SEA relative wages and choose the classification that produces values as close as possible to them. The criteria we employ in order to compare the classifications are shown in rows 4-10 of table 7. We consider (i) the number of observations for which data from both SEA and UNIDO are available (see: row 4), (ii) the average difference between the SEA and UNIDO relative wages (see: row 5), (iii) the percentage of observations for which the difference between SEA and UNIDO relative wages is larger than 1 or smaller than -1 (see: row 6), (iv) the number of observations that are smaller than 1 (see: row 7) since intuitively relative wages of high- to low-skilled individuals should exceed the value of 1, (v) the correlation (see: row 8) and (vi) spearman ranking correlation (see: row 9) between the SEA and UNIDO relative wages and, finally, (vii) the ratio of the UNIDO to the SEA standard deviation (see: row 10).

1995 2000 2005 AUS 0,162 0,156 0,190 AUT 0,443 0,382 0,370 BEL 0,344 0,305 0,279 BGR 0,554 0,590 0,630 BRA 1,761 1,432 1,085 CAN 0,286 0,260 0,129 CHN 0,923 0,851 0,750 CYP 0,382 0,320 0,447 CZE 0,277 0,187 0,031 DEU 0,403 0,276 0,139 DNK 0,467 0,467 0,501 ESP 0,794 0,568 0,531 EST 0,274 0,120 0,128 FIN 0,360 0,555 0,353 FRA 0,479 0,347 0,306 GBR 0,977 0,952 0,897 GRC 0,530 0,539 0,444 HUN 0,540 0,344 0,309 IDN 2,375 2,001 2,113 IND 3,961 4,332 4,295 IRL 0,344 0,299 0,284 ITA 0,692 0,661 0,589 JPN 0,262 0,220 0,232 KOR 0,243 0,180 0,174 LTU 0,199 0,153 0,114 LUX 0,447 0,487 0,490 LVA 0,403 0,432 0,345 MEX 1,795 1,639 1,422 MLT 1,161 1,168 1,172 NLD 0,238 0,222 0,246 POL 0,712 0,687 0,980 PRT 1,570 1,485 1,368 ROM 0,487 0,517 0,443 RUS 0,189 0,042 0,053 SVK 0,491 0,535 0,515 SVN 0,235 0,153 0,160 SWE 0,145 0,105 0,077 TUR 1,574 1,468 1,213 TWN 0,493 0,400 0,286