경제학석사학위논문

Inequality of Opportunity

in Educational Achievement:

A Cross-national Analysis using TIMSS data

학업성취도에 있어서의 기회불평등

-TIMSS 자료를 이용한 국제 비교-

2018 년 2월

서울대학교 대학원

경제학부 경제학 전공

옥 승 빈

Abstract

Inequality of Opportunity in Educational

Achievement:

A Cross-national Analysis using TIMSS data

Seungbin Ohk

Department of Economics

The Graduate School

Seoul National University

This study analyzes the trend in the degree of inequality of opportunity in educational

achievement during the past two decades, using Trends in International Mathematics and Science

Study (TIMSS) data set for Grade 8 students from 16 countries. Individual socioeconomic

background is measured using father’s level of education and the home learning environment

index, an aggregate index including factors relevant to parental support and resources. This study

first measures and compares the cumulative distributions, conditional on social background, using

stochastic dominance tools. Then, two inequality opportunity indices, the Gini Opportunity Index

(GOI) and Rags to Riches Index (RRI) are applied to track the extent of the inequality of

opportunity within countries and over time. The cross-national comparison is implemented by

ranking the countries according to the two inequality opportunity indices. The results show that

students from advantaged socioeconomic backgrounds are more likely to achieve academic

success in all countries, suggesting that no country obtains equality in terms of opportunity for

educational achievement. An example of a country with relatively low values of the opportunity

inequality indices is Hong Kong. England and New Zealand appear to be the most unequal

countries during the study period in terms of equality of opportunity. When the complete set of

countries is considered, the global trends in the two opportunity inequality indices show similar

patterns. While inequality in outcomes has increased, the inequality of opportunity has remained

relatively unchanged over the last two decades.

keywords: equality of opportunity, opportunity index, educational achievement, social mobility,

socioeconomic background

Student number: 2016-20156

Contents

1 Introduction ............................................................................................. 3

2 Equal Opportunity: Conception and Measurement ................................ 6

2.1 Definition of Equality of Opportunity ................................................................. 6

2.2 Opportunity Inequality Index ............................................................................... 7

2.2.1 The GOI...................................................................................................... 7

2.2.2 The RRI ...................................................................................................... 8

3 Data ......................................................................................................... 8

3.1 Data Set ................................................................................................................ 8

3.2 Social Background ............................................................................................... 9

3.2.1 Father’s Level of Education ..................................................................... 10

3.2.2 The HLEI.................................................................................................. 10

4 Empirical Results .................................................................................. 11

4.1 Inequality of Opportunity Related to Father’s Education .................................. 11

4.1.1 Conditional Distributions: Mathematics .................................................. 12

4.1.2 Conditional Distributions: Science........................................................... 13

4.1.3 The Stochastic Dominance Test ............................................................... 15

4.2 Inequality of Opportunity Related to the HLEI ................................................. 17

4.2.1 Conditional Distributions: Mathematics .................................................. 17

4.2.2 Conditional Distributions: Science .......................................................... 19

4.2.3 The Stochastic Dominance Test ............................................................... 20

4.3 Opportunity Inequality Index............................................................................. 23

4.3.1 Trend ........................................................................................................ 23

4.3.2 Rankings from 1995 to 2003 .................................................................... 25

4.3.3 Rankings from 2007 to 2015 .................................................................... 28

5 Conclusion ............................................................................................ 30

A Appendices

List of Tables

1 Stochastic Dominance Tests (Father's Education) ....................................................... 15

2 Stochastic Dominance Tests (HLEI) ............................................................................ 20

List of Figures

1. Math score Distributions Conditional on Father's Education ....................................... 13

2. Science score Distributions Conditional on Father's Education ................................... 15

3. Math score Distributions Conditional on HLEI ............................................................ 19

4. Science Score Distributions Conditional on the HLEI ................................................. 20

5. Inequalities in Outcomes and Opportunities conditional on father’s education ........... 24

6. Inequalities in Outcomes and Opportunities conditional on HLEI ............................... 25

7. Differences between Mathematics and Science ............................................................ 26

8. GOI in math 1995-2003 measured by father's education(left) and HLEI(right) ........... 27

9. GOI in Science 1995-2003 Measured by Father's Education (left) and HLEI (right) .. 27

10. RRI in math 1995-2003 measured by father's education(left) and HLEI(right) ........... 28

11. RRI in science 1995-2003 measured by father's education(left) and HLEI(right) ....... 28

12. GOI in math 2007-2015 measured by father's education(left) and HLEI(right) ........... 29

13. GOI in science 2007-2015 measured by father's education(left) and HLEI(right) ....... 29

14. RRI in math 2007-2015 measured by father's education(left) and HLEI(right) ........... 29

15. RRI in science 2007-2015 measured by father's education(left) and HLEI(right) ....... 30

1 Introduction

Education has been considered as a promising way of climbing up the social ladder, functioning

as a powerful weapon for encouraging social mobility. However, recently in Korea for over a

decade higher education has been regarded as an insurance against downward mobility rather than

a promise of upward social mobility. Parents with more economic and social resources support

their children for attaining higher academic achievement and to ensure that their child retain

superior position on the social ladder, leaving students from disadvantaged families with less

chance succeed in academic achievement. When the inequality of opportunity in educational

achievement prevails in a society, that is, the differences in the level of educational achievement

according to social background exist, an individual's socioeconomic background plays an

important role in determining her own social status. Inequality of opportunity results in lower

social mobility. Inequality of educational achievement across more or less advantageous socio-

economic family backgrounds are used to formulate opportunity inequality in educational

achievement. Using international test score data, we access opportunity inequality in Korea and

other countries. We also provide international comparison of opportunity inequalities.

Individual achievements result from circumstances and effort. A distinction can be made

(in terms of the sources of the inequality in achievements) between what individuals can and

cannot be held responsible for. Examples of the latter include inequalities resulting from race,

gender, and family background, which are beyond a person's control. The former are the

remaining factors that are relevant to individual’s choices, such as efforts, time, allocation,

strategies, habit formation, etc. Inequalities due to individual choices can be morally acceptable.

But inequalities due to reasons beyond one's control are not morally acceptable. Therefore,

identifying the sources of inequality is important when designing social policies that lesson such

inequality without reducing incentives for effort.

Roemer (1998) developed a model that determines the social policy that coordinates the

inequality of opportunities among various groups of individuals with different levels of

environmental factors that cannot be attributed to self-responsibility. The conceptual definition of

equality of opportunity in our study follows John Roemer's principles of leveling the playing field

and nondiscrimination principle. His leveling the playing field ensures children from

disadvantaged social backgrounds public supports for compensatory education so that they may

be able to compete for jobs with those from more advantaged backgrounds. Roemer views the

nondiscrimination principle, "as deriving from a particular interpretation of the leveling the

playing field principle". Morally irrelevant personal characteristics such as gender or race should

not affect one's eligibility for a position. According to Roemer, equality of opportunity should

focus on inequalities due to circumstances, compensating for possible disadvantages due to

factors related to social background.

While there is no agreement over how best to measure and compare the extent of equality

of opportunity, several concepts of equal opportunity have been developed. Based on the equal

opportunity policy proposed by Roemer (1998), Lefranc et al. (2008, 2009) use stochastic

dominance techniques to characterize and measure inequality of opportunity. They define equality

of opportunity as a situation in which income distributions that are conditional on social

backgrounds, the opportunities offered by different circumstances, “cannot be ranked according

to stochastic dominance criteria". Lefranc et al. (2008) compared conditional income distributions

across circumstances in OECD countries, defining the circumstances by the parental education

and occupation. They also introduced an index of inequality of opportunity, which is the Gini

index of the levels of well-being for all different social environments.

We investigate inequality of opportunity using data from the Trends in Mathematics and

Science Study (TIMSS), the large international comparative student achievement test. This data

set includes the assessment of student performance and family background questionnaires.

Unfortunately, family income is not included in the TIMSS data set. We indexify family

background by using three aspects of home environment: wealth, educational resources such as

the number of books and parents' education. The number of books in home can be treated as proxy

for family income and for the educational resources supported by parents. Then, students’ social

backgrounds are measured by students' home learning environment index (HLEI), which simply

aggregate the level of parents' education, the number of books, and the existence of home

possessions.

Because parents’ level of education affects the academic performance of their children,

both directly and indirectly, through family income, many previous studies including Lefranc et

al. (2008) also used parental education as a measure of social background. However, the HLEI,

is preferable, for two reasons, when using TIMSS data. First, the HLEI can make the composition

of environments as equal as possible across countries. One shortcoming of using parental

education as a measure of circumstances is that it leads to notable differences in the relative sizes

of groups across countries, which could limit the cross-country comparability of the findings.

When using the HLEI, the relative sizes of the groups become more balanced across countries.

For instance, in Korea, one group with a certain level of father's education represents less than

two percent of the overall population. Because non-parametric stochastic dominance tests require

a sufficiently large number of observations in each group, such measures might provide

unreasonable estimations.

Second, the home learning environment may have a distinct influence on educational

outcomes. For example, parents may have a low level of education, but may nevertheless have

high educational aspirations for their children and, thus, invest heavily in their children's

education. The HLEI ensures that high achievement in one factor compensates for low

achievement in another factor. The HLEI is designed to indicate parental support -the extent of

home resources and parents’ education which may have an important impact on academic

achievement.

Kim and Lee (2008) measured the extent of the equality of opportunities for income in

terms of parents’ level of education and father’s occupation in Korea. They compared the impact

of the fiscal policy in Korea- reducing inequality of opportunity for income - with those in 11

Western countries, which had been analyzed by Roemer et al. (2003). Ko and Lee (2011)

examined the degree of equality of opportunity for academic attainment and income in Korea.

They reported that the father's education accounts for 16 percent to 59 percent of the inequalities

for son's educational attainment and 2 percent to 12 percent of the inequality in the son's income.

Byun and Kim (2010) investigated the trends in educational inequality based on math

performance in South Korea using TIMSS data for three waves (1999, 2003, and 2007). They

compared the changes in the impact of the socioeconomic gap on student achievement in Korea

with those in the United States. Their results suggest that the effects of socioeconomic background

on student achievement have remained unchanged in the United States, but have increased over

time in Korea. Salehi-Isfahani et al. (2014) examined the level of inequality of opportunity in

educational achievement in math and science, focusing on the Middle East and North Africa,

using data from TIMSS (1999, 2003, and 2007). Their results showed that most countries in

Middle East and North Africa are less equal than European countries in terms of opportunity. Kim

et al. (2014) compared the influence of parents' education level on student's achievement in PISA

among OECD countries. They find that parental education is significantly related to students'

academic attainment in every OECD country. In addition, the level of inequality of opportunity

is relatively low in Korea.

Recent findings indicate that educational opportunity is a determinant of inequality and

intergenerational mobility. However, few studies have empirically examined and compared the

trends in the equality of opportunity for academic achievement across countries. In this context,

this study makes two contributions. First, it measures the extent of the inequality of opportunity

in terms of academic performance across time and countries using stochastic dominance tools.

Second, we compare the level of equality of opportunity for academic performances in 16

countries using two opportunity inequality indices: Gini Opportunity Index (GOI), developed by

Lefranc et al. (2008), and the Rags to Riches Index (RRI), introduced by Oh and Ju (2016).

Furthermore, the extent of intergeneration mobility is captured by comparing the values of the

opportunity indices, and particularly the RRI which provides clear information on the chances of

success of students in the lowest socioeconomic classes.

The remainder of this thesis is organized as follows. Section 2 discusses the model and

defines equality of opportunity for academic achievement and opportunity inequality indices.

Section 3 provides information on the datasets and describes the procedures used to estimate the

indices in practice. Section 4 presents the main results, and compares the levels of inequality of

opportunity in 16 countries. Section 5 concludes our investigation.

2 Equal Opportunity: Conception and Measurement

Although there is no single definition of fair equality of opportunity, there is widespread

agreement on its basic principles. While inequalities due to factors for which individuals are

accountable – a person’s level of effort- are considered morally acceptable, inequalities due to

circumstances that are beyond a person's control, but that affect the outcome of interest are unfair

and should be compensated for.

2.1 Definition of Equality of Opportunity

This study follows the same method proposed in Lefranc et al.(2008).1 Consider a society of

individuals, where each individual's academic achievement is determined by circumstances and

effort. Define a finite set T (i.e.,a type) as a set of individuals with similar circumstances.

Individuals within each type can differ only in their level of effort. The distribution of scores

within each type is regarded as the opportunity set open to the individuals of that type. Differences

in opportunity sets indicate the presence of inequalities in opportunities. All individuals with the

same level of effort should have the same chances of achieving the objective, regardless of their

type.

Let c denote a set of circumstances,e be an individual’s level of effort, and F(∙ |c, e)

be the conditional probability distribution of academic achievement, given c and e. Denote the

distribution of the test scores, conditional on circumstances c, by F(y|c). Considering the concepts

of opportunity equality, if the distribution of scores is independent of circumstances, then equality

of opportunities requires that F(∙ |𝑐, 𝑒) = F(∙ |𝑐′, 𝑒). However, this condition seems improbable

in practice. Lefranc et al. (2009) noted this is “a compelling case of equality of opportunity”. They

formalize equality of opportunity using stochastic dominance relations among the conditional

distributions (Lefranc et al.,2009):

Given 𝑐, 𝑐′ and 𝑒 , the first order stochastic dominance(FSD) holds between two

probability distributions F(∙ |𝑐, 𝑒) and F(∙ |𝑐′, 𝑒) if for all 𝑦,

F(𝑦|𝑐, 𝑒) ≥ F(𝑦|𝑐′, 𝑒)

with strict inequality for some y. This coincides with the property that for all 𝑢(𝑦) is

monotonically increasing,

∫ 𝑢(𝑦)𝑑𝐹(𝑦|𝑐, 𝑒) ≥ ∫ 𝑢(𝑦)𝑑𝐹(𝑦|𝑐′, 𝑒)

with strict inequality for at least one monotonically increasing u(y). Then circumstance 𝑐 is

always preferred to circumstance 𝑐′ by any student. When the FSD holds for all 𝑒, we say that

the first order opportunity inequality exists between the two circumstances, 𝑐 and 𝑐′ . The

1 A detailed explanation of the measurement and the GOI are given in Lefranc et al. (2008).

second order stochastic dominance (SSD) holds between the two probability distributions

F(∙ |𝑐, 𝑒) and F(∙ |𝑐′, 𝑒) if for all 𝑥,

∫ 𝐹(𝑦|𝑐, 𝑒)𝑑𝑦 ≥ ∫ 𝐹(𝑦|𝑐′, 𝑒)𝑑𝑦𝑥

0

𝑥

0

with strict inequality for some 𝑥 . This coincides with the property that all students with rick

averse and monotonically increasing utility functions prefer circumstance 𝑐 to circumstance 𝑐′.

When the SSD holds for all 𝑒, we say that the second order opportunity inequality exists between

the two circumstances, 𝑐 and 𝑐′.

The distribution of effort may be affected by circumstances. Under an extremely inferior

circumstance, it may be difficult to make enough effort for achieving high test-scores. Then non-

existence of stochastic dominances defined earlier does not seem to warrant opportunity equality.

To avoid this issue, we follow Roemer (1998) and Lefranc et al. (2008, 2009) and measure effort

in such a way that the distribution of effort does not depend on circumstances. When such a

measure of effort is used, the first and the second order opportunity inequalities have the following

necessary conditions, which are used in our investigation as conditions for opportunity

inequalities.

The First Order Opportunity Inequality Condition: For some circumstances c ,c ' , there exist first

order stochastic dominance between F (× |c ) and F (× |c ') .

The Second Order Opportunity Inequality Condition: For some circumstances c ,c ' , there exist

second order stochastic dominance between F (× |c ) and F (× |c ') .2

2.2 Opportunity Inequality Index

2.2.1 The GOI

Let the population be partitioned into K types by T = {𝑇1, 𝑇2, … , 𝑇𝐾}. Let 𝜇 denote the mean

score of the entire population, the mean of {𝜇1(1 − 𝐺1), 𝜇2(1 − 𝐺2), … , 𝜇𝐾(1 − 𝐺𝐾)},

G indicate the Gini coefficient, P be a population proportion, and the subscript t denote

circumstance t. Then 𝜇𝑡(1 − 𝐺𝑡) represents twice the area under the Generalized Lorentz curve

of circumstance t. Rank all environments in ascending order of 𝜇𝑡(1 − 𝐺𝑡). Then, the GOI is

expressed as follows:

GO =1

𝜇∑ ∑ 𝑃𝑖𝑃𝑗

𝑗>𝑖

𝑘

𝑖=1

(𝜇𝑗(1 − 𝐺𝑗) − 𝜇𝑖(1 − 𝐺𝑖))

The GOI is proportional to the sum of the differences between the areas of the opportunity sets.

2 The proof can be found in Lefranc et al. (2009).

Therefore, the closer the value is to zero, the more equal is the opportunity, and the closer the

value is to one, the more unequal is the opportunity.

2.2.2 The RRI

One of the most important issues related to opportunity equality is the way it increases the

problem of intergenerational mobility. If the probability of high performance is much lower

among students from a disadvantaged background, that is, if a less advantaged environment leads

to a lower possibility of higher educational attainment, then social mobility will decline as a result.

The RRI identifies how many students from the most disadvantaged background can ascend the

social ladder, and is measured as the number of students from the most disadvantaged

environment as a proportion of the highest-performing students.

Denote 𝑐 as the most disadvantaged circumstance, and 𝑞𝑐 as the population

proportion of the most disadvantaged group. Define p, the set of highest-performing students, as

those in top p percentile. Let n𝑝 denote the number of students in p , and n𝑝,𝑐, denote the

number of students from the most disadvantaged group in p.

𝑅𝑅𝑝 = 1 −n𝑝,𝑐, n𝑝⁄

𝑞𝑐

The value of the RRI ranges between zero and one3, with zero representing 0 percent inequality

of opportunity. This indicates that, the share of students from the lowest socioeconomic

background among the top p percent of the overall population by achievement is equal to the

share of students from the lowest socioeconomic background. Then, a value of one indicates the

highest level of opportunity inequality, where students from the lowest socioeconomic

background cannot achieve the top p percent of academic success. In this study, the highest-

performing students are defined as 20 percent of the population. A decrease in the RRI implies an

increase in the number of students from the least advantaged group who have achieved a first

quintile score on the test.

3 Data

3.1 Data Set

The Trends in International Mathematics and Science Study (TIMSS), an international

comparative study of student achievement in mathematics and science, represents the most

comprehensive international comparison. The TIMSS is designed to assess several criteria in

3 If the proportion of high-performing students from lowest social status to total high-performing students exceeds

the proportion of lowest social status population to total population, RRI might have negative value; the negative

values imply that students from lowest social status are more likely to achieve highest performance.

terms of students' characteristics, home environment, learning resources, and science and

mathematics achievements among Grades 4 and 8. The study has been administered every four

years by the International Association for the Evaluation of Educational Achievement (IEA) since

1995.

In this study, data from six waves of TIMSS (1995, 1999, 2003, 2007, 2011, 2015) are

employed to analyze the relationship between students’ academic performance and home

environment, which are drawn mainly from student background questionnaires. This study

focuses on 16 countries: Australia, Canada, Germany, England, Finland, France, Hong Kong, Italy,

Japan, Korea, the Netherlands, New Zealand, Norway, Singapore, Sweden, and the United States.

Consequently, the purpose of this study is to measure and compare the degree of the inequality in

opportunity (in science and mathematics achievement) among Grade 8 students in the 16 countries

who participated in the TIMSS assessment. All of these countries have participated in the TIMSS

assessment at least once, but not all countries participated in every round. For example, Hong

Kong, Korea, Singapore, and the Unites States joined TIMSS in 1995, and France and Germany

participated in the program in 1995 only. The inequality indices are computed using only those

countries that participated in that year. Therefore, when comparing these indices across countries,

this study will separate the data into two parts: from 1995 to 2003, and from 2007 to 2015.

3.2 Social Background

In this study, individual social background is measured by: (1) father’s level of education, as in

Roemer (1998) and Lefranc et al. (2008), and (2) the HLEI, which is derived from selected factors.

Since only restricted circumstances are available in TIMSS, our value of Inequality of opportunity

indices should be considered as lower bounds.

Most studies on the equality of opportunity that use a non-parametric approach, consider

a single variable (e.g., level of education, income, or parents’ occupation) as the social origin of

the inequality. This might be attributed to the requirements of a reasonable partition and large sub-

samples within each type. When partitioning the population into types (subsets of the population

that are homogeneous with respect to circumstances) to test for the existence of opportunity

inequality, the test suffers from a limited number of observations as the number of types increases.

This study develops a circumstance index, the HLEI, taking into account that several factors,

rather than parental income, occupation or education alone, influence the equality of opportunity

in education. The HLEI also solves the problem of a reasonable number of sub samples. The HLEI

is a composite measure that captures a positive home learning environment using three

dimensions: parents’ level of education, home educational materials (resources and facilities), and

the number of books in the home. Assuming that all factors included in HLEI may indicate parents’

aspirations and devotion to their child’s education, partitioning the population according to the

value of HLEI is meaningful, because it reflects the resources and environmental effects provided

by parents.

According to the mean scores conditional on the social background (i.e., father’s

educational attainment and the HLEI) students’ educational performance has been shown to be

related to their social background. In all countries, the mean scores of students from the more

privileged group are always higher than those of students from the less privileged group.

3.2.1 Father’s Level of Education

The data on students’ educational achievements are assigned to one of three categories based on

the first measurement: father’s level of education. The categories Low, Med, and High include

students whose fathers have less than or equal to lower secondary education, short-cycle tertiary

education or below, and a bachelor degree or above, respectively. Table 1 presents the descriptive

statistics (means and standard deviations) conditional on the father’s level of education.4

The proportion of students from disadvantaged socioeconomic backgrounds (Low) has

decreased dramatically in Korea. In 2015, the proportion of Korean students whose fathers have

a low level of education was 1.98 percent, and those whose fathers have a medium level of

education was 46.85 percent. The sum of these two groups is smaller than the percentage of

Korean students whose fathers have high level of education (51.17 percent). In fact, with the

exception of the United States, the proportion of students from low backgrounds has decreased

by more than half in all countries.

3.2.2 The HLEI

The HLEI reflects the level of the learning environment, and is based on three factors: number of

books at home, coded from 1 to 5, where 5 indicates having more books in the home; home

possessions,5 as dichotomous variables (the items asked were not the same in each year); and

parents’ education level. The responses to parents’ highest level of education are re-coded on a

seven-point scale so that high scores indicate higher levels of education. Then, each factor

receives a score from 0 to 1. The overall index value is the sum of the weighted scores for each

factor. In this study, each factor is simply weighted at 1: Factor1’s score × 1 + Factor2’s

score×1+Factor3's score×1. Thus, the HLEI value can range from 0 to 3. A higher score indicates

a more socioeconomically advantaged environment at home. Then, based on the scores derived

from the weighted factors, students are divided into three equally sized groups as much as that is

possible, where category 3(1) denotes the most advantaged (disadvantaged) social background.

When measuring circumstances using the HLEI, each group includes at least 25.92 percent and

4 Descriptive statistics for the remaining countries are presented in Appendix.

5 In 1995, 1997, and 2003: calculator, computer, study desk, and dictionary. In 2007: calculator, computer, study

desk, dictionary, and internet connection. In 2011: computer, study desk, own room, own books and internet

connection. In 2015: digital devices, own computer, computer, study desk, own room, internet connection and own

mobile phone.

at most 41.43percent of the total subpopulation.

4 Empirical Results

The degree of opportunity inequality can be analyzed using the curves of the distributions of the

test scores, conditional on the social backgrounds. When comparing these curves to check for

first-order inequality of opportunity, three situations can occur: the two curves are identical; the

two curves intersect; one curve lies above the other. Equality of opportunity is satisfied in the first

two cases, and is violated in the third case.

According to Lefranc et al.(2008), the distance between the distributions of the groups also

needs to be estimated and compared, because the gap reflects “the magnitude of the advantage

conferred by more privileged backgrounds over less privileged ones.” The gap between the

distributions of the different backgrounds varies between countries, suggesting that the extent of

the advantage given to the privileged group varies as well. In other words, if the three conditional

distributions for each category are close, differences in social background correspond to very

small differences in academic performance.

Differences in partitioning the individual social backgrounds into circumstances correspond

result in different findings. We have to keep in mind that a restrictive approach to partitioning

individual social backgrounds into circumstances is likely to lead to an underestimate of

inequality of opportunity: any inequality associated with unconsidered backgrounds (race, gender

or language) may remain within three types and would be attributed to effort.

Reporting visual inspections in terms of the FSD and second-order stochastic dominance

(SSD) for six rounds of TIMSS and as many as 16 countries for math and science takes a lot of

space. Therefore, this paper concentrates on comparing the dominance results using one or two

countries from each continent: Australia, Korea, Hong Kong, Sweden, and the United States are

presented and compared.6 Whether the gaps between the distributions of the different types have

narrowed can be seen clearly from a comparison of the curves for the first and the last test.

4.1 Inequality of Opportunity Related to Father’s Education

The cumulative distribution functions conditional on father’s education are presented in this

section. According to Figure 1 and 2, the CDF for individuals from the more privileged group

(students whose fathers have higher levels of education) is always below the CDF for individuals

from the less privileged group (students whose fathers have lower level of education). Note that

the distribution of the students in the latter category in 2015 includes samples that are relatively

6 Results for the remaining countries are included in the Appendix.

smaller than they were in 1995 for all countries except the United States. Students from lower

socioeconomic backgrounds are less likely to obtain higher levels of academic performance than

those from higher socioeconomic backgrounds.

4.1.1 Conditional Distributions: Mathematics

Figure 1 presents the conditional distributions for scores in mathematics in 1995 (left) and 2015

(right). The test scores are plotted on the horizontal axis and the percentiles on the vertical axis.

Except for the United States, the gaps between the three CDFs corresponding to the differences

in father’s levels of education appear to be widening further, indicating an increase in opportunity

inequality. In the case of Hong Kong, although it has not escaped the worldwide widening of the

gaps, the three conditional distributions for each category are closer than any of the other countries

in all rounds. Sweden seems to have a more equal distribution than those of other countries in

1995. However, the inequality of opportunity seems to increase to a point where it matches or

exceeds that of the United States. In Korea, the distance between Low and Med is closer than the

distance between Med and High, suggesting that there is more equality of opportunity at the

bottom of the social ladder.

4.1.2 Conditional Distributions: Science

Figure 2 shows the conditional distributions for scores in science in 1995 (left) and 2015 (right).

In nearly all cases, the cumulative distribution functions of science score conditional on father’s

education are similar to those of the mathematics scores. For Korea, the gaps in 1995 are relatively

smaller than those shown in Figure 1, but then become more similar to those in 2015.

Figure 1: Math score Distributions Conditional on Father's Education

Figure 2: Science score Distributions Conditional on Father's Education

4.1.3 The Stochastic Dominance Test

To complement the result offered by the cumulative distributions, the stochastic dominance test

results based on the SSD are presented in Table 3. Here, the top and bottom 2.5 percent of each

group are excluded. Thus, in 2015, the distribution for Korea cannot be ranked using the stochastic

dominance tool, because Korean students from a low social background form only about 1.97

percent of the total population.7 With the exception of this group, the equality of opportunity

measured using the SSD tests appear consistent with the comparisons obtained from the visual

inspection of CDFs. As shown in Table 3, the distributions of the less privileged groups are equal

in Hong Kong in 2003, but the degree of equality of opportunity seems to weaken.

Table 1: Stochastic Dominance Tests (Father's Education)

Mathematics Science

Country Category 1 2 3 1 2 3 Australia

1995

Low ≺1*** ≺1*** ≺1*** ≺1***

Med ≺1*** ≺1***

High

1999

Low ? ≺1***

≺2* ≺1***

Med ≺1*

≺1*

High

2003

Low ≺1* ≺1***

≺2*** ≺1***

Med ≺2***

≺1***

High

2007

Low ? ≺1***

≺2*** ≺1***

Med ≺1***

≺1***

High

7 The result of dominance tests conditional on HLEI - distributions of Korean students from more privileged group

dominates those from less privileged group, indicates that some results from Table3 have problems with small sample

size.

2011

Low ≺2*** ≺1***

≺1*** ≺1***

Med ≺1***

≺1***

High

2015

Low ≺1*** ≺1***

≺1*** ≺1***

Med ≺1***

≺1***

High

Hong

Kong

1995

Low ≺1*** ≺1*** ≺1** ≺2***

Med ≺2*** ?

High

1999

Low ≺1* ≺1**

= ≺1***

Med ?

≺1***

High

2003

Low = ?

= ≺1***

Med ?

≺1***

High

2007

Low ? ≺1**

≺2* ≺1**

Med ≺2**

≺2**

High

2011

Low ≺1** ≺1***

≺1** ≺1***

Med ≺1***

≺1***

High

2015

Low ? ≺1***

≺1** ≺1***

Med ≺1***

≺1***

High

Korea

1995

Low ≺1** ≺1*** ≺2* ≺1***

Med ≺1*** ≺1***

High

1999

Low ≺2*** ≺1***

≺1*** ≺1***

Med ≺1**

≺1***

High

2003

Low ≺1*** ≺1***

≺1** ≺1***

Med ≺1***

≺1***

High

2007

Low ≺2** ≺1***

≺2* ≺1***

Med ≺1***

≺1***

High

2011

Low ≺2** ≺1***

≺2** ≺1***

Med ≺1***

≺1***

High

2015

Low ? ≺1***

? ≺1***

Med ≺1***

≺1***

High

Sweden

1995 Low

≺2** ≺1** ≺2*** ≺1***

Med ≺2* ≺1∗∗

High

2003

Low ≺1* ≺1**

≺2* ≺1**

Med ≺2**

≺1*

High

2007

Low ≺2** ≺1**

≺1*** ≺1***

Med ?

?

High

2011

Low ≺1* ≺1***

≺1* ≺1***

Med ≺1***

≺1***

High

2015

Low ≺1* ≺1***

≺1*** ≺1***

Med ≺1**

≺2**

High

USA

1995

Low ≺1*** ≺1*** ≺1*** ≺1***

Med ≺1*** ≺1***

High

1999

Low ≺1*** ≺1***

≺1*** ≺1***

Med ≺1***

≺1***

High

2003

Low ≺1*** ≺1***

≺1*** ≺1***

Med ≺1***

≺1***

High

2007

Low ≺1*** ≺1***

≺1*** ≺1***

Med ≺1***

≺1***

High

2011

Low ≺1*** ≺1***

≺1*** ≺1***

Med ≺1***

≺1***

High

2015

Low ≺2*** ≺1***

≺1*** ≺1***

Med ≺1***

≺1***

High Notes ≺𝑖 : the column dominates the row for order i stochastic dominance. =: the distributions are equal. ?: the

distributions cannot be ranked using first- and second-order stochastic dominance. Father's education group

corresponds to social background. Low: lower secondary education or below, Med: short-cycle tertiary education or

below, High: bachelor degree or above.

4.2 Inequality of Opportunity Related to the HLEI

4.2.1 Conditional Distributions: Mathematics

Figure 3 shows the conditional distributions for scores in mathematics in 1995(left) and

2015(right). Category 1 is the bottom one-third of the population; Category 2 is the second one-

third of the population; and Category 3 is the upper one-third of the population.

Hong Kong exhibits the lowest degree of opportunity inequality. On the other hand, in

Australia, Korea, and the United States, the gaps between the three distributions are quite large in

both 1995 and 2015, suggesting that more advantages are offered to the privileged group. While

the gap in the United States remains unchanged and narrows somewhat in Korea, the gaps in

Australia, Hong Kong, and Sweden have roughly doubled in size.

Figure 3: Math score Distributions Conditional on HLEI

4.2.2 Conditional Distributions: Science

Figure 4 describes the conditional distributions for scores in science in 1995(left) and 2015(right).

Although the distances between the different types has widened in all countries, Hong Kong and

Korea display relatively small degrees of inequality.

Figure 4: Science Score Distributions Conditional on the HLEI

4.2.3 The SSD Test

The stochastic dominance test results according to the SSD are summarized in Table 4.

For all cases other than Hong Kong in 1995, the more privileged group first-order

stochastically dominates the less privileged group.

Table 2: Stochastic Dominance Tests (HLEI)

Mathematics Science

Country Category 1 2 3 1 2 3 Australia

1995

1 ≺1*** ≺1*** ≺1*** ≺1***

2 ≺1*** ≺1***

3

1999

1 ≺1* ≺1***

≺1*** ≺1***

2 ≺1**

≺1***

3

2003

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺2***

≺1***

3

2007

1 ≺1** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2011

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2015

1 ≺2*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

Hong

Kong

1995

1 ≺2*** ≺1*** = ≺1***

2 ≺2*** ≺2*

3

1999

1 ≺1*** ≺1***

≺1** ≺1***

2 ≺1**

≺2***

3

2003

1 ≺2** ≺1***

≺1* ≺1***

2 ≺1**

≺1*

3

2007

1 ≺1** ≺1***

≺2*** ≺1***

2 ≺1***

≺1*

3

2011

1 ≺1*** ≺1***

≺2*** ≺1***

2 ≺1***

≺1***

3

2015

1 ≺1** ≺1***

≺1* ≺1***

2 ≺1***

≺1***

3

Korea

1995

1 ≺1*** ≺1*** ≺1*** ≺1***

2 ≺1*** ≺1*

3

1999

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1**

≺1***

3

2003

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2007 1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2011

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2015

1 ≺1*** ≺1***

≺1** ≺1***

2 ≺1***

≺1**

3

Sweden

1995

1 ≺1*** ≺1*** ≺1*** ≺1***

2 ? ?

3

2003

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1**

≺1***

3

2007

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1**

≺1*

3

2011

1 ≺1** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2015

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

USA

1995

1 ≺1*** ≺1*** ≺1*** ≺1***

2 ≺1*** ≺1***

3

1999

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2003

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2007

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2011

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3

2015

1 ≺1*** ≺1***

≺1*** ≺1***

2 ≺1***

≺1***

3 Notes ≺𝑖 : the column dominates the row for order i stochastic dominance. =: the distributions are equal.?: the

distributions cannot be ranked using first- and second-order stochastic dominance. Categories refers to social

background. 1: bottom one-third. 2: second one-third. 3: upper one-third.

4.3 Opportunity Inequality Index

In this section, the GOI and the RRI are multiplied by 100 and 1000, respectively. Thus, zero

represents complete inequality and 100(1000) represents complete equalities in terms of the

GOI(RRI). The values of these indices are presented in the Appendix.

4.3.1 Trend

An important point, shown in both Figure 5 and 6, is that countries with a relative low GOI value

do not necessarily have low RRI value, and vice versa. Also, for Korea, the trends in RRI using

the father’s education differ to those measured using the HLEI.

Figure 5 displays inequalities in outcomes and opportunities for Korea, the United States

and 16 countries when the circumstances measure is father’s level of education. In Korea, the

value of the RRI shows an increasing trend, which implies that students whose fathers with low

level of education tend to be less likely to score in the 80th percentile on the test than before. The

average mathematics score for 16 countries in 2015 is higher than that in 2011. However, for

Korea, all 3 groups have a lower score in 2015 than in 2011. The decline has been greatest among

those in the most advantaged group. From the increased RRI, it seems that the slight decrease in

the GOI is due to the narrowing gap between the two more privileged groups. For the United

States, the gap between the students whose father has medium level of education and the students

whose father has low level of education has been narrowed.

Figure 7 shows the differences in the values of inequality indices between mathematics

and science. In most of the countries, there is no appreciable difference in the degrees and patterns

of the GOI regardless of the different subject areas. In terms of GOI, Japan, Korea and Singapore

are the exceptional cases where there are relatively noticeable differences in the level of

inequalities of opportunity according to the subject area. GOI for mathematics are slightly higher

than those for science in Japan and Korea. In Singapore, the case is the exact opposite. In terms

of RRI, the gap regarding to the subject area is somewhat smaller and not constant.

Figure 5: Inequalities in Outcomes and Opportunities conditional on father’s education

Figure 6: Inequalities in Outcomes and Opportunities conditional on HLEI

Figure 7: Differences between Mathematics and Science

4.3.2 Rankings from 1995 to 2003

In this section, the levels of opportunity inequality are compared by subject area, across-time

changes, and within each country. The rest of the paper is divided into two parts, focusing on the

first period (from 1995 to 2003), and on the second period (from 2007 to 2015).

In the following sets of figures, the results on the left represent the average values of the

GOI when circumstances are measured using father’s education level (GOI-edu), and those on

the right are obtained when circumstances are measured using the HLEI (GOI-HLEI). The GOI-

edu rankings are not always the same as the GOI-HLEI rankings, for several reasons. First, when

partitioning students into three categories according to father’s level of education, the differences

in the number of observations in each category underestimate or overestimate the GOI. As

mentioned in section 3.2.1, the relative size of each category based on father’s level of education

varies between countries, and the relative size of each category represents between 25 percent to

42 percent of the students based on the HLEI, which is an aggregate index including parental

education, home possessions, and the number of books in the home. Second, the two factors other

than father’s education influence the academic performance of students indirectly as a proxy for

income, representing the capacity to purchase goods and services for academic support. Third, the

other two factors also influence the academic performance of students directly. The use of devices

such as computers and dictionaries and an abundance of books may foster a higher level of

academic achievement.

Figure 8: GOI in math 1995-2003 measured by father's education(left) and HLEI(right)

Figure 9: GOI in Science 1995-2003 Measured by Father's Education (left) and HLEI (right)

Figure 8 presents the average value of the GOI from 1995 to 2003 for mathematics. As

shown in the graph on the left, Japan, England and the United States are among the most unequal

countries in terms of GOI based on circumstances measured by father’s education while Hong

Kong and Canada rank as the most equal nations. The graph on the right shows that, Hong Kong,

Canada, and France are the most equal countries. A comparison of GOI-edu and GOI-HLEI shows

a aignificant difference in the case of Japan and Korea. Japan ranks first, with a value of 2.3254

(GOI-edu), but ranks ninth out of 16 countries according to GOI-HLEI (2.738). In contrast, Korea

ranks seventh in terms of GOI-edu (2.1359), but ranks second in terms of GOI-HLEI.

Figure 9 shows the average values of the GOI from 1995 to 2003 for science. Similarly,

to the results for mathematics, Hong Kong, Finland, and the Netherlands, show a low degree of

inequality in terms of GOI-edu. The United States ranks first, followed by Singapore, in terms of

both GOI-edu and GOI-HLEI. In Japan and Singapore, unlike in other countries, different features

appear in relation to the subjects. Singapore, which has an intermediate level of inequality of

opportunity in mathematics scores, is one of the most unequal country in terms of science scores.

In Japan, father’s education levels tend to have a significant impact on their children’s

mathematics achievements, but almost no difference in the case of science.

Figure 10: RRI in math 1995-2003 measured by father's education(left) and HLEI(right)

Figure 11: RRI in science 1995-2003 measured by father's education(left) and HLEI(right)

In Figure 10 and 11, the GOI is replaced by the RRI. The findings are similar to those

reported in Figure 8 and 9. With regard to mathematics, the United States and Japan are the least

equal countries according to both GOI-edu and GOI-HLEI, while Hong Kong is the most equal

country. With regard to science, England and the United States have the highest values relative to

the other countries in terms of both RRI-edu and RRI-HLEI. Furthermore, Hong Kong has a

relatively low value of both RRI-edu and RRI-HLEI, and Germany is ranked as the second least

unequal country according to RRI-edu, and fourth most unequal country according to RRI-HLEI.

4.3.3 Rankings from 2007 to 2015

In this section, the figures show the degree of inequality of opportunity measured by the GOI and

RRI in terms of arithmetic average, from 2007 to 2015. France, Germany and the Netherlands did

not participate in the program between 2007 and 2015. Therefore, these three countries are

therefore omitted from the comparison for this period.

Figure 12: GOI in math 2007-2015 measured by father's education(left) and HLEI(right)

Figure 13: GOI in science 2007-2015 measured by father's education(left) and HLEI(right)

Figure 12 and Figure 13 show the average value of the GOI from 2007 to 2015 in

mathematics and science, respectively. England, Australia and New Zealand are the least equal

countries, and Hong Kong, Finland, Sweden and Norway are the most equal countries in both

mathematics and science. Canada, in mathematics, ranks eighth according to GOI-edu, but stand

out as the second most equal country according to GOI-HLEI.

Figure 14: RRI in math 2007-2015 measured by father's education(left) and HLEI(right)

Figure 15: RRI in science 2007-2015 measured by father's education(left) and HLEI(right)

According to Figure 14, showing the average value of the RRI in mathematics, Japan,

England and New Zealand are the most unequal countries, while Italy, Hong Kong, and Canada are

the least unequal countries. The United States ranks second when the social background is partitioned

by HLEI, but is considered to belong in intermediate unequal country when the social background is

interpreted by father’s education. While Japan shows serious inequities of opportunity in achievement

in mathematics, the degree of inequality of opportunity in science is relatively low. For the United

State, the results shown in Figure 14 and 15 are made more interesting by the fact that dividing social

backgrounds by father’s education or HLEI influences the rank of the level of inequality of opportunity

in mathematics achievement. However, such differences do not exist for science.

5 Conclusion

This study examines how the differences in levels of academic achievement are related to social

background, across time and countries. International comparisons of the degree of inequality in

opportunity are based on two opportunity inequality indices.

This study first measures and compares cumulative distributions conditional on social

background using stochastic dominance. Then the comparison is implemented by ranking

countries according to two opportunity inequality indices. The results indicate that not only social

backgrounds attributes to the access of education, but also to the chance to success in education.

The two indices reveal substantial variation in the extent to which different countries achieve

equality of educational opportunity for students from different social backgrounds. In addition, in

some countries, the level of inequality varied by subject areas, suggesting that social background

advantages in education may be related to systemic features of countries’ education systems.

Particularly in Japan and Korea, students from low social backgrounds are more likely to suffer

from lack of opportunities to develop mathematic ability, as both countries have high values of

RRI and GOI in mathematics compared to science. On the other hand, students from low social

backgrounds are more likely to suffer from lack of opportunities learning science than learning

mathematics in Singapore. England and New Zealand continuously display the greatest

opportunity inequality, while the United States ranked as one of the most unequal countries during

the period of 1995-2003, has improved in terms of opportunity inequality during the second phase,

2007-2015.

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A Appendices

A.1 Descriptive Statistics

A.1.1 Conditional on Father’s Education

Subject Mathematics Science

Country Category N Mean SD Total% N Mean SD Total%

Australi

a 1995

Low 3139 498.7 93.45 34.22 3139 508.3 102.9 34.22

Med. 3626 517.7 93.84 39.53 3626 531.6 102.4 39.53

High 2408 559.5 90.70 26.25 2408 568.6 102.4 26.25

1999

Low 816 516.3 72 34.29 816 534.4 84.09 34.29

Med. 809 535.1 75.72 33.99 809 551 81.30 33.99

High 755 569.5 70.34 31.72 755 579.8 75.25 31.72

2003

Low 639 482.3 78.35 24.29 639 508.9 74.87 24.29

Med. 1330 509.3 76.19 50.55 1330 532.8 67.35 50.55

High 662 548.5 77.40 25.16 662 569.5 67.29 25.16

2007

Low 554 479.5 72.13 27.56 554 501.6 74.67 27.56

Med. 1005 501.0 74.02 50.00 1005 520.6 74.34 50.00

High 451 554.9 74.50 22.44 451 573.2 70.73 22.44

2011

Low 340 462.9 80.89 10.57 340 476.7 78.37 10.57

Med. 1985 496.2 74.40 61.70 1985 516.2 75.99 61.70

High 892 577.3 83.23 27.73 892 590.4 78.98 27.73

2015

Low 482 461.1 84.83 11.77 482 469.8 85.14 11.77

Med. 2239 507.6 75.87 54.68 2239 515.7 75.13 54.68

High 1374 552.3 74.87 33.55 1374 559.9 76.20 33.55

Hong

Kong 1995

Low 3343 577.7 94.93 63.30 3343 510.4 85.27 63.30

Med. 1515 599.1 95.28 28.69 1515 525.6 84.76 28.69

High 423 621.5 90.89 8.010 423 540.5 83.74 8.010

1999

Low 2006 581.3 71.76 54.14 2006 530 69.23 54.14

Med. 1393 592.9 69.23 37.60 1393 534.5 68.70 37.60

High 306 613.2 68.55 8.260 306 565.4 65.33 8.260

2003

Low 1906 584.5 67.56 49.55 1906 554.5 64.21 49.55

Med. 1478 591.8 66.08 38.42 1478 559.8 61.49 38.42

High 463 618 72.09 12.04 463 578 65.15 12.04

2007

Low 1161 565.4 90 46.20 1161 527.9 81.52 46.20

Med. 1000 580.1 87.17 39.79 1000 537.2 77.53 39.79

High 352 613.4 86.79 14.01 352 561.6 73.78 14.01

2011

Low 970 571 80.16 35.69 970 526.2 71.91 35.69

Med. 1237 593.9 76.72 45.51 1237 540 69.69 45.51

High 511 632.5 68.73 18.80 511 574 63.19 18.80

2015

Low 732 580.3 77.45 27.58 732 531.4 72.42 27.58

Med. 1374 596.3 74.63 51.77 1374 546.4 68.26 51.77

High 548 630.5 67.44 20.65 548 581.7 66.90 20.65

Korea

1995

Low 1433 567 103.8 28.02 1433 536.2 91.61 28.02

Med. 2475 594.4 104.0 48.39 2475 552.1 92.48 48.39

High 1207 640.5 99.10 23.60 1207 577.9 90.10 23.60

1999

Low 1098 569.4 77.53 21.45 1098 533.7 81.83 21.45

Med. 2627 588.3 72.74 51.31 2627 552.8 81.45 51.31

High 1395 625.9 72.15 27.25 1395 586.9 83.27 27.25

2003

Low 527 545.4 86.99 11.19 527 525.9 73.54 11.19

Med. 2548 584.7 76.45 54.09 2548 554.6 65.24 54.09

High 1636 618.8 75.16 34.73 1636 583.2 65.80 34.73

2007

Low 189 553.1 96.50 5.500 189 521.6 80.12 5.500

Med. 1574 584.3 83.50 45.82 1574 545.5 72.49 45.82

High 1672 630.2 85.42 48.68 1672 579.8 70.89 48.68

2011 Low 169 573.1 93.18 4.550 169 526.4 78.77 4.550

Med. 1776 599.4 83.25 47.77 1776 553.6 72.52 47.77

High 1773 652.2 78.78 47.69 1773 591 71.58 47.69

2015

Low 66 570.3 83.42 1.980 66 523.3 72.34 1.980

Med. 1560 595.6 79.15 46.85 1560 547.7 70.19 46.85

High 1704 637.3 78.04 51.17 1704 583 73.75 51.17

Sweden

1995

Low 917 514.7 87.46 19.78 917 530.7 95.33 19.78

Med. 2496 527.9 86.09 53.84 2496 542.8 91.05 53.84

High 1223 548.9 89.31 26.38 1223 567.6 97.83 26.38

2003

Low 299 488.8 66.84 17.61 299 518.5 71.58 17.61

Med. 717 505.4 66.42 42.23 717 532.8 70.21 42.23

High 682 529.9 69.96 40.16 682 556.4 72.89 40.16

2007

Low 297 478.3 66.47 16 297 496.3 74.78 16

Med. 976 501.4 63.74 52.59 976 529.8 72.30 52.59

High 583 520.4 66.48 31.41 583 548.5 73.58 31.41

2011

Low 276 474.6 65.96 11.55 276 502.7 81.28 11.55

Med. 1269 495.1 63.12 53.12 1269 527.9 73.56 53.12

High 844 518 63.63 35.33 844 550.7 71.91 35.33

2015

Low 195 472.6 66.55 10.32 195 491.6 88.59 10.32

Med. 916 505.6 64.91 48.47 916 532.3 73.10 48.47

High 779 535.7 65.68 41.22 779 562.9 81.18 41.22

Canada

1995

Low 2737 503.7 81.51 24.02 2737 503.7 91.31 24.02

Med. 4550 516.1 82.75 39.93 4550 518 90.40 39.93

High 4107 532.1 84.02 36.05 4107 540.5 90.48 36.05

1999

Low 942 516.8 72.40 15.15 942 521.9 75.97 15.15

Med. 2518 533.7 70.38 40.49 2518 536.3 74.23 40.49

High 2759 550.2 70.61 44.36 2759 551.3 77.34 44.36

2015

Low 181 504.6 74.27 4.080 181 504.9 75.40 4.080

Med. 2355 523.9 63.88 53.05 2355 526.2 63.24 53.05

High 1903 565.3 62.95 42.87 1903 563.8 66.06 42.87

German

y 1995

Low 1813 498.4 84.19 53.80 1813 518.8 94.92 53.80

Med. 1167 519.6 83.96 34.63 1167 541.3 91.47 34.63

High 390 542.7 87.71 11.57 390 560.3 103.7 11.57

England

2011

Low 59 490.0 79.55 9.770 59 540.5 67.98 9.770

Med. 367 529.0 70.43 60.76 367 576.1 71.93 60.76

High 178 564.3 68.66 29.47 178 613.8 65.70 29.47

2015

Low 150 472.3 85.62 9.750 150 490.8 93.25 9.750

Med. 970 522.3 77.99 63.03 970 554.0 75.92 63.03

High 419 569.1 71.62 27.23 419 596.2 72.59 27.23

2003

Low 209 509.9 78.08 13.05 209 522.7 82.17 13.05

Med. 739 526.5 71.98 46.16 739 550.0 73.59 46.16

High 653 580.0 74.70 40.79 653 600.0 75.76 40.79

Finland

1999

Low 391 511.2 61.86 38.64 391 538.5 74.19 38.64

Med. 497 540.8 62.57 49.11 497 564.0 77.59 49.11

High 124 566.8 61.69 12.25 124 584.3 75.71 12.25

2011

Low 281 491.0 59.74 11.59 281 533.5 64.83 11.59

Med. 1399 517.1 61.48 57.69 1399 558.0 61.51 57.69

High 745 543.3 60.65 30.72 745 583.7 62.44 30.72

France

1995

Low 981 516.9 78.21 39.46 981 474.2 79.05 39.46

Med. 1085 539.5 74.05 43.64 1085 495.3 76.36 43.64

High 420 560 72.82 16.89 420 506.9 74.58 16.89

Italy

1999

Low 1591 465.0 83.45 53.10 1591 476.6 85.90 53.10

Med. 1165 498.8 80.16 38.89 1165 519.3 80.63 38.89

High 240 523.7 73.20 8.010 240 542.9 75.23 8.010

2003

Low 1733 463.1 74.89 45.25 1733 471.1 77.09 45.25

Med. 1486 500.5 71.02 38.80 1486 507.1 73.45 38.80

High 611 506.8 73.29 15.95 611 510.9 76.68 15.95

2007 Low 1484 459.6 75.15 40.85 1484 477.2 79.90 40.85

Med. 1485 500.7 68.74 40.88 1485 514.4 70.01 40.88

High 664 505.5 69.86 18.28 664 524.2 67.13 18.28

2011 Low 1238 483.9 70.74 38.32 1238 480.3 74.45 38.32

Med. 1431 505.8 70.33 44.29 1431 510.2 72.97 44.29

High 562 527.6 65.69 17.39 562 531.6 66.46 17.39

2015

Low 1178 478.8 72.28 35.41 1178 482.5 73.22 35.41

Med. 1600 506.7 68.65 48.09 1600 510.7 71.11 48.09

High 549 528.6 71.14 16.50 549 532.5 71.32 16.50

Netherl

ands 1995

Low 409 510.0 82.75 16.99 409 525.1 82.57 16.99

Med. 1629 539.5 82.54 67.65 1629 550.9 81.21 67.65

High 370 562.7 84.26 15.37 370 566.4 87.35 15.37

1999

Low 230 523.9 70.58 13.31 230 516.4 85.10 13.31

Med. 1227 553.3 64.51 71.01 1227 562.4 66.15 71.01

High 271 569.9 64.77 15.68 271 576.3 74.58 15.68

2003

Low 82 518.6 65.41 4.550 82 509.6 61.66 4.550

Med. 1333 544.1 63.40 73.89 1333 543.4 55.57 73.89

High 389 573.3 63.82 21.56 389 564.4 56.33 21.56

Norway

1995

Low 459 471.2 84.70 14.98 459 493.3 85.19 14.98

Med. 1638 488.9 80.76 53.44 1638 512.8 86.02 53.44

High 968 508.2 84.53 31.58 968 529.5 88.54 31.58

2003

Low 138 425.4 70.42 8.270 138 471.9 73.86 8.270

Med. 519 465.5 64.60 31.12 519 502.2 62.30 31.12

High 1011 489.2 65.60 60.61 1011 519.8 63.87 60.61

2007

Low 119 436.5 72.09 6.470 119 450.9 82.13 6.470

Med. 565 470.6 63.88 30.71 565 493.1 71.41 30.71

High 1156 490.5 60.59 62.83 1156 513.9 69.07 62.83

2011

Low 93 449.8 69.10 5.230 93 448.7 86.03 5.230

Med. 706 476.9 58.77 39.69 706 501.6 67.38 39.69

High 980 503.4 59.23 55.09 980 525.0 66.83 55.09

2015

Low 118 487.1 59.35 5.100 118 483.5 68.72 5.100

Med. 997 506.9 67.65 43.07 997 507.1 75.58 43.07

High 1200 537.8 65.88 51.84 1200 542.9 73.57 51.84

New

Zealand 1995

Low 1151 486.5 81.96 27.67 1151 501.5 92.03 27.67

Med. 1974 493.3 87.69 47.46 1974 512.0 99.41 47.46

High 1034 530.2 91.59 24.86 1034 545.3 100.8 24.86

1999

Low 605 484.7 81.66 28.06 605 501.3 84.95 28.06

Med. 924 489.0 82.99 42.86 924 514.7 82.35 42.86

High 627 536.4 84.71 29.08 627 555.5 88.67 29.08

2003

Low 170 480.6 74.29 11.64 170 500.6 61.07 11.64

Med. 914 500.3 69.66 62.56 914 533.4 66.73 62.56

High 377 540.8 75.45 25.80 377 566.8 66.94 25.80

2011

Low 365 463.7 81.08 20.61 365 487.6 81.86 20.61

Med. 971 497.2 81.54 54.83 971 521.8 81.88 54.83

High 435 543.9 79.77 24.56 435 566.5 80.71 24.56

2015

Low 447 479.1 86.38 18.55 447 499.6 92.05 18.55

Med. 1151 502.1 85.53 47.76 1151 526.7 91.62 47.76

High 812 548.3 88.84 33.69 812 568 91.88 33.69

Singapo

re 1995

Low 2614 601.3 91.47 31.80 2614 550.3 100.5 31.80

Med. 5096 627.9 91.92 62 5096 583.0 100.8 62

High 509 673.6 85.43 6.190 509 640.3 91.73 6.190

1999

Low 1465 592.6 78.42 39.10 1465 551.7 94.84 39.10

Med. 1890 609.3 74.53 50.44 1890 577.8 91.87 50.44

High 392 651.6 73.89 10.46 392 636.0 85.25 10.46

2003

Low 2658 598.0 77.49 63.62 2658 567.5 87.74 63.62

Med. 918 624.9 69.31 21.97 918 608.5 79.16 21.97

High 602 654.5 67.77 14.41 602 642.3 72.07 14.41

2007

Low 734 567.7 89.48 24.75 734 531.0 101.9 24.75

Med. 1587 600.6 85.06 53.51 1587 576.5 93.19 53.51

High 645 648.9 75.32 21.75 645 640 81.29 21.75

2011

Low 841 586.9 84.37 22.85 841 556.0 98.11 22.85

Med. 1837 615.3 74.98 49.92 1837 596.3 86.30 49.92

High 1002 651.2 70.60 27.23 1002 644.8 81.10 27.23

2015

Low 635 590.5 82.83 16.99 635 561.9 87.86 16.99

Med. 1857 617.6 77.19 49.69 1857 594.0 79.09 49.69

High 1245 664.8 63.93 33.32 1245 648.4 68.58 33.32

USA

1995

Low 1362 453 76.34 15.34 1362 483.3 92.97 15.34

Med. 5078 485.3 85.46 57.21 5078 522.3 102.6 57.21

High 2436 526.1 95.37 27.44 2436 557.4 104.2 27.44

1999

Low 739 462 78.11 11.71 739 480.2 89.31 11.71

Med. 3420 505.5 77.11 54.18 3420 518.2 87.65 54.18

High 2153 545.1 83.55 34.11 2153 563.1 90.98 34.11

2003

Low 804 458.6 69.98 13.85 804 482.2 73.19 13.85

Med. 2316 498.2 71.38 39.90 2316 522 72.31 39.90

High 2684 538.6 76.57 46.24 2684 562 76.28 46.24

2007

Low 776 470.8 66.54 16.62 776 472.3 74.41 16.62

Med. 1895 504.3 69.54 40.59 1895 519.8 74.36 40.59

High 1998 540.7 73.14 42.79 1998 553.9 76.86 42.79

2011

Low 968 476.2 70.32 15.47 968 487.5 79.03 15.47

Med. 2593 503.9 67.85 41.45 2593 524.5 73.70 41.45

High 2695 543.9 72.72 43.08 2695 562.7 74.54 43.08

2015

Low 1018 496.1 81.88 15.84 1018 505.1 80 15.84

Med. 2954 512.3 77.04 45.98 2954 525.9 78.01 45.98

High 2453 554.3 78.08 38.18 2453 564.1 76.41 38.18

A.1.2 Descriptive Statistics Conditional on HLEI

Subject Mathematics Science

Country Category N Mean SD Total% N Mean SD Total%

Australi

a 1995

1 3284 488.7 91.64 35.80 3284 497.2 99.28 35.80

2 2960 523.5 91.79 32.27 2960 535.2 101.3 32.27

3 2929 560.4 90.14 31.93 2929 573.9 100.6 31.93

1999

1 794 511.2 73.43 33.36 794 520.9 83.35 33.36

2 814 539.3 71.48 34.20 814 556.3 77.68 34.20

3 772 570.4 71.21 32.44 772 588.8 71.48 32.44

2003

1 901 479.2 78.93 34.25 901 502.4 71.25 34.25

2 881 517.9 77.19 33.49 881 538.2 65.11 33.49

3 849 542.3 72.35 32.27 849 569.8 64.99 32.27

2007

1 744 471.4 74.13 37.01 744 488.2 75.44 37.01

2 611 507.0 67.59 30.40 611 531.6 66.37 30.40

3 655 547.7 72.76 32.59 655 567.1 69.34 32.59

2011

1 1154 465.1 72.47 35.87 1154 478.4 72.00 35.87

2 1008 516.5 70.01 31.33 1008 534.7 67.77 31.33

3 1055 570.4 84.20 32.79 1055 592.2 75.75 32.79

2015

1 1375 476.1 83.09 33.58 1375 478.6 80.43 33.58

2 1400 517.7 70.23 34.19 1400 529.0 69.53 34.19

3 1320 560.4 69.01 32.23 1320 570.9 67.40 32.23

Hong

Kong 1995

1 1916 573.9 96.63 36.28 1916 508.0 84.61 36.28

2 1696 584.6 94.60 32.12 1696 514.6 85.56 32.12

3 1669 605.4 92.86 31.60 1669 530.2 85.01 31.60

1999

1 1287 571.2 71.77 34.74 1287 520.0 70.91 34.74

2 1327 588.3 68.75 35.82 1327 535.2 67.57 35.82

3 1091 609.1 67.66 29.45 1091 551.7 65.47 29.45

2003

1 1321 577.5 68.16 34.34 1321 547.1 65.38 34.34

2 1248 588.4 66.91 32.44 1248 558.8 61.57 32.44

3 1278 608.4 65.99 33.22 1278 572.7 61.15 33.22

2007

1 967 552.2 91.40 38.48 967 518.0 83.48 38.48

2 825 580.6 86.59 32.83 825 537.4 77.88 32.83

3 721 610.5 79.73 28.69 721 560.3 69.08 28.69

2011 1 976 566.1 83.10 35.91 976 521.5 74.66 35.91

2 915 593.1 74.08 33.66 915 539.6 66.48 33.66

3 827 624.6 68.58 30.43 827 567.1 64.15 30.43

2015

1 955 575.7 76.81 35.98 955 528.1 72.69 35.98

2 828 599.1 72.04 31.20 828 548.5 65.36 31.20

3 871 624.3 70.50 32.82 871 574.2 67.59 32.82

Korea

1995

1 1988 558.6 104.2 38.87 1988 527.8 92.11 38.87

2 1517 601.6 99.42 29.66 1517 557.8 90.56 29.66

3 1610 641.6 96.49 31.48 1610 581.8 87.09 31.48

1999

1 1737 561.6 75.02 33.93 1737 528.6 79.37 33.93

2 1700 596.0 69.08 33.20 1700 555.9 80.60 33.20

3 1683 627.1 70.44 32.87 1683 590.8 81.00 32.87

2003

1 1952 560.0 78.71 41.43 1952 535.1 66.57 41.43

2 1221 593.8 72.51 25.92 1221 563.1 62.44 25.92

3 1538 631.4 70.90 32.65 1538 593.1 62.77 32.65

2007

1 1149 560.8 87.62 33.45 1149 526.6 73.38 33.45

2 1203 607.9 78.88 35.02 1203 562.2 67.70 35.02

3 1083 648.6 77.80 31.53 1083 595.9 66.37 31.53

2011

1 1154 465.1 72.47 35.87 1154 478.4 72.00 35.87

2 1008 516.5 70.01 31.33 1008 534.7 67.77 31.33

3 1055 570.4 84.20 32.79 1055 592.2 75.75 32.79

2015

1 1375 476.1 83.09 33.58 1375 478.6 80.43 33.58

2 1400 517.7 70.23 34.19 1400 529.0 69.53 34.19

3 1320 560.4 69.01 32.23 1320 570.9 67.40 32.23

Sweden

1995

1 1607 504.1 83.29 34.66 1607 520.6 91.60 34.66

2 1585 537.7 85.88 34.19 1585 553.3 90.82 34.19

3 1444 553.2 87.93 31.15 1444 569.4 95.21 31.15

2003

1 567 476.8 63.89 33.39 567 503.4 68.02 33.39

2 573 518.0 64.72 33.75 573 543.8 68.40 33.75

3 558 541.5 64.51 32.86 558 571.4 66.02 32.86

2007

1 634 475.8 63.39 34.16 634 495.8 73.41 34.16

2 642 507.4 60.80 34.59 642 535.9 67.73 34.59

3 580 532.2 63.28 31.25 580 564.6 67.25 31.25

2011

1 850 474.0 65.16 35.58 850 499.6 77.00 35.58

2 745 500.3 57.64 31.18 745 532.5 65.89 31.18

3 794 529.0 59.68 33.24 794 568.3 65.41 33.24

2015

1 637 482.5 66.33 33.70 637 501.8 75.71 33.70

2 683 515.5 60.28 36.14 683 539.7 75.64 36.14

3 570 552.9 59.66 30.16 570 590.2 65.51 30.16

Canada 1995

1 4015 504.5 83.10 35.24 4015 495.1 88.21 35.24

2 3619 517.0 81.70 31.76 3619 524.8 91.10 31.76

3 3760 535.7 83.04 33 3760 549.5 87.77 33

1999 1 2187 520.7 71.48 35.17 2187 518.2 74.25 35.17

2 2097 538.1 68.89 33.72 2097 544.5 76.40 33.72

3 1935 557.8 70.16 31.11 1935 561.2 72.84 31.11

2015 1 1506 513.2 67.91 33.93 1506 510.9 66.49 33.93

2 1455 541.9 61.70 32.78 1455 542.9 60.98 32.78

3 1478 568.8 60.04 33.30 1478 572.9 60.75 33.30

German

y 1995 1 1303 480.5 80.30 38.66 1303 499.5 89.88 38.66

2 947 515.1 82.45 28.10 947 537.1 95.21 28.10

3 1120 541.4 83.20 33.23 1120 562.2 92.04 33.23

England 2011

1 203 501.8 72.95 33.61 203 548.4 70.85 33.61

2 202 543.4 66.16 33.44 202 587.7 62.82 33.44

3 199 563.4 69.51 32.95 199 617.2 68.39 32.95

2015 1 603 493.1 82.40 39.18 603 517.8 82.24 39.18

2 447 533.2 71.61 29.04 447 566.3 67.60 29.04

3 489 573.1 67.66 31.77 489 604.4 68.08 31.77

2003 1 547 500.4 72.72 34.17 547 516.2 72.05 34.17

2 529 549.1 68.56 33.04 529 573.4 69.08 33.04

3 525 592.3 67.20 32.79 525 614.5 68.53 32.79

Finland 1999

1 349 506.1 63.89 34.49 349 529.2 77.34 34.49

2 346 534.9 57.56 34.19 346 561.3 70.56 34.19

3 317 558.1 62.57 31.32 317 580.7 76.20 31.32

2011 1 847 498.1 59.97 34.93 847 536.4 61.28 34.93

2 792 524.9 60.18 32.66 792 565.7 59.83 32.66

3 786 544.8 60.30 32.41 786 588.7 59.97 32.41

France 1995

1 844 514.4 78.43 33.95 844 470.8 78.52 33.95

2 843 534.4 74.01 33.91 843 488.4 77.61 33.91

3 799 554.8 73.35 32.14 799 508.8 73.43 32.14

Italy 1999

1 1017 452.3 83.11 33.95 1017 462.7 84.23 33.95

2 1013 484.8 79.74 33.81 1013 497.9 82.21 33.81

3 966 513.2 77.16 32.24 966 537.1 76.24 32.24

2003 1 1415 454.6 73.35 36.95 1415 463.3 75.72 36.95

2 1139 487.8 71.40 29.74 1139 493.6 74.50 29.74

3 1276 514.8 69.33 33.32 1276 520.6 71.84 33.32

2007 1 1300 453.6 74.78 35.78 1300 468.9 78.27 35.78

2 1230 493.3 70.57 33.86 1230 509 71.47 33.86

3 1103 511.8 65.26 30.36 1103 529.5 65.16 30.36

2011 1 1143 472.4 70.30 35.38 1143 470.1 73.97 35.38

2 1073 504.3 67.18 33.21 1073 504.9 69.58 33.21

3 1015 530.8 63.78 31.41 1015 536.8 64.84 31.41

2015 1 1116 467.1 72.84 33.54 1116 468.8 73.88 33.54

2 1109 504.4 63.73 33.33 1109 508.4 63.55 33.33

3 1102 531.6 65.30 33.12 1102 538.3 66.96 33.12

Netherl

ands 1995 1 946 512.1 83.05 39.29 946 528.1 79.62 39.29

2 673 541.2 80.44 27.95 673 550.6 81.37 27.95

3 789 568.1 77.95 32.77 789 573.7 82.37 32.77

1999 1 598 530.5 66.09 34.61 598 532.7 72.28 34.61

2 622 552.8 66.05 36 622 562.3 68.69 36

3 508 575.2 59.75 29.40 508 582.0 68.98 29.40

2003 1 628 520.8 61.84 34.81 628 519.0 55.06 34.81

2 595 551.8 62.13 32.98 595 550.3 52.55 32.98

3 581 578.6 57.18 32.21 581 573.2 49.90 32.21

Norway

1995 1 1073 470.2 79.09 35.01 1073 494.6 84.82 35.01

2 1127 495.4 82.82 36.77 1127 518.5 87.15 36.77

3 865 516.4 82.74 28.22 865 536.8 85.41 28.22

2003 1 561 445.6 67.33 33.63 561 484.5 67.38 33.63

2 606 484.9 62.63 36.33 606 518.7 59.82 36.33

3 501 502.6 62.02 30.04 501 530.6 60.76 30.04

2007 1 618 450.3 65.75 33.59 618 466.6 75.12 33.59

2 668 491.8 55.92 36.30 668 514.6 60.78 36.30

3 554 502.7 58.21 30.11 554 532.3 65.20 30.11

2011 1 643 464.3 60.96 36.14 643 480.8 70.46 36.14

2 643 497.8 56.77 36.14 643 521.3 64.52 36.14

3 493 513.8 56.28 27.71 493 540.1 62.96 27.71

2015 1 820 492.1 66.06 35.42 820 488.9 74.66 35.42

2 751 523.2 65.04 32.44 751 527.1 69 32.44

3 744 553.5 59.41 32.14 744 561.0 68.49 32.14

New

Zealand 1995 1 1402 469.2 82.99 33.71 1402 483.6 93.87 33.71

2 1428 499.4 83.97 34.34 1428 517.4 94.51 34.34

3 1329 535.5 87 31.95 1329 553.5 96.74 31.95

1999 1 738 460.6 79.62 34.23 738 477.1 81.96 34.23

2 705 504.4 79.88 32.70 705 529.1 77.56 32.70

3 713 541.0 79.15 33.07 713 563.6 80.69 33.07

2003 1 491 479.3 68.76 33.61 491 506.1 61.50 33.61

2 503 501.6 69.63 34.43 503 533.9 64.37 34.43

3 467 544.5 69.79 31.96 467 574.7 63.28 31.96

2011 1 607 457.0 85.32 34.27 607 475.7 83.31 34.27

2 606 509.7 74.93 34.22 606 531.4 71.77 34.22

3 558 544.8 71.40 31.51 558 576.4 70.07 31.51

2015 1 822 463.7 87.16 34.11 822 480.6 93.50 34.11

2 800 522.9 80.94 33.20 800 547.9 84.08 33.20

3 788 560.2 73.55 32.70 788 586.0 71.76 32.70

1 2810 590.3 90.99 34.19 2810 536.5 97.08 34.19

Singapo

re 1995

2 2699 624.8 89.96 32.84 2699 575.9 97.54 32.84

3 2710 651.2 88.29 32.97 2710 615.4 97.53 32.97

1999 1 1277 578.6 76.81 34.08 1277 532.5 92.77 34.08

2 1257 606.2 73.96 33.55 1257 571.0 87.75 33.55

3 1213 636.6 71.85 32.37 1213 617.3 86.72 32.37

2003 1 1490 578.2 79.50 35.66 1490 542.2 90.82 35.66

2 1472 616.9 67.85 35.23 1472 593.4 76.03 35.23

3 1216 646.8 67.50 29.10 1216 634.1 71.13 29.10

2007 1 1071 558.3 88.30 36.11 1071 522.8 99.12 36.11

2 939 609.7 75.15 31.66 939 586.0 85.21 31.66

3 956 645.1 77.81 32.23 956 633.7 80.55 32.23

2011 1 1260 583.8 82 34.24 1260 552.3 94.53 34.24

2 1201 620.5 74.11 32.64 1201 602.1 83.61 32.64

3 1219 651.7 66.37 33.13 1219 646.8 75.33 33.13

2015 1 1280 591.5 81.51 34.25 1280 563.5 82.62 34.25

2 1222 629.3 74.09 32.70 1222 606.0 77.30 32.70

3 1235 665.9 61.39 33.05 1235 651.0 65.48 33.05

USA 1995

1 3019 452.6 77.65 34.01 3019 482.3 97.39 34.01

2 2908 487.4 84.96 32.76 2908 526.4 100.6 32.76

3 2949 532.6 89.30 33.22 2949 566.9 97.78 33.22

1999 1 2129 471.0 76.54 33.73 2129 481.1 88.03 33.73

2 2217 516.6 74.52 35.12 2217 533.8 84.33 35.12

3 1966 555.3 78.54 31.15 1966 573.7 83.17 31.15

2003 1 2024 470.3 71.05 34.87 2024 491.6 72.21 34.87

2 1863 513.4 68.86 32.10 1863 538.6 70.37 32.10

3 1917 552.1 73.66 33.03 1917 576.3 71.12 33.03

2007 1 1577 475.2 69.71 33.78 1577 482.0 77.11 33.78

2 1694 516.3 67.68 36.28 1694 530.7 71.28 36.28

3 1398 555.2 66.61 29.94 1398 570.7 68.73 29.94

2011 1 2086 479.9 67.40 33.34 2086 492.0 74.65 33.34

2 2321 516.9 69.31 37.10 2321 537.3 71.45 37.10

3 1849 557.4 67.65 29.56 1849 580.0 67.98 29.56

2015 1 2278 488.9 78.81 35.46 2278 500.0 79.18 35.46

2 2079 524.7 73.12 32.36 2079 537.1 72.91 32.36

3 2068 565.9 73.47 32.19 2068 576.6 71.07 32.19

A.2 Conditional Distributions

A.2.1 Conditional on Father’s Education

A.2.2 Conditional on HLEI

A.3 Opportunity Inequality Index

GOI RRI

Country Year Math Science Math Science

Australia 1995 3.0222 3.0222 65.7218 65.7218

1999 2.6125 2.0723 41.0067 62.3558

2003 2.8628 2.774 44.6446 61.2122

2007 2.3268 2.3268 41.0067 51.6599

2011 3.0222 3.0222 65.7218 63.8491

2015 3.0222 2.8628 63.8491 63.8491

Canada 1995 1.6628 2.6331 44.6446 44.6446

1999 1.7906 1.7015 62.3558 61.2122

2015 2.0723 1.7906 44.6446 47.1885

Germany 1995 2.6125 1.9167 41.0067 51.6599

England 1999 2.6331 2.6125 76.7166 69.5291

2003 2.774 2.6331 80.1462 80.1462

2007 2.774 2.774 61.2122 51.6599

Finland 2011 1.9167 1.7906 51.6599 65.7218

2015 1.7015 1.6628 47.1885 61.2122

France 1995 2.6331 2.3268 51.6599 47.1885

Hong Kong 1995 1.6628 2.6331 44.6446 44.6446

1999 1.7906 1.7015 62.3558 61.2122

2003 2.0723 1.7906 44.6446 47.1885

2007 2.6125 1.9167 41.0067 51.6599

2011

2015

1.7906

1.6628

1.6628

1.6628

37.5703

37.5703

37.5703

37.5703

Italy 1999 2.6331 2.774 44.6446 44.6446

2003 2.6125 2.6331 47.1885 44.6446

2007 1.9167 2.0723 37.5703 41.0067

2011 1.9029 2.3268 41.0067 37.5703

2015 1.9029 1.9167 37.5703 41.0067

Japan 2003 2.774 1.9167 63.8491 76.7166

2007 2.6331 1.9167 63.8491 65.7218

2011 2.3268 1.9167 63.8491 76.7166

2015 2.8628 2.3268 47.1885 80.1462

Korea 1995 2.8628 2.6125 47.1885 69.5291

1999

2003

2.0723

2.3268

1.9167

2.3268

63.8491

62.3558

47.1885

62.3558

2007 1.9029 1.9029 51.6599 62.3558

2011 2.6125 2.0723 61.2122 69.5291

2015 1.7906 1.6628 76.7166 69.5291

Netherlands 1995 1.9029 1.7015 76.7166 76.7166

1999

2003

1.7015

1.7015

1.9029

1.7015

65.7218

65.7218

63.8491

65.7218

Norway 1995 1.9167 1.7906 63.8491 62.3558

2003 2.0723 1.9029 61.2122 63.8491

2007 1.7906 1.7906 47.1885 61.2122

2011 1.7906 1.9029 69.5291 47.1885

2015 1.6628 1.9029 80.1462 76.7166

New Zealand 1995 2.3268 2.0723 62.3558 61.2122

1999 2.3268 2.3268 61.2122 51.6599

2003 1.9029 2.0723 80.1462 47.1885

2011 2.8628 2.774 62.3558 65.7218

2015 2.6125 2.6331 62.3558 62.3558

Singapore 1995

1999 2.0723

1.9029

2.774

2.6125

69.5291

47.1885

63.8491

41.0067

2003 1.9167 3.0222 41.0067 41.0067

2007 2.6125 2.6331 61.2122 47.1885

2011 2.0723 2.8628 51.6599 44.6446

2015 2.6331 3.0222 65.7218 61.2122

Sweden 1995

2003 1.7015

1.7906

1.9029

1.7906

61.2122

51.6599

41.0067

51.6599

2007 1.6628 1.7015 44.6446 44.6446

2011

2015

1.6628

1.9167

1.7015

2.0723

44.6446

69.5291

51.6599

65.7218

USA 1995 2.774 2.8628 80.1462 80.1462

1999

2003

2.774

3.0222

2.6331

2.8628

69.5291

69.5291

69.5291

80.1462

2007 2.0723 2.6125 62.3558 63.8491

2011 2.6331 2.6125 76.7166 62.3558

2015 2.3268 2.6125 51.6599 44.6446