VPs 2525
POLICY RESEARCH WORKING PAPER 2525
Measuring Education Equal access to education is a
basic human right. But in
Inequality many countries gaps in
education between various
Gini Coefficients of Education groups are staggering. An
education Gini index-a new
indicator for the distribution
Vinod Thomas of human capital and
Yan Wang welfare-facilitates
Xibo Fan comparison of education
inequality across countries
and over time.
The World Bank
World Bank Institute
Office of the Vice President
and
Economic Policy and Poverty Reduction Division H
January 2001
POLICY RESEARCH WORKING PAPER 2525
Summary findings
Thomas, Wang, and Fan use a Gini index to measure higher educational attainment are more likely to achieve
inequality in educational attainment. They present two equality in education than those with lower attainment.
methods (direct and indirect) for calculating an * A clear pattern of an education Kuznets curve exists
education Gini index and generate a quinquennial data if the standard deviation of education is used.
set on education Gini indexes for the over-15 population * Gender gaps are clearly related to education
in 85 countries (1960-90). Preliminary empirical analysis inequality, and over time, the association between gender
suggests that: gaps and inequality becomes stronger.
* Inequality in education in most of the countries * Increases in per capita GDP (adjusted for purchasing
declined over the three decades, with a few exceptions. power parity) seem to be negatively associated with
* Inequality in education as measured by the education inequality and positively related to the labor
education Gini index is negatively associated with force's average years of schooling, after controlling for
average years of schooling, implying that countries with initial income levels.
This paper-a joint product of the Office of the Vice President and the Economic Policy and Poverty Reduction Division,
World Bank Institute-is an extension of the paper "Measuring Educational Inequality: Education Gini Index from 1960
to 1990" (Vinod Thomas, Yan Wang, and Xibo Fan, World Bank, Washington, DC). This study was funded by the Bank's
Research Support Budget under the research project "The Quality of Growth" (RPO 682-02). Copies of this paper are
available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Agnes Datoloum, room
J4-259, telephone 202-473-6334, fax 202-676-98 10, email address adatoloumCaworldbank.org. PolicyResearchWorking
Papers are also posted on the Web at www.worldbank.org/research/workingpapers. The authors may be contacted at
vthomas@worldbank.org, ywang2aworldbank.org, or xfan@worldbank.org. January 2001. (37 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about
development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should he cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Center
Measuring Education Inequality: Gini Coefficients of Education
Vinod Thomas, Yan Wang, and Xibo Fan*
JEL Classification code: C43, D63, I32, J24, 011, 015
* Respectively, Vice President, senior economist, and consultant, at The World Bank Institute. This is an
extension of our paper, "Measuring Educational Inequality: Education Gini Index from 1960 to 1990."
mimeo, World Bank Institute. September 27, 1999. Washington D.C. The authors thank Ram6n E. L6pez
for collaborating a paper on this topic using data from 20 countries, Nancy Birdsall, Shaohua Chen, Deon
Filmer, Emmanuel Jimenz, Peter Moock, Martin Ravallion and The Quality of Growth team, for their
comments and suggestions, and the Bank's Research Committee for providing a part of the funding. The
findings, interpretations and conclusions expressed here are those of the authors. They do not necessarily
represent the views of the World Bank, its Executive Directors or the countries they represent. Comments
and questions should be sent to the corresponding authors, Yan Wang at vwang2( worldbank.or2 and/or
Xibo Fan at gini@egroups.com. The dataset is available at the World Bank's web page
http://www.worldbank.org/devforum/forum qog3.html.
1. Introduction
Equal access to education is among the basic human rights to which everyone is entitled. Yet,
the educational gaps between various groups in many countries are staggering, as shown by
many studies. If people's abilities are normally distributed, then a skewed distribution of
education opportunities represents large welfare losses. As with land and machinery, an
equitable distribution of human capital (basic literacy and nutrition/health) constitutes a
precondition for individual productivity and ability to rise above poverty.' Furthermore, an
equitable distribution of opportunities is preferable to a redistribution of existing assets or
incomes. This is because education builds new assets and improves social welfare by its spill-
over effect, without making anyone worse off. Ensuring access to educational opportunities by
attending to both the supply and demand sides, is a win-win policy gaining support in industrial
and developing countries. To support such an effort, an indicator that can be easily calculated and
monitored over time would be useful.
This paper aims at developing a measure for educational inequality, using the concept of
education Gini index based on school attainment data, for a large number of countries over time.
Education Gini could be used as one of the indicators of welfare, complementing average
educational attainment, health and nutrition, income per capita, and other indicators of welfare.
After reviewing the literature and discussing the methodology, we look into the relationship
between the education Gini index and average educational attainment, gender gaps, and the
standard deviation of education. As a narrowly focused technical paper, we do not attempt to
find a causal relationship between inequality in education and growth, as they could be jointly
determined and mutually reinforcing.
Standard deviations and Gini coefficients are often chosen as measures of inequality.
Standard divisions of school attainment were used in a few studies. Only four previous studies
were found to have used Gini coefficients in measuring education inequality. They estimated the
Gini coefficient based on either enrollment or education finance. To properly measure education
inequality, a Gini index should be based on educational attainment data. However, to our
knowledge, no study has estimated education Gini coefficient based on educational attainment
for a large number of industrial and developing countries. (See table 1 for a selective literature
review.)
2. Indicators to Measure Various Aspects of Education
Various indicators have been used to measure different aspects of education in cross country
analyses. These indicators include, among others, enrollment ratios, educational attainment,
quality by input of resources, and quality by cognitive test scores. On the distribution of
' There was a heated debate over the "Equity of what?" Amartya Sen (1980) sees individual's levels of functionings,
such as literacy and nutrition, as attributes to be equalized. Others see the opportunities people face as the attributes
to be equalized (Arneson 1989, Cohen 1989, and Roemer 1993). Yet others consider the amount of resources as the
attribute to be equalized (Dworkin 1981).
3
education, standard deviation of years of schooling was used, and lately, the education Gini
index, as a new indicator to measure education inequality. This section briefly explains the
usefulness and problems of the various indicators that measure different aspects of education.
Flow variable: Enrollment Ratios. At the early stage, the enrollment ratios for different
levels of schooling were used as indicators of human development (Barro 1991, Mankiw et al
1992, Levine and Renelt 1992, Levine and Zervos 1993). The most commonly used are the
primary- and secondary enrollment ratios. One problem of this approach is that enrollment ratio
only measures the flow of population's education or access to education. It does not show the
cumulated educational attainment/outcome. As a result, it is often inappropriate to use these
enrollment ratios in growth models. Measuring education inequality based on enrollment data is
also problematic as they do not reflect the stock of human capital.
Stock variable: Attainment measured by Number of Average Years of Schooling.
Psacharopoulos and Arriagada (1986) suggested that the proper indicator of human development
level is the stock of educational attainment defined as average years of schooling.
Psacharopoulos and Arriagada (1986) made the efforts of collecting the census information on
each country's schooling distribution over the entire population, and calculated educational
attainment. Barro and Lee (1991, 1993, and 1997) gathered more data and formalized the use of
educational attainment for growth regressions. Nehru, Swanson, and Dubey (1994) also created a
cross country database for educational attainment, through estimating the schooling distributions
over time for various countries. Measuring the distribution of education based on these
attainment data becomes feasible.
The Quality of Schooling. Educational attainment across countries may not be
comparable as the quality of schooling differ widely. Behrman and Birdsall (1983) and others
(Lockheed and Verspoor 1991; Card and Krueger 1992) warned that quantity alone is not
enough, quality must be taken into consideration when measuring the level of human
development. Two typical approaches were used to measure the quality of education, the input
approach and the output approach, each with its own problems and limitations.
The Input Approach (Resources for Schooling). One way to measure the education
quality is to see which country devotes more resources to education than others. Resources being
inputted into the education systems can be measured by pupil-teacher ratio, by expenditures on
teachers' wage, by spending on book and reading materials. One problem is that high volume of
input does not necessarily yield high quality. Another problem is that the inputs for schools are
not independent of the income. There is limited feasibility of using inputs of schooling as proxies
for education quality (Hanushek and Kim 1995).
The Output Approach (Test Score of Cognitive Performance). The output approach
directly measures the achievements of schooling by comparing the scores of cognitive
performance, which the students of the same-age group of various countries obtained through the
same international tests on the same subjects including mathematics and science. The tests to
assess student achievement in mathematics and science were conducted both by the International
Association for Evaluation of Educational Achievement (IEA) and by international Assessment
4
of Fiducation progress (1EAP).2 Two problems that prevented these measures to be widely used
include that first, they are only available for a dozen, mostly industrial, countries, and second,
they are not comparable over time. It is for these reasons, we cannot use them to control for the
quality of education in the education Gini index that we constructed.
The Distribution of Education: why important. The distributional dimension of education
is extremely important for both welfare consideration and for production. If an asset, say physical
capital, is freely traded across firms in a competitive environment, its marginal product will be
equalized through free-market mechanism. As a result, its contribution to output will not be
affected by its distribution across firms or individuals. If an asset is not completely tradable,
however, then the marginal product of the asset across individuals is not equalized, and there is
an aggregation problem. In this case, aggregate production finction depends not only on the
average level of the asset but also on its distribution. Because education/skill is only partially
tradable, the average level of educational attainment alone is not sufficient to reflect the
characteristics of a country's human capital. We need to look beyond averages and investigate
both the absolute dispersion and the relative dispersion of human capital.
Standard Deviation of Schooling: Absolute Dispersion. There is a small but growing
literature on schooling inequality or the distribution of education (see, for example, Lam and
Levinson 1991; Londofio 1990; Ram 1990). As data became available for measuring the
distribution of education, the disparities became more apparent. Standard deviations have been
used often to measure the absolute dispersion distribution of assets. Birdsall and Londono
(1997), investigating the impact of initial asset distribution on growth and poverty reduction,
found a significant negative correlation between education dispersion (measured by the standard
deviation of schooling) and income growth. In the Inter-American Development Bank (1999)
study on inequality in Latin America, the standard deviation of schooling is used to measure
inequality of education, and it was found that the larger the standard deviation of schooling, the
greater the income inequality--measured by income Gini. (See Table 1 for literature review). Rati
Ram used the standard deviations of schooling to illustrate the existence of an education Kuznuts
curve, and concluded that, "As the average level of schooling rises, educational inequality first
increases, and after reaching a peak, starts to decline. The tuming point is about seven years of
education" (Ram 1990). Londofno 1990 also used the same method.
2 Hanushek and Kim (1995) first transformed the test scores into unified scales, and then utilized the index to test
how much of the growth was affected by both the quantity and the quality of education. They found that both the
quantity and the quality of schooling positively contribute to the growth of income, at statistically significant levels.
The output approach measures the quality of education based on student cognitive performance, which was
regarded by Hanushek and Kim (1995) as a complement to the quantity of education developed by Barro and Lee
(1993). Lee and Barro (1997) investigated the determinants of school quality, and found that greater school inputs,
longer school terms, family background, and strong communities are positively related to student performance.
However, they cannot fully explain the better education outcomes in East Asian countries than in other developing
countries. It suggests other factors at play, including those associated with a more open and export-oriented
economic environment.
5
Education Gini: Measurement of Relative Inequality. Standard deviation of schooling
only measures the dispersion of schooling distribution in absolute terms. To measure the relative
inequality of schooling distribution, developing an indicator for education Gini is necessary.3
Four previous studies were found to have used Gini coefficient in measuring the
inequality of education. Education Gini, which are similar to the Gini coefficients widely used to
measure distributions of income, wealth, and land, ranges from 0, which represents perfect
equality, to 1, which represents perfect inequality. Education Gini coefficients can be calculated
using enrollment, financing, or attainment data. Maas and Criel (1982) estimated Gini
coefficients based on enrollment data for 16 East African countries. First, they found that the
degree of inequality in education opportunity varied enormously from one country to another.
Second, enrollment Gini coefficients were negatively related with the average enrollment rate in
a country. In other words, the higher the average enrollment, the lower the inequality. This is
consistent with what we found on average educational attainment and education inequality using
a different method. Ter Weele (1975) estimated Gini coefficients using education finance data
for several East African countries. Rosthal (1978) summarized four indicators for the distribution
of education estimated for the United States and Gini index was one of them. Sheret (1982 and
1988) estimated the Gini coefficient of enrollment for Papua New Guinea. However, the above-
mentioned Ginis were calculated based on enrollment or education financing, not on the
distribution of school attainment.
In this paper, we calculate an education Gini index that is based on educational
attainment of the concerned population (or labor force). Thanks to the painstaking efforts made
by a group of pioneers including Barro and Lee (1991, 1993, and 1997), Psacharopoulos and
Arriagada (1986), and Nehru, Swanson and Dubey (1995), the data is now available on
proportions of population with various level of educational attainment for major developing and
industrial countries. Lopez, Thomas and Wang (1998) were among the first to try Gini
coefficients of education for 12 countries, by utilizing the educational attainment data. The
dataset was then updated/revised and expanded to 20 countries in a later version (May 1999). In
this paper, education Gini indexes are calculated for 85 countries for the period from 1960-1990,
using a consistent method which is discussed below.
3 Both the income Gini and the wealth Gini coefficients have been widely used in studies of growth, poverty and
inequality. For example, Deininger and Squire (1996) constructed a new data set on inequality in the distribution of
income. They found a systematic link between growth and changes in aggregate inequality, and a strong positive
relationship between growth and reduction of poverty. Li, Squire, and Zou (1998) tried to explain income inequality
mainly by three variables: financial depth, civil liberty, and land ownership inequality (land Gini). They found that
higher concentration of land contributed to higher income inequality. On the other hand, after adding a dummy
variable for the region of Latin America, the Inter-American Development Bank (1999) de-emphasized the
significance of land concentration with respect to income inequality. Lundberg, and Squire (1999) utilized twenty
variables of 120 countries, tested various specifications both for poverty and for growth, and come out with two
strong conclusions. First, growth is much more sensitive to policy intervention than to inequality is. Second, even a
moderate change in inequality coupled certain growth is of tremendous impact on alleviating poverty.
6
3. Education Gini: Concept and Methodology
Starting with income Gini coefficient, there are two ways to calculate an income Gini, the direct
method (Deaton 1997) and the indirect method. Mathematically, the direct method states that the
income Gini is defined as "the ratio to the mean of half of the average over all pairs of the
absolute deviations between [all possible pairs ofl people" (Deaton 1997). The indirect method
first constructs the income Lorenz curve, with the cumulative percentage of the income on the
vertical axis, and the cumulative percentage of the population on the horizontal axis. The forty-
five degree line is called the egalitarian line for it represents a completely equal society with
respect to the distribution of income. And then the Gini coefficient is calculated as the ratio of
two areas, with the area of the egalitarian triangle as the denominator and the area between
Lorenz curve and the egalitarian line as the numerator. The geometric representation of the
income Gini definition is shown in Figure 1.
Similarly, both the direct method and the indirect method can also applied to the
education Gini. As an analogue to Deaton's definition, education Gini measures the ratio to the
mean (average years of schooling) of half of the average schooling deviations between all
possible pairs of people. The mathematical representation of this definition is shown in Equation
(Il). 4
3.1 The Direct Method for Calculating Gini Coefficient
The direct method uses the following formula to calculate Gini coefficient (Deaton 1997).
(1) GINI -,uN(N-1), E
Where,
GINI is the Gini index;
F' is the mean of the variable (income, e.g.);
N is the total number of observations;
For income Gini, yi and y, are dollar values of income of individuals;
For education Gini, yi and yj are years of school attainment of individuals.
3.2 The Indirect Method through the Construction of Lorenz Curve
The indirect method first constructs the education Lorenz curve, with the cumulative percentage
of the schooling years on the vertical axis, and the cumulative percentage of the population on
the horizontal axis. The forty-five degree line is the education egalitarian line for it represents a
completely equality of schooling. The Gini coefficient is defined as the ratio of the area formed
4 To promote usage by noneconomists, this section does not require any prior knowledge on gini coefficient.
7
by the Lorenz curve and the egalitarian line to the area of the entire egalitarian triangle (see
Figure 1).
(2) GINI = Area of A (between Egalitarian and Lorenz)
Area of OWQ (Egalitarian Triangle)
Figure 1. The Lorenz Curve and Income Gini
100 S W
S 0ahrt 00
8. ~~~~Line /
n < Lo~~~~~~~renz Curve Q
30 0 1X0
Cumulatw proportion of population (9/6f)
3.3 Limitations of Traditional Methods
The distribution of schooling has several special characteristics. Even though the concept of
education Gini is the same as the income Gini, several obstacles have prevented us from applying
the conventional income Gini methods for calculating education Gini.
(1) First, household / individual surveys on educational attairnment are not available for many
countries, which implies that that the equation (1) cannot be directly applied for the
calculation of education Gini.5 Barro and Lee (1991) divided the population into 7
categories, no-schooling (or illiterate), partial primary, complete primary, partial
5If the objective is to calculate education gini for one or a few countries, equation I can be used on household
survey data.
8
secondary, complete secondary, partial tertiary, and complete tertiary. The seven groups
are both mutually exclusive and collectively inclusive. To accommodate the special
feature of this educational attainment data, a new formula has to be worked out from the
Gini definition of Equation (1).
(2) Second, the educational attainment in years of schooling is a discrete variable, not a
continuous variable, whereas income is a continuous variable. Usually, a country's
income distribution is standardized into quintiles or deciles. The World Banks
Development Research Group developed a software for calculating income Gini, by way
of estimating a continuous Lorenz curve function based on a country's scattered income
distribution. However, the levels of schooling are discrete variables and they have both a
lower boundary (zero) and an upper boundary (around 15 to 20 years). As a result, the
education Lorenz curve is a kinked line with seven kink points. It is not necessary to
estimate a continuous curve to approximate the education Lorenz Curve.
(3) Third, the education Lorenz Curve is truncated along the horizontal axis (Figures 2, 4, 5).
In many developing countries a big proportion of population is illiterate (schooling=0), as
shown in the education Lorenz curves for India in Figure 4. The software package
developed by the World Bank's Development Research Group for calculating Gini cannot
be used due to the truncation problem at the horizontal axis (schooling=O). We have to
develop our unique formula to accommodate the special features of the schooling
distribution data. 6
3.4 The First Formula for Calculating Education Gini
The education Gini formula used in this paper is shown in equation (3).
E ~~n i-l
(3) EL = (-) E Pi 'y - YJI Pi
P1 i=2 j=
Where,
EL is the education Gini based on educational attainment distribution, large population;
p. is the average years of schooling for the concerned population;
pi and p, stand for the proportions of population with certain levels of schooling;
y1 and yj are the years of schooling at different educational attainment levels;
n is the number of levels/categories in attainment data, and n = 7 in this paper. Barro and
Lee (1991) divided the population into seven categories including no-schooling (or igiterate),
partial primary, complete primary, partial secondary, complete secondary, partial tertiary, and
complete tertiary. The seven groups are both mutually exclusive and collectively inclusive for the
concerned population.
6 We thank Shaohua Chen at Development Research Group of the World Bank, for sharing their Gini software with
us. Due to the truncation problem at the horizontal axis (when years of schooling=O), the computer program
frequently runs into "overflow". So we had to develop our own formula.
9
Expanding equation (3) gets the detailed summation process of the first education
Gini formula, shown in equation (4). '
(4) EL
=(1/4) [ P2 (Y2-YI) PI
+ P, (Y3-YI) PI+ P3 (Y3-Y2) P2
+ P7 (Y7-Y,) PI+ P, (Y7-Y2) P2+ P7 (Y7-Y3) P3+ P7 (Y7-Y4) P4+ P7 (Y7-Y5) P5+ P7 (Y7-Y6) P6]
Where,
p, is the proportion of population with no schooling,
P2 is the proportion of population with partial primary education;
p7 is the proportion of population with complete tertiary education.
y, is years of schooling for an individual with no schooling, y,=O;
Y2 is years of schooling for an individual with partial primary education;
y, is years of schooling for an individual with complete tertiary education.
The formula for calculating the years of schooling at the seven levels of education:
(5.1) Illiterate: y1= 0
(5.2) Partial-Primary: Y2= Y, + 0.5Cp = 0.5Cp
(5.3) Complete-Primary: Y3= YI + Cp = Cp
(5.4) Partial-Secondary: y4= y3 + 0.5C, = Cp + 0.5CS
(5.5) Complete-Secondary: y5= y3 + C, = Cp + Cs
(5.6) Partial-Tertiary: Y6= y5 + 0.5Ct = Cp + C, + 0.5Ct
(5.7) Complete-Tertiary: y7= y5 + Ct =Cp+ Cs + ct
Where,
Cp is the cycle of the primary education;
C, is the cycle of the secondary education; and
Ct is the cycle of the tertiary education.
The data on cycles of schooling (Cp , Cs , Ct ) is obtained from Psacharopoulos and
Arriagada (1986). People who receive partial education is assumed to get half of the schooling
cycle in their years of schooling, shown in equation (5.2), (5.4), and (5.6).
' For the underlying assumptions and the detailed logic of the methodology, please refer to the sister paper "The
Formula for Calculating Education Gini Index" (Xibo Fan 2000).
10
3.5 The Second Formula for Calculating Education Gini
The value of Gini is sensitive to population size N if the population size is too small. The
sensitivity is reflected by a factor of [N/(N-1)]. The education Gini formula for a small
population is shown in equation (6).
(6) E= N * (I) E Pi |yi-YI Pi N-I) L
Where,
E is the education Gini based on educational attainment distribution;
N is the number of individuals in the concerned population.
Multiplying equation (4) with a factor of [N/(N-1)] gives us the detailed summation
process for the second education Gini formula of equation (6).
Theoretically, when population size N approaches infinite, [N/(N-1)] =1, and the second
formula becomes the first formula. Practically, when population size is large enough, the first
formula is good enough to achieve a high level of accuracy. The beauty of the first formula is
that the exact number of the population size is irrelevant to the value of Gini as long as we know
the concerned country has a large population.
The average years of schooling (AYS) can be calculated as follows.
n
(7) p = AYS = piYi
i=l
We also calculated the standard deviation of schooling (SDS) by using formula (8).
(8) cf=SDS = Pi(Yi _ )
3.6 The Education Lorenz Curve
The education Lorenz curve in Figure 2 is constructed by putting the cumulative proportion of
population on the horizontal axis, and by putting the cumulative proportion of schooling on
vertical axis. The cumulative proportion of population at each level is as the following.
11
(9.1) Illiterate: Q= Pt
(9.2) Partial-Primary: Q2 P + P2
(9.3) Complete-Primary: Q3 PI + P2 + P3
(9.7) Complete-Tertiary: Q7 P + P2 + P3+ P4+ P5+ P6+ p7 = 100%
The cumulative proportion of schooling at each level of schooling is as follows.
(IO.1) Illiterate: SI =(p,y,)/, 0
(10.2) Partial-Primary: S2 =(PiYI +P2Y2)/9,
(10.3) Complete-Primary S3 = (PI YI + P2Y2 + P3 Y3)/ .
(10.7) Complete-Tertiary: S7 = (Py pl2y2 + P3Y3 + P4Y4+ PsY5 + P6y6 + Pv Y7 ) / j
= p/= 100%
Figure 2. The Education Lorenz Curve
S (Q7,S7) W
100
S~~~~~~~
//
0
Ue - . / (Q5,S5)
0
r_ Egalitarian /
.50L Une /
°c / A (Q4,S4)
50
0. / /
> 10 / Education
E / / Lorenz Curve
/ ^(Q3,S3)
M'0
(QO,PS9 ) _ 2,52) Q
O0 (Q1,1 50 1 1°
Cumulative proportion of population (/)/4
After constructing the education Lorenz curve, the calculation of education Gini is
straightforward based on equation (2). This is the indirect method without using equations (3)
and (6).
12
4. Education Gini: Stylized Facts and Empirical Results
We generated the education Gini dataset by utilizing both the schooling distribution data of
Barro and Lee (1991, 1993, and 1997) and the schooling cycle data of Psacharopoulos and
Arriagada (1986). The quinquennial dataset contains education Gini for 85 countries, for the
population aged over fifteen, within the time span from 1960 to 1990. In addition to the data on
education Gini, we also calculated the average years of schooling and the standard deviations of
schooling, for the same number of countries and years. In this section, we investigate the
behavior of these variables over time and the relationships among some of them. We made the
following observations.
* Inequality in educational attainment for most of the countries had been declining during the
three decades of 1960-1990, with a few exceptions.
* There is a negative relation between the education Gini index and the average years of
schooling. This implies that countries with a higher educational attainment level are most
likely to achieve better education equality than those with lower attainment levels.
* An educational Kuznets Curve exists if the standard deviation of education is used.
* Gender-gaps were clearly related to the education inequality, and over time, the impact of
gender-gaps on inequality has become stronger.
* It is found that education inequality is negatively associated with per capita GDP increments
in PPP terms, and that educational attainment in years of schooling is positively associated
with the per capita GDP (PPP) increments, after controlling for initial income levels.
4.1 The Historical Trends of Education Inequality Measured by Education Gini
Education Gini indexes allow us to observe how education inequality in various countries have
changed overtime during the period of 1960 to 1990 (Figure 3). The first stylized fact is that the
education inequality measured by education Gini has been declining, albeit slowly, for most of
the countries. Whereas they were worsened only in a small number of countries during certain
periods. From 1960 to 1990, education Ginis were declining rapidly in some countries, such as
Korea, Tunisia, and China, but slowly in other cases such as India, Mali, Pakistan.
Korea had the fastest expansion in education coverage and the fastest decline in the
education Gini coefficient; it dropped from 0.55 to 0.22 in 30 years. Tunisia also had a rapid
improvement in the distribution of education, with Gini index declined from 0.94 in 1960 to 0.61
in 1990. India's education Gini coefficient declined moderately, from 0.79 in 1960 to 0.69 in
1990. Education Gini coefficients for Colombia, Hungary, Peru, and Venezuela have been
increasing slowly since the 1 980s, showing that inequality is on the rise (see Figure 3).
13
Figure 3. Historical Trends of Education Gini, Selected Countries
1.0 Mali
.. India
0.8- * x :-. -. . . Tunisia
_* - |---.--- Colombia
0.6 _.~ Venezuela
0.4 ;---E}- ~~~~~~~China
0.4
Thailand
Korea
0 *.2 ><- .~..... Bulgaria
...1...Hungary
0.0
1960 1965 1970 1975 1980 1985 1990 ; _ United States'
Source of data: Authors' calculation. Data available on the web and upon request.
4.2 Education Lorenz Curves of India and Korea
The improvement of education equality can be shown by the shifting of a country's education
Lorenz curve. An examination of education Lorenz curves for India and Korea in 1990 shows a
great range among developing countries.
The Case of India. Despite progress in expanding primary and secondary enrollment in
India, more than half of the population (age 15 and older) did not receive any education while 10
percent of the population received nearly 40 percent of total cumulated years of schooling. This
made its education Lorenz Curve steep, located far away from the egalitarian line, leading to a
large education Gini (Figure 4). Education Gini being among one of the highest in the world,
providing universal access to basic education remains a huge challenge for the country.
A distribution of education as skewed as that of India implies a huge social loss from the
underutilization of potential human capital. Assuming that ability or talent is normally
distributed across population groups, production increases to its optimum when the dispersion of
education matches the distribution of human ability. When the distribution of education is too
skewed to match the distribution of ability, there is a deadweight loss to the society of
14
underdeveloped and underutilized talent. In this case, societies would be better off to massively
expand basic education, especially by improving access to education for the poor.
Figure 4. Education Lorenz Curves, India, 1960 and 1990
s w 100 s w
100 ~~100 100,0 100
0 India 1960 9 1.5 India1990 ,/909
80) Mean=1.09 years / |5an=2.95years
._ 80 Education gini=0.79 / ° Educaton gini=0.69 18/
0
/75.7.
60 /60 /
.0
o0 / / 633
040 / 040 /
o2 / 37.1/ .
20 /20 23.7
E /0i 0 Ee
/0~~~~
0 .Q C. 0 '1Q
0 0 20 40 60 80 100 0 0 20 40 60 80 100
Cum ulative proportion of population (%/o) Cumulative proportion of populabon (0/4
Source: Authors' calculation.
The Case of Korea. Korea expanded its basic education rapidly and eliminated illiteracy
successfully. In the early 1 960s and 70s, over two thirds of government expenditure on education
were concentrated on primary and secondary schooling. Over the three decades from 1960 to
1990, the mean years of schooling doubled and a large proportion of the population became
literate. Comparing to other countries, Korea's education Lorenz curve have shifted much closer
toward the forty-five degree egalitarian line.
In the 1990s, Korea enjoyed a more equitable distribution of education than India, as
indicated by a flatter Lorenz curve and a smaller Gini coefficient. Even in 1960, when Korea's
per capita income was similar to that of India, Korea's education Gini coefficient was 0.55, much
lower than that of India in 1990. Note that the distribution of education in Korea was more
equitable than that of income, but the distribution of education in India was much more skewed
than that of income between 1970 and 1990.
15
Figure 5 Education Lorenz Curves, Korea, 1960 and 1990
s wI00 s w IO0
ax__oo 94__ _4 100
Korea 1960 / " Korea 1990 A
.' MItean1.29 years 90.3 ['80 Mean=10.04 years ,
o ~ Educaton gini=0.55 / o Education gini=0.22 a 3
'as0- / / l x&6 20oso86
6 6~~0
t) o i 4 /° °iZ648.2 0* 404 2
0 6 -
C0 CO
00 2 r.~2
CL 40 40 .60
0 0 20 42600 - 0 0 6 8 0
CumubUvNe proportion of population (0/4 Cumulaive proportion of popubation (afh)
Source data: Authors' calculation.
4.3 The Historical Trends of School Attainment
The data on the number of average years of schooling also shows improvement of educational
attainment. The average years of schooling had been increasing for most of the countries.
However, Afghanistan was one of countries that had the lowest school attainment. And even
worse, its schooling attainment was still on the path of declining (See Figure 6).
Figure 6. Historical Trends of School Attainment for Population age 15 and over
14 + .. United States'
l~ + Canada
12 A Romania
l / Poland
10 == _ Bulgana
\ + Hungary
8 . Philippines !
-Mexico
6 -Malaysia
. China
4 = Brazil
4 Colombia
2 . K-- -X--- Tunisia
:::+:. +-+ K..... Pakistan
0 + India
1960 1965 1970 1975 1980 1985 1990 ....... Afghanistan
16
Source: Authors' calculation.
4.4 International Comparison of Education Inequality
Examining the cross-country pattern of the distribution of education, we found that education
Gini coefficients decline as the average education levels increase, although there clearly are other
possibilities using other indicators (next section). In addition to the industrial countries,
Argentina, Chile, and Ireland had relatively low education Gini coefficients throughout the whole
period from 1960 to 1990. The Gini coefficient for education in Korea, Tunisia and some other
countries declined dramatically. Only a few countries-Colombia, Costa Rica, Peru, and
Venezuela-have seen a significant worsening of the education Gini coefficient. Among 85
countries for which education Gini coefficients were calculated, Afghanistan and Mali had the
least equitable distributions in the 1990s at approximately 0.90, while most industrial countries
were at the lower end, with the United States and Poland having the most equitable distribution
(Figure 7).
Figure 7. Education Gini and Average Attainment in 1990
r
*, 1.0
* 0.9 MLI
u AFG
0.8
0.7 ENIND
MR'
.c 0.6 MCDZAl
o. . SOL. KWA
.2 0.5 J
(U~~~~~~~~~\U
04 - 4 0 2 1
w
0.3HK
0.2 -KRCU
POL ~~USA
0.1
0 2 4 6 8 10 12 14
Average years of schooling, age over 15 (1990)
Source of data: Authors' calculation.
17
This implies that the countries with higher average years of schooling are most likely to
achieve a more equitable education than those with a lower average years of schooling. It can
also be found that the education inequality in low-income countries is most likely to be worse
than that of high-income countries, measured by education Gini. The inverse relationship
between the education Gini (education inequality) and the mean years of schooling (educational
attainment) is found in every cross section from 1960 to 1990.
The panel data regression results in Table 4.1 also show a statistically significant evidence
for this negative association between educational attainment and education Gini. The
relationship is robust no matter whether we use fixed effect or random effect models, or whether
we control for time-specific (column 1, fixed effect) or country-specific factors (column 2 and 3).
By using fixed effect model, we have controlled for country-specific left-out variables such as
initial income, thus controlling for heterogeneity.
Furthermore, this result has a strong policy implication. Moving any person out of
illiteracy improves the society's education Gini index and at the same time increase the country's
level of educational attainment. As we can see below, this is one of the advantage of using
education Gini, not the standard deviation, as a measure of inequality.
4.5 Educational Kuznets Curve
Does the distribution of education have to get worse before it gets better? As suggested by
Londofio (1990) and Ram (1990), there is a "Kuznetsian tale" with distribution of education.
That is, as a country moves from the zero to maximum level of education, the variance first
increases and then declines. However, we cannot find this Kuznets curve if education Gini
coefficients are used to measure inequality.
Using the standard deviation of education, a clear pattern of educational Kuznets curve
exists, being shown in a scatter diagram below and by panel regressions. Figure 8 shows the
1990 educational Kuznets curve illustrated by cross-country data. As the average number of
years of schooling increases, the standard deviations of schooling first rise, reaching a peak at
around 6-7 years of schooling, and then decline. (See Figure 8). This observation is fairly
consistent with what was observed by Ram (1990). We have observed seven similar educational
Kuznets curves, one each for the five-year intervals from 1960 to 1990.
When running panel regressions, both the fixed effect and the common effect models
confirm the existence of an inverted U-shape educational Kuznets curve. This is shown in Table
4.2, by the positive coefficient on the mean year of schooling, and the negative coefficient for the
mean-year-of-schooling squared, both significant. (Table 4.2). This relationship is robust no
matter whether we run fixed effect or random effect method, or whether we control for time-
specific or country-specific factors (column 2 and 3).
18
Figure 8. Educational Kuznets curve, Standard Deviation of Schooling, 1990
6
*
0 5* * ..
0,
03
0
*0
'>2-
'E-
0
0 2 4 6 8 10 12 14
Average Years of Schooling, age over 15 (1990)
Source of data: Authors' calculation.
4.6 The Historical Trends of Standard Deviation of Schooling
Over time, we found no clear pattern for the standard deviations of schooling within the
time horizon of 1960 - 1990. The standard deviations were rising for most of the 85 countries,
and declining for the others (See Figure 9).
The standard deviations of schooling for India, Tunisia and several others rose drastically
over time, showing a widening spread of educational attainment. For Thailand it was a "U"-
shaped curve, declining first and rising later. For Korea it was an inverted "U"-shape, rising first
and declining later. It was declining continuously for Canada, Romania, and Poland.
Intuitively, the standard deviation of schooling seems to be a more volatile, and sometimes
misleading, indicator. It does not provide a consistent picture of whether the distribution of
education in a country is improving or not.
19
Figure 9 Time Trends for Standard Deviations of Schooling
5
Colombia
----- ------- XX Korea
sQ4 -ZK India
0 n
o *-0.. Sr Thailana
c i( Japan
o /1 /+ Brazil
.o A China
p 3 - i- . - Romania
A--- Hungary
cU X . . ~... - United States I
-- -Canada
A .. -A-- Poland
2
1960 1965 1970 1975 1980 1985 1990
Source: Authors' calculation, data available on the web and upon request.
An interesting observation could be made after comparing the behaviors of education Gini,
and standard deviations in sections 4.4, 4.5 and 4.6.
* For a poor country that has a low but relatively equal school attainment (such as Tunisia),
helping more people to become educated may enlarge the standard deviation of schooling.
The spread of education will be widened as some people are getting higher education. The
standard deviation of education would rise. But this would improve the distribution of
education as measured by education Gini.
* For a country that already has a high average schooling (years>7), it would have to reduce the
spread (i.e. the standard deviation) of schooling in order to raise the average level, as there is
a upper ceiling of 16 to 20 years in education.
* In both cases, education Gini will decline. Therefore, education Gini is a more robust and
better measurement for the distribution of education.
20
4.7 Gender-Gaps and Education Inequality
The dataset on education Gini also allows us to examine the linkage between gender inequality
and education inequality. Here the gender gap is measured by the difference between female
illiteracy rate and male illiteracy rate. The bigger the difference of the two illiteracy rates, the
larger the gender gap. We calculated the correlation between education Gini and this special
gender illiteracy gap index. And two observations can be made. First, gender gaps are positively
associated with education inequality measured by Gini coefficients. Second, the association
between gender-gaps and education inequality had become stronger over time, as the correlation
coefficients were becoming larger, from 0.53 in the 1970s to 0.69 in the 1990s (both significant)
(See Figure 10).
The regression in the Table 4.3 also confirms these two points and these results are robust
no matter whether we use fixed or random effect. The results imply that while educational
inequality has been declining, gender inequality accounts for much of the remaining inequality in
education. Reducing gender gaps in education is crucial to addressing the inequality in
education.
Figure 10. Gender Gaps and Education Inequality, 1970 and 1990
1.0 1.0
0.8 *0.8
0.6 0.6
c0.4 *. 0.4
0 * a~~~~~~~~
0.0 . 0.0
-40 -20 o 20 40 60 -40 -20 o 20 40 60
Difference of Illiteracy Pate Difference of Illiteracy Rate
(female4 nale, °/4 (female-male, 4 1U
(1970, correlation=0.53) (1990, correlation=0.69)
Source: education Gini: authors' calculation. Illiteracy data: World Bank central database.
21
4.8. Education Inequality and Changes in GDP Per Capita.
While Mincerian microeconomic tests confirm a positive relation between schooling and income,
the macroeconomic empirical tests on education's contribution to GDP growth have not yielded
conclusive and robust results. Many have found that additional years of education per person
increase real output or growth rates. But a few studies have found that human capital
accumulation has an insignificant or negative impact on economic growth and productivity
growth (Benhabib and Spiegel 1994; Islam 1995; Pritchett 1996). Many studies have attempted
to address this puzzle including our own (Lopez, Thomas and Wang 1999).8
Lopez, Thomas and Wang argue that the distribution of education is important for
production and growth process because education is only partially tradable. If an asset, say
physical capital, is freely traded across firms in a competitive environment, its marginal product
will be equalized through free-market mechanism. If an asset is not completely tradable,
however, then the marginal product of the asset across individuals is not equalized, and there is
an aggregation problem. In this case, aggregate production function depends not only on the
average level of the asset but also on its distribution.9 For a theoretical model incorporating the
distribution of education in the production function, see Lopez, Thomas and Wang (1999).
In addition, we suggest here that growth may not be an appropriate indicator to measure the
contribution of human capital. For a high-income country, the base of the rich country's current
income is so high that a increment bigger in magnitude than that of a poor country might only
shows a tiny growth rate. On the contrary, for a low-income country, the base of the poor
country's current income is so low that an increment smaller than that of a rich country might
imply a high growth rate. In the absence of data on GDP in purchasing-power-parity (PPP)
terms, growth rate became the only standard indicator for making cross-country comparisons,
even though it may be misleading in many sense. We suggest that per capita PPP GDP
increment is a more appropriate measure than growth rate for testing education's contribution. In
the recent years, many economists have conducted painstaking work in converting the GDP data
into international dollar (PPP) terms. Today, the cross-country analysis on per capita GDP
increment is made feasible by the availability of the PPP GDP data.
In the scatter diagrams consisting of both the per capita PPP GDP five-year increments (in
the preceding five-year period) and the education Gini, we find that there is always a downward-
sloping curve for each of the four periods. The regression results shown in Table 4.4 are
consistent with this point. The education inequality is negatively associated with the per capita
8 Only recently, Barro (1999b) found a clear result educational attainment contributes positively to economic
growth.
9 Similarly as many pointed out, even capital is not perfectly tradable in an incomplete financial market where credit
rationing and liquidity constraint exist, especially for the poor. That is why margiiial product of capital is not
equalized, and the distribution of capital or assets should enter the production function. We thank Martin Ravallion
for this point. See Ravallion 1998 and 2000.
22
PPP GDP increments no matter whether we use fixed or random effect. By using the PPP GDP
increments in the preceding five-year period, we have to some extent controlled for endogenuity.
Similarly, there is a positive relationship between the average educational attainment and per
capita PPP GDP increments (in the preceding period). The regression results are shown in Table
4.5. This positive relationship exists no matter whether we use fixed or random effect, and
whether we control for time or country-specific effects.
We then regress the per capita PPP GDP increments (in the preceding five-year period) on
the average educational attaimnent and education Gini, the results are mixed (Table 4.6). The
coefficients for average educational attainment remain positive and significant, but those for
education Gini become insignificant. Since we are fully convinced that our rationale of
incorporating the distribution of education in the production function is correct, there could be at
least two explanations. First, the theory tells us that there is an aggregation problem when
marginal product of education for each individual is not equalized, and the function form for
aggregation might be nonlinear. (See also Ravallion 1998, and 2000) But empirically we have
only estimated a linear function. There might be a mis-specification problem. Second, there is a
negative correlation between average years of education and education Gini (shown in Figure 7
and Table 4.1). When putting both into one linear function, there is a multicolinearity and
consequently the coefficients may have low significance levels, and they "will have the wrong
sign or an implausible magnitude." (Greene 1990, p.279). '
Figure 11. Education Gini, Attainment and per capita PPP GDP Increments
10000 1 10000
9000 .5 9000
° 6000 C.o) 8000
2 = 500° ] L . X -o 7000 t , ,IL .
0 - 370
7 000 a; = 7 000 .. *
000a
C ~5000o (9 X000
E ~~~ 0
0.0 0 2 E 5000
- - 400 0 4aC 4
41 3 * - 4000
m ~ ~ i 195EuaioItanLet(vrg
CD ~~~~~~~~~~~~CL
)- 0. ~~~~~~~~~~~~'I
1.O 000
0.0..a 2 0U.0 .8 i.2-000I
03 1000 09~~~~~~~~~~~01 5678 0111 3 41
Years of Schooling) in 1985
Source: education Gini: authors' calculation. GDP per capita data: World Bank central database
'° This paper focuses on generating an indicator on the distribution of education as a welfare indicator. It is beyond
our scope to test the causal relationship between education gini and income growth, which was attempted in Lopez,
Thomas and Wang 1999 using data from 20 countries, and an interesting topic for future studies.
23
4.9 The Time-Space Two Dimensional Comparison: The Case of Tunisia
We created the time-space two-dimensional diagram for education Gini to allow the readers to
compare one special country's education status in time-dimension against the World's education
status in space-dimension, shown in Figure 12. Take the case of Tunisia as an example." In
this diagram we can show that the education Gini and attainments for Tunisia were changing
from 1960 to 1990 along the time-dimension. The education Ginis and attainments for the World
were changing across various countries in space-dimension, but at the fixed time point of the
year 1990.
According our data, Tunisia is among the best performers in terms of expanding the
average level of education and in improving the distribution of education opportunities, as
compared to the history of itself. However, Tunisia started from a position that was one of the
worst. Compared to other countries, Tunisia's educational attainment level was still relatively
low in 1990, education inequality relatively high. But the country is on the right track: a
dramatic improvement in educational opportunities has taken place, and is likely to continue, if
past performance is a basis for the future. The time-space two-dimension education Gini
international comparison diagram allows the readers to understand the harmony of the above
seemingly contradictory claims. It would be interesting in an future study to identify those
educational policies that contributed to the rapid decline in education inequality in Tunisia.
Similar time-space two-dimensional comparison for other countries might look much
different from that of Tunisia, with a much slower decline in education Gini over time. This
could provide an effective tool to show where a country stands, comparing with other countries
in the world, in term of providing equal opportunities in education to its own people.
"We thank Jeffrey Waite and his colleagues for this section. It is their valuable comments and suggestions that
prompt us to do some additional work on Tunisia.
24
Figure 12 Time-Space Two-dimensional Comparison of Education Gini, Tunisia (1960-90)
and World (1990)
1.0
0 TUN,O
0.9 Ml4 U
0.8
. \ a tUN85
0.7 IUN,<
-0.6
0 * TURt N Exponential Trendline
.1 0.5 . . * * , + Tunisia 1960-1990
| **¢ ** . Edu Gini = 0.9974eO.11
I0.4 . **. R2=0.9946
0.3
Exponential Trendline * -
0.2 World 1990 *
Edu Gini = 1.0067e- 1563" PO. L USA
0.1 R2 = 0.9054
0.0
0 2 4 6 8 10 12 14
Education Attainment: Number of Average Years of Schooling (AYS)
World Twisia -World Trarlir. _TLsiaTrerdlire I
Source: education Gini and average years of schooling by authors' calculation.
25
5. Concluding Remarks
This paper presents two methods of calculating education Gini, a direct formula and an indirect
methodology of calculating education Gini though the construction of education Lorenz curve. It
then generates a quinquennial dataset on education Gini, for the population age over fifteen, for
85 countries within the time span from 1960 to 1990. In addition, this paper also calculates the
data on average years of schooling and the standard deviations of schooling.
First stage empirical analysis finds that, first, inequality in educational attainment for most of the
countries declined over the three decades of 1960-1990, with a few exceptions. Second,
inequality in education is negatively associated with the average years of schooling, implying
that countries with higher educational attainment levels are most likely to achieve better
education equality than countries with lower attainment level. Data also shows that the
education inequality in low-income countries is likely to be worse than that of high-income
countries. Third, an educational Kuznets Curve exists if the standard deviation of education is
used, which is also shown in regression results. Fourth, gender-gaps are closely associated to the
education inequality, and over time, the association between gender-gaps and inequality becomes
stronger. Fifth, per capita PPP GDP increments seem to be negatively associated with inequality
in education, and seem to be positively related to the labor force's average years of schooling.
However the effects are not robust due to problems including multicolinearity.
We are not able to incorporate the quality aspect into this particular Gini index, nor did
we try to find any causal relationship between education Gini and income growth, which are
challenges for future studies. We are continuing the work on education Gini along the following
directions. (1) Expand the current data set to include additional countries and male and female
separately. (2) Update the current dataset to cover 1991-2000 as Barro and Lee (2000) have just
released their updated education data for 1960-2000. (3) Conduct econometric analysis to explore
relationship between education inequality and other aspects of development, such as income
inequality, income level and growth, gender gaps, education-related policies, and poverty.
The education Gini index can be considered a new indicator for the distributional
dimension of human capital and welfare, which facilitates comparison cross countries and over
time. Compared with the standard deviation of schooling, education Gini is a more effective
indicator that reflects the improvement in the distribution of educational opportunities which is
crucial for generating income. It complements the average stock and quality variables on
education, not substituting them, and together they reflect a more complete picture on the
educational development of a country.
26
Table 1.1. Selected Studies on Distributions of Education and Health/Nutrition
Authors Methodology Major Findings
Studies used indicators of distribution of education inequality
Maas and Criel The distribution of primary school enrollment 1) Enrollment Ginis varied enormously across
(1982) was examined for Eastern African countries. countries; and
Gini coefficients of enrollment were estimated 2) There is a negative link between the average
for 16 Eastern African countries. enrollment and its distribution--the higher the
average enrollment the lower the Gini coefficient.
Ram (1990) Calculated standard deviations of education As the average level of schooling rises,
for about 100 countries. educational inequality first increases, and
after reaching a peak, starts to decline. The
turning point is about seven years of
education.
O'Neill (1995) 1. Assuming the stock of human capital is the Among the developed countries, convergence in
accumulation of the past education, not education levels has resulted in a reduction in
sensitive to current income level. income dispersion. However, for the world as a
2. Using the variance of income and that of whole, incomes have diverged despite substantial
human and physical capitals convergence in education levels.
3. Using both quantities and prices of human
and physical capitals.
Lopez, Thomas A asset allocation model is constructed, and 1. The distribution of education matters for income
& Wang (1998) Gini coefficient of educational attainment was levels as well as for growth.
estimated for 12 countries. Used quinquennial 2. Economic reforms improved the productivity of
data, linkage between distribution of human capital in growth models.
education and growth is investigated
controlling for physical capital, labor and etc.
Birdsall & Cross-country analysis using a traditional Initial levels of educational inequality and land
Londono (1997) growth model, controlled for capital Gini have strong negative impacts on economic
accumulation, initial income and initial growth and income growth of the poorest.
education levels, and natural resources.
Inter-America Regression, Income inequality (Gini) is negatively related to
Development Land Gini, income Gini, education, standard land Gini if the Latin American counties are
bank (1998) deviation of education differentiated by latitude, and positively to
standard deviation of education.
Strauss and I .Using both height and body mass index Some evidence for the causal relation from income
Thomas (1998) (BMI-weight divided by height) as to the distribution of health outcome (BMI).
indicators of health.
2. Using wage as indicator of productivity
Source: Compiled by authors.
27
Table 4.1 Educational attainment and education inequality
(Dependent Variable: Education Gini)
Panel regression Panel regression
Variables stacked by date Variables stacked by country
Fixed effects Fixed effects Random effects
Variables
Average years of schooling .0.075**** -0.051**** -0.056****
(-55A5) (-28.7) (-35.20)
Intercept(s) Fixed effects Fixed effects Random effects
0.76****
(66.84)
Year 1960 0.83 Algeria 0.87 0.11
Year 1965 0.84
Year 1970 0.84 China 0.71 -0.03
Year 1975 0.85
Year 1980 0.87 India 0.85 0.09
Year 1985 0.87
Year 1990 0.88 Mexico 0.72 -0.02
USA 0.71 0.01
Zambia 0.73 -0.01
Adjusted R-squared 0.86 0.97 0.97
Log likelihood 611.50
Included observations 81 countries 7 (1960,65,70,75,80,85,90)
Number of cross-sections 7 (1960,65,70,75,80,85,90) 85 countries
Total panel observations 550(unbalanced panel) 583(unbalanced panel)
* Significant at the 10 percent level
** Significant at the 5 percent level
*** Significant at the I percent level
**** Significant at the 0.5 percent level
t-statistics in parenthesis
Education inequality: education Gini is by authors' calculation
Educational attainment- average years of schooling is by authors' calculation
28
Table 4.2 Educational Kuznets curve
(Dependent Variable: Standard Deviation of Schooling)
Panel regression Panel regression
Variables stacked by date Variables stacked by country
Fixed effects Fixed effects Random effects
Variables
Average Years of Schooling 0.064**** 0.091**** 0.085****
(20.77) (31.01) (29.04)
(Average Years of Schooling)2 -0.048**** .0.054**** -0.054****
(-17.6) (-21.53) (-20.96)
Intercept(s) Fixed effects Fixed effects Random effects
1.15****
(12.40)
Year 1960 1.79 Algeria 1.81 0.76
Year 1965 1.83
Year 1970 1.90 China 0.86 -0.06
Year 1975 2.03
Year 1980 2.15 India 1.58 0.52
Year 1985 2.23
Year 1990 2.31 Mexico 1.11 0.19
USA -0.20 -0.80
Zambia 1.11 0.13
Adjusted R-squared 0.55 0.90 0.91
Log likelihood 425.66
Included observations 81 countries 7 (1960,65,70,75,80,85,90)
Number of cross-sections 7 (1960,65,70,75,80,85,90) 85 countries
Total panel observations 557(unbalanced panel) 583(unbalanced panel)
* Significant at the 10 percent level
* * Significant at the 5 percent level
** Significant at the I percent level
* Significant at the 0.5 percent level
t-statistics in parenthesis
Standard deviation of schooling is by authors' calculation
Educational attainment: average years of schooling is by authors' calculation
29
Table 4.3 Gender-Gaps are Associated with Education Inequality
(Dependent Variable: Education Gini)
Panel regression Panel regression
Variables stacked by date Variables stacked by country
Fixed effects Fixed effects Random effects
Variables
Gender-Gap 0.0097**** 0.0088**** 0.091****
(14.57) (9.06) (11.29)
Intercept(s) Fixed effects Fixed effects Random effects
0.40****
(19.42)
Algeria 0.46 0.04
Year 1970 0.43 China 0.46 -0.13
Year 1975 0.41
Year 1980 0.39 India 0.49 0.08
Year 1985 0.38
Year 1990 0.37 Mexico 0.40 0.00
Zambia 0.32 -0.09
Adjusted R-squared 0.41 0.94 0.95
Log likelihood 163.56
Included observations 66 countries 5 (1970,75,80,85,90)
Number of cross-sections 5 (1970,75,80,85,90) 66 countries
Total panel observations 327(unbalanced panel) 327(unbalanced panel)
* Significant at the 10 percent level
** Significant at the 5 percent level
*** Significant at the I percent level
**** Significant at the 0.5 percent level
t-statistics in parenthesis
Education inequality: education Gini is by authors' calculation
Gender-gap: difference of illiteracy rates between female and male, from World Bank central database.
Only the developing countries are included in the regression.
30
Table 4.4 Education Inequality and Changes in Per Capita PPP GDP
(Dependent Variable: Per Capita PPP GDP Increments over a Five-year Interval)
Panel regression Panel regression
Variables stacked by date Variables stacked by country
Fixed effects Fixed effects Random effects
Variables
Initial Per Capita GDP (1975) 0.53****
(13.33)
Education Gini -881.66* -2222.81* -4364.58****
(-1.87) (-1.61) (-6.74)
Intercept(s) Fixed effects Fixed effects Random effects
3470****
(10.75)
Algeria 2217 174
China 1681 -613
Year 1975 617
Year 1980 106 India 1973 48
Year 1985 1062
Year 1990 817 Mexico 2188 -246
USA 5153 1663
Zambia 1228 -937
Adjusted R-squared 0.62 0.70 0.76
Log likelihood -2164.87
Included observations 65 countries 4 (1975,80,85,90)
Number of cross-sections 4 (1975,80,85,90) 72 countries
Total panel observations 260 (balanced panel) 277(unbalanced panel)
* Significant at the 10 percent level
* * Significant at the 5 percent level
Significant at the I percent level
**** Significant at the 0.5 percent level
t-statistics in parenthesis
Education inequality: education Gini is by authors' calculation
Per Capita PPP GDP is quoted from the World Bank central database.
The Per Capita PPP GDP increments over a Five-year interval are forward changes.
For example,
(1975 Five-year Increments of Per Capita PPP GDP)
(1980 Per Capita PPP GDP) - (1 975 Per Capita PPP GDP)
31
Table 4.5 Educational attainment and Changes in Per Capita PPP GDP
(Dependent Variable: Per Capita PPP GDP Increments over a Five-year Interval)
Panel regression Panel regression
Variables stacked by date Variables stacked by country
Fixed effects Fixed effects Random effects
Variables
Initial Per Capita GDP (1975) 0.47****
(10.00)
Average years of schooling 114.09**** 214.76** 372.55****
(2.86) (2.33) (9.02)
Intercept(s) Fixed effects Fixed effects Random effects
-545.02**
(-2.14)
Algeria 39.50 78
China -313.16 -339
Year 1975 -218.21
Year 1980 -776.49 India -166.10 -7
Year 1985 164.39
Year 1990 -106.25 Mexico 43.65 -185
USA 2343.95 837
Zambia -693.42 -559
Adjusted R-squared 0.63 0.70 0.76
Log likelihood -2163
Included observations 65 countries 4 (1975,80,85,90)
Number of cross-sections 4 (1975,80,85,90) 72 countries
Total panel observations 260 (balanced panel) 277 (unbalanced panel)
* Significant at the 10 percent level
* * Significant at the 5 percent level
*** Significant at the I percent level
**** Significant at the 0.5 percent level
t-statistics in parenthesis
Educational attaimnent: average years of schooling is by authors' calculation
Per Capita PPP GDP is quoted from the World Bank central database.
The Per Capita PPP GDP increments over a Five-year Interval are forward changes.
For example,
(1975 Five-year Increments of Per Capita PPP GDP)
= (19S0 Per Capita PPP GDP) - (1975 Per Capita PPP GDP)
32
Table 4.6 Educational attainment, education inequality, and changes in per capita PPP GDP
(Dependent Variable: Per Capita PPP GDP Increments over a Five-year Interval)
Panel regression Panel regression
Variables stacked by date Variables stacked by country
Fixed effects Fixed effects Random effects
Variables
Initial Per Capita GDP (1975) 0.46***
(9.51)
Average years of schooling 189.12** 303.84* 512.43***
*
(2.42) (1.78) (5.07)
Education Gini 1022.32 1571.57 2149.22
(1.12) (0.62) (1.50)
Intercept(s) Fixed effects Fixed effects Random effects
-2283.9*
(-1.93)
Algeria -1306 -47
China -1462 -263
Year 1975 -1044
Year 1980 -1619 India -1525 -135
Year 1985 -682
Year 1990 -962 Mexico -1146 -169
USA 1089 682
Zambia -1832 -461
Adjusted R-squared 0.63 0.70 0.76
Log likelihood -2162
Included observations 65 countries 4 (1975,80,85,90)
Number of cross-sections 4 (1975,80,85,90) 72 countries
Total panel observations 260 (balanced panel) 277 (unbalanced panel)
* Significant at the 10 percent level
** Significant at the 5 percent level
*** Significant at the I percent level
* Significant at the 0.5 percent level
t-statistics in parenthesis
Educational attainment: average years of schooling is by authors' calculation
Education inequality: education Gini is by authors' calculation
Per capita PPP GDP is quoted from the World Bank central database.
The Per Capita PPP GDP increments over a five-year interval are forward changes.
For example,
(1975 Five-year Increment of Per Capita PPP GDP)
= (1980 Per Capita PPP GDP) - (1975 Per Capita PPP GDP)
33
References
Anand, Sudhir; and Kanbur, S. M. R. 1993. "The Kuznets Process and the Inequality-Development
Relationship." Journal of Development Economics; v40, n 1, February 1993, pp. 25-52.
Arneson, Richard. 1989. "Equity and Equality of Opportunity for Welfare." Philosophical Study 56: 77-
93.
Atkinson, A. B.; Rainwater, L.; and Smeeding, T. 1995. "Income Distribution in European Countries."
University of Cambridge, Department of Applied Economics Working Paper, Amalgamated
Series: 9535 November 1995, pp. 36.
Barro, Robert J. 1991. "Economic Growth in a Cross Section of Countries." Quarterly Journal of
Economic; 106 (May 91): 407-443.
Barro, Robert J. 1996. "Determinants of Economic Growth: A Cross-Country Empirical Study." National
Bureau of Economic Research Working Paper: 5698, August 96, pp. 71.
Barro, Robert J. 1999a. "Inequality, Growth, and Investment." National Bureau of Economic Research
Working Paper: 7038, March 1999, pp. 71.
Barro, Robert J. 1999b. " Inequality and Growth in a Panel of Countries." National Science Foundation,
available on the web.
Barro, Robert J.; and Lee, J. W. 1993. "International Comparisons of Educational Attainment."Journal of
Monetary Economics; 32, no.3 (December 93). 363-394.
Barro, Robert J.; and Lee, J. W.. 1997. "International Measures of Schooling Years and Schooling
Quality." American Economic Review; Papers and Proceedings, 86(2), pp. 218-223.
Barro, Robert J.; and Lee, J. W. 2000. "International Data on Educational Attainment: Updates and
Implications." CID working paper no. 42, Center for International Development at Harvard
University, April and August.
Behrman, Jere. 1987. "Schooling in developing countries: Which countries are the over and
underachievers and what is schooling impact? " Economics of Education Review; 6(2):1 11-127.
Behrman, Jere; and Birdsall, Nancy. 1983. "The Quality of Schooling. Quantity Alone Is Misleading."
American Economic Review; 73(5):928-946.
Bhagwati, jagdish. 1973. "Education, Class Structure, and Income Inequality." World Development
1(5):21-36.
Birdsall, Nancy and Londofio, Juan Luis. 1997. " Asset Inequality Matters: An Assessment of the World
Bank's Approach to Poverty Reduction." American Economic Review 87(2): 32-37.
Bonilla-Chacin, Maria. And Jeffrey Hammer. 1999. "Life and Death among the Poorest." Paper
presented at the World Bank Economist Forum, May 3-4, Washington, DC.
British Council. Various Years. Education Profile.
Chong, Albert; and Cesar Calder6n. 1997. "Empirical tests on Causality and feedback between
Institutional Measures and Economic Growth." Mimeograph. Washington, DC: World Bank.
Cohen, G. A. 1989. "On the Currency of Egalitarian Justice." Ethics 99: 906-944.
Dahan, Momi. 1996. "The Effect of Macroeconomic Variables on Income Distribution in Israel."Bank of
Israel Economic Review;vO, n69, March 1996, pp. 19-43.
Dasgupta, Partha. 1990. "Well-being and the Extent of its Realization in Developing Countries."
Economic Journal 100(4, supplement): 1-32.
Deaton, Angus. 1997. The Analysis of Household Surveys: A Microeconomic Approach to Development
Policy. Johns Hopkins University Press, Baltimore and London.
Deininger, Klaus; and Squire, Lyn. 1996. "A New Dataset Measuring Income Inequality." World Bank
Economic Review; 10(3), September 565-91.
Deininger, Klaus; and Squire, Lyn. 1998. "New Ways of Looking at Old Issues: Inequality and Grow[lh."
Journal of Development Economics; v57, n2, December 1998, pp. 259-87.
34
Dubey, Ashutosh, and Elizabeth M. King. 1996. " A New Cross-Country Education Stock Series
Differentiated by Age and Sex." Journal of Educational Planning and Administration II (1): 5-
24.
Dworkin, Ronald. 1981. "What is Equity: Part 2. Equality of Resources." Philos. & Public Affairs; 81,
10. pp.283-345.
Easterly, William. 1999. "Life during Growth." Journal of Economic Growth 4(3): 239-79.
Fan, Xibo. 2000. "The Formula for Calculating Education Gini Index." Working paper, The World Bank
Institute, Washington, DC.
Fields, Gary. 1980. Poverty, Inequality, and Development. Cambridge: Cambridge University Press.
Galor, Oded; and Zeira, J. 1993. "Income Distribution and Macroeconomics." Review of Economic
Studies; LX: 35-52.
Galor, Oded; and Tsiddon, Daniel. 1996. "Income Distribution and Growth: The Kuznets Hypothesis
Revisited." Economica; v63, n250, Supplementary, 1996, pp. S103-17.
Glomm, Gerhard. 1997. "Whatever Happened to the Kuznets Curve? Is It Really Upside Down?" Journal
of Income Distribution; v7, nl, 1997, pp. 63-87.
Greene, William H. 1990. Econometric Analysis. MacMillan Publishing Company, New York.
Haddad, Lawrence; and Kanbur, Ravi. 1992. "Is There an Intrahousehold Kuznets Curve? Some
Evidence from the Philippines." Public Finance; v47, nO, Supplementary, 1992, pp. 77-93.
Hanushek, Eric A.; and Kim, Dongwook. 1995. "Schooling, Labor Force Quality, and Economic
Growth." National Bureau Of Economic Research paper 5399.
Inter-American Development Bank. 1999. Facing up to Inequality in Latin America: Economic and
Social Progress in Latin America, 1998-99 Report. Johns Hopkins University Press.
Kaneko, M. 1986. "The Education Composition of the World Population." Education and Training
Report, World Bank. Washington, DC. April 86.
Komen, Marinus H. C.; Gerking, Shelby; Folmer, Henk. 1997. "Income and Environmental R&D:
Empirical Evidence from OECD Countries." Environment and Development Economics; v2, n4,
October 1997, pp. 505-15.
Kuznets, Simon. 1955. "Economic Growth and Income Inequality."American Economic Review; March
19'5, pp 1-28.
Kuznets, Simon. 1963. "Quantitative Aspects of the Economic Growth of Nations: VIII, Distribution of
Income by Size." Economic Development and Cultural Change; January 1963, pt.2, pp. 1-80.
Kuznets, Simon. 1966. Modern Economic Growth. New Haven: Yale University Press.
Kuznets, Simon. 1976. "Demographic Aspects of the Size Distribution of Income." Economic
Development and Cultural Change; October 1976, pp. 1-94.
Lam, David and Deborah Levison. 1991. "Declining Inequality in Schooling in Brazil and its Effects on
Inequality in Earnings." Journal of Development Economics 37(1-2): 199-225.
Lanjouw, Peter and Nicholas Stem. 1998. Economic Development in Palanpur Over Five Decades. New
York: Oxford University Press.
Lee, Jong-Wha; and Barro, Robert J. 1997. "Schooling Quality in a Cross Section of Countries."
Working paper no. 6198. National Bureau of Economic Research, Cambridge, MA.
Levine, Ross; and Renelt, David. 1992. "A sensitive analysis of cross country growth regression."
American Economic Review; 82 (Sept. 1992). No.4. 942-63
Levine, Ross; and Zervos, Sara J. 1993. "What we have learned about policy and growth from cross-
country regressions?" American Economic Review; 83. May 1993. No.2 426-30.
Li, Hongyi; Squire, Lyn; and Zou, Heng-fu. 1998. "Explaining International and Intertemporal Variations
in Income Inequality." Economic Journal; 108:26-43.
Lockheed, E. Marlaine, and Adriaan M. Verspoor. 1991. Improving Primary Edtication in Developing
Countries. New York: Oxford University Press.
35
L6pez, Ram6n; Thomas, Vinod; and Wang, Yan. 1998. "Addressing the Education Puzzle: The
Distribution of Education and Economic Reform." Policy Research Working Paper #2031. The
World Bank, Washington, D.C.
Londoflo, Juan Luis, 1990. "Kuznetsian Tales with Attention to Human Capital." Paper presented at the
Third Inter-American Seminar in Economics, Rio de Janeiro, Brazil.
Lundberg, Mattias; and Squire, Lyn. 1999. "Growth and Inequality: Extracting the Lessons for Policy-
Makers." Unpublished. The World Bank, Washington, D.C.
Maas, Jacob van Lutsenburg, and Ceert Criel. 1982. Distribution of Primary School Enrollments in
Eastern Africa. World Bank Staff Working Papers no.511. The World Bank, Washington DC.
Mankiw, N. Gregory; Romer, David; and Weil, David. 1992. "A contribution to the empirics of economic
growth." Quarterly Journal of Economics; (May 1992). 407-3 7.
Nehru, Vikram; Swanson, Eric; and Dubey, Ashutosh. 1995. "A new database on human capital stock:
sources, methodology and results." Journal of Development Economics; v46, n2, April 1995, pp.
379-401.
Ogwang, Tomson. 1995. "The Economic Development-Income Inequality Nexus: Further Evidence on
Kuznets' U-Curve Hypothesis." American Journal of Economics and Sociology; v54, n2, April
1995, pp. 217-29.
O'Neill, Donal. 1995. "Education and Income Growth: Implications for Cross-Country Inequality."
Journal of Political Economy 103(6): 1289-1301.
Park, Walter G.; Brat, David A. 1995. "A Global Kuznets Curve?" Kyklos; v48, nI, 1995, pp. 105-31.
Prichett, Lant. 1997. "Where has All the Education Gone?" World Bank Working Paper 1581. World
Bank, Washington, DC.
Psacharopoulos, G. 1984. " The Contribution of Education to Economic Growth: International
Comparisons." In J.W. Kendrick (ed.) International Comparisons of Productivity and Causes of
the Slowdown. Cambridge, Mass: Ballinger Publishing Co.
Psacharopoulos, G.; Tan, J. P.; and Jimenez, E. 1986. Financing Education in Developing Countries: An
Exploration of Policy Options. Washington, D.C: World Bank.
Psacharopoulos, George; and Arriagada, Ana-Maria. 1986. "The educational attainment of the labor
force: an international comparison." The World Bank, October 86. Report No.: EDT38.
Quan, Nguyen T.; and Koo, Anthony Y. C. "Concentration of Land Holdings: An Empirical Exploration
of Kuznets' Conjecture." Journal of Development Economics; v18, nl, May-June 1985, pp. 101-
17.
Ram, Rati. 1988. "Economic Development and Income Inequality: Further Evidence on the U-Curve
Hypothesis." World Development; v16, nl 1, November 1988, pp. 1371-76.
Ram, Rati. 1989. "Level of Development and Income Inequality: An Extension of Kuznets-Hypothesis to
the World Economy." Kyklos; v42, nl, 1989, pp. 73-88.
Ram, Rati. 1990. "Educational Expansion and Schooling Inequality: international edidence and some
implications". The Review of Economics and Statistics; 72(2), 1990, pp.266-74.
Ram, Rati. 1991."Kuznes's Inverted-U Hypothesis: Evidence from a Highly Developed Country."
Southern Economic Journal; v57, n4, April 1991, pp. 1112-23.
Ram, Rati. 1992. "Intercountry Inequalities in Income and Basic-Needs Indicators: A Recent
Perspective." World Development; v20, n6, June 1992, pp. 899-905.
Ram, Rati. 1997. "Level of Economic Development and Income Inequality: Evidence from the Postwar
Developed World." Southern Economic Journal; v64, n2, October 1997, pp. 576-83.
Ram, Rati. 1997. "Reply to the Comment on Rati Ram's Test of the Kuznets Hypothesis." Economic
Development and Cultural Change; v46, n 1, October 1997, pp. 191-95.
Ravallion, Martin. 1997. "A Comment on Rati Ram's Test of the Kuznets Hypothesis." Economic
Development and Cultural Change; v46, n 1, October 1997, pp. 187-90.
36
Ravallion, Martin. 1998. "Does the Aggregation hide the harmful effects of inequality on growth?"
Economics Letters 61(1998): 73-77.
Ravallion, Martin. 2000. "Growth, Inequality and Poverty: Looking Beyond Averages." Working paper,
Development Research Group, The World Bank, Washington, DC.
Ravallion, Martin, and Gaurav Datt. 1999. "When is Growth pro-poor? Evidence from the Diverse
Experiences of India's States." Policy Research Working papers no. 2263. World Bank,
Development Research Group. Washington, DC.
Roemer, John E. 1993. "A Pragmatic Theory of Responsibility for the Egalitarian Planner." Philosophy
and Public Affairs 22: 146-66.
Rosthal, Richard A. 1978. "Measures of Disparity. A Note." Research report published by Killalea
Associates, Inc. Available at EDRS Price, ED 149482, ERIC database.
Sen, Amartya K. 1980. "Equality of What?" In S. McMurrin, ed., Tanner Lectures on Human Values, vol
I. Cambridge, U.K.: Cambridge University Press.
Sheret, Michael. 1988. "Equality Trends and Comparisons for the Education System of Papua New
Guinea." Studies in Educational Evaluation, v.14 (1):91-112.
Strauss, John and Duncan Thomas. 1998. "Health, Nutrition and Economic Development", Journal of
Economic Literature, Vol XXXVI (June 1998):766-817.
Thomas, Vinod et al. 2000. The Quality of Growth. New York: Oxford University Press.
UNESCO. Various years. Statistical Yearbook. Paris.
Williamson, Jeffrey G. 1998. "Growth, Distribution, and Demography: Some Lessons from History."
Explorations in Economic History; v35, n3, July 1998, pp. 241-71.
World Bank. 1999. Education Sector Strategy. Washington, DC.
World Bank. 2000a. Engendering Development. New York: Oxford University Press.
World Bank. 2000b. Attacking Poverty. The World Development Report 2000/01. New York: Oxford
University Press.
37
Policy Research Working Paper Series
Contact
Title Author Date for paper
WPS2505 Family Altruism and Incentives Roberta Gatti December 2000 R. Bonfield
31248
WPS2506 Ethnicity and Wage Determination Abigail Barr December 2000 R. Bonfield
in Ghana Abena Oduro 31248
WPS2507 Public Expenditures and Gunnar S. Eskeland December 2000 H. Sladovich
Environmental Protection: When Is 37698
the Cost of Funds Irrelevant?
WPS2508 Sources of Financial Assistance for Mattias Lundberg December 2000 V. Soukhanov
Households Suffering an Adult Mead Over 35271
Death in Kagera, Tanzania Phare Mujinja
WPS2509 How Tax Policy and Incentives Jacques Morisset December 2000 N. Busjeet
Affect Foreign Direct Investment: Neda Pirnia 33997
A Review
WPS251 0 Environmental Protection and Gunnar S. Eskeland December 2000 H. Sladovich
Optimal Taxation 37698
WPS2511 Monetary Policy under Flexible Pierre-Richard Agenor December 2000 M. Gosiengfiao
Exchange Rates: An Introduction to 33363
Inflation Targeting
WPS2512 Quantifying the Impact of Technical Keith E. Maskus December 2000 L.Tabada
Barriers to Trade: A Framework for John S. Wilson 36896
Analysis Tsunehiro Otsuki
WPS2513 Do State Holding Companies Facilitate Michel Kerf December 2000 M. Leon
Private Participation in the Water Sector? 36151
Evidence from Cote d'lvoire, the Gambia,
Guinea, and Senegal
WPS2514 Intersectoral Dynamics and Economic Norbert M. Fiess January 2001 A. Pillay
Growth in Ecuador Dorte Verner 88046
WPS2515 Firm-Level Survey Provides Data on Mary Hallward-Driemeier January 2001 E. Khine
Asia's Corporate Crisis and Recovery 37471
WPS2516 Does Decentralization Increase Jean-Paul Faguet January 2001 H. Sladovich
Responsiveness to Local Needs? 37698
Evidence from Bolivia
WPS2517 The Effect of International Monetary William Easterly January 2001 K. Labrie
Fund and World Bank Programs 31001
on Poverty
Policy Research Working Paper Series
Contact
Title Author Date for paper
WPS2518 Can Reforming Global Institutions Andres Solimano January 2001 R. Bonfield
Help Developing Countries Share 31248
More in the Benefits from
Globalization?
WPS2519 Is Investment in Africa Too Low or Shantayanan Devarajan January 2001 H. Sladovich
Too High? Macro and Micro Evidence William R. Easterly 37698
Howard Pack
WPS2520 Wage Effects of Unions and Industrial Kristin F. Butcher January 2001 P. Sader
Councils in South Africa Cecilia Elena Rouse 33902
WPS2521 Labor Market Rigidity and the Alvaro Forteza January 2001 P. Sader
Success of Economic Reforms Martin Rama 33902
across More than 100 Countries
WPS2522 Trade in International Maritime Carsten Fink January 2001 L. Tabada
Services: How Much Does Policy Aaditya Mattoo 36896
Matter? Ileana Cristina Neagu
WPS2523 Can Duty Drawbacks Have a Olivier Cadot January 2001 L. Tabada
Protectionist Bias? Evidence from Jaime de Melo 36896
Mercosur
WPS2524 Racing to the Bottom? Foreign David Wheeler January 2001 D. Wheeler
Investment and Air Pollution in 33401
Developing Countries