WPS6735
Policy Research Working Paper 6735
Outcomes, Opportunity and Development
Why Unequal Opportunities and Not Outcomes Hinder
Economic Development
Ezequiel Molina*
Ambar Narayan
Jaime Saavedra-Chanduví
The World Bank
Poverty Reduction and Economic Management Network
Poverty Reduction and Equity Unit
December 2013
Policy Research Working Paper 6735
Abstract
This paper studies the relationship between inequality of educational opportunities that incorporates inequality
of opportunity and development outcomes in a cross- between “types” or circumstance groups. Theories from
country setting. Scholars have long debated the impact economic history are used to instrument for this type of
of inequality on growth, development, and the quality inequality in a large cross-country dataset. The results
of institutions in a society. The empirical relationships seem to confirm the hypothesis that this measure of
are however confounded by the notion that “inequality” inequality of opportunity is a better fit for structural
can be seen as a composite of inequality arising from inequality than the Gini index of income. The results
differences in effort and ability, which would tend to suggest that inequality of endowments at the outset
encourage competition and productivity, and inequality of history led to unequal educational opportunities,
attributable to unequal opportunities, particularly in which in turn affected development outcomes such as
terms of access to basic goods and services, which might institutional quality, infant mortality, and economic
translate to wasted human potential and lower levels of growth. The findings are robust to several checks on the
development. The analysis in this paper applies a measure instrumental variable specification.
This paper is a product of the Poverty Reduction and Equity Unit, Poverty Reduction and Economic Management
Network. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to
development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://
econ.worldbank.org. The authors may be contacted at ezequielmolina@worldbank.org.
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names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Outcomes, Opportunity and Development
Why unequal opportunities and not outcomes hinder
economic development
Ezequiel Molina *
Ambar Narayan
Jaime Saavedra-Chanduví
JEL Classification Codes: O11, O15, D63
Key words: inequality; equity; opportunity; growth; institutions; education
Sector Board: Poverty Reduction (POV)
*
Corresponding author: ezequielmolina@worldbank.org; The World Bank Group, 1818 H Street NW, Washington
DC 20433, USA. The authors would like to thank Alejandro Hoyos Suarez and Claudio Montenegro for providing
access to data from all over the world, and Joao Pedro Azevedo, Jose Molinas and Amer Hassan for advice and
support in the computation of Human Opportunity Index. Insightful comments on earlier drafts and presentations
were received from Martin Ardanaz, Carles Boix, John Londregan, Pedro Olinto, Eliana Rubiano, Carolina Sanchez-
Paramo, and participants at the World Bank Equity Conference of 2012. The findings, interpretations, and
conclusions are entirely those of the authors. They do not necessarily represent the view of the World Bank Group,
its Executive Directors, or the countries they represent.
1. Introduction
Do unequal opportunities among different members or groups in a society hinder economic and social
development? Using recently developed distributional measures of opportunity, this paper studies the
relationship between opportunities for a country’s citizens and its development outcomes.
For years scholars have discussed whether the way wealth is distributed has an impact on the level of
economic development of society as well as the quality of its institutions. Aided by increasing availability
of data on income inequality, many researchers have studied this relationship empirically. The
relationship is however complicated by the notion that inequality of outcomes can be thought of as
combining elements of “good” and “bad” inequality (World Bank, 2005). “Good” inequality is the one
traced to differences in effort or talent, which drives investment and competition that play a key role to
increase productivity. “Bad” inequality is the one caused as a consequence of some individuals not having
basic opportunities to develop their human potential, due to circumstances beyond their control. If this
were true, one could argue that net of the effect of opportunities, inequality of outcomes can even be good
for economic development. In other words, once the effect of “bad” inequality is accounted for, inequality
of outcomes could drive competition and efficiency, and encourage economic growth.
In this paper we argue that most of the existing empirical studies have been missing an important
variable – given that the theoretical link between inequality and development is based on the concept of
unequal opportunities rather than unequal outcomes. We present results that appear to confirm this
hypothesis – once we account for the effect of unequal opportunities, inequality of outcomes does not
appear to play any role in hindering economic development.
The World Development Report 2006 on Equity and Development (World Bank, 2005) focused on
equality of opportunity and concluded that institutions and policies that promote a level playing field,
where all members of society have similar chances to become socially active, politically influential, and
economically productive, contribute to sustainable growth and development. However, as there were no
indicators that could be computed for a large number of countries with the data that were available, there
was no rigorous empirical evidence to show that higher equality of opportunity causes social and
economic development at the country level. The WDR 2006 was followed by several World Bank reports
measuring equality of opportunity for different countries and regions. These analytical studies developed
several indicators to measure how countries rank in terms of distribution of opportunities among groups
in each society.
Whether there is a causal link between inequality of opportunity in a country and its overall level of
development remains an open question that has been examined only to a limited extent in existing
literature. This paper intends to make a contribution to this literature, by using the recently developed
measures of opportunities to investigate the causal link between (the level and distribution of)
opportunities and development outcomes, such as gross domestic product per capita and institutional
quality. It examines the extent to which empirical evidence supports a hypothesis that relates historical
factors to the distribution of opportunities, in explaining a country’s development trajectory. The
hypothesis, drawn from seminal literature on the history of economic development of nations, is based on
the idea that factor endowments at the outset of history influenced the type of human capital institutions
2
that each country developed. The quality of a country’s institutions was manifested in the distribution of
opportunities among its population, which in turn has had an effect on its level of development.
2. Motivation and links to recent literature
The empirical literature at the individual level is unambiguous. People who face better opportunities
in life, attend better schools, have a more customized educational experience, and enjoy a better family
environment are more likely to be able to develop their full human potential, achieving better outcomes in
terms of income, education, and so on. Furthermore, increasing opportunities for disadvantaged groups
has proved to increase cognitive as well as non-cognitive skills, including improvements in personality,
social and emotional traits. This general set of skills has also been proved to be essential in producing
social and economic success (Herrnstein et al, 1994, Heckman et al, 2006 and Borghans et al, 2008).
Interventions to equalize opportunities earlier in life are also found to be significantly more cost-
effective and successful than those attempted later in life. Research shows that preschoolers with low
levels of cognitive development have lower school achievement and earn lower wages in adulthood
(Currie and Thomas, 1999; Case and Paxson, 2006). More recent studies suggest that early childhood
education has substantial long-term impacts, ranging from adult earnings to retirement savings (Chetty et
al., 2010). Reynolds et al. (2003) present a comprehensive review of the impact of early childhood
programs directed toward disadvantaged children. Their findings also support a causal link between
opportunities and productivity. Lost opportunities during childhood cannot always be compensated for.
Child malnutrition, for example, can generate life-long learning difficulties, poor health and lower
productivity and earnings over a lifetime (Alderman et al, 2006 and Hoddinott et al, 2008). But do these
findings at the individual level extend to the aggregate level? Our paper attempts to address this question
by empirically analyzing whether countries where opportunities are more widely available and distributed
independent of an individual’s circumstances at birth have better development outcomes.
Extrapolating from the micro-level evidence mentioned above, one would expect that increased
opportunities in childhood in a country would have positive impacts on its growth prospects. The rich
cross-country empirical literature linking economic growth with human capital has relevance to this
hypothesis. For example, Barro (2001) finds growth to be positively related to the average years of school
attainment of adult males at the secondary and higher levels at the beginning of the period, in a panel of
100 countries observed from 1965 to 1995. While “quantity” of schooling is important, quality of
schooling as measured by internationally comparable test scores is even more so. A number of studies in
recent years have shown the effect of health on economic growth to be important (see Grimm, 2011 for an
overview).
Thus improving opportunities for children – by improving coverage and reducing inequality of
opportunity – is not just about “fairness” and building a “just society”, important as these principles are,
but also about realizing a society’s aspirations of economic prosperity. Notably, the dividends of
investing in opportunities among children, micro and macro level evidence seems to suggest, are likely to
accumulate over time and across generations.
The empirical literature on inequality and economic development has largely neglected the role of
opportunities and focused on the relationship between inequality of outcomes and economic development,
3
with inconclusive findings (see Banerjee and Duflo, 2003 and Boix, 2010). In contrast, our paper
combines the literature on equality of opportunity – brought into prominence by John Roemer’s seminal
1998 book “Equality of Opportunity” 1 – with recent theoretical and empirical work on the effect of the
historical distribution of wealth and its effects on economic development. Our paper is also related to
preceding work by scholars who have argued for a change in focus from inequality of outcomes to
inequality of opportunities. In particular, Ferreira and Walton (2006) argue for inequality of opportunity
as a more suitable concept to test the leading theories on economic development. 2 They provide a detailed
account of the literature where the empirical tests rely on measures of inequality of outcomes, even
though the best theoretical fit would be a measure of opportunities.
A case in point is the theory suggested by Engerman and Sokoloff (1997). In their seminal study, they
argue that historical dominance of some crops like wheat in agriculture lead to more equal societies over
time; while that of others, like sugarcane, which have large economies of scale, are associated with the
growth of large plantations and structural inequality. These inequalities later translate to inferior
education systems, weaker institutions and less democratic societies. Weak institutions, which are
persistent, have a negative impact on economic growth and development. Easterly (2007) tested the
Engerman and Sokoloff theory empirically, measuring structural inequality as the Gini coefficient of a
country averaged over the period 1960–98. Using an agricultural endowment instrument for factor
endowments, he assesses the causal effect of inequality of outcomes on development outcomes, namely
GDP per capita, institutional quality and secondary enrollment.
Several other studies have complemented the theory suggested by Engerman and Sokoloff, suggesting
alternate plausible channels through which inequality can affect economic development. Acemoglu et al.
(2001, 2002 and 2005) highlighted the importance of unequal power in the process of economic
development. Differences in settlers’ mortality led Europeans to establish different institutional set-ups,
with extractive institutions in places where they could not settle and inclusive institutions in places they
could. As a consequence, some societies enjoy equal distribution of power among members while others
were ruled by the elites. These elites maximize their power by blocking enfranchisement and reforms to
the education system that the rest of the population can benefit from. In contrast, Glaeser et al. (2004)
argue that human capital is a more fundamental source of growth than political institutions, and human
capital accumulation is the key factor that leads to institutional improvement and economic development.
Galor et al. (2009) formally model the mechanisms through which inequality in the distribution of
land ownership negatively impacts the development of institutions that promote human capital (such as
public schooling and child labor regulation), delaying the transition from agricultural to industrial society.
Ferreira (2001) develops a model that highlights the political economy channel through which unequal
educational opportunities may affect institutions and economic development. Educational opportunities
are modeled as a function of wealth, and low educational opportunities translate into political inequality.
Under some assumptions, the author finds opportunity traps, where low levels of wealth translate into low
educational opportunities and political inequality, which in turn perpetuates inequalities in wealth,
generating a vicious cycle.
1
For more on this literature, see, for example, Roemer (2002), Van der Gaer (1993) and Ferreira and Gignoux
(2011).
2
Deininger and Olinto (2000) make a similar argument that what matters for growth is not inequality of outcomes
but assets, which might be a better proxy for opportunity.
4
The above papers have something in common. Structural inequality, educational inequality and
inequality of power are symptoms of a more encompassing concept: inequality of opportunity.
The hypothesis we empirically test in this paper is compatible with the above literature. It is based on
the idea that factor endowments at the outset of history influenced the type of human capital institutions
that each country developed and as a result of that, affect education opportunities among its population.
Low and unequal education opportunities tend to create a failure in the political market due to multiple
agents (citizens) who vastly differ in their bargaining power, through no fault of their own. All agents do
not have the same power to influence the principal (government), since the political power of influence is
a function of information, resources and the capability to mobilize groups. In countries where broad
segments of the population do not have information, resources or capabilities for mobilization, the
politicians are likely to be less accountable, as they recognize that the population is not able to monitor
and punish them for their misdeeds.
A recent paper (Jakiela et al. 2010), finds experimental evidence in favor of the idea that improving
educational opportunities creates a better environment to design institutions. They combine data from a
field experiment and a laboratory experiment to measure the causal impact of educational opportunity on
respect for earned property rights. The paper finds that higher academic achievement reduces the
willingness of young Kenyan women to appropriate others' labor income, and shifts players toward a 50-
50 split norm in the dictator game.
Thus it seems reasonable to suggest that greater equality of opportunity promotes more engaged
citizens, who have more respect for property rights and more information and intellectual resources to
“punish” corrupt principals. To empirically assess such an argument in a cross-country setting, we
analyze the extent to which equality of opportunity, which we proxy with measures of educational
opportunities, have an impact on development outcomes – namely, the level of economic development
and institutional quality at the country level. We also assess the extent to which inequality of outcomes
explains variation in GDP per capita or institutional quality, once the level and distribution of
opportunities are controlled for (using recently developed measures that are new to the cross-country
literature).
While research establishing a causal link between inequality of opportunity and growth in a cross-
country framework is at a nascent stage, the evidence so far seems to suggest that inequality of
opportunity has an adverse impact on growth and development. Marrero and Rodríguez (2013), using
income-based measures of inequality of opportunity that are quite different from ours, have found such
evidence in an entirely different data set. They test the hypothesis that inequality of opportunity
(attributable to two circumstances, namely parental education and race) and inequality of effort affect
economic growth in different directions, using refined data of the PSID database for 26 states distributed
throughout the United States in 1970, 1980 and 1990. They find robust support for a negative relationship
between inequality of opportunity and growth and a positive relationship between inequality of effort and
growth. While the results are encouraging, the authors acknowledge the need for caution because only
two circumstances were used in the analysis, which implies that the results shed no light on the impact of
other opportunity-related inequalities (for example, those attributable to parental occupation or
5
geographical location) on growth. 3 The likely underestimation of inequality of opportunity could also lead
to their measure of inequality of effort containing some amount of inequality of opportunity. This would
imply that their finding of a positive impact of inequality of returns to effort on growth merits more
scrutiny through research, as the authors themselves point out.
Also of relevance is a paper by Grimm (2011), which assesses the effect of inequality in health on
economic growth, using a cross-national panel data set of 62 low and middle-income countries between
1985 and 2007. The gradient in child mortality over mothers’ education groups, used as a proxy for
disparity in health conditions to which different socioeconomic groups of a country are exposed, is
closely related to inequality in health opportunities. Even with such a narrow measure, the paper finds a
significant negative effect of health inequality (between different socioeconomic groups) on economic
growth, which is robust to different specifications, estimation methods, and time spells.
3. Methodological approach
Data and measures of equality of opportunity
This paper incorporates new measures of opportunities. The first is the Human Opportunity Index
(henceforth, HOI), which is a measure developed by Barros et al. (2009). The HOI is a composite
indicator that combines two elements:
(i) The level of coverage of basic opportunities necessary for human development, such as
primary education, water and sanitation, and electricity.
(ii) The degree to which the distribution of those opportunities is conditional on circumstances
exogenous to children, such as gender, parental income, or household characteristics.
The formula to compute this index is
= ̅ (1 − )
where ̅ is the average coverage of an opportunity and is the Dissimilarity Index (henceforth, D-Index)
that measures inequality in opportunity due to circumstances that are exogenous. D is defined by: 4
1
= � | − ̅ |
2̅
=1
where is the coverage rate for group k (where each group is defined by a set of circumstances unique
to that group), and is the share of group k in total population. The D-Index is then a measure of the
weighted average of the distance between group access and population access. It ranges from 0 to 100, in
percentage terms, and in a situation of perfect equality of opportunity, takes the value zero. The D-Index
has an interesting interpretation as the fraction of all available opportunities that need to be reallocated
3
Also, the likely underestimation of inequality of opportunity could lead to their measure of inequality of effort
containing some amount of inequality of opportunity. This would imply that their finding of a positive impact of
inequality of returns to effort on growth needs to be subjected to more scrutiny through research.
4
We also make use of the geometric version of the D-Index, which is more sensitive to inequalities within each
subgroup and is decomposable by subgroups.
6
from circumstance groups (or “types”, as defined in the inequality of opportunity literature) with coverage
rate higher than ̅ to groups with coverage rate lower than ̅ to restore equal opportunity across all groups.
HOI has a number of desirable properties, including sensitivity to scale and inequality and its reward
to Pareto improvements (see Barros et al. 2010). Of particular relevance is its sensitivity to inequality.
HOI improves when inequality between types decreases with a fixed number of opportunities in a society,
or when the number of opportunities increases and inequality among types stays constant.5 The D-Index,
on the other hand, improves if inequality among types, for a given number of total opportunities, declines.
Importantly, while D is an indicator of inequality of opportunity, it is not independent of the level of
coverage. Clearly, as the coverage of an opportunity increases, the share of total opportunities allocated
unequally among types is likely to fall, which is to say D is likely to fall. This is an inevitable
consequence of the opportunity being a binary (zero-one) indicator, which implies that the coverage of an
opportunity has an upper limit (100 percent). It also implies that the estimated effect of D on level of
development will also reflect, in part, the effect of the level (coverage) of the opportunity, albeit to a
much smaller extent than for the estimated effect of HOI.
Computing D and HOI when the number of circumstances is relatively large, as is the case here,
requires an econometric exercise to obtain a prediction of HOI from observed access to the opportunity
and circumstances among children (see Barros et al., 2010). This involves running a logistic regression
model to estimate the relationship between access to a particular opportunity and the circumstances of the
child, on the full sample of children for whom the HOI measure will be constructed. The estimated
coefficients of the regression are used to obtain for each child his/her predicted probability of access to
the opportunity, which is then used to estimate the coverage rate ̅ , D and HOI (see Appendix 2).
We compute the HOI and the D-Index using data from the Program for International Student
Assessment (PISA). PISA surveys 15-year-olds and assesses the extent to which students near the end of
compulsory education have acquired the knowledge and skills essential for full participation in society.
This is done through the use of standardized test scores. The scores range from 0 to 700, and six cut-off
values or levels have been established by PISA. An “opportunity” is defined as achieving proficiency of
Level 2 for the topics covered in all three tests (Mathematics, Reading and Science), which indicates a
basic level of understanding of the topics covered. 6 The circumstances used are a measure of household
wealth, calculated using principal component methodology based on asset ownership; gender of the child;
parental education; school location; 7 and occupation of the head of the child’s household. For the child,
these are all attributes s/he has no control over and are likely to have been determined at birth.
One of the drawbacks of using PISA is that the standardized tests are not carried out in all countries.
To expand the sample of countries to a larger set, we also make use of Montenegro 8 et al. (2011)
5
The D-index and HOI are sensitive to the set of circumstances chosen for analysis. But this is mitigated by an
additional property: the D-Index (HOI) will not be lower (higher) if more circumstances are added to the existing set
of circumstances in the analysis. This implies that the computed D-index serves as a lower bound to the “actual”
inequality if all circumstances of interest could be included in the analysis.
6
The results are robust to the use of proficiency levels 3 or 4. See PISA 2009 for a description of what proficiency
level 2 implies for each test.
7
The location of the school is classified as: a) Village, b) Small Town, c) Town, d) City or e) Large City.
8
Not all surveys had the necessary variables to compute the indicator. As a result, we end up with 80 surveys in
which we could compute it.
7
Harmonized Micro data from Household Surveys that cover almost 100 developing countries to compute
the HOI for another set of indicators: completing sixth grade on time, school attendance for children 10–
14 years old, and starting primary school on time for children between 6 and 7 years old. While these
opportunities are not as attractive as PISA scores, since they cannot capture the quality of learning, they
are reasonable proxies for educational opportunities. This is particularly true for timely completion of
sixth grade (or six years of education), which correlates with variables like timely start to school and
(absence of) grade repetition that are useful predictors for learning achievement. Taking advantage of the
richer information available from household data, the circumstances considered here are: gender of the
child, location, head of household education, per capita family income, number of children in the
household and family structure (presence of both parents in the household).
Appendix 1 includes a description of the variables (with basic statistics included) for all the relevant
measures used in the study, as well as a brief explanation of how these were constructed. Furthermore,
Table A.2-2 in Appendix 2 shows correlations between all the opportunity measures computed for the
study.
Identification strategy
Below we present our structural equation model for identification.
= 1 + + 1 + 1 (1)
= 2 + 2 + 2 (2)
Equation (1) denotes our outcome variable “ ” indicating level of GDP, institutional quality, or
infant mortality. These outcomes can be explained by different control variables (Xi) as well as our main
variable of interest (Ei), which proxies for unequal opportunities.
The problem with estimating equation (1) is the possibility that the outcome variables also affect
unequal opportunities, meaning that we have an endogenous variable. This would imply that if we replace
in Equation (1) we will end up with
= 1 + (2 + 2 + 2 ) + 1 + 1 (3)
= 3 + 3 + 3 (4)
where 3 = 1 + 2 , 3 = 1 + 2 and 3 = 1 + 2 (5)
In order to be able to use an Ordinary Least Squares (OLS) approach, we need the classical
assumptions to hold, which would require 1 to be independent of 2 . Since we suspect that our variable
is endogenous, we know the errors from Equations (1) and (2) will not be independent. As a result, OLS
results would be biased. To address this problem we use Instrumental Variables (IV). In Equations (6)
and (7) the instrument is represented by .
= 1 + 1 + + 1 + 1 (6)
= 2 + 2 + 2 + 2 (7)
8
For the IV approach to be valid and allow valid inferences of our variables of interest, we need two
conditions to hold.
a) Exclusion Restriction: The instrument is uncorrelated with the error term, that is, ( , 1 ) =
0 . Or, to put it differently, the instrument has no direct effect on . This means that β1 = 0 in
Equation (6).
b) is correlated with , our opportunity measure. ( , ) ≠ 0.
The literature on economic development suggests a few different potential instruments.
a) Log of Wheat Sugar Suitability Ratio: Abundance of land suitable for growing wheat relative to
that suitable for growing sugarcane (Easterly, 2007).
b) Share of Tropical Land. Percentage of land area in geographical tropics (Sachs, 1997). 9
c) Ethnic Fractionalization. Ranges from 0 and 1 and describes how ethnically segregated a society
is (Alesina et al., 2003).
d) Legal Origin. 10
e) Latitude of Country Centroid. 11
f) Longitude of Country Centroid. 12
Table A.2-3 in Appendix 2 presents a correlation table across all these measures. We choose
agricultural endowments as our preferred instrument, which was first introduced by Easterly (2007). The
variable “wheat–sugar suitability ratio” is defined as
LWHEATSUGAR=log[(1+share of arable land suitable for wheat) / (1+share of arable land suitable
for sugarcane)].
The idea behind this instrument is that the higher the ratio (share of arable land suitable for wheat to
sugar in total arable land) in a society, the lower would be economies of scale in production, and the
society would be less likely to need structural inequality (in its most extreme form, slavery) for efficiency.
As a result, societies with a higher wheat-sugar ratio of arable land are likely to be more equal in terms of
opportunities.
As Easterly points out, the wheat–sugar ratio could simply be proxying for whether the country is in
the tropics. There is certainly a strong correlation (correlation= −0.66, t-statistic= −10.75), but also
enough variation in this measure within tropical and non-tropical areas alike to suggest that the two
measures are not the same. The measure comes from FAO and takes into account factors like soil,
rainfall, temperature and elevation. Easterly (2007), using different studies, argues that this measure has
9
This instrument is similar to settler mortality, so we will not use it to avoid concerns about the validity of the
historical data in the latter. See Acemoglu et al. (2012) and Albouy (2012) for a debate on the validity of settler
mortality data.
10
Indicates which type of legal system the country ascribes to: British, French, Germany, Scandinavian or
Communist.
11
Ranges from 0 at the Equator to 90 (North or South) at the poles and refers to a geographic coordinate that
specifies the north-south position of a point on the Earth's surface.
12
Ranges from −180 to 180 and refers to the angle between a plane containing the Prime Meridian and a plane
containing the North Pole, South Pole and the location in question.
9
remained constant over time. Hence, he can use current data on agricultural endowment to construct this
measure, as the data would be highly correlated with historical agricultural endowments.
In order for it to qualify as a good instrument, we need to argue that the two necessary conditions
stated above hold. The first condition, namely the exclusion restriction, captures the notion that any effect
of the instrument on the outcome must occur via the effect of the instrument on the treatment. In other
words, we argue that conditional on the controls included in the regression, the wheat–sugar ratio has no
effect on GDP per capita today, other than the effect through opportunities. The second condition, namely
the nonzero average causal effect of the instrument on the treatment, implies that there should be a
relationship (linear in this case) between the wheat–sugar ratio and educational opportunity. If the
relationship is weak, we would have weak instruments. In our case, the correlations are strong (see
Figures 1 and 2) between the log wheat–sugar ratio and our measures of educational opportunities,
namely the HOI and D-Index for PISA scores (Level 2 proficiency).
Figure 1 Figure 2
Relation between Agricultural Endowments and Equality of Opportunity Relation between Agricultural Endowments and Inequality of Opportunity
Log of Wheat Sugar Suitability Ratio
Log of Wheat Sugar Suitability Ratio
.6
.6
r = 0.576*** r = -0.542***
.4
.4
.2
.2
0
0
-.2
-.4 -.2
-.4
0 20 40 60 80 100 0 10 20 30 40
Human Opportunity Index - PISA D-Index - PISA
Fitted values Americas Fitted values Americas
East Asia, South Asia & Pacific Europe & Central Asia East Asia, South Asia & Pacific Europe & Central Asia
Middle East and Africa Middle East and Africa
Finally, for our theory to be consistent, we need to show that firstly, factor endowments are related
with historical measures of unequal educational opportunities; and secondly, there is persistence of
unequal educational opportunities from those historical measures to our current measures of unequal
opportunities.
For historical data on educational achievement, we use Tutu Vanhanen’s data (in press). In particular,
we use the Index of Knowledge Distribution, which is computed as the arithmetic mean of the percentage
of students and literates in the country. The number of students refers to students in universities and other
higher education institutions, per 100,000 inhabitants of the country. 13 Using this data comes at the cost of
possible inaccuracies and methodological problems involved in using data from many different sources.
However, the data are valuable for testing whether our story about a high endowment of wheat land
relative to sugarcane land predicts a high value of the index of knowledge distribution. As this index is
itself a measure of unequal opportunities, we can also perceive whether there is persistence over time,
which is to say, whether today's educational opportunities are correlated with those in the past.
13
Two ways are used to calculate the percentage of Students (%): before the year 1988 the value 1000 of the
variable “number of students” is equivalent to 100%; and between the years 1988-1998 the value 5000 of the same
variable is equivalent to 100%. For percentage of literates we use all the adult population.
10
Table 1 shows a positive and strong correlation between our measure of factor endowments and
educational achievement, as measured by the aforementioned Index of Knowledge Distribution, over a
long period of history between 1858 and 1998. Countries with a higher wheat-sugar ratio of arable land
have had a higher percentage of students and literates throughout this period (measured with 10-year
intervals). Tables 2A and 2B show strongly positive correlations between educational achievement during
the period 1858-1998 (measured once every 10 years) and our measures of equality of opportunity (HOI
and D-Index) using PISA data from 2009. Thus unequal educational opportunities appear to persist over
time, all the way to our current measures of unequal opportunities. Taken together, the two types of
correlation in Tables 1 and 2 seem to support the use of our measure of factor endowments, the wheat-
sugar ratio of arable land, as an instrument for educational opportunities.
4. Empirical results
We start by showing the strong correlations between our measures of Equality of Opportunity and
GDP per capita. The HOI and D-Index (derived from PISA test scores or timely completion of primary
school) have strong positive and negative correlation, respectively, with the log of GDP per capita (Figure
3) – consistent with our hypothesis. The correlations with GDP are weaker for measures derived from
school attendance (10-14 years) and starting primary school on time (6-7 years) (Figure 4). 14
Figure 3
Opportunities and Economic Development Using PISA Test Scores
Logaritm of GDP pc at Current USD (2005-2010)
Logaritm of GDP pc at Current USD (2005-2010)
14
14
r = 0.766*** r = -0.713***
12
12
10
10
8
8
6
6
4
4
0 20 40 60 80 100 0 10 20 30 40
Human Opportunity Index - PISA Test Scores Dissimilarity Index - PISA Test Scores
Fitted values Americas
East Asia, South Asia & Pacific Europe & Central Asia
Middle East and Africa
These graphs show the strong economical and statistical correlation (p-value is equal to zero in both cases)
between our measures of equality of opportunity and economic development
14
See Appendix 2, Figures A-2.1 and A-2.2.
11
Figure 4
Opportunities and Economic Development - Completing Six Years on Time
Logaritm of GDP pc at Current USD (2005-2010)
Logaritm of GDP pc at Current USD (2005-2010)
12
12
r = 0.695*** r = -0.697***
10
10
8
8
6
6
4
4
0 20 40 60 80 100 0 20 40 60 80
HOI - Completing Six Years of Education On Time D-Index - Completing Six Years of Education On Time
Fitted values Americas
East Asia, South Asia & Pacific Europe & Central Asia
Middle East and Africa
Before introducing our IV results, some results using OLS are helpful in setting the stage. Table 3
with the OLS results shows that once we take into account the effect of educational opportunity,
measured by the HOI or D-Index using PISA data, inequality of outcomes (as measured by the Gini index
of income) does not have a relationship with the level of economic development.15
The next step is to assess the effect of unequal opportunities on development outcomes using the
wheat–sugar ratio as an instrument for opportunities. The first stage regression shows a highly significant
relationship between the wheat–sugar endowment ratio and the two measures of equality of opportunity.
The F-statistics for the first stage regressions are above the critical values identified by Stock and Yogo
(2005), which indicates a problem with weak instruments. 16
Table 4 shows the IV estimates of the effect of equality of opportunity (as measured by the HOI and
D-Index) on economic development, measured by GDP per capita. Higher influence of circumstances on
available opportunities is associated with lower degree of economic development. Once we account for
the effect of opportunities, inequality of outcomes – measured by the Gini coefficient of income – has no
causal effect on economic development. The relationship between opportunities and economic
15
The results are similar with equality of opportunity measures constructed with other variables (e.g. timely
completion of primary school). But for the sample of countries for which we have those variables, the Gini
coefficient does not have a significant negative relationship with GDP per capita in OLS regressions. Then we
cannot make the case that accounting for equality of opportunity makes the Gini insignificant.
16
Staiger and Stock (1997) suggest that the F-statistic in the first stage regression should exceed 10. In most of our
specification this value holds true for our case. For some specifications the F from the first stage are below 10, we
also conduct sensitivity analysis for weak instruments and compute alternative confidence intervals following
Chernozhukov and Hansen (2008). This confidence intervals are larger but produce the same insight the once we
found using the small sample robust statistics we report in this paper.
12
development is also robust to inclusion of the Gini coefficient, which is averaged over 1960-2010 to
mitigate the noise associated with the measure. 17
Following up from the discussion earlier (in Section 3), the effect of HOI on GDP per capita is a
combination of the effects of coverage and inequality of educational opportunity. The effect of the D-
Index on GDP, on the other hand, reflects the effect of inequality of opportunity, which is however also
related (in part) to coverage in the sense that inequality by this measure is likely to be higher when
coverage is lower and vice-versa. Given this feature, should the IV estimates of the D-Index be
interpreted as the effect of inequality of opportunity on economic development?
We would argue that such an interpretation is correct, because of the way opportunities are defined
here – as binary variables, where coverage is bounded above (at 100 percent). This is due to the nature of
these variables – the rate of school completion or attainment of proficiency cannot exceed 100 percent –
and the type of data available. Given the binary nature of these variables, an intuitive measure of
inequality of opportunity cannot be fully independent of coverage. Rather the measure should capture the
notion that inequality of educational opportunity in a country is likely to be higher when the basic
proficiency level in education is not universal, and that there would be no inequality when every child
attains the basic proficiency level. 18 Therefore, the estimated effect of the D-Index on per capita GDP
does reflect the effect of inequality of opportunity, even though the measure of the D-Index itself is partly
dependent on coverage.
As in Easterly (2007), Table 4 also expands on the basic results by adding two quick robustness
checks. The first check excludes the Western Hemisphere, to which Engerman and Sokoloff's original
case study was limited. Excluding countries from this region, the hypothesis that inequality of
opportunities inhibits development with the wheat–sugar ratio as an instrument holds “out of sample” for
the rest of the world. The second check involves the inclusion of three regional dummy variables – a
classification that is exogenous to the level of development of countries. 19 The results are robust to both
the changes in specifications, although the results with the regional dummies have smaller F-statistics that
could imply weak instruments.20
Similar results are obtained when the HOI and D-Index are constructed using timely completion of
six years of education as an alternative indicator of educational opportunity (see Table 5). 21 In this case,
we use the “share of tropical land” as an instrument, which is related to the previously used wheat-sugar
ratio, but allows for a larger number of observations for this particular opportunity measure. For all
17
As controls, we also use Gini coefficient adjusted to gain comparability across countries and surveys following
Easterly (2007) and an alternative adjustment proposed by Solt (2009). Both of these measures produce very similar
results as the one using the World Development Data.
18
Note that this would not apply when education proficiency is not a binary variable, but rather a continuous and
unbounded variable reflecting that learning achievement is, in fact, unbounded.
19
The dummies correspond to Americas (includes Latin America & Caribbean region, Canada and United States);
Europe and Central Asia (includes Western Europe), and Middle East & Africa; the omitted region is East Asia &
Pacific (includes Japan, Australia and New Zealand).
20
All specifications compute robust standard errors to account for potential heteroscedasticity. See also footnote 13
regarding weak instruments.
21
This is interesting as the sample of countries is not the same between PISA data and Montenegro et al. (2011).
13
instruments that are correlated with our measure, we find a significant positive effect on the level of GDP
per capita, with similar coefficients in every case.22
Next, we examine the relationship between equality of opportunity and other development outcomes,
namely institutional quality and infant mortality. 23 Table 6A presents the results. Higher equality of
opportunity (measured using PISA scores) predicts higher institutional quality of a country (see Appendix
2 for how this variable was created). Controlling for inequality of outcomes with the Gini index of
income, whose coefficient is not statistically significant, the coefficients of both the HOI and the D-Index
remain statistically significant. These coefficients also increase in size once we take into account the Gini
of income. Interestingly, the magnitude of the effects is higher using IVs than for OLS, suggesting that
the causal effect of inequality of opportunity on development outcomes is actually understated by the
OLS estimation.
Table 6B shows the results from the same analysis as above, re-defining the “opportunity” as timely
completion of six years of education. Equality of opportunity measured with this variable does not have a
clear relationship with institutional quality, with some specifications having significant results and others
not. For the other development outcomes, infant mortality and malnutrition, the results are clear: equality
of opportunity measured by the HOI or D-Index of timely completion of six years of education predicts
lower infant mortality and malnutrition rates.24
Estimated magnitude of economic impacts
How much does equality of opportunity matter as a driver of development? Using the data from
PISA, a one standard deviation increase in the Human Opportunity Index (33 percentage points) increases
income by 0.718 standard deviations, increases institutional quality by 0.814 standard deviations, and
reduces infant mortality by almost one standard deviation (Table 7). An increase of one point (9.4
percentage points) in inequality of opportunity or the D-Index reduces per capita income by almost 10
percentage points and institutional quality by 2.3 percentage points, and increases infant mortality by
almost 3 percentage points. By these estimates, the extent to which inequality of opportunity hinders
development is economically meaningful, in addition to being statistically significant.
We also compute the elasticity of GDP per capita to HOI and find that a 1 percent higher HOI for a
given country would lead to 2.3 percent higher GDP per capita. This means, for example, that if the
current HOI for Argentina were higher by 1 percent (around 0.4 points), its GDP per capita would be
higher by 150 USD.
22
With school attendance (10-14 years) or starting primary school on time (6-7 years) as the indicator of
opportunity, there appears to be no causal relation. We believe this result is due to the fact that attendance in school
and timely start to schooling are not good proxies for education achievement, which is what determines
opportunities. Therefore, in the rest of the paper we use only the measure derived from PISA test scores and timely
completion of six years of schooling.
23
For this specification we do not use malnutrition as a development outcome as only few observations were
available to estimate the first stage.
24
As results with D-Index are very similar, we omit them from Table 6B to reduce the number of tables. Results are
available upon request.
14
Using our alternative opportunity variable of completing sixth grade on time, we find that increasing
the Human Opportunity Index by one point increases GDP per capita by 3.8 percentage points, reduces
infant mortality rate by 0.6 percentage points, and reduces malnutrition by 0.8 percentage points. A one
point increase in inequality of opportunity or the D-Index (4 percentage points) reduces per capita income
by 6.7 percentage points, and increases infant mortality by 1.12 percentage points and malnutrition by
1.46 percentage points.
5. Robustness of the results
Testing different model specifications
To test the robustness of our results in more detail, we first explore how sensitive the findings are to
the choice of different model specifications. As we suggested when introducing the instrumental variable
approach, there are some plausible competing alternatives to our theory of equality of opportunity being a
key variable in explaining development outcomes. In particular, the literature has highlighted the role of
inequality of outcomes, ethnic fractionalization, legal origins, latitude and longitude as well as tropical
location (see Section 3). To test the alternative variables against our hypothesis, we adopt the approach of
controlling for each variable in turn (taking them as exogenous), while continuing to run an IV regression
of development outcomes on the inequality measures with the wheat–sugar endowment ratio as an
instrument for the PISA test scores data.
Tables 8A and 8B show the estimated effects of the HOI and D-Index (based on PISA test scores) on
log of GDP per capita, after controlling for the effects of ethnic fractionalization, legal origin, share of
tropical land, latitude and longitude, in succession. When the effects of ethnic fractionalization are
controlled for, the coefficients on the HOI and D-Index drop modestly but still have high statistical and
economic significance. Introducing dummies for British, French and German or Scandinavian legal origin
(Socialist legal origin is the omitted category) also leaves the significance of the HOI and D-Index
unchanged, and actually increases the magnitude of the coefficients. The tropical location measure – the
share of a country's cultivated land area in tropical climate zones 25 – was introduced by Sachs and
coauthors. The tropics variable is not significant and its inclusion does not affect the significance of the
HOI and D-Index. The inclusion of latitude and longitude variables reduces the coefficients on the HOI
modestly and increases the coefficients on the D-Index.
Therefore, the effects of equality of opportunity – measured by the HOI and D-Index of PISA test
scores – are robust to the exclusion of different variables that provide competing explanations for
economic development. Interestingly, three of these variables – ethnic fractionalization, share of tropical
land and latitude – have strong and significant effects on GDP per capita when the opportunity variables
are not included in the specification, which disappear upon the inclusion of the HOI or D-Index.
25
Tropical climate zone is characterized as “hot and humid with no winter”, which is the most precise measure of
tropical conditions.
15
As before, the same exercise is repeated defining the opportunity as timely completion of sixth grade
(results available upon request). The coefficients on the HOI and D-Index are always statistically and
economically significant with only modest reductions seen when ethnic fractionalization is controlled for.
Tables 9A and 9B show the estimates for the effects of the HOI and D-Index PISA test scores on
institutional quality using the same controls as before. As in Tables 8A and 8B, the coefficients on the
HOI and D-Index are always statistically and economically significant, with modest reductions in the
coefficients seen when ethnic fractionalization is controlled for. 26
< Tables 9A and 9B here>
Overidentification test
To check the robustness of our results, we also need to test the validity of our instruments in more
detail. For an IV approach to work, the instrument must be: (i) uncorrelated with the unobserved error
term and (ii) correlated with the endogenous explanatory variable. As shown in Section 3, our instrument,
the wheat-sugar suitability ratio in arable land, appears to satisfy the second condition quite well.
The first requirement, however, cannot be tested definitively as it arises from a correlation between
the instrument and an unobserved component of the error. One of the most problematic parts of any IV
exercise is establishing that the selected instrument meets this so-called exclusion restriction. In our case
it would imply that conditional on the pre-treatment controls, the wheat–sugar ratio affects the outcome,
i.e. GDP per capita today, infant mortality or institutional quality, only through its effect on educational
opportunities and not through any other variable. And it would imply that the share of tropical land does
not directly affect the level of development, infant mortality and institutional quality, other than through
its effect on the HOI and D-Index of completing sixth grade on time.
If we have more than one instrumental variable, we can effectively test whether these are uncorrelated
with the structural error, with the null hypothesis being that all instruments are uncorrelated with the error
term. The usual econometric approach is to run a test of overidentification. These tests are far from
definitive, as “passing the test” merely implies a failure to reject the exclusion restriction. To run the test,
we need an alternative instrument for equality of opportunity. The variable “share of tropical land”
described earlier is a good candidate, as it is used as an instrument for the variable completing sixth grade
on time. There is considerable consensus in the literature that the tropics variable affects income through
social and political institutions rather than directly. For the tropics variable to be of use here as an
instrument, its effects on institutions also must go through equality of opportunity rather than through any
other mechanism.
The results on the over-identification tests fail to reject the exclusion restriction, by a considerable
margin in all of the specifications, when the outcome variable is GDP per capita, institutional quality or
malnutrition (see Table 10). When the outcome variable is infant mortality, the over-identification tests
fail to reject the exclusion restriction in all cases but one. 27 Thus in almost all cases the over-identification
26
Results are qualitatively similar using other development measures as well as the different measures of equality of
opportunity used in this paper. These regression outputs are available upon request.
27
The one where the hypothesis of exclusion restriction is rejected is for the case for infant mortality using the HOI
and D-Index for PISA test scores data. However, the overidentification test fails to reject the hypothesis when the
opportunity is defined as completing sixth grade on time, using data from household surveys.
16
tests, even as they are less than definitive due to the nature of the test, yield results favorable to the
validity of the instruments.
6. Final Remarks
The findings of this paper suggest that the conflicting results in the literature on inequality of
outcomes and economic growth can be attributed to the omission of an important variable – what really
matters is inequality of opportunities and not of outcomes. A recent paper (Marrero and Rodriguez, 2013)
finds evidence in favor of this hypothesis using a measure of inequality of opportunity that is derived
from a decomposition of income. Our innovation is to apply a measure of educational opportunities that
incorporates inequality between “types” or circumstance groups, using theories from economic history to
instrument for this type of inequality. We argue that our measure of inequality of opportunity is a better
fit for structural inequality than the Gini index of income, and the results seem to support this argument.
Consistent with the hypothesis of the literature, our paper supports the prediction that agricultural
endowments – specifically the relative abundance land suitable for wheat to that suitable for sugarcane –
predict unequal educational opportunities and this, in turn, predicts development outcomes. After
controlling for the measures for unequal opportunity we construct, the Gini index that measures income
inequality has no explanatory power. We test the robustness of our results using different country samples
and sources of data, measures of opportunity and development outcomes, and controlling for the effects
of other variables that have been shown in earlier literature to influence economic development. For
almost all cases, our results remain statistically and economically significant.
Although the IV approach using cross-country data may not be the best identification strategy to
establish causality, the results in this paper support a well-defined a priori hypothesis at the individual and
aggregate levels, whereby unequal educational opportunities hinder development. The validity of the
instrument, the wheat-sugar land ratio or the share of tropical land, both of which have been used in past
literature, is typically a subject of debate in work such as ours. The evidence we offer on the instrument
satisfying the condition of the exclusion restriction, which is the failure to reject the overidentifying
restrictions in the system, is subject to important caveats about the power of such tests. In spite of these
tests being less than definitive by their very nature, we find it encouraging that they fail to find evidence
of the wheat–sugar land ratio having any effect on underdevelopment other than its effect through the
opportunity variables defined on the basis of PISA test scores. The tests also fail to find evidence that the
share of tropical land has any effect on underdevelopment other than through equality of opportunity,
measured by timely completion of sixth grade from household survey data.
Future research could focus on disentangling the effects of higher coverage of opportunities (the
level) from pure inequality of opportunities (which is independent of the level), which is not possible in
the model we estimate. A related question to examine will be whether the relative importance of reducing
inequality or increasing coverage is related to the existing level of opportunities in a society or the level of
development. It is possible to argue, for example, that inequality in educational opportunity is relevant for
development only after a country reaches a certain threshold level of education and/or income level.
17
Whether such an argument has any merit is an empirical question that could be a subject of future
research.
18
Tables
TABLE 1
Historical Equality of Opportunity and Agricultural Endowments
Regression Dependent Variable:Log of Wheat Sugar Ratio Sustainability
OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS
Index of Knowledge Distribution (1858) 0.00913***
(0.00)
Index of Knowledge Distribution (1868) 0.00847***
(0.00)
Index of Knowledge Distribution (1878) 0.00889***
(0.00)
Index of Knowledge Distribution (1888) 0.00894***
(0.00)
Index of Knowledge Distribution (1898) 0.00913***
(0.00)
Index of Knowledge Distribution (1908) 0.00887***
(0.00)
Index of Knowledge Distribution (1918) 0.00816***
(0.00)
Index of Knowledge Distribution (1928) 0.00776***
(0.00)
Index of Knowledge Distribution (1938) 0.00681***
(0.00)
Index of Knowledge Distribution (1948) 0.00602***
(0.00)
Index of Knowledge Distribution (1958) 0.00610***
(0.00)
Index of Knowledge Distribution (1968) 0.00438***
(0.00)
Index of Knowledge Distribution (1978) 0.00538***
(0.00)
Index of Knowledge Distribution (1988) 0.00405***
(0.00)
Index of Knowledge Distribution (1998) 0.00435***
(0.00)
Number of Observations 35 37 39 40 40 43 46 53 53 62 71 92 100 101 116
R-squared 0.341 0.323 0.379 0.409 0.443 0.425 0.398 0.409 0.355 0.321 0.357 0.288 0.14 0.197 0.202
* p<0.05, ** p<0.01, *** p<0.001
19
TABLE 2A - Persistance of Equality of Opportunity in History
Regression Dependent Variable: Human Opportunity Index - Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS
Index of Knowledge Distribution (1858) 0.782***
(0.18)
Index of Knowledge Distribution (1868) 0.774***
(0.17)
Index of Knowledge Distribution (1878) 0.756***
(0.16)
Index of Knowledge Distribution (1888) 0.735***
(0.16)
Index of Knowledge Distribution (1898) 0.762***
(0.15)
Index of Knowledge Distribution (1908) 0.855***
(0.14)
Index of Knowledge Distribution (1918) 0.890***
(0.14)
Index of Knowledge Distribution (1928) 0.891***
(0.14)
Index of Knowledge Distribution (1938) 0.881***
(0.14)
Index of Knowledge Distribution (1948) 0.632***
(0.14)
Index of Knowledge Distribution (1958) 0.765***
(0.13)
Index of Knowledge Distribution (1968) 0.723***
(0.14)
Index of Knowledge Distribution (1978) 0.725***
(0.15)
Index of Knowledge Distribution (1988) 0.822***
(0.15)
Index of Knowledge Distribution (1998) 0.801***
(0.19)
Number of Observations 24 26 28 29 29 33 34 39 38 41 44 45 51 51 59
R-squared 0.455 0.46 0.463 0.455 0.493 0.55 0.56 0.543 0.52 0.339 0.457 0.397 0.334 0.387 0.242
* p<0.05, ** p<0.01, *** p<0.001
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
20
Table 2B - Persistance of Equality of Opportunity in History
Regression Dependent Variable: Dissimilarity Index - Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS OLS
Index of Knowledge Distribution (1858) -0.258**
(0.07)
Index of Knowledge Distribution (1868) -0.253**
(0.07)
Index of Knowledge Distribution (1878) -0.246***
(0.06)
Index of Knowledge Distribution (1888) -0.235***
(0.06)
Index of Knowledge Distribution (1898) -0.243***
(0.06)
Index of Knowledge Distribution (1908) -0.292***
(0.06)
Index of Knowledge Distribution (1918) -0.305***
(0.06)
Index of Knowledge Distribution (1928) -0.302***
(0.06)
Index of Knowledge Distribution (1938) -0.297***
(0.06)
Index of Knowledge Distribution (1948) -0.207***
(0.05)
Index of Knowledge Distribution (1958) -0.254***
(0.05)
Index of Knowledge Distribution (1968) -0.234***
(0.05)
Index of Knowledge Distribution (1978) -0.258***
(0.05)
Index of Knowledge Distribution (1988) -0.275***
(0.06)
Index of Knowledge Distribution (1998) -0.266**
(0.08)
Number of Observations 24 26 28 29 29 33 34 39 38 41 44 45 51 51 59
R-squared 0.362 0.361 0.367 0.354 0.382 0.448 0.466 0.446 0.423 0.268 0.387 0.323 0.318 0.325 0.161
* p<0.05, ** p<0.01, *** p<0.001 21
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
Table 3 - Basic Results for Development Outcomes ( Ordinary Least Squares)
Equality of Opportunity Measures versus Inequality of Outcomes Measures
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
OLS OLS OLS (Comparison Sample) OLS OLS
Human Opportunity Index* 0.038*** 0.038*** 0.042***
(0.004) (0.005) (0.004)
Gini Index, Average 1960-2010 -0.050*** -0.047** 0.005 -0.005
(0.013) (0.016) (0.013) (0.012)
Americas - LAC plus Canada and United States 0.656**
(0.191)
Europe and Central Asia 0.273
(0.182)
Middle East and Africa 1.101
(0.738)
constant 7.163*** 10.140*** 11.308*** 6.915*** 6.664***
(0.287) (0.538) (0.580) (0.675) (0.664)
R-sqr 0.587 0.093 0.135 0.599 0.647
Number of Observations 63 152 59 59 59
0.000 0.000 0.000 0.000 0.000
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
OLS OLS OLS (Comparison Sample) OLS OLS
Dissimilarity Index* -0.094*** -0.090*** -0.097***
(0.012) (0.013) (0.013)
Gini Index, Average 1960-2010 -0.050*** -0.047** -0.004 -0.018
(0.013) (0.016) (0.013) (0.013)
Americas - LAC plus Canada and United States 0.624*
(0.271)
Europe and Central Asia 0.159
(0.225)
Middle East and Africa 0.863
(0.832)
constant 10.672*** 10.140*** 11.308*** 10.706*** 11.030***
(0.156) (0.538) (0.580) (0.444) (0.468)
R-sqr 0.508 0.093 0.135 0.522 0.557
Number of Observations 63 152 59 59 59
* p<0.05, ** p<0.01, *** p<0.001
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
22
Table 4 - Basic results for Development Outcomes (Instrumental Variables - Log of Wheat Sugar Sustainability)
Human Opportunity Index
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
IV IV IV Excluding Americas IV
Human Opportunity Index* 0.035*** 0.033** 0.040*** 0.034***
(0.006) (0.012) (0.009) (0.008)
WDI Gini Index - Average for 1960-2010 -0.008
(0.021)
Americas - LAC plus Canada and United States 0.465
(0.302)
Europe and Central Asia 0.357
(0.259)
Middle East and Africa 0.136
(0.433)
constant 7.243*** 7.696*** 6.852*** 6.997***
(0.425) (1.477) (0.610) (0.621)
Number of Observations 49 46 39 49
F-statistics from first stage 23.43 20.58 14.51 7.87
D-Index
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
IV IV IV Excluding Americas IV
D-Index* -0.097*** -0.086** -0.122*** -0.091***
(0.019) (0.034) (0.028) (0.023)
WDI Gini Index - Average for 1960-2010 -0.012
0.019
Americas - LAC plus Canada and United States 0.517
(0.375)
Europe and Central Asia 0.424
(0.315)
Middle East and Africa 0.013
(0.504)
constant 10.590*** 10.910*** 10.770*** 10.151***
(0.219) 0.423 (0.267) (0.348)
Number of Observations 49 49 39 49
F-statistics from first stage 19.6 19.95 10.33 6.37
* p<0.05, ** p<0.01, *** p<0.001
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
Gini Index
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
IV IV IV Excluding Americas IV
Gini* -0.157*** 0.078 -0.246*** -0.295**
(0.030) (0.071) (0.044) (0.099)
Human Opportunity Index* 0.061**
(0.018)
Americas - LAC plus Canada and United States 4.286**
(1.335)
Europe and Central Asia -0.126
(0.746)
Middle East and Africa 0.872
(0.957)
constant 14.526*** 2.732 17.418*** 19.001***
(1.199) (3.682) (1.656) (3.763)
Number of Observations 112 48 89 112
F-statistics from first stage 57.27 15.09 37.44 42.47
* p<0.05, ** p<0.01, *** p<0.001
*Average 1960-2010
23
Table 5 - Basic results for Development Outcomes . (Instrumental Variables - Share of Tropical Land)
Human Opportunity Index
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
IV IV IV Excluding Americas IV
Human Opportunity Index* 0.038*** 0.050*** 0.049** 0.039***
(0.01) (0.01) (0.02) (0.01)
WDI Gini Index - Average for 1960-2010 0.039*
(0.02)
Americas - LAC plus Canada and United States 0.901**
(0.31)
Europe and Central Asia 0.294
(0.75)
Middle East and Africa 0.133
(0.29)
constant 6.154*** 4.126*** 5.704*** 5.797***
(0.29) (0.66) (0.32) (0.37)
Number of Observations 70 68 53 70
F-statistics from first stage 11.776 9.648 9.19 6.055
D-Index
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
IV IV IV Excluding Americas IV
D-Index* -0.067*** -0.084*** -0.075*** -0.083***
(0.02) (0.02) (0.02) (0.02)
WDI Gini Index - Average for 1960-2010 0.039**
(0.01)
Americas - LAC plus Canada and United States 0.992**
(0.30)
Europe and Central Asia -0.053
(0.69)
Middle East and Africa 0.379
(0.26)
constant 8.789*** 7.485*** 8.791*** 8.734***
(0.41) (0.80) (0.49) (0.50)
Number of Observations 70 68 53 70
F-statistics from first stage 18.386 15.004 17.007 8.216
* p<0.05, ** p<0.01, *** p<0.001
*Completing Six Years of Education on Time - HHS
Gini Index
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
IV IV IV Excluding Americas IV
Gini* -0.178*** -0.028 -0.265*** -0.487
(0.03) (0.04) (0.04) (0.28)
Human Opportunity Index* 0.031***
(0.01)
Americas - LAC plus Canada and United States 7.026
(3.76)
Europe and Central Asia -1.133
(1.77)
Middle East and Africa 2.467
(2.17)
constant 15.285*** 7.576*** 18.116*** 26.001*
(1.12) (1.65) (1.62) (10.52)
Number of Observations 142 68 116 142
F-statistics from first stage 78.67 6.656 49.503 3.01
* p<0.05, ** p<0.01, *** p<0.001
*Average 1960-2010
24
Table 6A - Basic results for Development Outcomes . (OLS and Instrumental Variables using Log of Wheat Sugar Sustainability)
Human Opportunity Index controlling for Gini Index
Regression Dependent Variable: Institutional Index, Average WBGI 2009
OLS OLS (Comparison Sample) OLS IV IV IV
Human Opportunity Index* 0.775*** 0.783*** 0.806*** 0.842*** 0.890***
(0.07) (0.09) (0.12) (0.23) (0.14)
Gini Index* -1.014** 0.052 0.108
(0.31) (0.23) (0.46)
Americas - LAC plus Canada and United States 12.512*
(6.06)
Europe and Central Asia 3.288
(4.90)
Middle East and Africa 7.808
(5.88)
constant 18.992*** 106.242*** 16.461 15.907* 9.649 5.27
(5.00) (11.28) (12.32) (7.84) (30.37) (10.17)
R-sqr 0.659 0.162 0.658
Number of Observations 63 59 59 49 49 49
Wald F-statistics from first stage 21.945 6.304 9.514
Regression Dependent Variable: Infant Mortality
OLS OLS (Comparison Sample) OLS IV IV IV
Human Opportunity Index* -0.358*** -0.355*** -0.436*** -0.538*** -0.510***
(0.03) (0.04) (0.06) (0.09) (0.08)
Gini Index* 0.515*** 0.006 -0.308*
(0.14) (0.11) (0.14)
Americas - LAC plus Canada and United States -3.469
(4.11)
Europe and Central Asia 1.704
(3.33)
Middle East and Africa -4.663
(4.15)
constant 34.486*** -7.145 34.234*** 40.159*** 57.996*** 44.950***
(2.38) (5.16) (6.03) (4.70) (10.37) (6.57)
R-sqr 0.649 0.194 0.645
Number of Observations 61 58 58 49 49 49
Wald F-statistics from first stage 21.945 6.304 9.514
D-Index controlling for Gini Index
Regression Dependent Variable: Institutional Index, Average WBGI 2009
OLS OLS (Comparison Sample) OLS IV IV IV
Dissimilarity Index* -1.853*** -1.762*** -2.221*** -2.219** -2.383***
(0.22) (0.26) (0.46) (0.76) (0.56)
Gini Index* -1.014** -0.165 -0.002
(0.31) (0.26) (0.47)
Americas - LAC plus Canada and United States 13.884
(6.97)
Europe and Central Asia 5.049
(5.27)
Middle East and Africa 4.586
(6.24)
constant 89.681*** 106.242*** 94.410*** 92.457*** 92.523*** 87.858***
(2.87) (11.28) (8.56) (4.82) (10.73) (6.69)
R-sqr 0.544 0.162 0.544
Number of Observations 63 59 59 49 49 49
Wald F-statistics from first stage 14.806 4.999 6.916
Regression Dependent Variable: Infant Mortality
OLS OLS (Comparison Sample) OLS IV IV IV
Dissimilarity Index* 0.866*** 0.805*** 1.203*** 1.420*** 1.367***
(0.10) (0.12) (0.25) (0.39) (0.34)
Gini Index* 0.515*** 0.108 -0.237
(0.14) (0.12) (0.20)
Americas - LAC plus Canada and United States -4.256
(3.73)
Europe and Central Asia 0.693
(2.39)
Middle East and Africa -2.815
(3.93)
constant 1.776 -7.145 -1.243 -1.3 4.976 -2.432
(1.36) (5.16) (3.97) (1.94) (4.72) (3.52)
R-sqr 0.551 0.194 0.553
Number of Observations 61 58 58 49 49 49
Wald F-statistics from first stage 14.806 4.999 6.916
* p<0.05, ** p<0.01, *** p<0.001
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
*Gini Index: Average 1960-2010
25
Table 6B - Basic results for Development Outcomes. (OLS and Instrumental Variables using Share of Tropical Land)
Human Opportunity Index controlling for Gini Index
Regression Dependent Variable: Institutional Index, Average WBGI 2009
OLS OLS (Comparison Sample) OLS IV IV IV
Human Opportunity Index* 0.348*** 0.378*** 0.303 0.536* 0.373
(0.06) (0.08) (0.21) (0.22) (0.24)
Gini Index* 0.34 0.32 0.35
(0.23) (0.20) (0.23)
Americas - LAC plus Canada and United States 10.483
(6.28)
Europe and Central Asia 0.768
(13.76)
Middle East and Africa 3.378
(4.68)
constant 25.313*** 19.555 11.044 25.728*** 5.237 19.492**
(2.57) (10.26) (9.05) (5.15) (10.37) (6.44)
R-sqr 0.268 0.03 0.283
Number of Observations 82 74 74 70 68 70
Wald F-statistics from first stage 11.776 9.648 6.055
Regression Dependent Variable: Infant Mortality
OLS OLS (Comparison Sample) OLS IV IV IV
Human Opportunity Index* -0.999*** -1.178*** -1.036** -1.183*** -0.791*
(0.11) (0.14) (0.35) (0.33) (0.39)
Gini Index* (0.47) (0.39) (0.42)
(0.51) (0.36) (0.49)
Americas - LAC plus Canada and United States -21.276
(13.41)
Europe and Central Asia -8.194
(20.76)
Middle East and Africa 20.969*
(8.94)
constant 87.795*** 82.214*** 108.719*** 88.882*** 111.057*** 77.130***
(4.40) (22.94) (16.53) (9.17) (18.81) (9.46)
R-sqr 0.506 0.012 0.512
Number of Observations 82 74 74 70 68 70
Wald F-statistics from first stage 11.776 9.648 6.055
Regression Dependent Variable: Malnutrition
OLS OLS (Comparison Sample) OLS IV IV IV
Human Opportunity Index* -0.275*** -0.278*** -0.365** -0.453*** -0.424*
(0.05) (0.05) (0.11) (0.12) (0.17)
Gini Index* -0.384* -0.402** -0.430*
(0.16) (0.13) (0.16)
Americas - LAC plus Canada and United States -14.360**
(5.21)
Europe and Central Asia -8.778
(8.82)
Middle East and Africa -11.196**
(3.53)
constant 25.389*** 35.754*** 43.137*** 27.308*** 48.249*** 38.653***
(1.75) (7.24) (6.12) (2.95) (7.79) (4.36)
R-sqr 0.296 0.082 0.385
Number of Observations 66 65 65 62 61 62
Wald F-statistics from first stage 11.805 11.248 5.528
* p<0.05, ** p<0.01, *** p<0.001
*Completing Six Year of Education on Time, Household Survey Data
*Gini Index: Average 1960-2010
26
Table 7 - Magnitude of Effect on Development Outcomes
Human Opportunity Index - Average Mathematics, Reading and Science Outcomesfor Level 2 - PISA 2009
Dependent Variable Coefficient on HOI in IV Change in dependent variable Ratio to 1 standard deviation % change as a result of % change as a result of
regression (for whole sample in response to 1 standard dependent variable a 1 point increase in HOI a 1 % increase in HOI
without regional dummies) deviation change in HOI
Log of GDP per capita, Average 2005-2010 0.035 0.773 0.718 3.50 2.31
Institutional Index, Average WBGI 2009 0.806 17.8 0.814 0.82 0.54
Infant Mortality -0.436 -9.6 -0.956 -1.03 -0.68
D-Index - Average Mathematics, Reading and Science Outcomesfor Level 2 - PISA 2009
Dependent Variable Coefficient on HOI in IV Change in dependent variable Ratio to 1 standard deviation % change as a result of % change as a result of
regression (for whole sample in response to 1 standard dependent variable a 1 point increase of D-Index a 1 % increase in HOI
without regional dummies) deviation change in HOI
Log of GDP per capita, Average 2005-2010 -0.097 -0.827 -0.767 -9.70 -1.02
Institutional Index, Average WBGI 2009 -2.221 -18.930 -0.865 -2.27 -0.24
Infant Mortality 1.203 10.253 1.017 2.85 0.30
Human Opportunity Index - Completing Six Year of Education on Time
Dependent Variable Coefficient on HOI in IV Change in dependent variable Ratio to 1 standard deviation % change as a result of % change as a result of
regression (for whole sample in response to 1 standard dependent variable a 1 point increase in HOI a 1 % increase in HOI
without regional dummies) deviation change in HOI
Log of GDP per capita, Average 2005-2010 0.038 0.910 0.803 3.76 0.99
Infant Mortality -1.036 -25.079 -0.646 -0.63 -0.16
Malnutrition -0.365 -8.836 -0.773 -0.84 -0.22
D-Index - Completing Six Year of Education on Time
Dependent Variable Coefficient on HOI in IV Change in dependent variable Ratio to 1 standard deviation % change as a result of % change as a result of
regression (for whole sample in response to 1 standard dependent variable a 1 point increase of D-Index a 1 % increase in HOI
without regional dummies) deviation change in Dindex
Log of GDP per capita, Average 2005-2010 -0.067 -0.894 -0.789 -6.70 -1.65
Infant Mortality 1.846 24.641 0.635 1.12 0.28
Malnutrition 0.63 8.409 0.736 1.46 0.36
27
Table 8A - Robustness Checks: Effect of Equality of Opportunity on Economic Development
Human Opportunity Index - Average Mathematics, Reading and Science Outcomesfor Level 2 - PISA 2009
Controlling for Ethnic Fractionalization
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
Index of Ethnic Fractionalization (0-Low to 1-high) -2.505*** 0.343 -1.075
(0.43) (0.47) (0.66)
Human Opportunity Index* 0.040*** 0.028**
(0.01) (0.01)
constant 9.420*** 6.942*** 8.054***
(0.22) (0.44) (0.81)
R-sqr 0.158 0.577
Number of Observations 183 60 48
Wald F-statistics from first stage 13.591
Controlling for Legal Origin
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
Human Opportunity Index* 0.038*** 0.043***
(0.00) (0.01)
British Legal System -0.344 0.658*** 0.673**
(0.36) (0.17) (0.22)
French Legal System -0.467 0.579*** 0.626***
(0.32) (0.14) (0.15)
Germany Legal System 2.267** 0.692** 0.606
(0.72) (0.22) (0.33)
Scandinavian Legal System 2.653*** 1.082*** 0.975***
(0.72) (0.22) (0.25)
constant 8.246*** 6.545*** 6.252***
(0.26) (0.20) (0.35)
R-sqr 0.199 0.875
Number of Observations 142 55 48
Wald F-statistics from first stage 21.485
Controlling for Share of Tropical Land
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
% land area in geographical tropics -1.927*** 0.075 -0.237
(0.23) (0.33) (0.64)
Human Opportunity Index* 0.038*** 0.031*
(0.01) (0.02)
constant 9.116*** 7.133*** 7.536***
(0.15) (0.36) (1.12)
R-sqr 0.315 0.58
Number of Observations 158 59 49
Wald F-statistics from first stage 3.306
Controlling for Latitud
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
latitude of country centroid 0.030*** 0 0.002
(0.01) (0.00) (0.00)
Human Opportunity Index* 0.038*** 0.034***
(0.01) (0.01)
constant 7.565*** 7.179*** 7.253***
(0.15) (0.30) (0.44)
R-sqr 0.207 0.58
Number of Observations 158 59 49
Wald F-statistics from first stage 17.839
Controlling for Longitude
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
longitude of country centroid -0.002 -0.003 -0.003**
(0.00) (0.00) (0.00)
Human Opportunity Index* 0.039*** 0.036***
(0.00) (0.01)
constant 8.250*** 7.154*** 7.242***
(0.14) (0.29) (0.37)
R-sqr 0.006 0.599
Number of Observations 158 59 49
Wald F-statistics from first stage 21.201
28
* p<0.05, ** p<0.01, *** p<0.001
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
Table 8B - Robustness Checks: Effect of Equality of Opportunity on Economic Development
Dissimilarity Index - Average Mathematics, Reading and Science Outcomesfor Level 2 - PISA 2009
Controlling for Ethnic Fractionalization
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
Index of Ethnic Fractionalization (0-Low to 1-high) -2.505*** 0.192 -1.004
(0.43) (0.51) (0.73)
Dissimilarity Index* -0.095*** -0.079*
(0.01) (0.03)
constant 9.420*** 10.622*** 10.714***
(0.22) (0.20) (0.19)
R-sqr 0.158 0.496
Number of Observations 183 60 48
Wald F-statistics from first stage 11.346
Controlling for Legal Origin
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
Dissimilarity Index* -0.092*** -0.115***
(0.01) (0.02)
British Legal System -0.348 0.679** 0.600*
(0.36) (0.20) (0.29)
French Legal System -0.494 0.489** 0.548**
(0.32) (0.16) (0.19)
Germany Legal System 2.213** 0.852** 0.682*
(0.72) (0.25) (0.31)
Scandinavian Legal System 2.599*** 1.193*** 1.016***
(0.72) (0.25) (0.25)
constant 8.300*** 10.070*** 10.342***
(0.27) (0.16) (0.24)
R-sqr 0.2 0.82
Number of Observations 142 55 48
Wald F-statistics from first stage 12.814
Controlling for Share of Tropical Land
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
% land area in geographical tropics -1.927*** -0.119 -0.207
(0.23) (0.35) (0.66)
Dissimilarity Index* -0.090*** -0.088*
(0.01) (0.04)
constant 9.116*** 10.623*** 10.520***
(0.15) (0.17) (0.37)
R-sqr 0.315 0.503
Number of Observations 158 59 49
Wald F-statistics from first stage 2.313
Controlling for Latitude
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
latitude of country centroid 0.030*** 0.002 0.003
(0.01) (0.00) (0.00)
Dissimilarity Index* -0.089*** -0.093***
(0.01) (0.02)
constant 7.565*** 10.530*** 10.451***
(0.15) (0.26) (0.35)
R-sqr 0.207 0.505
Number of Observations 158 59 49
Wald F-statistics from first stage 11.074
Controlling for Longitud
Regression Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
longitude of country centroid -0.002 -0.002 -0.003*
(0.00) (0.00) (0.00)
Dissimilarity Index* -0.094*** -0.099***
(0.01) (0.02)
constant 8.250*** 10.684*** 10.650***
(0.14) (0.17) (0.22)
R-sqr 0.006 0.517
Number of Observations 158 59 49
Wald F-statistics from first stage 14.576
* p<0.05, ** p<0.01, *** p<0.001 29
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
Table 9A - Robustness Checks: Effect of Equality of Opportunity on Institutional Quality
Human Opportunity Index - Average Mathematics, Reading and Science Outcomesfor Level 2 - PISA 2009
Controlling for Ethnic Fractionalization
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
Index of Ethnic Fractionalization (0-Low to 1-high) -44.247*** 0.073 -9.338
(6.76) (8.06) (11.02)
Human Opportunity Index* 0.783*** 0.740***
(0.09) (0.17)
constant 67.794*** 18.444* 23.131
(3.44) (7.60) (14.37)
R-sqr 0.188 0.658
Number of Observations 187 60 48
Wald F-statistics from first stage 13.591
Controlling for Legal Origin
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
Human Opportunity Index* 0.762*** 0.957***
(0.08) (0.12)
British Legal System 2.821 9.493* 7.547
(5.75) (4.29) (4.46)
French Legal System -6.042 9.046* 11.288*
(5.14) (3.54) (4.92)
Germany Legal System 42.788*** 10.966 7.406
(11.44) (5.54) (8.22)
Scandinavian Legal System 51.321*** 19.569*** 16.394**
(11.44) (5.53) (4.95)
constant 44.444*** 11.598* -1.385
(4.21) (5.37) (9.17)
R-sqr 0.239 0.79
Number of Observations 144 55 48
Wald F-statistics from first stage 21.485
Controlling for Share of Tropical Land
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
% land area in geographical tropics -26.318*** 1.676 12.03
(3.92) (5.77) (9.74)
Human Opportunity Index* 0.794*** 1.005***
(0.09) (0.23)
constant 58.603*** 17.599** 1.051
(2.65) (6.33) (16.23)
R-sqr 0.219 0.655
Number of Observations 163 59 49
Wald F-statistics from first stage 3.306
Controlling for Latitud
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
latitude of country centroid 0.376*** -0.09 -0.119
(0.08) (0.07) (0.10)
Human Opportunity Index* 0.830*** 0.878***
(0.08) (0.15)
constant 37.923*** 18.646*** 15.343
(2.63) (5.13) (7.67)
R-sqr 0.12 0.665
Number of Observations 163 59 49
Wald F-statistics from first stage 17.839
Controlling for Longitude
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
longitude of country centroid -0.043 -0.055* -0.082*
(0.04) (0.03) (0.03)
Human Opportunity Index* 0.803*** 0.821***
(0.07) (0.11)
constant 46.779*** 18.086*** 15.866*
(2.21) (5.04) (7.11)
R-sqr 0.008 0.678
Number of Observations 163 59 49
Wald F-statistics from first stage 21.201
* p<0.05, ** p<0.01, *** p<0.001
30
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
Table 9B - Robustness Checks: Effect of Equality of Opportunity on Institutional Quality
Dissimilarity Index - Average Mathematics, Reading and Science Outcomesfor Level 2 - PISA 2009
Controlling for Ethnic Fractionalization
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
Index of Ethnic Fractionalization (0-Low to 1-high) -44.247*** -4.193 -7.488
(6.76) (9.35) (13.41)
Dissimilarity Index* -1.794*** -2.069**
(0.26) (0.61)
constant 67.794*** 90.581*** 93.098***
(3.44) (3.57) (4.32)
R-sqr 0.188 0.541
Number of Observations 187 60 48
Wald F-statistics from first stage 11.346
Controlling for Legal Origin
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
Dissimilarity Index* -1.744*** -2.573***
(0.23) (0.55)
British Legal System 2.821 10.711* 5.979
(5.75) (5.10) (5.98)
French Legal System -6.042 7.527 9.748
(5.14) (4.19) (6.76)
Germany Legal System 42.788*** 15.047* 9.146
(11.44) (6.50) (8.12)
Scandinavian Legal System 51.321*** 22.728** 17.319**
(11.44) (6.53) (5.42)
constant 44.444*** 79.935*** 89.522***
(4.21) (4.08) (6.41)
R-sqr 0.239 0.703
Number of Observations 144 55 48
Wald F-statistics from first stage 12.814
Controlling for Share of Tropical Land
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
% land area in geographical tropics -26.318*** -3.104 12.987
(3.92) (6.55) (17.30)
Dissimilarity Index* -1.792*** -2.815**
(0.26) (1.04)
constant 58.603*** 89.347*** 96.860***
(2.65) (3.14) (8.55)
R-sqr 0.219 0.538
Number of Observations 163 59 49
Wald F-statistics from first stage 2.313
Controlling for Latitude
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
latitude of country centroid 0.376*** -0.041 -0.102
(0.08) (0.08) (0.11)
Dissimilarity Index* -1.901*** -2.392***
(0.25) (0.58)
constant 37.923*** 91.473*** 97.848***
(2.63) (4.83) (8.69)
R-sqr 0.12 0.539
Number of Observations 163 59 49
Wald F-statistics from first stage 11.074
Controlling for Longitud
Regression Dependent Variable: Institutions, Average WBGI 2009
Instrument: Log of Wheat Sugar Sustainability OLS OLS IV
longitude of country centroid -0.043 -0.048 -0.087*
(0.04) (0.03) (0.04)
Dissimilarity Index* -1.893*** -2.267***
(0.23) (0.42)
constant 46.779*** 90.692*** 93.971***
(2.21) (3.17) (4.34)
R-sqr 0.008 0.554
Number of Observations 163 59 49
Wald F-statistics from first stage 14.576
* p<0.05, ** p<0.01, *** p<0.001
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009 31
Table 10 - Overidentification Test
A) GDP per capita B) Institutional Quality
Dependent Variable: Logaritm of Per Capita Income, Average 2005-2010 Dependent Variable: Institutions, Average WBGI 2009
IV IV
Human Opportunity Index* - PISA Test Scores 0.036*** Human Opportunity Index* - PISA Test Scores 0.749***
0.005 0.109
Constant 7.17*** Constant 19.61**
0.354 7.107
Number of Observations 49 Number of Observations 49
Wald F Statistic (First Stage) 46.515 Wald F Statistic (First Stage) 46.515
Overidentification test p-value: Overidentification test p-value:
Hansen J Statistic 0.668 Hansen J Statistic 0.203
D-Index* - PISA Test Scores -0.099*** D-Index* - PISA Test Scores -2.053***
0.021 0.4308713
Constant 10.62*** Constant 90.682***
0.222 4.725435
Number of Observations 49 Number of Observations 49
Wald F Statistic (First Stage) 16.832 Wald F Statistic (First Stage) 16.832
Overidentification test p-value: Overidentification test p-value:
Hansen J Statistic 0.740 Hansen J Statistic 0.329
* p<0.05, ** p<0.01, *** p<0.001
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
Human Opportunity Index** - Six Grade on Time 0.042*** **Completing Six Year of Education on Time, Household Survey Data
0.010 C) Infant Mortality
Constant 6.06***
0.298 Dependent Variable: Infant Mortality
Number of Observations 53 IV
Wald F Statistic (First Stage) 4.853 Human Opportunity Index* - PISA Test Scores -0.367***
Overidentification test p-value: 0.057
Hansen J Statistic 0.286 Constant 35.61***
4.141
Dissimilarity Index** - Six Grade on Time -0.07*** Number of Observations 49
0.012 Wald F Statistic (First Stage) 46.515
Constant 8.98*** Overidentification test p-value:
0.280 Hansen J Statistic 0.012
Number of Observations 53
Wald F Statistic (First Stage) 10.635
Overidentification test p-value: D-Index* - PISA Test Scores 1.00***
Hansen J Statistic 0.933 0.203
* p<0.05, ** p<0.01, *** p<0.001 Constant 0.8
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009 1.815
**Completing Six Year of Education on Time, Household Survey Data Number of Observations 49
Note: two-stage least square regressions of development outcomes on inequality Wald F Statistic (First Stage) 16.832
with share of tropical land intrument in addition to log of wheat sugar suitability ratio Overidentification test p-value:
D) Malnutrition Hansen J Statistic 0.038
Dependent Variable: Malnutrition
IV
Human Opportunity Index** - Six Grade on Time -0.49*** Human Opportunity Index** - Six Grade on Time -1.16***
0.146 0.315
Constant 30.24*** Constant 89.69***
4.053 9.675
Number of Observations 48 Number of Observations 53
Wald F Statistic (First Stage) 4.405 Wald F Statistic (First Stage) 4.853
Overidentification test p-value: Overidentification test p-value:
Hansen J Statistic 0.303 Hansen J Statistic 0.128
Dissimilarity Index** - Six Grade on Time 0.843*** Dissimilarity Index** - Six Grade on Time 2.00***
0.145 0.465
Constant -3.83944 Constant 8.813
3.226 10.326
Number of Observations Number of Observations 53
Wald F Statistic (First Stage) 8.649 Wald F Statistic (First Stage) 10.635
Overidentification test p-value: Overidentification test p-value:
Hansen J Statistic 0.979 Hansen J Statistic 0.589
* p<0.05, ** p<0.01, *** p<0.001 * p<0.05, ** p<0.01, *** p<0.001
*Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009 *Average Mathematics, Reading and Science Outcomes Level 2 - PISA 2009
**Completing Six Year of Education on Time, Household Survey Data **Completing Six Year of Education on Time, Household Survey Data
32
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35
Appendix 1
Table A1 - 1 - Description of Variables
Equality of Opportunity Measures
INDICATOR NAME DESCRIPTION
A basic opportunity is defined as achieving level 2 understanding of the topics cover in
each test, Mathematics, Reading and Science. Level 2 indicates very basic understanding
of the topics covered that should be covered in class. The circumstances used are the
following: A measure of wealth, calculated using principal component methodology based
HOI - Level 2 PISA Test
on asset ownership, gender, parental education, school location and head of household
Scores
occupation. The formula to compute this index is
HOI=p ̅(1-D)
where p ̅ is the average access and D is the Dissimilarity Index (henceforth, D-Index) that
measures the inequality in access due to circumstances that are exogenous
Dindex HOI - Level 2 PISA
See the formula used to compute this formula in the text.
Test Scores
In this case the opportunity is completing six grade on time. It is considered that the
HOI, Dindex, Coverage - opportunity is met if for the population of children between 12 and 16 years old they
Completing Six Years of achieve at least six years of education. The circumstances used are: gender of the child,
Education on Time location, head of household education, per capita family income, number of children in the
household, family structure (both parents present).
In this case the opportunity is school attendance for children between 10 and 14 years
HOI, Dindex, Coverage -
old.The circumstances used are: gender of the child, location, head of household education,
School Attendance for children
per capita family income, number of children in the household, family structure (both
among 10-14 years old
parents present).
In this case the opportunity is starting the educational experience on time. It is considered
that the opportunity is met if for the population of children between 6 and 7 years old is
HOI, Dindex, Coverage -
currently attending school and this is his/her first year of education or more. The
Starting Educational
circumstances used are: gender of the child, location, head of household education, per
Experience on Time
capita family income, number of children in the household, family structure (both parents
present).
Historical Proxies for Equality of Opportunity Measures
INDICATOR NAME DESCRIPTION
Tutu Vanhanen’s index of knowledge distribution. The index is computed by
calculating the arithmetic mean of Students and Literates. Number of students:
the variable denotes how many students there are in universities and other
higher education institutions per 100.000 inhabitants of the country. Two ways
Index of Knowledge Distribution
are used to calculate the percentage of Students (%): before the year 1988 the
value 1000 of the variable Number of students is equivalent to 100% and
between the years 1988-1998 the value 5000 of the same variable is equivalent
to 100%. 4) Literates (%) (as a percentage of adult population).
36
Historical Proxies for Institutional Quality
INDICATOR NAME DESCRIPTION
Tutu Vanhanen’s measure on political competition. Measure used to denote the
electoral success of the smaller parties, i.e., the proportion of the votes won by
those parties in parliamentary and/or presidential elections, to indicate the
VHcomp
degree of competition in a given political system. This figure is calculated by
subtracting the percentage of the votes won by the largest party from 100
percent.
Tutu Vanhanen’s measure on political participation. The percentage of the
population that actually voted in these elections is used as a measure of the
degree of electoral participation. It should be noted that this percentage is
VHpart calculated from the total population, not from the adult population or from the
enfranchised population. Because these two variables are assumed to represent
different dimensions of democratization, it is plausible to assume that a
combination of the two would be a more realistic indicator of democratization
than either of them alone.
Tutu Vanhanen’s index of democracy. The index is computed by multiplying
Index of Democratization the competition and participation variables and by dividing the outcome by
100.
Revised Combined Polity Score: This variable is a modified version of the
POLITY variable added in order to facilitate the use of the POLITY regime
measure in time-series analyses. It modifies the combined annual POLITY
Polity Index score by applying a simple treatment, or ““fix,” to convert instances of
“standardized authority scores” (i.e., -66, -77, and -88) to conventional polity
scores (i.e., within the range, -10 to +10). Please See POLITY codebook for
more details
Development Outcome Measures
INDICATOR NAME DESCRIPTION
Average Indicator Institutional Quality Average for 2009 of all 6 measures of World Bank Governance Indicator. The
(WBGI) explanation of the six component is describe below. Source WGI- World Bank
Voice and Accountability: Measures the extent to which country’s citizens are
able to participate in selecting their government, as well as freedom of
Voiceacc expression, freedom of association, and a free media. Coded from -2.5 to 2.5
with higher values corresponding with better governance outcomes. Source
WGI- World Bank
Political Stability: Measures the perceptions of the likelihood that the
government will be destabilized or overthrown by unconstitutional or violent
Polstab
means, including domestic violence and terrorism. Coded from -2.5 to 2.5
with higher values corresponding with better governance outcomes. Source:
WGI- World Bank
Government Effectiveness: Measures the quality of public services, the quality
of the civil service and the degree of its independence from political pressures,
the quality of policy formulation and implementation, and the credibility of the
Govteffec
government’s commitment to such policies. Coded from -2.5 to 2.5 with higher
values corresponding with better governance outcomes. Source: WGI-World
Bank
Regulatory Quality: Measures the ability of the government to formulate and
implement sound policies and regulations that permit and promote private
Regqual
sector development. Coded from -2.5 to 2.5 with higher values corresponding
with better governance outcomes. Source: WGI-World Bank
Rule of Law: Measures the extent to which agents have confidence in and
Ruleoflaw abide by the rules of society, in particular the quality of contract enforcement,
the police, and the courts, as well as the likelihood of crime and violence.
Coded from -2.5 to 2.5 with higher values corresponding with better
37
governance outcomes. Source: WGI- World Bank
Corruption Control: Measures the extent to which public power is exercised for
private gain, including petty and grand forms of corruption, as well as
Corruptcont “capture” of the state by elites and private interests. Coded from -2.5 to 2.5
with higher values corresponding with better governance outcomes. Source:
WGI- World Bank
GDP (constant 2005 US$). Log GDP per capita is the sum of gross value
added by all resident producers in the economy plus any product taxes and
minus any subsidies not included in the value of the products. It is calculated
without making deductions for depreciation of fabricated assets or for
depletion and degradation of natural resources. Data are in constant 2005 U.S.
Log of GDP per capita
dollars. Dollar figures for GDP are converted from domestic currencies using
2005 official exchange rates. For a few countries where the official exchange
rate does not reflect the rate effectively applied to actual foreign exchange
transactions, an alternative conversion factor is used. I use the average from
2005-201 of this measure. Source: World Bank national accounts data, and
OECD National Accounts data files.
Gini index measures the extent to which the distribution of income (or, in some
cases, consumption expenditure) among individuals or households within an
economy deviates from a perfectly equal distribution. A Lorenz curve plots the
cumulative percentages of total income received against the cumulative
number of recipients, starting with the poorest individual or household. The
Gini index measures the area between the Lorenz curve and a hypothetical line
Average GINI 1960-2010
of absolute equality, expressed as a percentage of the maximum area under the
line. Thus a Gini index of 0 represents perfect equality, while an index of 100
implies perfect inequality. Source: World Bank staff estimates based on
primary household survey data obtained from government statistical agencies
and World Bank country departments. For more information and
methodology, please see PovcalNet
(http://iresearch.worldbank.org/PovcalNet/jsp/index.jsp).
Malnutrition prevalence, weight for age (% of children under 5). Prevalence of
child malnutrition is the percentage of children under age 5 whose weight for
Malnutrition age is more than two standard deviations below the median for the
international reference population ages 0–59 months. The data are based on the
WHO’s new child growth standards released in 2006. Source: World Health
Organization, Global Database on Child Growth and Malnutrition.
Mortality rate, infant (per 1,000 live births). Infant mortality rate is the number
of infants dying before reaching one year of age, per 1,000 live births in a
Infant Mortality given year. Source: Harmonized estimates of the World Health Organization,
UNICEF, and the World Bank, based mainly on household surveys, censuses,
and vital registration, supplemented by World Bank estimates based on
household surveys and vital registration.
38
Appendix 2
Computation of the HOI and D-Index
We estimate the HOI and D-Index econometrically as follows. To obtain the conditional probabilities of
access to an opportunity for each individual in the sample based on his/her circumstances, a logistic
model is estimated, linear in the parameters β, where the event I corresponds to accessing the opportunity
and x the set of circumstances:
{ = 1| = (1 , … … , )}
ln � � = �
1 − { = 1| = (1 , … … , )}
=1
where xk denotes the row vector of variables representing n circumstances and a corresponding column
vector of parameters. From the estimation of regression above, one obtains estimates of the parameters
̂, �, where m denotes the sample size. Given the estimated coefficients, one can
{ }, denoted as �
obtain for each individual in the sample his/her predicted probability of the opportunity in consideration:
̂ �
�
̂ , =
1 + � ̂ �
Using the predicted probabilities (̂ ) and sample weights ( ), we can find the predicted overall coverage
� ) as:
̂ ) and D-index (
rate (̅
̂ = � ̂,
̅
=1
1
�= ̂ = ̅ )
̂ ̅ ∑=1 �̂ ,
2
− ̅ � (Note: ̅
� = ̅ �1 −
��
An important caveat is that the list of regressors does not include any interaction terms between
circumstances (e.g. between parental education and location). Given the number of circumstances we
have (all of which are dummy variables), limited sample sizes, and the large number of countries and
opportunities for which these regressions have to be run, including interactions would lead to intractable
problems in at least some of the cases. The interaction terms are thus omitted, even though translating the
exact definition of D-Index to the logistic regression model would require including these terms. If the
interactions were included, it would result in a higher D-Index (and lower HOI), just as it would happen if
more circumstances were added. This in turn implies that the estimated D-Index for all countries and
opportunities is the lower bound of inequality of opportunities (and the estimated HOI is the upper bound)
for a given set of circumstances.
39
Table A.2-1: Summary statistics of the Variables
Variable Name N Mean Std. Dev. Min Max
Equality of Opportunity Measures
Human Opportunity Index - Level 2 PISA Test Scores 65 67.32 21.98 9.61 95.47
Dissimilarity Index - Level 2 PISA Test Scores 65 10.08 8.29 1.41 42.46
Coverage - Level 2 PISA Test Scores 65 73.02 19.92 16.53 96.83
Geometric HOI - Level 2 PISA Test Scores 65 70.16 22.24 8.99 96.58
Geometric D- Index - Level 2 PISA Test Scores 65 6.1 8.78 0.2 46.77
HOI - Completing Six Years of Education on Time 82 29.57 26.96 0.72 90.85
D-Index - Completing Six Years of Education on Time 82 22.91 13.65 1.55 65.73
Coverage - Completing Six Years of Education on Time 82 34.33 27.22 1.45 93.34
Geometric HOI - Completing Six Years of Education on Time 82 31.44 27.87 0.6 92.99
Geometric D-Index - Completing Six Years of Education on Time 82 17.38 14.79 0.09 66.1
HOI - School Attendance for children 10-14 69 74.38 20.6 13.46 98.94
D-Index - School Attendance for children 10-14 69 6.33 6.28 0.3 28.9
Coverage -School Attendance for children 10-14 69 78.27 18.49 17.88 99.24
Geometric HOI - School Attendance for children 10-14 69 77.11 19.81 14.13 99.24
Geometric D-Index - School Attendance for children 10-14 69 5.24 6.72 0 30.44
HOI - Starting Educational Experience on Time 78 48.4 29.09 3.14 99.24
D-Index - Starting Educational Experience on Time 78 11.24 8.77 0.1 38.48
Coverage - Starting Educational Experience on Time 78 52.18 28.58 4.26 99.4
Geometric HOI - Starting Educational Experience on Time 78 50.78 29.26 3.39 99.34
Geometric D-Index - Starting Educational Experience on Time 78 5.51 6.97 0 30.44
Historical Proxies for Equality of Opportunity Measures
Index of Knowledge Distribution (1858) 37 13.54 15.4 0.5 47.5
Index of Knowledge Distribution (1868) 39 15.21 15.92 0.5 48.5
Index of Knowledge Distribution (1878) 41 17.5 16.74 0.5 49.5
Index of Knowledge Distribution (1888) 42 19.43 17.25 0.5 53
Index of Knowledge Distribution (1898) 42 21.69 17.68 1 56
Index of Knowledge Distribution (1908) 47 24.85 17.8 1.5 60
Index of Knowledge Distribution (1918) 51 26.77 18.4 0.5 65
Index of Knowledge Distribution (1928) 59 29.59 19.18 0.5 66
Index of Knowledge Distribution (1938) 60 32.42 20.52 0.5 75.5
Index of Knowledge Distribution (1948) 71 33.35 21.26 1 92.5
Index of Knowledge Distribution (1958) 83 35.24 21.53 1.5 98.5
Index of Knowledge Distribution (1968) 113 34.45 25.2 0.5 99
Index of Knowledge Distribution (1978) 114 41.02 27.37 1 99.5
Index of Knowledge Distribution (1988) 145 40.8 22.14 0 99.5
Index of Knowledge Distribution (1998) 172 48.42 20.82 9.5 99.5
Development Outcomes
Log of GDP per capita at current USD - Average for 2005-2010 195 8.34 1.64 4.88 12.04
Average Indicator Institutional Quality (WBGI) 210 49.9 26.51 0.4 97.95
Infant Mortality 191 38.1 35.9 2.08 165
Malnutrition 104 16.51 12.25 0.6 43.5
40
Table A.2-2: Correlations Among Different Measures of Equality of Opportunity
HOI - Dindex - HOI - PISA- Dindex - HOI - Finish DIndex -
PISA 2009 PISA 2009 Geometric PISA- 6 on Time - Finish 6 on
Geometric Geo Time - Geo
HOI PISA 2009 1 -0.969*** 0.998*** -0.864*** 0.4156 -0.4854
p-value 0.00000 0.00000 0.00000 0.00000 0.1791 0.1097
Number of Observations 65 65 65 65 12 12
D Index - PISA 2009 -0.969*** 1 -0.969*** 0.966*** -0.4775 0.5764*
p-value 0.00000 0.00000 0.00000 0.00000 0.1164 0.0498
Number of Observations 65 65 65 65 12 12
Coverage - PISA 2009 0.998*** -0.962*** 0.998*** -0.869*** 0.39 -0.4626
p-value 0.00000 0.00000 0.00000 0.00000 0.2100 0.13
Number of Observations 65 65 65 65 12 12
HOI - Finish 6 on Time 0.4216 -0.4863 0.4594 -0.5276 0.999*** -0.851***
p-value 0.1722 0.1089 0.1329 0.0779 0.00000 0.00000
Number of Observations 12 12 12 12 82 82
DIndex - Finish 6 on Time -0.507 0.6056* -0.5429 0.6353* -0.764*** 0.978***
p-value 0.0925 0.0369 0.0681 0.0264 0.00000 0.00000
Number of Observations 12 12 12 12 82 82
Coverage - Finish 6 on Time 0.4031 -0.4604 0.4411 -0.5049 0.996*** -0.844***
p-value 0.1938 0.1321 0.1512 0.0941 0.00000 0.00000
Number of Observations 12 12 12 12 82 82
HOI - Attendance 10-14 -0.1031 0.2176 -0.1195 0.2264 0.531*** -0.613***
p-value 0.7918 0.5738 0.7594 0.558 0.00000 0.00000
Number of Observations 9 9 9 9 69 69
* p<0.05, ** p<0.01, *** p<0.001
41
Table A.2-3: Correlations Among Different Instruments
Log of Wheat Share of Legal Ethnic Longitude Latitude
Sugar Tropical Land Origin Fractional.
Sustainability
Share of Tropical Land -0.7437*** 1
p-value 0.00000
Number of Observations 115 168
Legal Origin 3 of 5 5 of 5 1
p-value
Number of Observations 109 141 144
Ethnic Fractionalization -0.3398*** 0.5020*** 3 of 5 1
p-value 0.0002 0.0000
Number of Observations 117 157 144 189
Longitude 0.1312 -0.223** 2 of 5 -0.1256 1
p-value 0.1623 0.004 0.1169
Number of Observations 115 164 141 157 164
Latitude 0.498*** -0.622*** 5 of 5 -0.335*** 0.0747 1
p-value 0.0000 0.0000 0.0000 0.3419
Number of Observations 115 164 141 157 164 164
* p<0.05, ** p<0.01, *** p<0.001
Table A.2-4: Correlations Among Different Instruments and Measures of Equality of Opportunity
Log of Wheat Share of Tropical Ethnic Latitude Longitude Legal Origin -
Sugar Ratio Land Fractionaliz. Fstat
Human Opportunity Index PISA 2009 0.5768*** -0.4873*** -0.4842*** 0.421*** 0.1402 4.62**
p-value 0.0000 0.0001 0.0001 0.0009 0.2894 0.0029
Number of Observations 49 59 60 59 59 56
D Index - PISA 2009 -0.5425*** 0.4587*** 0.4859*** -0.394*** -0.1296 3.43*
p-value 0.0000 0.0003 0.0001 0.0020 0.3278 0.0148
Number of Observations 49 59 60 59 59 56
HOI - Finish 6 on Time 0.2259 -0.441*** -0.383*** 0.0564 -0.1002 1.72
p-value 0.0972 0.0001 0.0005 0.6430 0.4091 0.1873
Number of Observations 55 70 79 70 70 64
DIndex - Finish 6 on Time -0.1639 0.449*** 0.426*** -0.1925 0.0955 3.21
p-value 0.2318 0.0001 0.0001 0.1103 0.4316 0.047*
Number of Observations 55 70 79 70 70 64
HOI - Attendance 10-14 -0.0643 -0.0831 -0.311* -0.1925 0.0955 2.38
p-value 0.6642 0.5313 0.011 0.1103 0.4316 0.1027
Number of Observations 48 59 66 70 70 54
* p<0.05, ** p<0.01, *** p<0.001
42
Table A.2-5: Effects of Geometric Measures of HOI or D-Index on Development Outcomes
Geometric Human Opportunity Index - Average Mathematics, Reading and Science Outcomes for Level 2 - PISA 2009
Dependent Variable Coefficient on HOI or D in IV Change in dependent variable Ratio to 1 standard % change as a % change as a result
regression (for whole sample in response to 1 standard deviation dependent result of a 1 of a 1 % increase in
without regional dummies) deviation change in HOI or D variable point increase in HOI or D
HOI or D
Log of GDP per capita, Average 2005-2010 0.034 0.767 0.677 3.41 2.35
Institutional Index, Average WBGI 2009 0.781 17.6 1.025 0.80 0.55
Infant Mortality -0.423 -9.5 -0.943 -1.00 -0.69
Geometric D-Index - Average Mathematics, Reading and Science Outcomes for Level 2 - PISA 2009
Log of GDP per capita, Average 2005-2010 -0.096 -0.888 -0.824 -9.56 -0.62
Institutional Index, Average WBGI 2009 -2.186 -20.301 -0.927 -2.23 -0.14
Infant Mortality 1.184 10.995 1.091 2.80 0.18
Geometric Human Opportunity Index - Completing Six Year of Education on Time
Log of GDP per capita, Average 2005-2010 0.038 0.910 0.803 3.76 0.99
Infant Mortality -1.036 -25.079 -0.646 -0.63 -0.16
Malnutrition -0.365 -8.836 -0.773 -0.84 -0.22
Geometric D-Index - Completing Six Year of Education on Time
Log of GDP per capita, Average 2005-2010 -0.066 -0.887 -0.782 -6.64 -1.63
Infant Mortality 1.829 24.418 0.629 1.11 0.27
Malnutrition 0.615 8.210 0.718 1.42 0.35
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Figure A.2-1
Opportunities and Economic Development - School Attendance
Logaritm of GDP pc at Current USD (2005-2010)
Logaritm of GDP pc at Current USD (2005-2010)
12
12
r = 0.505*** r = -0.446***
10
10
8
8
6
6
4
4
20 40 60 80 100 0 10 20 30
HOI - Attendance for 10-14 Years Old D-Index - Attendance for 10-14 Years Old
Fitted values Americas
East Asia, South Asia & Pacific Europe & Central Asia
Middle East and Africa
Figure A2-2
Opportunities and Economic Development - Start Education on Time
12
12
Logaritm of GDP pc at Current USD (2005-2010)
Logaritm of GDP pc at Current USD (2005-2010)
r = 0.479*** r = -0.516***
10
10
8
8
6
6
4
4
0 20 40 60 80 100 0 10 20 30 40
HOI - Start Educational Experience on Time D-Index - Start Educational Experience on Time
Fitted values Americas
East Asia, South Asia & Pacific Europe & Central Asia
Middle East and Africa
44