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Higher Test Scores or More Schooling? Another Look at the Causes of Economic Growth

Author(s): Theodore R. Breton

Source: Journal of Human Capital , Vol. 9, No. 2 (Summer 2015), pp. 239-263

Published by: The University of Chicago Press

Stable URL: https://www.jstor.org/stable/10.1086/681911

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https://www.jstor.org/stable/10.1086/681911

Higher Test Scores or More Schooling? Another Look at the Causes

of Economic Growth

Theodore R. Breton Universidad EAFIT

I use a dynamic augmented Solow model to estimate the effect of international test scores and investment in schooling and tutoring on economic growth rates in 55 countries during 1985–2005. Either test scores or investment in schooling and tutoring can explain growth rates in the full data set or in countries that had less than 8 years of schooling in 1985. In countries with more schooling in 1985, in- vestment in schooling has a small effect and test scores have no effect on growth rates. In the 24 countries with scores above 470, higher scores have no effect on growth rates.

I. Introduction

Analyses of the effect of human capital on national income and growth

rates using aggregate cross-country data are valuable because they estimate the external as well as the direct effects of human capital ðKrueger and Lin- dahl 2001Þ. Until relatively recently, these analyses relied almost entirely on school enrollment rates and average years of schooling to represent the flow and the stock of human capital in an economy. In a series of articles, Hanushek and Kimko ð2000Þ and Hanushek and

Woessmann ð2008, 2011a, 2011b, 2012a, 2012bÞ use an innovative measure of human capital, students’ average scores on international tests, to esti- mate the effect of human capital on rates of economic growth. They ar- gue that average test scores provide a much more accurate measure of a nation’s human capital than adults’ average years of schooling attainment ðhereafter schooling attainmentÞ. In all of their articles, Hanushek and Woessmann compare the effect of

test scores and schooling attainment on growth rates and obtain similar results. Hanushek and Woessmann ð2008, 2012aÞ show that over the pe-

I thank Richard Rogerson, Mikael Lindahl, George Psacharopoulos, Michael Jetter, Andrew Breton, and four anonymous referees for helpful comments on earlier versions of

this manuscript.

239

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riod 1960–2000, average test scores explain three times the variation in growth explained by schooling attainment ð73 percent vs. 25 percentÞ. They also show that when test scores and schooling attainment are in-

240 Journal of Human Capital

cluded in the same model, test scores explain all the variation in growth. They conclude from these results that higher cognitive skills at ages 9–15 cause growth and more schooling often does not. Breton ð2011Þ challenges the validity of these results. He argues that

Hanushek and Woessmann’s ð2008Þ comparison of the effect of test scores and schooling attainment is flawed. Since Hanushek and Woessmann ð2008, 2011a, 2011b, 2012a, 2012bÞ use the same methodology to esti- mate the effect of these measures, his criticism is applicable to the more recent analyses as well. The most evident flaw in the methodology is that Hanushek and Woess-

mann compare the effect of students’ test scores from 1964–2003, and primarily from 1990–2003, to the effect of adults’ schooling attainment in 1960. These two measures are not remotely comparable. As an example, students who were tested at age 9 in 2003 and remained in school until they were 18 would have entered the workforce in 2012. Because of the lag between the testing of the students and their entry into the workforce and their subsequent 40-year working life, average test scores from 1964–2003 are a proxy for a country’s human capital in about 2010, or 50 years later than adults’ schooling attainment in 1960. The average scores from 1990– 2003, which they use for most of the less educated countries, are a proxy for a country’s human capital around 2020. The less evident flaw in the methodology is that their growth model is

misspecified. The model includes the initial level of human capital, which is included in some endogenous growth models, but it also includes initial income, which is included in dynamic neoclassical models to control for conditional convergence. The empirical results in Hanushek and Kimko ð2000Þ and Hanushek and Woessmann ð2008, 2011b, 2012a, 2012bÞ sup- port the lagged income variable and reject the initial level of schooling. Hanushek and Woessmann ð2012bÞ include the initial level of physical capital in the model, and this variable is also rejected. So their results con- sistently reject the initial levels of capital found in some endogenous growth models and accept the lagged income variable included in the dynamic neoclassical growth model. The capital variables in the dynamic neoclassical growth model are the

flow of capital into the economy during the growth period, not the ini- tial capital stock ðBreton 2011Þ. The implication is that in the Hanushek- Kimko/Hanushek-Woessmann model, students’ average test scores at ages 9–15 during 1964–2003 represent the flow of human capital into the economy during 1970–2010, or about 6–7 years after the testing period. The comparable schooling measure is the average rate of enrollment or the rate of investment in schooling during 1964–2003, not the schooling attainment of adults in 1960. Their model also lacks an analogous flow of physical capital into the economy. As a consequence, Hanushek and

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Kimko’s and Hanushek and Woessmann’s estimates of the effects of test scores and schooling attainment on growth are likely to be severely biased. In this paper I reexamine whether higher test scores or more schooling

Higher Test Scores or More Schooling? 241

causes growth, using a dynamic augmented Solow growth model, compa- rable measures for test scores and investment in schooling, and data for these measures that are appropriate for the period of estimation.1 I also examine whether private tutoring affects growth and whether there are nonlinearities in the education-growth relationship that lead to different results in the complete data set than in subsets of countries with different levels of schooling.2 As far as I know, these analyses have not been per- formed in the existing empirical literature. I begin my analysis by examining the quantitative relationships between

three measures of a nation’s human capital stock: average adult schooling attainment, the financial stock of human capital per adult, and students’ average test scores. I examine the relationship between stocks rather than flows because stocks measure the cumulative effect of flows over a long period. I show that while these three measures are correlated, they have very

different patterns across countries, which suggests that they quantify dif- ferent aspects of a nation’s human capital. The measures increase to- gether in countries with relatively little schooling, but test scores stabilize once countries have more than 9 years of schooling attainment or have invested more than $100,000 per adult ð2005 US$Þ in schooling. As a re- sult, these measures relate to growth rates differently in countries with different levels of schooling. Subsequently, I estimate the effects of higher test scores and more

investment in schooling on growth rates, using Mankiw, Romer, and Weil’s ð1992Þ dynamic version of the augmented Solow model. This model has a structure that is compatible with Hanushek and Woessmann’s test score data and their empirical results, and the validity of this model is supported by considerable recent empirical evidence ðCohen and Soto 2007; Ding and Knight 2009; Breton 2010, 2011, 2013b, 2013c, 2015; Gennaioli et al. 2013Þ.3 Since the Mankiw et al. model is a well-defined structural model, the nature, the form, and the vintage of the data required for its estima- tion are clearly specified. Since most of Hanushek and Woessmann’s test scores for less educated countries were obtained after 1990, I estimate the growth model over the 1985–2005 period to ensure consistency with the vintage of their data.

1 The flow of human capital into the economy is exogenous in the Solow growth model. Ehrlich and Kim ð2007Þ specify a complex endogenous growth model in which human cap-

ital determines economic growth.

2 Castelló-Climent ð2010Þ finds evidence that human capital inequality affects rates of in- vestment in human capital differently in high- and low-income countries.

3 Breton ð2013bÞ challenges Klenow and Rodriguez-Clare’s ð1997Þ and Hall and Jones’s ð1999Þ arguments that Mankiw et al.’s empirical results overestimate the effect of schooling on national output.

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I confirm Hanushek and Kimko’s and Hanushek and Woessmann’s findings that average test scores explain cross-country growth rates quite well in the complete sample of countries. But I find that investments in

242 Journal of Human Capital

schooling ðand private tutoringÞ also explain growth rates quite well. In both models the estimated parameters for the augmented Solow model are consistent with theoretical expectations and with estimates in other cross-country studies. These results reject Hanushek and Kimko’s and Hanushek and Woessmann’s findings that more schooling is not reliably correlated with growth. Perhaps more importantly, when I analyze the effect of higher test

scores and more investment in schooling in countries with different levels of schooling, I find that these measures explain growth rates well only in countries with relatively low levels of schooling and test scores. Average test scores cannot explain growth rates during 1985–2005 in countries that had more than 8 years of schooling attainment in 1985 or in countries that had average test scores over 470. These results call into question Hanu- shek and Woessmann’s ð2011aÞ claim that raising students’ test scores at ages 9–15 is an attractive growth strategy for OECD countries. In con- trast, rates of investment in schooling can explain growth rates in coun- tries with more than 8 years of schooling, but its estimated effect is smaller than in countries with less schooling. The paper is organized as follows: Section II examines the quantitative

relationship between the various measures of human capital. Section III presents the growth model used in the analysis, and Section IV describes the data used in this analysis. Section V presents the results. Section VI presents conclusions.

II. Measures of Human Capital

A country’s human capital is analogous to its physical capital but is much

more difficult to measure. A large fraction of human capital is created through the formal schooling process, particularly in higher-income coun- tries, but human capital is also created in informal settings, such as in the home or on the job. Expenditures on formal schooling or on tutoring can be measured, but historically such data have not been collected as care- fully or as regularly as expenditures on physical capital. The earnings that students forgo while in school are an additional, unmeasured investment in schooling. And some kinds of schooling are an element of consump- tion rather than an investment in productive capital.4 Owing to all these complications, estimates of a country’s rate of investment in human cap- ital or of its human capital stock inherently have more measurement error than analogous estimates for physical capital.

4 The United Nations system of national accounts classifies education as an element of

consumption.

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There are three measures of human capital that have been used in cross- country income and growth studies. The first is the average years of school- ing attainment of the adult population for the ages 15–64, over 15, or

Higher Test Scores or More Schooling? 243

over 25. The second is the average international score on tests of differ- ent skills for a student population with ages between 9 and 15. The third is the net cumulative investment in formal schooling of the population of working age, assuming a 40-year working life after the completion of schooling. Most cross-country growth studies use schooling attainment as a proxy

for a country’s human capital because it is the only quantitative measure of workers’ skills available for most countries for long historic periods.5

Despite its limitations, this measure has acquired legitimacy because the effect of an additional year of schooling on workers’ incomes ðthe Mincer- ian returnÞ is relatively consistent across countries ðPsacharopoulos and Patrinos 2004Þ. The other two measures are available for many fewer coun- tries and only for recent time periods. Growth analyses using the average schooling attainment measure al-

most always utilize the Mincerian log-linear relationship between income and schooling. In these models, each additional year of schooling has an exponential effect on income. As a consequence, the marginal contribu- tion of an additional year of schooling to a nation’s productivity and out- put is much greater in a country with higher average attainment ðlike Ja- panÞ than in a country with lower average attainment ðlike PeruÞ. These models implicitly take into account the higher average investment per year of schooling and the related higher schooling quality in countries with higher average schooling attainment. The main weakness in these analyses is that they implicitly assume that

a year of schooling has the same quality in countries that have the same schooling attainment, for example, in the United States and Canada. One indicator of how much schooling quality might vary in countries with the same schooling attainment is the variation in cumulative investment in schooling per adult in countries with the same average schooling attain- ment. Countries that invest more in each year of schooling ðadjusted for differences in purchasing powerÞ are more likely to provide higher-quality schooling. The cumulative investment measure of human capital could capture differences in schooling quality to a greater degree than the av- erage attainment measure, although there are differences in investment due to institutional characteristics that are not related to schooling quality. Figure 1 shows the relationship in 2005 between the log of Breton’s

ð2013aÞ estimates of the financial stock of human capital per adult of work- ing age and Cohen and Soto’s ð2007Þ estimates of the schooling attain- ment of the population aged 15–64.6 Breton’s measure of human capital

5 Morrisson and Murtin ð2009Þ present average schooling attainment data for 74 countries for the period 1870–2010.

6 The estimates of average schooling attainment in 2005 are the average of schooling

attainment in 2000 and 2010.

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is analogous to the standard financial measure of the stock of physical capital. It is created from the sum of the prior 40 years of investment in schooling and a depreciation rate of 2.5 percent per year. Since the in-

Figure 1.—Logðhuman capital per adultÞ versus average schooling attainment in 2005

244 Journal of Human Capital

vestment is calculated from national income in Penn World Table 6.3 ðHeston, Summers, and Aten 2009Þ, the estimates of the stocks of human capital are adjusted for purchasing power differences across countries. The relationship in the figure is clearly linear, and the two data sets are

highly correlated ðr 5 :91Þ. If a nation’s cumulative investment in school- ing accounts for the quality of its schooling, then the very high correlation between the log of human capital per adult and average schooling attain- ment indicates that a log-linear relationship between income and aver- age schooling implicitly accounts for the higher average quality of school- ing in more educated countries.7

The data in figure 1 show that South Korea, Japan, and the United King- dom have invested less per year of schooling than other highly educated countries, but their investment in schooling does not include their ex- penditures on private tutoring, which are substantial ðDang and Rogers 2008Þ. As will be addressed later, stocks or flows of human capital calcu- lated from investment in schooling are underestimated in countries that spend considerable amounts on private tutoring. As also shown in the figure, the differences in the financial measure of

human capital per adult can be quite large in countries with the same av-

7 The trend in the relationship shows that countries with 2 years of schooling in 2005 had invested about $2,000 per adult, and countries with 13 years of schooling had invested about $130,000 per adult, or 10 times as much per year of schooling.

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erage schooling attainment, and the range is particularly large in coun- tries in which average schooling attainment is between 4 and 9 years. These data suggest that the quality of schooling is much higher in Argen-

Higher Test Scores or More Schooling? 245

tina than in the Philippines and much higher in Costa Rica than in Syria. Breton ð2013bÞ estimates Mankiw et al.’s ð1992Þ static version of the aug-

mented Solow model across countries in 1990 using the financial stock of human capital per adult and schooling attainment. Both measures ex- plain the variation in national income quite well, but the financial mea- sure explains more of the variation, suggesting that across countries it accounts for differences in schooling quality somewhat better than the schooling attainment measure. If the financial stock of human capital per adult is a more accurate mea-

sure of human capital than average schooling attainment, then it could be a more accurate measure of human capital than average test scores, particularly in countries with high average levels of schooling. Figure 2 shows the relationship between Hanushek and Woessmann’s measure of average test scores and the financial stock of human capital per adult in 2005 in 46 countries. These two measures are correlated ðr 5 :70Þ, but the mathematical relationship between them is not linear or log linear. The data show that average test scores at ages 9–15 rise as countries raise their investment in human capital per adult, but only up to about $100,000 per adult ð2005 US$Þ. Beyond that level of investment, average scores tend to decline, although not by a substantial amount. Figure 3 shows the relationship between Hanushek and Woessmann’s

measure of students’ average test scores obtained over the period 1964–

Figure 2.—Hanushek and Woessmann’s average test scores versus human capital per adult in 2005.

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2006 and the average schooling attainment of the adult population in 1985, the midpoint of the testing period. Average scores on internationa tests at ages 9–15 increase across countries as the average schooling of the

Figure 3.—Average student test score versus average schooling attainment in 1985

246 Journal of Human Capital

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population aged 15–64 rises to a level of about 9 years, and then scores stabilize at a mean of about 500. These patterns suggest that a nation’s average test scores at ages 9–15

and its average schooling attainment are measuring different aspects of its human capital. Average test scores measure students’ competence in basic skills, while schooling attainment and the financial stock of human capital measure the overall educational level of the adult population. These measures rise together in countries with limited postsecondary schooling, but they diverge in more educated countries. The data in fig- ures 2 and 3 demonstrate that the test score measure cannot discern the differences in human capital in countries with widely differing levels of postsecondary schooling. The test score measure also has limitations in countries where many stu-

dents do not complete secondary schooling. In these countries, average test scores are not representative of the skills of the entire school-age pop- ulation. As an example, in Hanushek and Woessmann’s data, India has rel- atively high average scores, but in the testing period, its secondary school enrollment rate was under 50 percent.8 As a consequence, India’s average test scores overestimate the skills of the school-age population. Although there is no way to eliminate this measurement error in countries with low

8 World Bank data used are school enrollment, primary ð% grossÞ, secondary ð% grossÞ, and tertiary ð% grossÞ.

enrollment rates, it can be minimized by using Hanushek and Woess- mann’s average test scores to estimate growth during the latest possible period when a larger share of the school-age population attended second-

Higher Test Scores or More Schooling? 247

ary school. These patterns in the data suggest that students’ cognitive skills at ages

9–15 are an incomplete measure in countries with a financial stock of human capital per adult above $100,000 or with more than 9 years of av- erage schooling attainment. As a consequence, test scores may not be a sufficiently accurate measure to permit estimation of the effect of hu- man capital on national income or on economic growth in more educated countries. Since all measures of human capital have their limitations, which measure best represents cross-country human capital is an empir- ical issue that can be determined only in a properly specified income or growth model.

III. Growth Model Specification

In this analysis I utilize Mankiw et al.’s ð1992Þ augmented Solow model to

compare the effect of higher test scores and more investment in schooling on national output:

ðY =LÞ t 5 ðK=LÞa

t ðH=LÞb

t ðA0egtÞ12a2b: ð1Þ

In this model, output ðYÞ changes in response to changes in physical cap- ital ðKÞ, human capital ðHÞ, labor ðLÞ, and total factor productivity ðAÞ, which is assumed to grow at a constant rate gð1 2 a 2 bÞ. Breton ð2013bÞ shows that when H=L is defined as the financial stock of human capital per adult, b 5 0:36 and a 1 b 5 0:7. His results support Mankiw et al.’s assumption that a 1 b < 1, and they are consistent with Mankiw et al.’s results, in which human capital has large external effects on national in- come. Mankiw et al. ð1992Þ derive a dynamic version of their model in which

economic growth is modeled as convergence to the steady state yt 5 y*, where yt 5 Y =ðegtLÞ and l is the rate of convergence to the steady state:

log ðytÞ 2 log ðy0Þ 5 ð1 2 e2ltÞlog ðy*Þ 2 ð1 2 e2ltÞlogðy0Þ: ð2Þ They show that y* is a function of the shares of GDP invested in physical and human capital ðsk and shÞ, the labor growth rate ðnÞ, and the capital depreciation rates ðdk and dhÞ:

y* 5 a=ð1 2 a 2 bÞ½logðskÞ=ðn 1 g 1 dkÞ� 1 b=ð1 2 a 2 bÞ½logðshÞ=ðn 1 g 1 dhÞ�:

ð3Þ

Substitution of equation ð3Þ into equation ð2Þ and rearrangement creates a growth model, which contains a lagged income variable, similar to the variable in the Hanushek-Kimko and Hanushek-Woessmann analyses:

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log ðY =LÞ t 2 logðY =LÞ

5 c 1 ð1 2 e2ltÞa=ð1 2 a 2 bÞ½logðskÞ=ðn 1 g 1 dkÞ�

248 Journal of Human Capital

1 ð1 2 e2ltÞb=ð1 2 a 2 bÞ½logðshÞ=ðn 1 g 1 dhÞ� 2 ð1 2 e2ltÞlogðY =LÞ

0 1 ε:

ð4Þ

When this model is estimated over a period 0 to t, sk, sh, and n are the averages of these rates during the growth period. The shares of invest- ment sk and sh measure the flow of physical and human capital resources into the economy during this period. The average test score for a cohort of students aged 9–15 can be

employed as a measure of the human capital flow into the economy in each country 5–10 years later. Hanushek and Woessmann’s ð2012aÞ data for average test scores are based on international tests taken between 1964 and 2003, but as described below, most of the scores in the less educated countries were obtained between 1990 and 2003. As a consequence, their average scores for developed countries and a few developing countries are representative of the flow of human capital during 1970–2010, while most of their average scores for developing countries are representative of the flow of human capital into the workforce during 1995–2010. I estimate Mankiw et al.’s growth model over the 1985–2005 period.

This period corresponds relatively well to the period when most of the test scores were obtained and certainly much better than the earlier 1960– 2000 period that Hanushek and Woessmann use in their analyses. The test scores also are more representative of the flow of human capital in the less educated countries in the later period because a much higher fraction of students remained in school until age 15 in these countries in 1985 than in 1960. As a consequence, there is less measurement error in Hanushek and Woessmann’s test score measure when it is used to explain growth during 1985–2005 than when it is used to explain growth during 1960–2000. Figure 4 shows the relationship between average test scores and logðshÞ

in the data set. Although the correlation between these two data sets is not very high, the pattern in the data indicates that the relationship between investment in schooling and average test scores could be log-linear. I rep- resent logðshÞ in equation ð4Þ by the average test score rather than by the log of the average test score because it provides better results. Hanushek and Woessmann ð2012bÞ use a linear-exponential relationship between growth rates and test scores in their analyses for the same reason. As mentioned earlier, a limitation of the rate of investment in schooling

measure is that some countries expend considerable resources on private tutoring to improve students’ cognitive skills. Since rates of investment in schooling do not include these expenditures, they underestimate the rate of investment in human capital in these countries, and as shown later in the empirical results, the failure to include the tutoring expenditures in the growth model substantially changes the estimated effect of investment

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in schooling. Since cross-country time-series data on expenditures on tu toring are not available, I control for the effect of tutoring by including a dummy variable for countries with high expenditures on tutoring.

Mankiw et al.’s growth model assumes that investment in physical capita

Figure 4.—Average test score versus logðinvestment in schooling/GDPÞ

Higher Test Scores or More Schooling? 249

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Figure 5 shows the relationship between the growth rate over the 1985– 2005 period and the average test score variable for the 55 countries in the data set. The scores exhibit regional patterns that could indicate that un- known factors affected growth rates. Average test scores are relatively high in the Asian countries and relatively low in the Latin American countries. I include dummy variables for these regions in some models to test for possible omitted variables.

IV. Data Creation and Selection

and human capital, growth in workers, and the initial level of income are the only factors that affect growth. The model also assumes that factors of production are paid their marginal products. Countries that have cen- trally planned economies, have income largely determined by oil exports, have serious civil conflicts, or are tax havens have characteristics affecting income and growth rates that are not included in the model. These coun- tries are likely to be outliers in the model’s growth-investment relation- ships. Particularly in estimates of the model with small data samples, these outliers can substantially bias the estimated coefficients and reduce their statistical significance. Hanushek and Kimko and Hanushek and Woessmann had similar con-

cerns when they estimated their growth models, so they excluded many

countries from their data sample. Hanushek and Woessmann ð2008Þ re- port that 77 countries participated in international tests of mathematics andscienceduring the 1964–2003period.Theyexcluded 27ofthese coun-

Figure 5.—Economic growth rate in 1985–2005 versus test the score variable in the growth model.

250 Journal of Human Capital

tries from their sample because 15 were communist countries; three were predominantly oil exporters; six were small, were newly created, or lacked output data; and two were outliers in their growth regressions. Their re- maining data set includes 50 countries. Hanushek and Woessmann ð2012bÞ create average scores for an addi-

tional nine Latin American countries based on regional tests of mathe- matics and reading skills in fourth and sixth grades taken during 1997 and 2006. These scores are less reliable since they correspond to tests of dif- ferent subjects, correspond to a later period, and had to be adjusted to merge them with the international scores. I use most of these scores, but I test whether their use changes the regression results. I began with these 59 countries and excluded four for the same reasons

as Hanushek and Woessmann. I excluded China and Romania because they were communist countries and Venezuela because it was predomi- nantly an oil exporter.9 I excluded Jordan because it is an outlier in the growth regressions as a result of the heavy migration of refugees from Israel and Iraq during the 1985–2005 period. Since these refugees add human capital to the labor force that is not measured in the test scores or the investment rates, the inclusion of Jordan in the data set would bias

9 China’s average test scores correspond to tests taken in Shanghai, which is a relatively educated region.

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the results. So my initial estimates of the effect of test scores on growth are based on the scores in 55 countries. Hanushek and Woessmann’s international test scores are the simple

Higher Test Scores or More Schooling? 251

arithmetic average of any available scores on tests of mathematics and sci- ence for students between 9 and 15 during the 1964–2003 period. The age distribution of the students tested may be different in each country, but they argue thatthisisnot a problem because scores ondifferent testswithin the same country are highly correlated ðHanushek and Woessmann 2008, 2012aÞ. Another concern is that the students participating in international tests are not always a representative sample of the school population in the less educated countries. But Hanushek and Woessmann ð2011bÞ present analyses showing that sample selectivity problems have not unduly biased their results. Since the international tests began as a means to compare students’

skills in the more educated countries, there are few scores for less edu- cated countries prior to 1990. My data set with test scores includes 18 highly educated countries and 37 less educated countries. Only seven of the less educated countries have test scores prior to 1990 ðHanushek and Woess- mann 2008Þ, and eight of the 37 countries have scores only for the period 1997–2006 ðHanushek and Woessmann 2012bÞ. The shares of GDP invested in physical capital and human capital are

conceptually identical in the growth model, but obtaining estimates of the investment rate for human capital is much more difficult. Time-series data on the investment/GDP ratio in non-OECD countries are available only for public schooling and are intermittent or unreliable in many countries. In addition, there is a considerable lag between the investment in a stu- dent’s schooling and the student’s entry into the workforce. This lag var- ies across countries, depending on the amount of schooling provided, the structure of the economy, and practices related to child employment. Forthe averagerateof investment inschoolingvariableðshÞ during1985–

2005, I use the average rate of investment during 1980–2000. I use an investment period that is 5 years earlier than the growth period to account for the delay between the expenditures on students’ schooling and the entry of these students into the workforce.10

Breton ð2013bÞ estimates human capital per adult in 1990 for 61 mar- ket economies from the shares of GDP invested in schooling from 1950 to 1985, using UNESCO data on expenditures for public education ðper- centage of GDPÞ, increased by factors to account for private schooling, the opportunity cost of capital while students are in school, and students’ for- gone earnings. I use the data elements from these estimates to calculate

10 Five years is a reasonable average lag from a financial standpoint since unit schooling

costs rise with the level of schooling and the delay between expenditures and entry into the workforce is shorter at higher levels of schooling.

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the average rate of investment in schooling, but with additional UNESCO data on expenditures in public education for the period 1990–2000.11

Dang and Rogers ð2008Þ survey the extent of private tutoring in 23

252 Journal of Human Capital

countries, including estimates of either total expenditures or shares of the student population that participate in private tutoring. I include a dummy variable for tutoring expenditures in the eight countries that expend at least 0.5 percent of GDP on tutoring or that provide tutoring to at least 25 percent of the student population ðEgypt, Greece, Hong Kong, Japan, South Korea, Singapore, Turkey, and the United KingdomÞ. Hanushek and Woessmann’s ð2012a, 2012bÞ data provide test scores for

47 of the 61 countries in Breton’s data set. After Jordan is excluded, the sample of countries with data for both test scores and investment rates is reduced to 46. These countries provide the basis for the initial comparison of the effect of average test scores and investment in schooling on growth rates. I use Cohen and Soto’s ð2007Þ data on average schooling attainment

in the population aged 15–64 to calculate average attainment in 1985, and I then separate the countries into subsets with more and less than 8 years of schooling attainment at the beginning of the growth period. Four of the 55 countries with test score data ðHong Kong, Iceland, Israel, and TaiwanÞ are not included in Cohen and Soto’s average schooling attainment data. I estimate average attainment for these countries from Barro and Lee’s ð2013Þ data on average attainment in the population over 15. I use economic data from Penn World Table 6.3 ðHeston et al. 2009Þ. I

use the population over 15 as the proxy for workers, which I estimate from data on GDP per capita ðrgdpchÞ and GDP per equivalent adult ðrgdpqaÞ. I then calculate n from the growth in this population over the 1985–2005 period. I use the average investment rate ðciÞ over the period 1985–2004 as the investment share sk during the growth period. I assume g 5 0.01, dh 5 0:025, and dk 5 0:06. The rate g is the average rate derived from the Solow residual during 1910–2000 in Breton ð2013cÞ. The depreciation rate for human capital is based on a 40-year work life, as described in Breton ð2013bÞ. The depreciation rate for physical capital is from Caselli ð2005Þ. The data used in the models are shown in the Appendix.

V. Empirical Results

The mathematical structure of the Mankiw et al. ð1992Þ model implies that

a and b are the shares of national income that accrue to the stock of physical capital ðKÞ and human capital ðHÞ, and the rate of income convergence l is mathematically related to the values of a, b, n, g, dk, and dh. One of the desirable features of their model relative to unstructured models, such as those specified by Hanushek and Woessmann, is that the

11 I use the investment/GDP ratio in 1980, 1985, 1990, 1995, and 2000 to estimate the average ratio in each 5-year period and then average these four ratios to obtain the 20-year average.

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validity of the Mankiw et al. model can be evaluated on the basis of whether the estimated parameters of the model are consistent with its theoretical predictions.

Higher Test Scores or More Schooling? 253

Table 1 presents ordinary least squares ðOLSÞ estimates of the growth model in equation ð4Þ and shows the implied values of a, b, and l in the estimated coefficients. The first two columns in the table present the mod- el’s results with the test score data. Column 1 shows the effect with the 55- country data set, and column 2 shows the effect with the 46-country data set used to estimate the effect of investment in schooling in columns 3–5. The estimated coefficients for the two models with the test score mea-

sure are very similar, have estimated coefficients that are highly statistically significant, and have implied parameters for the effect of physical capital, human capital, and the rate of convergence that are consistent with ex- pectations for the Mankiw et al. model. The implied values of a are 0.35– 0.37, which are very consistent with Bernanke and Gurkaynak’s ð2001Þ and Gollin’s ð2002Þ estimates of the share of national income accruing to phys- ical capital, which is about 0.35 across countries. The implied values of b are 0.27, which is consistent with, but somewhat lower than, Breton’s ð2013bÞ estimates. The implied values of l, the rate of convergence to the steady state, range from 0.016 to 0.018, which are consistent with theoret- ical expectations and with Barro’s ð2012Þ estimates of actual average con- vergence rates ð1.7 percentÞ in 80 countries since the 1960s. Although not shown, the calculated parameter values are statistically significant at the 1 percent level.

TABLE 1

Effect of Human Capital Measures on Growth Rates, 1985–2005

Dependent Variable D logðGDP per AdultÞ Test Scores Investment/GDP Both

ð1Þ ð2Þ ð3Þ ð4Þ ð5Þ ð6Þ Countries 55 46 46 46 46 44 ln½sk=ðn 1 g 1 dkÞ� .29* .28** .51** .46** .31** .31**

ð.12Þ ð.09Þ ð.10Þ ð.07Þ ð.08Þ ð.08Þ ln½sh=ðn 1 g 1 dhÞ� .21* .30** .13 .21*

ð.10Þ ð.07Þ ð.09Þ ð.09Þ Tutoring dummy .22** .11 .05

ð.08Þ ð.08Þ ð.08Þ ln ½exptest=ðn 1 g 1 dhÞ� .22** .22** .18** .16**

ð.04Þ ð.03Þ ð.05Þ ð.05Þ lnðY/L 2 1985Þ 2.28** 2.30** 2.29** 2.32** 2.34** 2.37**

ð.05Þ ð.04Þ ð.08Þ ð.06Þ ð.06Þ ð.06Þ R2 .49 .60 .42 .52 .62 .64 Implied a .37 .35 .50 .43 .32 .30 Implied b .27 .27 .21 .28 .32 .35 Implied l .016 .018 .017 .019 .021 .023

Note.—Robust standard errors are in parentheses. * Statistically significant at the 5 percent level. ** Statistically significant at the 1 percent level.

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Columns 3 and 4 present the OLS estimates of the effects of investment in schooling and private tutoring on growth rates. The results in column 3 without the tutoring dummy are all statistically significant and acceptable

254 Journal of Human Capital

conceptually except the value of a, which is too high. When the tutoring dummy is added in column 4, the results become acceptable. All the co- efficients, including the coefficient on the dummy variable, are statistically significant at the 1 percent level. The results in columns 2 and 4, which are based on the same 46 coun-

tries, show that the model with test scores and the model with investment in schooling and tutoring provide very similar empirical results, although the model with test scores explains somewhat more of the variation in growth rates ðR2 5 .60 vs. .52Þ. Columns 5 and 6 show the results when test scores and investment in

schooling ðand tutoringÞ are included in the same model. In column 5 the effects of investment in schooling and tutoring are positive, but only the effect of test scores is statistically significant. The effect of tutoring is only half as large when test scores are included, indicating that tutoring affects growth in part through its effect on test scores.12

In the 46-country sample, Hong Kong and Singapore are outliers in that they have high economic growth rates but relatively low rates of investment in schooling. Hong Kong became a Special Administrative Region of China in 1997, with additional legal protection for private investment des- tined for mainland China. Singaporeis considered a tax haven. Sothe high growth rates in these jurisdictions may be due in part to the reporting of income that is earned elsewhere. Column 6 shows the results for both measures in a 44-country sample

that excludes Hong Kong and Singapore. In these results the effect of both test scores and investment in schooling is large and statistically sig- nificant. The implied values of the parameters in these models continue to be consistent with the expectations for the Mankiw et al. model. Table 2 presents additional tests of the same models. Columns 1 and 4

show the results when dummy variables for the Asian and Latin American regions are included in the model. Hanushek and Woessmann ð2012bÞ show that the effect of a Latin America dummy is negative in models that included adult schooling attainment in 1960, and they argue that this is due to the low quality of schooling in this region. In the results with the investmentinschoolingmeasureðcol.4Þ,thecoefficientontheLatinAmer- ica dummy is negative, but it is small and not statistically significant, sug- gesting that Hanushek and Woessmann’s ð2012bÞ results were due to the misspecification of their growth model. The effect of the Asia dummy is larger and positive but not statistically significant with both measures. The estimated coefficients on the physical capital and human capital variables

12 Alternatively, large investments in tutoring may be an indicator that the educational system is test based. If students work harder to raise their skills in these countries, it may be that the coefficient on tutoring is capturing the effect of the additional effort students

expend in a test-based system rather than just the effect of the tutoring.

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ontinue to be statistically significant, and the parameters continue to be cceptable when the regional dummies are included in the models. Column 2 shows the results for the test score measure when the Latin

TABLE 2 Sensitivity Tests: Effect of Human Capital Measures on Growth Rates, 1985–2005

Dependent Variable: D lnðGDP per AdultÞ Test Scores Investment/GDP

ð1Þ ð2Þ ð3Þ ð4Þ ð5Þ ountries 55 46a 59 46 47 ½sk=ðn 1 g 1 dkÞ� .24* .22* .33* .34** .53**

ð.118Þ ð.10Þ ð.13Þ ð.10Þ ð.09Þ ½sh=ðn 1 g 1 dhÞ� .27* .30**

ð.10Þ ð.07Þ utoring dummy .15 .22**

ð.09Þ ð.08Þ ½exptest=ðn 1 g 1 dhÞ� .21** .24** .21**

ð.05Þ ð.06Þ ð.04Þ ðY/L 2 1985Þ 2.22** 2.28** 2.29** 2.24* 2.35**

ð.07Þ ð.05Þ ð.06Þ ð.09Þ ð.07Þ atin America dummy .05 2.04

ð.09Þ ð.09Þ sia dummy .14 .14

ð.10Þ ð.12Þ 2 .51 .53 .51 .55 .54 plied a .33 .30 .40 .40 .45 plied b .29 .33 .25 .32 .27 plied l .012 .016 .017 .014 .022

ote.—Robust standard errors are in parentheses. Excludes Latin America. Statistically significant at the 5 percent level. * Statistically significant at the 1 percent level.

Higher Test Scores or More Schooling? 255

c a

C ln

R Im Im Im

N a

* *

American countries whose scores were calculated from regional tests are removed from the data set. These results are almost identical to the results for the full 55-country data set ðcol. 1 of table 1Þ. Column 3 shows the model results for Hanushek and Woessmann’s complete 59-country data set, including the four countries I had eliminated. The effect of test scores is smaller, but the results continue to provide acceptable, statistically sig- nificant parameters. Column 5 shows the model results for the investment in schooling measure when Jordan is included in the data set. The esti- mated parameters are similar to the parameters in the 46-country data set, but the effect of investment in schooling is slightly smaller. The data patterns for the human capital measures in figures 2, 3, and 4

suggest that the estimated effects of test scores in table 1 could be the average of different effects in countries with high and low levels of school- ing. Since test scores do not continue to rise once countries achieve 9 years of schooling attainment or a financial stock of human capital of $100,000 per adult, growth in the more educated countries may be caused by more investment in schooling rather than by increases in test scores. To investigate this possibility, I separate the countries into two groups

with less and more than 8 years of schooling attainment in 1985. I split the

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groups at 8 rather than 9 years to increase the sample size of the more ed- ucated countries. I use schooling attainment in 1985 to divide the coun- tries because the flow measures during the growth period do not provide

256 Journal of Human Capital

any indication of the level of education in the countries at the beginning of the growth period. Table 3 presents the results for three subsets of the countries, those with

less and more than 8 years of schooling in 1985 and those with test scores above 470 during 1964–2003. The results in the two subsets of countries with less and more schooling attainment show that the effects of higher test scores and more investment in schooling in the complete data set are due to the effects in countries that had less than 8 years of schooling in 1985. The implied values of the parameters are acceptable in this subset of countries, and all the human capital measures continue to be highly sta- tistically significant. The results for the more educated countries in columns 4 and 5 are very

different. None of the measures of human capital have any statistical sig- nificance. The 24 countries with more than 8 years of schooling have an average test score of 498, with a range from 405 to 545, so there should be enough variation to explain growth rates if there were a strong relation- ship. As shown in column 4, there is no evidence that higher test scores affected growth rates in these countries during the 1985–2005 period. There are 20 countries with more than 8 years of schooling in 1985 that had data on rates of investment in schooling, and again there is no evi- dence that these rates affected growth rates. The growth model explains about 60 percent of the variation in growth

rates in these countries, but this variation is explained by the rate of in- come convergence, which is quite rapid. Since test scores and investment rates have no effect, the convergence effect is absolute rather than condi- tional. In these two subsets of countries, the results show slow conditional income convergence in the less educated countries and rapid absolute income convergence in the more educated countries. In such a small data set, outliers can seriously affect the results. A review

of the residuals in the regressions with investment rates reveals that three countries, Hong Kong, Ireland, and Norway, are outliers. Hong Kong has an unusual legal status in China, Ireland is a tax haven for companies in the European Union, and Norway’s GDP is substantially affected by oil prices. These characteristics raised reported GDP growth rates beyond what can be explained by the variables in the model. Columns 6 and 7 show the results when a dummy variable is included

to control for the omitted factors contributing to higher growth rates in these three countries. In these two models the rate of investment in school- ing is statistically significant at the 5 percent level, but the effect is rela- tively small and investment in physical capital still has no effect. In col- umn 7 the effect of test scores on growth rates continues to be small and insignificant.

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T A B L E 3

E f f e c t o f H u m a n C a p i t a l M e a s u r e s o n G r o w t h R a t e s , 1 98

5 – 20

05 D e p e n d e n t V a r i a b l e : D l n ðG

D P p e r A d u lt Þ

S ch

o o li n g < 8 Ye a rs

S ch

o o li n g > 8 Ye a rs

T e st

S co

re > 4 7 0

ð8 Þ

ð1 Þ

ð2 Þ

ð3 Þ

ð4 Þ

ð5 Þ

ð6 Þ

ð7 Þ

C o u n tr ie s

3 1

2 6

2 4

2 0

2 4

ln ½s k = ðn

1 g 1

d k Þ�

.2 7 *

.4 6 * *

.2 5 * *

2 .0 4

.0 4

.0 1

2 .0 5

.0 8

ð.1 4 Þ

ð.0 7 Þ

ð.0 5 Þ

ð.1 7 Þ

ð.1 8 Þ

ð.1 5 Þ

ð.1 3 Þ

ð.1 8 Þ

ln ½s h = ðn

1 g 1

d h Þ�

.3 6 * *

.2 0

2 .1 6

.1 2 *

.1 1 *

ð.1 0 Þ

ð.1 1 Þ

ð.1 6 Þ

ð.0 4 Þ

T u to ri n g d u m m y

.3 2 * *

.1 7 *

2 .0 5

ð.1 0 Þ

ð.0 7 Þ

ð.1 1 Þ

ln ½ex

p te st = ðn

1 g 1

d h Þ�

.2 2 * *

.2 1 * *

.0 7

.0 6

2 .1 4

ð.0 6 Þ

ð.0 4 Þ

ð.0 7 Þ

ð.0 8 Þ

ð.1 7 Þ

H ig h -i n co

m e d u m m y

.3 2 * *

ð.0 5 Þ

ln ðY / L 2

1 9 8 5 Þ

2 .2 1 * *

2 .3 0 * *

2 .2 6 * *

2 .5 2 * *

2 .4 8 * *

2 .5 6 * *

2 .5 9 * *

2 .5 4 * *

ð.0 6 Þ

ð.0 7 Þ

ð.0 4 Þ

ð.0 7 Þ

ð.1 0 Þ

ð.0 9 Þ

ð.1 1 Þ

ð.0 8 Þ

R 2

.4 9

.6 3

.8 2

.6 4

.5 9

.8 6

.6 6

Im p li e d a

.3 9

.4 1

.2 7

.0 1

Im p li e d b

.3 1

.3 2

.4 5

.1 7

Im p li e d l

.0 1 2

.0 1 8

.0 1 5

.0 3 7

.0 3 3

.0 4 1

.0 4 5

.0 3 9

N o te .—

R o b u st st an

d ar d e rr o rs

ar e in

p ar e n th e se s.

* S ta ti st ic al ly si g n ifi ca n t at

th e 5 p e rc e n t le ve l.

* * S ta ti st ic al ly si g n ifi ca n t at

th e 1 p e rc e n t le ve l.

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Column 8 shows the effect of test scores on growth in countries with av- erage scores above 470. Again what we see in the results is absolute con- vergence in income levels, regardless of the level of test scores. Since the

258 Journal of Human Capital

data sets for highly educated countries are so small ð20–24 countriesÞ, these results cannot be considered definitive, but they call into question Hanushek and Woessmann’s ð2011aÞ claim that highly educated OECD countries can raise their growth rates by raising their students’ average test scores. It is instructive to examine why Hanushek and Woessmann ð2011aÞ

found a positive effect from test scores on growth in 24 OECD countries during 1960–2000, while this analysis does not find this effect in two slightly different sets of 24 countries during 1985–2005. There are several reasons for the different results, but two stand out. First, two OECD coun- tries with high test scores, Japan and Switzerland, had much lower growth rates during 1985–2005 than during 1960–2000. Second, Mexico and Tur- key, two OECD countries with low test scores and low growth rates during 1960–2000, are not included in the current analysis, while one non-OECD country, Chile, which had low test scores and a high growth rate during 1985–2005, is included in this analysis. In such small data sets, these changes are sufficient to completely change the statistical relationships in the results. Figure 6 shows the relationship between growth rates in 1985–2005 and

test scores for the 28 countries included in either of these analyses. An ex- amination of the data in this figure reveals that the more educated OECD

Figure 6.—Economic growth rates versus average test scores during 1985–2005

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countries, excluding South Korea, had similar growth rates during this period, which were not related to their average test scores. This same pat- tern is evident in figure 2 in Hanushek and Woessmann ð2011aÞ during

Higher Test Scores or More Schooling? 259

the 1960–2000 period.In these analyses the statistical relationship between growth rates and test scores is very sensitive to the inclusion or exclusion of certain countries that are outliers relative to the traditional OECD group of highly educated countries. There is a possible explanation for the lack of correlation between test

scores and growth rates in countries with scores above 470. Experiments with students at different grade levels in the more educated countries show that average scores on the same international tests rise by about 32 points after students complete an additional year of schooling ðWoessmann 2003; Jürges and Schneider 2004; Fuchs and Woessmann 2007Þ. The implication is that intensive efforts to raise students’ scores in some of the more educated countries accelerate by 1–2 years the increase in students’ skills that otherwise occurs as students continue their schooling. It is not clear whether the skill advantage at ages 9–15 in the countries with higher aver- age scores continues later or whether it diminishes with time. Since there is no noticeable effect of scores above 470 on economic growth in the results, the skill advantage may be temporary. Alternatively, it may be that in countries with average scores of at least 470, there are enough students with high skills to meet the economy’s requirement for highly skilled workers. The lack of any effect from test scores on growth rates in the more ed-

ucated countries is not surprising given the data patterns in figures 2 and 3, but the small or negligible effect of investment in physical capital and human capital is unexpected. It appears that in these countries differences in other factors not included in the model had a larger effect on reported growth rates during the 1985–2005 period than differences in capital in- vestment rates.

VI. Conclusions

Hanushek and Woessmann argue that students’ cognitive skills at ages 9–

15, as measured on international tests, determine a nation’s rate of eco- nomic growth, and Hanushek and Woessmann ð2008, 2012aÞ show that increased schooling attainment explains only one-third of the variation in growth rates explained by higher average test scores. Breton ð2011Þ argues that their results are severely biased because their methodology is flawed. In this paper I reexamine the effects of higher test scores and more

schooling on growth rates using a dynamic neoclassical growth model, con- ceptually appropriate measures of schooling, and a time period more ap- propriate for the vintage of the test scores. I find that in the complete data set, either average test scores or more investment in schooling can explain growth rates over the 1985–2005 period. Test scores explain more of the variation in growth rates, but the variation explained by the two measures

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is similar once the effect of private tutoring is taken into account. These results are consistent with Hanushek and Woessmann’s finding that in- creases in students’ test scores cause growth, but they reject their finding

260 Journal of Human Capital

that increases in schooling do not reliably cause growth. When I examine the effect of higher test scores and more investment in

schooling in subsets of countries with low and high levels of schooling attainment, I find that the effect of these measures during 1985–2005 occurs almost entirely in countries that had schooling attainment below 8 years at the beginning of the growth period. In these countries, either higher test scores or more investment in schooling and private tutoring explains a high share of the variation in economic growth rates. I find that countries that expend considerable resources on private tu-

toring have higher growth rates. The results indicate that investment in schooling and private tutoring are substitutes for raising students’ cogni- tive skills and for increasing growth rates in countries with average school- ing attainment below 8 years. More research should be undertaken to de- termine whether it is the substantial private tutoring or the greater focus on testing ðor bothÞ in these countries that raises the scores. In contrast, I find no evidence that increases in average test scores affect

growth rates in countries with more than 8 years of schooling or in coun- tries with average scores above 470. These results call into question Ha- nushek and Woessmann’s ð2011aÞ argument that OECD countries can raise their growth rates by increasing students’ cognitive skills at ages 9–15. I find some evidence that more investment in schooling raises growth

rates in countries with more than 8 years of schooling, but the effect is smaller than in the less educated countries. Over the 1985–2005 period, income per adult in these countries tended to converge. Countries with lower income per adult grew faster, regardless of their rates of investment in physical capital and schooling or their level of test scores. The small ef- fect of human capital in these results could be due to the diminishing re- turns to investment in human capital or to the failure of the human capital measures to adequately represent the human capital characteristics that are most relevant in highly educated countries.

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Appendix

TABLE A1

Data Used in the Analysis

Country dlnya lnskngdk testngdh lnshngdh lnya85 attain85 Score

Argentina .2116 .6712 6.9127 .7861 9.6127 7.61 3.920 Australia .3970 1.2473 8.0840 1.4971 10.2663 12.48 5.094

Austria Belgium

Boli Braz Can Chil Chin Colo Cost Cyp Den Ecu Egyp El S Finl Fran Gha Gre Gua Hon Hon Icela Indi Indo Iran Irela Israe Italy Japa Jord Kore Mal Mex Mor Neth New Nor Pan Para Peru Phil Port Rom Sing Sou Spai Swe Swit Taiw Tha Tun

��

.3683

.4098

��216.27 All

1.3124 1.2994

This con .113.144 on use subject

8.2997 8.2981

tent downlo Sun, 06 Feb to https://abo

1.4167

aded from 2022 23:48: ut.jstor.org/t

10.2240 10.1438

53 UTC�� erms

10.63 9.64

��

5.089 5.041

via

.1302

.1007

5.4342

.8415

8.5179

6.65

2.640

.0354

.4415

6.4922

.8347

9.3914

5.40

3.638

ada

.3409

1.1239

8.0651

1.5807

10.3044

11.98

5.038

.8398

.9403

6.9869

1.2188

9.1898

8.66

4.049

1.3197

1.1755

7.8849

7.6977

4.939

mbia

.1829

.3992

6.9890

.6091

9.0548

5.46

4.152

a Rica

.2895

.8209

7.2695

.9067

9.3285

5.30

4.486

rus

.6528

1.3632

7.5840

9.6342

7.57

4.542

mark

.3742

1.2996

8.2369

1.8099

10.2123

11.29

4.962

ador

2.0464

.7537

5.6132

.6579

9.1042

6.73

2.852

.4240

2.1135

6.7946

.8423

8.5388

3.94

4.030

alvador

.1159

.5338

6.0315

.3590

8.9121

4.07

3.243

and

.3873

1.3393

8.3591

1.4584

10.1044

10.11

5.126

.3108

1.1664

8.2062

1.5522

10.1602

11.46

5.040

.1311

2.3988

6.3146

.3443

7.7003

4.59

3.603

ece

.3607

1.2178

7.7638

.6352

9.9396

8.22

4.608

temala

.0751

.6498

5.6343

2.0352

9.1219

3.29

2.855

duras

2.0713

.8884

5.1193

8.7115

4.37

2.453

g Kong

.6013

1.1204

8.1316

.5685

10.0968

9.78

5.185

.4277

1.2920

7.9705

10.3711

9.35

4.936

.6280

.4913

7.1411

.5421

7.8853

2.88

4.281

nesia

.5324

.7450

6.7247

8.3088

4.89

3.880

.1959

.9780

6.9689

.5814

9.2600

3.01

4.219

.9117

1.2394

8.0508

1.2472

9.8821

9.24

4.995

.3280

1.1021

7.4336

10.0175

11.68

4.686

.3051

1.3504

8.0235

1.2807

10.0810

8.53

4.758

.2512

1.5091

8.4690

1.2355

10.1984

11.57

5.310

2.4545

.3033

6.7212

.8810

9.3464

4.264

a, Republic

.9410

1.5838

8.3232

.9367

9.2732

9.52

5.338

aysia

.7915

1.0116

7.6196

.9177

9.3186

7.10

4.838

ico

.0306

.8584

6.8286

.7073

9.6084

6.48

3.998

occo

.0539

.4238

6.0775

.9415

8.8684

1.96

3.327

erlands

.4094

1.1822

8.2874

1.4458

10.1867

10.50

5.115

Zealand

.3171

1.0989

8.0367

1.4412

10.0338

10.87

4.978

way

.4857

1.4411

8.0417

1.6584

10.4627

11.94

4.830

ama

.2159

.8375

5.8042

1.0040

9.1277

7.37

2.985

guay

2.1160

.3776

5.7508

.1999

9.0226

5.59

3.031

.0387

.6741

5.9410

.6279

8.9932

6.93

3.125

ippines

.1835

.4643

6.4181

.4231

8.5774

6.72

3.647

ugal

.5040

1.4031

7.7078

1.1552

9.5473

5.74

4.564

ania

2.0283

1.3161

7.7802

9.2145

4.562

apore

.8058

1.4634

8.0996

.7043

9.9257

6.12

5.330

th Africa

.0259

2.0539

5.9059

9.5138

5.40

3.089

.5488

1.3886

7.9823

1.0710

9.8881

7.95

4.829

den

.3634

1.0459

8.2523

1.7655

10.1585

11.65

5.013

zerland

.1777

1.4119

8.3095

1.3467

10.4738

12.72

5.142

.9204

.9159

8.4317

9.3989

9.19

5.452

iland

.6900

1.3383

7.4796

.7715

8.6315

5.19

4.565

isia

.4042

.4778

6.5832

.9768

9.0233

3.03

3.795

TABLE A1 (Continued)

Country dlnya lnskngdk testngdh lnshngdh lnya85 attain85 Score

262 Journal of Human Capital

Turkey .3062 .8486 6.9426 .0459 8.9009 4.69 4.128 United Kingdom .4793 1.0216 8.1928 1.3926 10.0367 11.93 4.950

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4.107

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