ï»¿ WPS6304
Policy Research Working Paper 6304
Inequality of Opportunity, Income
Inequality and Economic Mobility
Some International Comparisons
Paolo Brunori
Francisco H. G. Ferreira
Vito Peragine
The World Bank
Development Research Group
Poverty and Inequality Team
January 2013
Policy Research Working Paper 6304
Abstract
Despite a recent surge in the number of studies income inequality, and intergenerational mobility. The
attempting to measure inequality of opportunity in analysis finds evidence of a â€œKuznets curveâ€? for inequality
various countries, methodological differences have so of opportunity, and finds that the IEO index is positively
far prevented meaningful international comparisons. correlated with overall income inequality, and negatively
This paper presents a comparison of ex-ante measures with measures of intergenerational mobility, both in
of inequality of economic opportunity (IEO) across incomes and in years of schooling. The HOI is highly
41 countries, and of the Human Opportunity Index correlated with the Human Development Index, and its
(HOI) for 39 countries. It also examines international internal measure of inequality of opportunity yields very
correlations between these indices and output per capita, different country rankings from the IEO measure.
This paper is a product of the Poverty and Inequality Team, Development Research Group. 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 fferreira@worldbank.org, peragine.vito@gmail.com and paolo.brunori@gmail.com.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should 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
Inequality of opportunity, income inequality and economic mobility:
Some international comparisons
Paolo Brunori
Francisco H. G. Ferreira
Vito Peragine 1
Keywords: Equality of opportunity, income inequality, social mobility
JEL classification: D71, D91, I32
Sector Board: Poverty Reduction
1
Brunori and Peragine are at the University of Bari. Ferreira is with the Development Research Group at the World
Bank and IZA, Bonn. This paper was prepared for a volume on â€œThe Triple Challenge of Development: Changing the
rules in a global worldâ€?, which draws on a conference held at Mount Holyoke College in March 2012. We are
grateful to Michael Grimm, Peter Lanjouw, Branko Milanovic and Eva Paus (the editor) for various helpful
comments and suggestions. We are also grateful to Ambar Narayan and Alejandro Hoyos Suarez for help with the
data on human opportunity indices and to Tor Eriksson and Yingqiang Zhang for providing us additional estimates
for China. Ferreira would like to acknowledge support from the Knowledge for Change Program, under project
grant P132865. All errors are exclusively our own. The views expressed in this paper are those of the authors, and
they should not be attributed to the World Bank, its Executive Directors, or the countries they represent.
Correspondence: fferreira@worldbank.org, peragine.vito@gmail.com and paolo.brunori@gmail.c3om.
1. Introduction
The relationship between inequality and the development process has long been of interest, and
both directions of causality have been extensively investigated. The idea that the structural
transformation that takes place as an economy develops may lead first to rising and then to falling
inequality â€“ known as the Kuznets (1955) hypothesis â€“ was once hugely influential. The view that
inequality may, conversely, affect the rate and nature of economic growth has an equally distinguished
pedigree, dating back at least to Kaldor (1956). In the 1990s, a burgeoning theoretical literature
suggested a number of mechanisms through which wealth inequality might be detrimental to economic
growth: when combined with credit constraints and increasing returns; through political channels;
fertility effects; etc. See Voitchovsky (2009) for a recent survey of that literature.
But popular concern about inequality in developing (and developed) countries does not originate
exclusively â€“ or even primarily â€“ from its possible instrumental effects - on growth, on the growth
elasticity of poverty, on health status, on crime, or on any number of other factors that are possibly
influenced by the distribution of economic well-being. Many of those who worry about inequality do so
because they consider it â€“ or at least some of it â€“ â€œunjustâ€?. Most development economists, however,
share the broader professionâ€™s discomfort with normative concepts such as justice and, until recently
and with some distinguished exceptions, have had little to say about it.
That is a pity. Behavioral economics has taught us that notions of fairness and justice affect
individual behavior â€“ in the precise and well-documented sense that they induce sizable deviations from
the behaviors predicted by models based on the assumption of purely self-regarding preferences (e.g.
Fehr and Schmidt, 1999; Fehr and Gachter, 2000; Fehr and Fischbacher, 2003). Some recent
experimental evidence suggests that, when assessing outcome distributions, people do distinguish
between factors for which players can be held responsible, and those which are beyond their control
(Cappelen et al., 2010). If fairness matters to economic agents and alters their behavior, then
understanding fairness ought to matter even to the purest positive economist. If people assess
distributional outcomes differently depending on how much of the inequality they observe is thought to
be â€œfairâ€? or â€œunfairâ€?, then it may be useful to measure the extent to which inequality is unfair.
Efforts in this direction have already taken place. Drawing primarily on the welfare economics
literature on â€œinequality of opportunityâ€? (I. Op.), researchers have started to measure unfair inequality
in both poor and rich countries. In that literature, there is now widespread agreement on the basic
principle of what equality of opportunity refers to: inequalities due to circumstances beyond individual
control are unfair, and should be compensated for, while inequalities due to factors for which people
can be held responsible (sometimes called â€œeffortsâ€?), may be considered acceptable. But this broad
concept can be interpreted in a number of different ways, some of which have been shown to be
mutually inconsistent. And there is an array of actual indices that have been proposed to implement
these concepts, and used to measure inequality of opportunity in different countries or at different
times. The relatively high ratio of different (and incomparable) approaches to actual empirical
applications means that it has so far been difficult to make a reasonably broad comparison of inequality
of opportunity levels across countries.
2
This paper takes a first step towards making such a comparison, by drawing on two specific
approaches that have been relatively widely used. The first is the measurement of ex ante inequality of
economic opportunity. The second is the measurement of (childrenâ€™s) access to basic services adjusted
for differences associated with circumstances â€“ commonly known as the Human Opportunity Index
(HOI). The latter is not a measure of inequality of opportunity per se; it is better seen as a development
index that is designed to be sensitive to inequality of opportunity. Our objective is a modest one: we
collect and summarize the results of empirical applications of these two measures to as many countries
as possible, and describe the correlations between these measures and a number of other indicators of
interest, including GDP per capita, overall income inequality, and two measures of intergenerational
mobility.
We hope that the collected evidence on the degree of inequality of opportunity in different
countries, and its pattern of association with other variables, might help to shed light on the nature of
the (often increasing) inequalities observed today in many areas of the world. The paper is organized as
follows. Section 2 contains a brief overview of the concepts and approaches to the measurement of
inequality of opportunity. This provides essential background not only for an understanding of where
the inequality of opportunity measures come from and what they do, but also of what they do not do,
and the concepts they do not capture. Section 3 contains our review of inequality of opportunity
measures for 41 countries, and examines how they correlate with other indicators. Section 4 presents a
comparison of HOI applications across 39 developing countries, and how it correlates with other
relevant indices, including the United Nationsâ€™ Human Development Index (HDI). Section 5 contains a
discussion of the results and some concluding remarks.
2. Concepts and measurement
The economics literature on inequality of opportunity builds explicitly on a few key contributions
from philosophy, including Dworkin (1981a, b), Arneson (1989) and Cohen (1989). The basic idea, as
noted above, is that outcomes that are valued by all or most members of society (such as income,
wealth, health status, etc.), and which are often termed â€œadvantagesâ€?, are determined by two types of
factors: those for which the individual can be held responsible, and those for which she cannot. 2
Inequalities due to the former - which we will call â€œeffortsâ€? - are normatively acceptable, whereas those
due to the latter - which we call â€œcircumstancesâ€? - are unfair, and should in principle be eliminated. 3
However, as economists sought to formalize this idea so as to make it more precise, they quickly
faced some fundamental choices, both conceptual and methodological. Some of these are actually
choices between mutually inconsistent principles or approaches. Following Fleurbaey (1998, 2008) and
Fleurbaey and Peragine (2012) we focus on two such fundamental dichotomies: the distinction between
2
Which factors belong to which category is a subject of considerable debate in the philosophical literature.
3
The terminology of advantages, circumstances and efforts follows Roemer (1998). Other authors prefer the term
â€œresponsibility factorsâ€? to efforts, for example.
3
the compensation and reward principles, and the distinction between the ex-ante and ex-post
approaches. 4
In order to understand these distinctions, it is helpful to introduce the concepts of types and
tranches, using some simple notation. For simplicity, consider the basic set up in which there is a single
advantage y and a vector of discrete circumstance variables, C. Let effort be measured by a continuous
scalar variable e. Then suppose that all determinants of y, including various different forms of luck, can
be classified into either the vector C or the scalar index e. The theory of inequality of opportunity is built
upon the idea that these circumstances and efforts determine advantage, as follows:
y = g(C, e) (1)
Because C is a vector with a finite number of elements, each of which is discrete, we can partition
the population into a set of groups that are fully homogeneous in terms of circumstances. Formally, this
is the partition Î = {T1 , T2 ,...,TK } such that Ci = C j , âˆ€i, j i âˆˆ Tk , j âˆˆ Tk , âˆ€k . Each of these subgroups,
indexed by k, is called a type Tk , and clearly individuals within each type can differ only in their effort
level eik. Let Fk (y) denote the advantage distribution in type k and í µí±ží µí±˜ denote its population share. The
overall distribution for the population as a whole is í µí°¹ (í µí±¦) = âˆ‘í µí°¾
í µí±˜=1 í µí±ží µí±˜ í µí°¹í µí±˜ (í µí±¦).
Effort variables have been treated in a number of different ways in the literature. In this
exposition, we follow the influential approach due to Roemer (1993, 1998), in which effort is treated as
unobserved. Roemer argues that the absolute level of effort í µí±’í µí±–í µí±˜ is not actually an appropriate basis for
comparison across individuals, because the average level of effort expended in each type may vary. The
children of well-educated parents may on average dedicate greater effort to their studies than those of
less educated parents, for example. Roemer argues that such average differences in effort levels should
be treated as characteristics of the types, rather than of the individuals â€“ effectively as unobserved
circumstances. He proposes that effort comparisons be based instead on relative effort, which he
equates with the percentile of the distribution of advantage within each type: í µí±?í µí±˜ = í µí°¹í µí±˜ (í µí±¦). This is known
in the literature as the Roemer Identification Assumption. It naturally gives rise to an alternative
partition of the population, by grouping in separate tranches all those who are at identical percentiles of
the advantage distribution, across types: Î˜ = {R1 , R2 ,..., RP } .
So we have a population of individuals, each of whom is fully characterized by the triple (y, C, e).
This population can be partitioned in two ways: into types (within which everyone shares the same
circumstances), and into tranches (within which everyone shares the same degree of effort). Figure 1
provides a simple illustration, in which there are three types, T1, T2 and T3. The (inverse) cumulative
-1
advantage distribution of each type is given by Fk , and their means are indicated on the vertical axis,
where advantages (or incomes) are mapped. Tranches are not shown in the figure but, under the
Roemer Identification Assumption, they would correspond to â€˜verticalâ€™ sections across the three type
distributions, at each percentile pk on the horizontal axis. With this very basic toolkit, we are ready to
4
This section is intended as a brief non-technical overview. It cannot â€“ and is not intended to â€“ do justice to the
recent literature. Two excellent full-length reviews of the literature on the measurement of I. Op. are Pignataro
(2011) and Ramos and van de Gaer (2012).
4
understand the distinction between the compensation and reward principles, and between ex-ante and
ex-post approaches.
The compensation principle states the first basic idea of inequality of opportunity as follows:
"inequalities due to circumstances should be eliminated". There are two main versions of this principle
in the literature. The ex-ante approach to compensation (associated with van de Gaer, 1993) seeks to
evaluate â€“ i.e. attribute a numerical value vi to â€“ the opportunity set faced by individual i. Inequality of
opportunity would then be eliminated when all types faced opportunity sets with the same value:
vi = v, âˆ€i . If that did not hold, inequality of opportunity could be measured by computing an
appropriate inequality measure I(.) over the counterfactual distribution where each personâ€™s advantage
is replaced by the value of his or her opportunity set, vi:
ï¿½ ), where í µí±¦
í µí°¼ (í µí±¦ ï¿½í µí±– = í µí±£í µí±– (2)
Under this ex-ante compensation approach, then, there are two questions left before a precise
measure can be proposed. First, how should opportunity sets be valued, i.e. how should be chosen?
And second, what inequality index I(.) should be applied to the counterfactual distribution? Most
attempts to evaluate the opportunity set faced by individuals in a given type k are based on information
on the typeâ€™s advantage distribution Fk . The advantage prospect of individuals in the same type is
interpreted as the set of opportunities open to each individual in that type. A specific version of this
model, extensively used in empirical analyses, further assumes that the value of the opportunity set
can be summarized by a single statistic such as its mean, Âµk . 5 In that case, í µí±£í µí±– = í µí¼‡í µí±˜ , âˆ€í µí±– âˆˆ í µí±‡í µí±˜ .
Hence, starting from a multivariate distribution of income and circumstances, a smoothed
distribution is obtained, which is interpreted as the distribution of the values of the individual
opportunity sets. In this model, measuring opportunity inequality with Equation (2) simply amounts to
measuring inequality in the smoothed distribution6. Clearly, focusing on the mean imposes full
neutrality with respect to inequality within types.
There are also alternatives with respect to the inequality index: van de Gaer (1993) argues for a
measure with infinite inequality aversion, effectively min vk. Other authors have suggested alternative
inequality measures, such as a transformation of the Gini coefficient (Lefranc et al., 2008), a rank
dependent mean (Aaberge et al., 2011), or the mean logarithmic deviation (Checchi and Peragine, 2010;
Ferreira and Gignoux, 2011).
The ex-post approach to compensation, on the other hand, argues that inequalities should be
eliminated among any individuals who exert the same degree of effort. Under this approach there is no
need to evaluate opportunity sets, but one must observe (or agree on a measure of) effort. Under
Roemerâ€™s identification assumption, eliminating ex-post inequality of opportunity would require
eliminating all income differences among individuals at a given percentile of their typeâ€™s advantage
5
Alternative approaches propose to use the equally distributed equivalent income (EDEI), see Atkinson (1970), or
other welfare indicators (see Lefranc et al. 2008)
6
The concept of smoothed (and standardized) distributions is introduced by Foster and Shneyerov (2000). In the
present context, a smoothed distribution is one where individual incomes are replaced by their subgroups means.
5
distribution, across types: í µí±¦ í µí±˜ (í µí±?) = í µí±¦(í µí±?), âˆ€í µí±˜, âˆ€í µí±?. Inequality of opportunity can be measured by applying
an inequality measure I(.) to the distribution of advantages within each tranche, and then aggregating
across tranches.
In terms of our illustration in Figure 1, eliminating ex-ante inequality of opportunity (when
í µí±£í µí±– = í µí¼‡í µí±˜ ) would be achieved by shifting those inverse distribution curves up or down (i.e. transferring
incomes between individuals of different types) until they had the same mean. Eliminating ex-post
inequality of opportunity, on the other hand, would require making those distributions identical to one
another. The latter requirement clearly demands a more complex set of transfers, so that inequality is
eliminated within each and every tranche. Indeed, ex-post equality of opportunity implies ex-ante
equality of opportunity, but not the reverse. In this example:
Fk (y) = Fl (y), âˆ€k, l â‡’ Âµk (y) = Âµl (y) (3)
Let us now briefly turn to the reward principle, which maintains that "inequalities due to unequal
effort should be considered acceptable". This is, in some sense, the other side of the coin (from the
compensation principle) of the basic idea of inequality of opportunity expressed in the first paragraph of
this section. This principle too can be formalized in various ways, the two most prominent ones being
the liberal reward principle that "inequalities due to unequal effort should be left untouched" ---
prohibiting redistribution between individuals with identical circumstances --- and the utilitarian reward
principle that "inequalities due to unequal effort do not matter" --- advocating a sum-maximizing policy
among subgroups with identical circumstances 7.
An interesting recent result from the theoretical literature (see Fleurbaey, 2008, and Fleurbaey
and Peragine (2012), is that both of these reward principles are incompatible with the ex-post
compensation principle: full respect for the differences in reward to effort within each type is not
consistent with full equality within tranches. Although the result is proved for a more general set up, its
essence is easily understood from Figure 1 again, focusing on types 1 and 2. The liberal reward principle
requires that policy makers do nothing about the differential rewards between high and low percentiles
within each of those types. The ex-post compensation principle requires that the two distributions
become identical â€“ with the functions lying on top of each other. Those two things cannot both be
achieved.
Figure 1 is also suggestive of another result in Fleurbaey and Peragine (2012): there is no such
clash between the ex-ante compensation principle and the reward principles. One could â€œre-scaleâ€? the
advantage distributions across types so that they would all have the same mean (or some other value),
without changing the absolute advantage differences (the rewards to effort) across percentiles within
each type. The ex-post approach to the compensation principle is more demanding, but a conceptual
7
These various distinctions are discussed in detail in Fleurbaey (2008).
6
price must be paid for its stringency, namely consistency with the reward principles that also underpin
the theory of equality of opportunity. 8
Most measures of inequality of opportunity computed in practice have followed an ex-ante
approach. A notable exception is Checchi and Peragineâ€™s (2010) work on inequality of opportunity in
Italy, which reports both ex-ante and ex-post measures. There is also a related literature that
acknowledges the incompatibility between ex-post compensation and reward, and proposes fair
allocation rules that satisfy somewhat weakened versions of those principles. If one treats these fair
allocation rules as income norms (that individuals would have received under that particular definition
of fairness) then unfair inequality can be defined as some aggregate of the differences between actual
and norm incomes across the population. See Ramos and van de Gaer (2012) for an excellent discussion
of these measures, and Almas et al. (2011) and Devooght (2008) for examples of the approach. 9 But
neither ex-post compensation nor norm-based measures have been computed in similar ways across
many countries.
In contrast, the particular version of the ex-ante approach where equation (2) is computed with
vi = Âµk , has been applied to at least some forty countries, by a number of authors. The measure I(.)
used does vary across some of the papers but most use the mean logarithmic deviation, following
Checchi and Peragine (2010) and Ferreira and Gignoux (2011). In a few cases, as detailed below, the
Theil (T) index and even the variance are employed. Despite these differences, as well as a variety of
caveats on data comparability across â€“ or even within â€“ studies, the eight papers reviewed in Section 3
comprise the most closely comparable sources on actual I. Op. measures across countries that we are
aware of.
In closing this section, we turn to another approach that has been applied to a number of
countries in recent years, namely the Human Opportunity Index of Barros et al. (2009, 2011). This index
is defined over a different set of advantages (which, confusingly, are sometimes referred to as â€˜basic
opportunitiesâ€™), namely access to certain basic services, such as piped water, electricity or sanitation. In
í µí±—
a discrete population of size n, let í µí¼‹í µí±– denote the probability that person i has access to service j.
1
j
ï¿½j = âˆ‘i Ï€i then denotes the expected coverage of service j in the population. In practice, probabilities
Ï€
n
are often estimated econometrically from binary data on access, and Ï€ ï¿½j can be interpreted as the
average coverage of service j. Let this population also be partitioned into K types, by Î = {T1 , T2 ,...,TK }as
before. Denote the population share of type k by wk, and the average coverage of service j in type k as
jk 1
ï¿½ =
Ï€ âˆ‘ Ï€j . Then the human opportunity index for service j is defined as:
nk iâˆˆk i
1 í µí±—í µí±˜
í µí°» í µí±— = í µí¼‹
ï¿½ í µí±— ï¿½1 âˆ’ í µí°· í µí±— ï¿½ where í µí°· í µí±— = âˆ‘í µí°¾ í µí±¤ ï¿½í µí¼‹
ï¿½ ï¿½ í µí±— ï¿½
âˆ’ í µí¼‹ (4)
ï¿½ í µí±— í µí±˜=1 í µí±˜
2í µí¼‹
8
There is also a potential practical price to be paid in empirical exercises of measuring inequality of opportunity.
Because the ex-post approach requires a partition into types and tranches, it is more demanding on the data.
When many circumstance variables are observed, precision is harder to achieve for ex-post measures. See Ferreira,
Gignoux and Aran (2011) for a discussion.
9
Brunori and Peragine (2011) compare the norm-based measures with the ex-ante and ex-post measures.
7
In equation (4), í µí°· í µí±— is a version of the dissimilarity index commonly used in sociology. In this
application, it simply computes an appropriately normalized (and population-weighted) average
deviation in service coverage from the mean, across types. The HOI (for service j) itself, denoted by Hj, is
simply the average access rate in the population, penalized by the degree of dissimilarity in that
coverage across types. It is clearly analogous to the Sen welfare function, where mean outcomes are
adjusted by one minus a measure of inequality. Sometimes an aggregate index is calculated as an
average of Hj across a number of different services, j âˆˆ {1, â€¦ , J}. 10 Various versions of the HOI have now
been computed for at least 39 countries, and basic results are compared in Section 4 below.
3. Ex-ante inequality of opportunity in 41 countries
As noted above, the ex-ante approach to the measurement of inequality of opportunity essentially
consists of computing an inequality measure over a counterfactual distribution, where individual
advantages are replaced with some valuation of the opportunity set of the type to which the individual
belongs. In this section, we review eight papers that have adopted this approach and applied it, in total,
to 41 countries, ranging from Guinea and Madagascar (with annual per capita GNIs of PPP$980, to
Luxembourg, with a per capita GNI of almost PPP$ 64,000). The eight papers are Checchi et al. (2010);
Ferreira and Gignoux (2011); Ferreira et al. (2011); Pistolesi (2009); Singh (2011); Belhaj-Hassine (2012),
Cogneau and Mesple-Somps (2008) and Piraino (2012).
All of these papers use a measure of economic well-being as the advantage indicator: household
per capita income, household per capita consumption, or individual labor earnings. All use the mean
value of this indicator for each type as the value of the typeâ€™s opportunity set. We refer to the measure
generated by this specific version of the ex-ante approach as an index of inequality of economic
opportunity (IEO). There are, in fact, two closely related versions of the index: the absolute or level
estimate of inequality of opportunity (IEO-L) is given simply by the inequality measure computed over
the smoothed distribution, where each person is given the mean income of their types: í µí°¼ (í µí±¦ ï¿½ ). The ratio
of IEO-L to overall inequality in the relevant advantage variable (e.g. household per capita income) yields
the relative measure, IEO-R 11:
ï¿½)
I(y
IEOR = I(y) (5)
The partition of types varies across studies, ranging from six types to 7,680 (although in four of
the eight studies, the range is a more comfortable 72-108 types). Because in some cases the data sets
are not large enough to yield precise estimates of í µí¼‡í µí±˜ for all types, some authors compute IEO-L using a
parametric shortcut. After estimating the reduced-form regression of income on circumstances:
y = CÎ² + Ïµ (6)
10
However, see Ravallion (2011) on the potential pitfalls of such arbitrary aggregate indices or, as he calls them,
â€œmashup indicesâ€? of development.
11
Ferreira and Gignoux (2011) refer to the corresponding measures that are obtained when the mean log
deviation is used as the inequality measure I(.) as IOL and IOR. They also note that IEO-R is an application of a
standard between-group inequality decomposition, which has long been familiar. See e.g. Bourguignon (1979).
8
and obtaining coefficient estimates Î² ï¿½ , these authors use predicted incomes as a parametric
approximation to the smoothed distribution:
í µí°¼ (í µí±¦
ï¿½), where í µí±¦ Ì‚
ï¿½í µíº¤ = í µí°¶í µí±– í µí»½ (7)
Parametric estimates are also presented either as levels (IEO-L) or ratios (IEO-R), analogously. This
approach follows Ferreira and Gignoux (2011), which in turn draws on Bourguignon et al. (2007).
Empirically, parametric estimates of inequality of opportunity tend to be a little lower than their non-
parametric counterparts but, at least in the case of Latin America, the differences are not great:
proportional differences between the two average 6.6% in Ferreira and Gignoux (2011).
The fact that the parametric estimates are conservative â€“ i.e. generally lower than the non-
parametric ones â€“ is consistent with another important property of these estimates of IEO-R and IEO-L.
They are, in each and every case, lower-bound estimates of inequality of opportunity. A formal proof of
the lower-bound result is contained in Ferreira and Gignoux (2011), but the intuition is straight forward.
The set of circumstances which is observed empirically - and used for partitioning the population into
types - is a strict subset of the theoretical vector of all circumstance variables. The existence of
unobserved circumstances â€“ virtually a certainty in all practical applications â€“ guarantees that these
estimates of I.Op. â€“ whether parametric or non-parametric â€“ could only be higher if more circumstance
variables were observed.
As discussed in Ferreira and Gignoux (2011), the existence of effort variables, observed or
unobserved, is entirely immaterial to this result, since (6) is written as a reduced-form equation, where
any effect of circumstances on incomes through their effects on effort (such as years of schooling or
hours worked) is captured by the regression coefficients, and hence influence the smoothed
distribution. In a setting where some variables are treated as observed efforts (as in Bourguignon et al.
2007), Equations (6) and (7) capture the reduced-form influence of circumstances on advantages, both
directly and indirectly through efforts. By construction, therefore, the only omitted variables that matter
for IEO are omitted circumstances. 12
Table 1 presents the estimates of IEO-L and IEO-R for each of the forty-one countries studied by
the eight aforementioned papers. The table also lists their gross national income (GNI) per capita;
overall inequality and, when available, a measure of intergenerational earnings elasticity (IGE) reported
in the literature; a measure of the intergenerational correlation of education from Hertz at al. (2007);
and the Human Opportunity Index. Overall inequality is measured by whatever index was used in the
construction of the IEO indices for each country. Except where indicated, this measure was the mean
logarithmic deviation, also known as the Theil-L index, and a member of the generalized entropy class of
inequality measures. Whereas overall inequality, IEO-L and IEO-R come from the eight studies
mentioned above, the other variables come from other sources. GNI per capita comes from the World
Bankâ€™s World Development Indicators database. Our measure of intergenerational correlation of
12 ï¿½ . First, these coefficients are
Of course, this does not hold for the estimates of the individual coefficients Î²
reduced-form, rather than structural, estimates. In addition, they are likely to be biased (upwards or downwards)
even as reduced-form estimates, by the omission of unobserved circumstances. The lower-bound result applies
only to the overall measures of inequality of opportunity, IEO-L and IEO-R.
9
education is simply the correlation coefficient between the parentsâ€™ education and the childâ€™s education,
where both are measured by years of completed schooling, as reported by Hertz et al. (2007). Parental
education is the average of motherâ€™s and fatherâ€™s attainment â€œwherever possibleâ€? (Hertz et al, 2007,
p.11). The correlation we report is what the authors call a measure of â€œstandardized persistenceâ€?.
The measures of intergenerational earnings elasticity reported in Table 1 come from eleven
different studies published over the last ten years, namely Azevedo and Bouillon (2010); Cervini Pla
(2009); Christofides et al. (2009); Corak (2006); Dâ€™Addio (2007); Dunn (2007); Ferreira and Veloso (2006);
Grawe (2004); Hnatkovskay et al. (2012); Hugalde (2004); NuÃ±ez and Miranda (2006); and Piraino
(2007). Denoting parental earnings (or income) by yf , and the adult childâ€™s earnings by ys , these
elasticity estimates generally come from an equation of the form:
log ys = Î² log yf + Îµ (8)
An elasticity (Î²) of 0.4, for example, would mean that income differences of 100% between two
fathers (say), would lead to a 40% gap between their sons (on average). As in the case of the IEO
measures, the datasets and econometric methods used for estimating this elasticity are not
homogeneous across studies. This comparative exercise is very much in the same spirit as Corak (2012),
and the same caveats he discusses are applicable here. The values for the Human Opportunity Index
reported in Table 1 come from Molinas et al. (2011) for Latin America, and World Bank (2012a, b) for
Africa.
Table 1 should be read in close conjunction with Table 2, which provides some basic information
on each of the eight studies used to construct the inequality of opportunity estimates in Table 1. Table 2
describes which countries are studied in each paper; the specific data sets (including survey year); the
precise income and circumstance variables used; whether the estimation was parametric or otherwise,
and the number of types included in each calculation. The table highlights a number of problems for
comparability across these studies. First is the nature of the advantage variable (y) itself: whereas
Checchi et al. (2010), Pistolesi (2009), Singh (2011) and Belhaj-Hassine use labor earnings, Ferreira and
Gignoux (2011) and Piraino (2012) use incomes, Cogneau and Mesple-Somps (2008) use consumption,
and Ferreira et al. (2011) use imputed consumption. And the definitions of earnings and incomes are not
exactly the same across each of these papers either.
These distinctions are not immaterial: in a comparison of six Latin American countries, Ferreira
and Gignoux (2011) found substantially higher estimates of IEO-R for consumption expenditure than for
income distributions, in the same countries. 13 They attributed this finding to the fact that income
inequality measures are thought to contain greater amounts of measurement error, as well as transitory
income components, which are less closely correlated with circumstances than permanent income or
consumption might be. Bourguignon et al. (2007) also noted differences between estimates for
individual earnings and for household per capita incomes, which they attributed to the fact that unequal
opportunities affect the latter not only through earnings, but also through assortative mating, fertility
decisions, and non-labor income sources.
13
Similarly, Singh (2010) finds a higher IEO-L for consumption than for earnings in India.
10
Second, the studies differ in the number of types used for the decomposition and, naturally, in the
exact set of circumstances used in each case. On one extreme, the Cogneau and Mesple-Somps study
has a mere three types for Uganda, based on fatherâ€™s occupation and education levels, while on the
other Pistolesi has 7,680 types, constructed on the basis of information on age (20 levels), parental
education (4 levels for the mother and 4 for the father), occupational group of the father (6 categories),
individual ethnic group (2 categories), individual region of birth (2 categories). There is, fortunately, a
middle range of studies which account for most countries in the sample, with 72 to 108 types each.
Nevertheless, results for Africa and the US should certainly be interpreted with caution, in light of the
number of types used in each case. Finally, a third comparability caveat, on which we have already
dwelled, is the fact that some studies use non-parametric estimates while others use parametric ones.
Bearing these caveats in mind, Table 1 nevertheless illustrates the substantial variation in
inequality levels across countries â€“ both in advantages and in opportunities. The mean log deviation for
incomes (or the corresponding advantage indicator) ranges from 0.083 in Denmark to 0.675 in South
Africa. Norway, Slovenia and Sweden also have comparatively low levels of overall inequality, while
Brazil and Guatemala stand out at the upper end. Inequality of opportunity levels (IEO-L) range from
0.003 in Norway and 0.005 in Slovenia to 0.199 in Guatemala and 0.223 in Brazil. In other words, the
level of inequality in the distribution of values of opportunity sets across types (the smoothed
distribution described in Section 2) in Brazil is almost three times as large as the inequality (measured by
the same index) in the distribution of actual incomes in Denmark. One can also observe substantial
differences in IEO-L among countries at closer levels of development, and more methodologically
comparable: Madagascarâ€™s level of inequality of opportunity is twice that of Ghana; those of the US and
the UK are ten times those of Norway and almost four times higher than Denmarkâ€™s.
The ratio of these two inequality measures, i.e. the (lower bound) share of the overall inequality
due to inequality of opportunity (IEO-R), also varies substantially, from 0.02 in Norway to 0.34 in
Guatemala. Slovenia also has a remarkably low inequality of opportunity ratio, at 0.05, while Brazil
closely follows Guatemala in the upper tail, at around 0.32. Figure 2 shows the range of relative
measures of inequality of opportunity graphically, for the entire sample, highlighting those countries
where consumption (actual or predicted) was used instead of earnings or incomes.
It may be of interest to look at how these measures of inequality of opportunity correlate with
some other important variables. Output per capita, overall income inequality, and measures of
intergenerational mobility â€“ a concept closely related to I.Op. â€“ are natural candidates. Figures 3, 4, 5
and 6 depict the associations between the relative measure of inequality of opportunity (IEO-R) and four
other variables â€“ log per capita GNI, total inequality, the intergenerational elasticity of income, and the
intergenerational correlation of education. Figure 3 reveals a non-linear relationship between inequality
of opportunity and the level of development, as measured by log per capita income levels. In fact, the
association appears to have an inverted-U shape, much as the â€œKuznets curveâ€? that used to be
hypothesized for the relation between income inequality and the â€œlevel of developmentâ€?. The
regression of IOR on a quadratic of log GNI is shown in the figure; the coefficient on the linear term is
0.32 (p-value: 0.05), and that on the quadratic term is -0.017 (p-value: 0.05).
11
A very similar relationship (not shown) is found between IEO-L and log per capita GNI (with a
coefficient of 0.37 on the linear term, and on the square term of -0.02, both significant at the one
percent level). While the poorest countries in this figure are all located in Africa, the middle income
countries near the turning point of the inverted-U include a number of Latin American countries, as well
as Egypt, South Africa and Turkey. The richer part of the sample is dominated by European countries and
the United States. Although these tend to be more I. Op. egalitarian, there is still a considerable spread
among them.
It is, of course, impossible to interpret this inverted-U pattern solely on the basis of the
information available in our data. One can weave hypotheses: the non-linearity might reflect two
opposite effects at play, the relative strengths of which change as incomes grow. Perhaps at very low
levels of development, new income opportunities are initially captured by a narrow privileged group â€“ a
few well-educated families, or a small ruling ethnic group. During that phase, disparities across types
may grow even faster than overall income inequality. At some point, however, the grip of the elite on
economic opportunities must weaken if growth is to continue. Such mechanisms have been modeled
formally: the transition can occur when, at a certain point, the elite decides that the costs of expanding
education to â€œthe massesâ€? (in terms of their own share of political power) is outweighed by the likely
economic gains from a more skilled labor force (Bourguignon and Verdier, 2000) Alternatively, the
threat of revolution may impose the franchise and a broader sharing of political influence, even upon a
less enlightened elite (Acemoglu and Robinson, 2000). There is also some evidence that lower inequality
of opportunity may be associated with faster growth, at least in richer countries (see, e.g., Marrero and
Rodriguez, 2010, for a sample of US states).
But these are only hypotheses consistent with the pattern in Figure 3. It is equally possible, of
course, that the pattern is spurious: other variables may cause inequality of opportunity first to rise, and
then decline with GNI. As we have learned from work on the (income) Kuznets hypothesis, it would also
be foolhardy to infer much about the time-series pattern in any given country from a simple cross-
sectional association. At some level, in fact, it is probably fruitless to look for evidence of causal
relationships between two variables at such a high order of aggregation. Both overall output levels (GNI)
and inequality of opportunity are summary statistics, jointly determined by the full general equilibrium
of the economy, including all of the key political economy processes that determine policy variables
such as tax rates and spending allocations. It is likely that one can more easily find causality at the
microeconomic level. From that vantage point, disentangling causality in the relationship depicted in
Figure 3 may well be pointless, even if the correlation between the two aggregate variables reflects
genuine economic processes, which are both real and important.
Another question that naturally arises is whether there is any observable empirical relationship
between inequality of opportunity and income inequality. Since the former is measured as a component
of the latter there is a mechanical aspect to the relationship in levels, but it is not obvious that there is
any mechanical reason to expect a correlation between income inequality levels and the relative extent
of inequality of opportunity. Figure 4 shows the association between overall inequality (in economic
advantage) and the share of that inequality associated with inequality of opportunity (IEO-R). The
correlation coefficient is 0.523 (p-value: 0.0004). A number of possible mechanisms might drive this
12
correlation as well. One that appears eminently plausible is the notion that todayâ€™s outcomes shape
tomorrowâ€™s opportunities: large income gaps between todayâ€™s parents are likely to imply bigger gaps in
the quality of education, or access to labor market opportunities, among tomorrowâ€™s children (Ferreira,
2001). Naturally, the reverse causality probably holds too: if opportunity sets differ a great deal among
people, then individual outcomes are also likely to be unequal. Inequalities in income and opportunities
are both endogenously determined: once again, the quest for causality at the aggregate level may be
futile, even if the correlation reflects real underlying political and economic processes. 14
The use of the links between parentsâ€™ and childrenâ€™s incomes to describe an important
manifestation of inequality of opportunity suggests that the concept should be closely related to
intergenerational mobility. Indeed, if we wrote y = log ys and í µí°¶ = log í µí±¦í µí±“ , equations (6) and (8) would
be identical suggesting that, if the set of observed circumstances becomes restricted to parental income,
then our lower-bound measure of inequality of opportunity is very closely related to the commonest
measure of intergenerational mobility, namely the IGE. It can easily be checked that the R2 of (8) is
identical to the IEO-R measure defined by (5) and (7) when the variance of logarithms is used as the
inequality index.
Figure 5 documents the association between IEO-R and (inverse) economic mobility, as measured
by the intergenerational elasticity of earnings (or incomes). The correlation across the 23 countries for
which we have both variables in Table 1 is 0.5853 (p-value: 0.0172). Of course, the two measures are not
exactly the same, in part because the vector of circumstances C used to partition types and generate
IEO-R is not the same as a measure of parental income or earnings. In fact, C does not contain that
variable for any of the 41 countries in Table 1. It does, however, usually contain parental education (and
in some cases parental occupation), which are themselves determinants of log parental incomes. And it
often contains additional information, such as race or the region of the personâ€™s birth.
For these reasons, we expected the correlation in Figure 5 to be strong, but not perfect. Given the
likely correlation between most circumstances and parental economic status, it would be surprising if
this association turned out to be weak. Given the isomorphism between the ex-ante measurement of
inequality of opportunity and the measurement of intergenerational mobility, we find it intriguing that
these comparisons do not appear to have been made before.
It should also be noted that Figure 5 is close in spirit to Figure 2 in Corak (2012), which plots the
intergenerational earnings elasticity against income inequality (measured by the Gini coefficient) across
countries. 15 Instead of plotting the estimates of IGE against overall inequality, we plot the
intergenerational elasticity of income against a broader measure of inequality of opportunity.
14
If an inverted U-shaped relationship is observed between income inequality and per capita GNI levels across
countries â€“ i.e. if a cross-sectional â€œKuznets curveâ€? holds empirically - then the positive association between
income inequality and IEO-R shown in Figure 4 actually implies the inverted U shape in Figure 3. We are grateful to
Branko Milanovic for pointing this out.
15
Corakâ€™s figure has rapidly become well-known, in part because Alan Krueger, Chairman of President Obamaâ€™s
Council of Economic Advisers, referred to it in a speech as â€œthe Great Gatsby curveâ€?, relating the distance between
the rungs of the economic ladder, and the ease with which it is climbed.
13
Reassuringly, a very similar correlation is found between the same measure of inequality of
opportunity (IEO-R) and a different gauge for intergenerational (im)mobility, namely the correlation
between parental and child schooling attainment. As noted earlier, the intergenerational correlations of
education reported in Table 1 come from Hertz et al. (2007), and use the average years of schooling
completed by a personâ€™s mother and father as the measure of parental education. Figure 6 shows the
scatter-plot for the 23 countries for which data on both variables is available. The correlation coefficient
is 0.5965 (p-value: 0.0021). So, inequality of economic opportunity, as measured by IEO-R, is clearly
negatively associated with two independent measures of intergenerational mobility (as opposed to
persistence), one based on incomes and the other on educational attainment.
4. Measuring development with a penalty for unequal opportunities
The country composition of Table 1 was determined by the availability of information on ex-ante
measures of inequality of opportunity, IEO-L and IEO-R, and drew on the eight papers listed in Table 2.
The last column of Table 1 contains estimates of the aggregate Human Opportunity Index, defined as a
weighted average of the dimension-specific HOI. 16 This information was only available for ten of the 41
countries in Table 1, largely because the index has not been calculated in rich countries.
In Table 3, however, we list the component (or dimension-specific) human opportunity indices for
a larger set of countries, and for the following advantages (or â€œbasic opportunitiesâ€?, or â€œservicesâ€?):
school attendance (10-14 year olds); access to water; access to electricity; access to sanitation; and
whether or not the child finished primary school on time (i.e. with zero grade-age delay). The indices are
multiplied by 100, so the possible range is 0-100. The 39 countries included - all of them in either Africa
or Latin America - is the full set available at the time of writing. As noted earlier, they come from
Molinas Vega et al. (2011) for Latin America, and World Bank (2012a, b) for Africa. Following the
authors, the table also reports the simple average of the school attendance and primary school
completion indices, as the HOI for education, and the simple average of the other three indices as the
HOI for housing conditions. The simple average of these two numbers in turn yields the overall HOI
reported in the last column of the table.
The motivation behind the HOI, as initially proposed by Barros et al. (2009), was to measure the
extent to which children in various developing countries have access to basic opportunities. Although
the authors do not motivate it this way, one could view the index as an example of the ex-ante approach
applied to a multidimensional advantage space, with each dimension corresponding to access to a
particular service â€“ such as water or schooling â€“ and the valuation of the opportunity set of each type
being given by the coverage of the service in that type. The particular inequality index applied to that
smoothed distribution of probabilities is the dissimilarity index (see equation 4).
16
The averaging procedure is the same suggested by Barros et al. (2011) for the HOI summary index: first calculate
a HOI for education obtained as the mean of the two education components and a HOI for housing conditions (the
mean of the other three components). Then obtain a summary HOI as a simple average of the two.
14
Although the dissimilarity index might therefore be seen as a measure of inequality of
opportunity, the HOI itself clearly cannot. 17 It is intended â€“ and defined â€“ as a measure of average
access, adjusted (or penalized) by inequality of opportunity. Unsurprisingly, therefore, it is closely
correlated with other indicators of â€œlevel of developmentâ€?. This association is already clear in Figure 7,
which ranks the average HOI for all countries in Table 3, ranging from 9.6 in Niger, to 91.6 in Chile. There
is almost no overlap in HOI between the African and the Latin American sub-samples, and the
correlation between the HOI and GNI per capita for these countries is 0.89 (p-value: 0.0005).
Perhaps more striking is the correlation with the UNDPâ€™s Human Development Index which is even
higher (at 0.94) and highly statistically significant. Figure 8 presents the scatter plot. This is remarkable
because the two indices are constructed on the basis of completely different data. Until 2010 (the year
used in Figure 8), the Human Development Index was calculated as a simple average of three normalized
indices in the dimensions of health, income and education. 18 The income index used GNP per capita,
and the health index was based on life expectancy at birth, while the education index combined
information on literacy and the gross school enrolment ratio. Of these four basic components, only one
is close to the indicators used to construct the HOI, namely gross enrolment ratio, which is related to the
â€œschool attendanceâ€? data used in the first column of Table 3. The other four components of the HOI,
listed above, do not enter directly into the computation of the HDI, and neither does the latter explicitly
adjust for dissimilarity across types in any way. Conversely, life expectancy at birth, GDP per capita and
literacy do not enter the HOI explicitly.
A correlation of 0.94 between these two indices, albeit calculated only over a non-representative
sample of 39 countries in two of the worldâ€™s regions, suggests two things. First, it suggests that the
average coverage rates of services like access to water, electricity, etc. are highly correlated with the
constituent elements of the HDI. Second, it suggests that the HOI is determined, to a very large extent,
ï¿½j ï¿½1-Dj ï¿½. In fact, the correlations between average coverage and the
by the first term in the product Ï€
component-specific HOI in this sample are extremely high: they are greater than 0.99 for school
attendance; access to water; access to electricity; and having finished primary school on time. It is 0.987
for access to sanitation. This implies, of course, that the penalty for inequality of opportunity, ï¿½1-Dj ï¿½,
accounts for a much smaller share of the variance in the HOI than mean coverage.
A final international comparison issue our data can shed light on is the association between the
dissimilarity index (the measure of inequality of opportunity contained within the HOI) and the index of
inequality of economic opportunity (IEO-R). The dissimilarity index can be interpreted as the proportion
17
A possible caveat with viewing the dissimilarity index within the HOI as a measure of inequality of opportunity is
that the index is typically calculated â€œfor childrenâ€?. This justifies the use of certain variables - like geographic
location or education of the adults in the household - as circumstances, which are clearly in the realm of choices
for the adults. The argument is that the index applies to children, and these are circumstances from their
perspective. But this then raises the issue of age of responsibility, and whether or not all inequalities in access to
services for children below a certain age should not be considered inequality of opportunity. Under that view,
unequal access to water or sanitation among five-year olds within the same type (i.e. sharing identical observed
circumstances) should also be counted as inequality of opportunity.
18
The correlation with the inequality-adjusted Human Development Index introduced for the first time in 2011 is
almost the same: 0.95.
15
of â€œbasic opportunitiesâ€? that is improperly allocated, relative to equal access across all types (Barros et
al. 2011). In other words, it is a measure of how much re-distribution in access to a particular service
would be required to move from the observed allocation to one in which average access was the same
across types. Subject to the caveat in footnote 17, this is a perfectly plausible measure of between-type
inequality in a particular dimension (that of service j). IEO-R, on the other hand, measures inequality of
opportunity as the between-type share of income (or consumption) inequality. How do these two
measures correlate? Do they yield essentially the same country ranking, even though their information
bases are quite different, as appears to be the case with the HDI and the HOI?
It is probably too early to answer this question in cross-country terms. The overlap between the
country samples in Table 1 (for which we have estimates of IEO-R) and in Table 3 (for which we have
estimates of the dissimilarity index) is only ten countries, six in Latin America and four in Africa. Very
little can be said, even about descriptive correlations, on the basis of such a small and unrepresentative
sample. Nevertheless, for what it is worth, Figure 9 plots the IEO-R index against the dissimilarity index,
averaged across its five dimensions. The correlation is -0.6989 (p-value: 0.0245), suggesting that the two
alternative approaches to measuring inequality of opportunity can yield very different country rankings.
It is true, of course, that in this sample the negative correlation is driven primarily by a dichotomy
between Africa and Latin America, where the latter has lower dissimilarity in access to services, but a
higher share of income inequality driven by unequal opportunities. Given that the IEO-R data for Africa
in our sample is based on coarser partitions than in most other cases, one really should not read too
much into this correlation. Nevertheless, it equally cannot be taken for granted that the IEO-R and the
part of the HOI which seeks to capture inequality of opportunity are measuring the same things.
5. Concluding remarks
Inequality of opportunity is a complex concept that can be measured in a number of different
ways. A number of measures have recently been proposed, both under the ex-ante and the ex-post
approaches, or indeed seeking a compromise between them. But most of these approaches have been
applied to a single country or a very small group of countries, making cross-country comparisons
impossible. Two exceptions are ex-ante measures of inequality of economic opportunity (IEO), and the
Human Opportunity Index (HOI). Our review of this empirical literature yielded (roughly) comparable
measures of the IEO for forty-one countries, and of the HOI for thirty-nine. Most countries in the first set
are in Europe and Latin America, but there are examples from North America, Asia, Africa and the
Middle-East. The second set covers countries in Africa and Latin America exclusively, and the overlap
between the two samples is ten countries.
The evidence reviewed suggests that an important portion of income inequality observed in the
world today cannot be attributed to differences in individual efforts or responsibility. On the contrary, it
can be directly ascribed to exogenous factors such as family background, gender, race, place of birth,
etc. There was considerable cross-country variation in the (lower-bound) relative measure of inequality
of economic opportunity: Brazilâ€™s share (0.32) is sixteen times as large as Norwayâ€™s. Although there
certainly is noise in these measures, and various comparability caveats, there appears to be some signal
as well.
16
In addition, the data reveal a positive correlation between inequality of opportunities and income
inequality. Countries with a higher degree of income inequality are also characterized by greater
inequality of opportunity. This result is consistent with the empirical literature on social mobility, which
considers only one exogenous circumstance (family background measured on the basis of income or
social status of the parents) and finds a negative correlation between inequality and mobility (see the
â€œGreat Gatsby Curveâ€? of Corak, 2012): less unequal countries are also those that have a higher degree
intergenerational mobility.
In fact, the IEO-R measure is strongly positively correlated with two different measures of
intergenerational persistence (the converse of mobility): the intergenerational elasticity of income, and
the correlation coefficient of parental and child schooling attainment. It bears emphasis that these
measures of intergenerational transmission refer to different variables, collected in different data sets,
and reported by different studies. This suggests that the cross-country association between inequality of
economic opportunity and intergenerational mobility is rather robust.
In a sense, this is not surprising: inequality of opportunity is the missing link between the concepts
of income inequality and social mobility: if higher inequality makes intergenerational mobility more
difficult, it is likely because opportunities for economic advancement are more unequally distributed
among children. Conversely, the way lower mobility may contribute to the persistence of income
inequality is through making opportunity sets very different among the children of the rich and the
children of the poor.
We also found an inverted-U relationship between per capita GNI and inequality of economic
opportunity, reminiscent of the old Kuznets curve for income inequality. We argued that it is impossible
to treat that relationship as causal (in either direction), but that this is due primarily to the order of
aggregation of the two variables. It is quite possible that the relationship is underpinned by real
economic processes, although it is likely that disentangling them requires looking for specific
relationships among well-defined microeconomic variables.
Our international comparison exercise also revealed some interesting differences between the
IEO-R index and the Human Opportunity Index, even though both can be thought of as belonging to the
ex-ante family of I.Op. measures. These differences fall into at least three categories. First, the
advantage space for the IEO index is unidimensional, and usually refers to a measure of economic well-
being, such as income or consumption, while the HOI focuses on binary indicators of access to services.
If it is constructed as an average of the measure for different services, it can be thought of as having a
multidimensional advantage space (although aggregation across them is fairly ad-hoc).
Second, the HOI is deliberately constructed as a development index, with a functional form
analogous to Senâ€™s welfare index: a mean penalized by an inequality measure. The HOI is not a measure
of inequality of opportunity; it contains a measure of inequality of opportunities (in the space of access
to services), which is the dissimilarity index. As we have seen, however, most of the cross-country
variation in the HOI is driven by the mean coverage term, with correlations above 0.98 for each of the
five main dimensions usually included. Partly as a result, the HOI is very highly correlated with the HDI,
another famous aggregate development index, at least over the currently available sample of countries.
17
It is not obvious that the extent of this correlation is well-understood by the analysts working on either
approach.
Third, over the (small and unrepresentative) sample of countries for which both measures are
available, the dissimilarity index and the IEO-R â€“ each an ex-ante measure of inequality of opportunity,
albeit with respect to different advantage spaces â€“ are actually negatively correlated. While sample size
and comparability issues preclude taking this correlation too seriously, it may nevertheless serve as a
cautionary tale that different ways of measuring inequality of opportunity can measure (very) different
things, and yield widely disparate country rankings.
We argued in the introduction that fairness matters to people, and affects individual behavior.
There is also (anecdotal) evidence that measures of fair or unfair inequality matter to governments, and
international institutions like the World Bank increasingly use measures of inequality of opportunity in
country dialogue. We hope that this simple description of how the two most commonly-used measures
vary across countries, and co-vary with related indicators, may both contribute to greater clarity in those
discussions and help spur further analytical work.
18
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22
Table 1: Inequality of opportunity, income inequality and economic mobility in 41 countries
Intergenerational
GNI per Total Intergenerational
Country IEO-L IEO-R Method correlation of HOI
capita PPP inequality income elasticity
education
Austria (1) 39,410 0.1800 0.0390 0.2167 parametric
Belgium (1) 37,840 0.1450 0.0250 0.1724 parametric 0.400
Brazil (3) 10,920 0.6920 0.2230 0.3223 parametric 0.5733 0.590 75.90
Colombia (3) 9,000 0.5720 0.1330 0.2325 parametric 0.590 79.25
Cyprous (1) 30,160 0.1700 0.0510 0.3000 parametric 0.3430
Czec Rep. (1) 23,620 0.1760 0.0190 0.1080 parametric 0.370
Denmark (1) 40,140 0.0830 0.0120 0.1446 parametric 0.0710 0.300
Ecuador (3) 9,270 0.5800 0.1500 0.2586 parametric 0.610 76.25
Egypt (5) 5,910 0.4230 0.0491 0.1160 non parametric 0.500
Estonia (1) 19,500 0.2430 0.0260 0.1070 parametric 0.400
Finland (1) 37,180 0.1360 0.0130 0.0956 parametric 0.1353 0.330
France (1) 34,440 0.1630 0.0210 0.1288 parametric 0.4100
Germany (1) 38,170 0.1910 0.0350 0.1832 parametric 0.2130
Ghana (2) 1,600 0.4000 0.0450 0.1125 non parametric 0.390 39.30
Greece (1) 27,360 0.2000 0.0340 0.1700 parametric
Guatemala (3) 4,610 0.5930 0.1990 0.3356 parametric 51.73
Guinea (2) 980 0.4200 0.0560 0.1333 non parametric
Hungary (1) 19,280 0.2080 0.0210 0.1010 parametric 0.490
India (8) 3,560 0.4218 0.0822 0.1949 parametric 0.5500
Ireland (1) 32,740 0.1880 0.0420 0.2234 parametric 0.460
Italy (1) 31,090 0.1960 0.0280 0.1429 parametric 0.4095 0.540
Ivory Coast (2) 1,650 0.3700 0.0500 0.1351 non parametric
Latvia (1) 16,360 0.2290 0.0280 0.1223 parametric
Lithuania (1) 17,880 0.2280 0.0350 0.1535 parametric
Luxemburg (1) 63,850 0.1480 0.0350 0.2365 parametric
Madagascar (2) 980 0.4400 0.0920 0.2091 non parametric 22.62
Netherlands (1) 42,580 0.1920 0.0360 0.1875 parametric 0.2200 0.360
Norway (1) 57,130 0.1300 0.0030 0.0231 parametric 0.2050 0.350
Panama (3) 12,980 0.6300 0.1900 0.3016 parametric 0.610 63.98
Peru (3) 8,940 0.5570 0.1560 0.2801 parametric 0.6000 0.660 69.18
Poland (1) 19,020 0.2710 0.0250 0.0923 parametric 0.430
Portugal (1) 24,710 0.2470 0.0300 0.1215 parametric
Slovakia (1) 23,140 0.1320 0.0180 0.1364 parametric 0.370
Slovenia (1) 26,970 0.1040 0.0050 0.0481 parametric 0.520
South Africa (6) 10,280 0.6750 0.1690 0.2504 parametric 0.7055 0.440 58.09
Spain (1) 31,550 0.2160 0.0420 0.1944 parametric 0.4533
Sweden (1) 39,600 0.1060 0.0120 0.1132 parametric 0.2125 0.400
Turkey (4) 14,580 0.3620 0.0948 0.2620 parametric
Uganda (2) 1,230 0.4300 0.0400 0.0930 non parametric 27.00
UK (1) 36,580 0.2040 0.0420 0.2059 parametric 0.4760 0.310
US (7) 47,020 0.2200 0.0409 0.1860 semiparametric 0.4800 0.460
Notes: The source for inequality and IEO measures for each country is given in parentheses after the country's name, and refers to the studies
below. GNI per capita is from the World Bank's World Development Indicators, for the year 2010, using PPP exchange rates for 2005. Total
inequality is measured by the mean logarithmic deviation in all cases except those from source (2), which use the Theil-T index. IEO indices are
always based on the same inequality measure used for total inequality in that country. Sources for the numbers in the last three columns are given
in the text.
(1) Checchi et al. (2010)
(2) Cogneau and and Mesple-Somps (2008)
(3) Ferreira and Gignoux (2011)
(4) Ferreira et al. (2011)
(5) Belhaj-Hassine (2012)
(6) Piraino (2012)
(7) Pistolesi (2009)
(8) Singh (2011)
23
Table 2: Comparing eight studies of ex-ante inequality of opportunity across 41 countries.
Number of
References Countries Data sources Outcome Method Circumstances
types
Austria, Belgium, Czech Republic, Germany,
Denmark, Estonia, Greece, Spain, Finland, parental education,
post-tax
Checchi et al. France, Hungary, Ireland, Italy, Lithuania, parental occupation,
1 EU-Silc 2005 individual parametric 72
(2010) Latvia, Netherlands, Norway, Poland, gender, nationality,
earnings
Portugal, Sweden, Slovenia, Slovakia, geographical location
United Kingdom.
Ivory Coast, EPAMCI, 1985-88
Cogneau and Ghana, 1998, GLSS per capita 3 groups based on
Ivory Coast, Ghana, Guinea, Madagascar, 6
2 Mesple-Somps Guinea, 1994, EICVM household non parametric fatherâ€™s occupation and
Uganda. (3 Uganda)
(2008) Madagascar, 1993, EPAM consumption education, region of birth
U d 1992 NIHS
Brazil, PNAD 1996;
Colombia, ECV 2003; gender, ethnicity,
Ferreira and Brazil, Colombia, Ecuador, Guatemala, Ecuador ECV 2006; household per parental education, 108
3 parametric
Gignoux (2011) Panama, Peru Guatemala, ENCOVI 2000; capita income fatherâ€™s occupation, (54 Peru)
Panama, ENV 2003; region of birth.
Peru, ENAHO 2001
urban/rural, region of
Ferreira, imputed per
birth, parental education,
4 Gignoux, Aran Turkey TDHS 2003-2004 and HBS 2003 capita parametric 768
mother tongue, number
(2011) consumption
of sibling
gender, fatherâ€™s
education, motherâ€™s
Belhaj-Hassine total monthly
5 Egypt ELMPS 2006 non parametric education, fatherâ€™s 72
(2012) eraning
occupation, region of
birth.
Individual gross
6 Piraino (2012) South Africa NIDS 2008-2010 parametric race, father's education 24
income
age, parental education,
individual annual
7 Pistolesi (2009) US PSID 2001 semiparametric father's occupation, 7,680
earnings
ethnicity, region of birth
fatherâ€™s education,
household per fatherâ€™s occupation, caste,
8 Singh (2011) India IHDS 2004â€“2005 parametric 108
capita earnings religion, geographical
area of residence.
Table 3: The Human Opportunity Index for five service indicators and 39 countries
HOI HOI
HOI HOI HOI HOI
School Finished HOI
Country Period Access to Access to Access to Housing HOI
Attendance primary on Education
Water Electricity Sanitation conditions
(10-14 yrs) time
Argentina 2008 96.80 97.30 100.00 64.40 82.60 89.70 87.23 88.47
Brazil 2008 97.30 82.50 96.40 78.20 34.90 66.10 85.70 75.90
Cameroon 2004 79.11 4.91 24.38 1.89 24.50 51.80 10.40 31.10
Chile 2006 98.40 93.90 99.20 86.10 82.00 90.20 93.07 91.63
Colombia 2008 93.00 54.00 100.00 77.00 70.00 81.50 77.00 79.25
Costa Rica 2009 95.50 95.40 98.80 92.80 66.40 80.95 95.67 88.31
Dem. Rep. Congo 2007 72.92 2.73 5.33 1.65 18.64 45.78 3.24 24.51
Dominican Republic 2008 96.50 70.10 95.40 48.80 53.40 74.95 71.43 73.19
Ecuador 2006 85.90 67.60 90.90 50.90 79.50 82.70 69.80 76.25
El Salvador 2007 89.40 18.30 83.00 18.60 42.50 65.95 39.97 52.96
Ethiopia 2011 69.09 0.93 5.61 0.14 15.75 42.42 2.23 22.32
Ghana 2008 84.59 4.90 36.70 3.91 42.26 63.42 15.17 39.30
Guatemala 2006 80.40 63.90 68.20 21.10 24.40 52.40 51.07 51.73
Honduras 2006 82.00 19.70 53.20 25.60 45.10 63.55 32.83 48.19
Jamaica 2002 95.00 23.40 85.40 35.70 93.00 94.00 48.17 71.08
Kenya 2008-09 93.34 8.36 4.92 1.53 47.31 70.32 4.93 37.63
Liberia 2007 59.10 1.03 1.04 4.70 8.45 33.78 2.26 18.02
Madagascar 2008-09 72.49 0.83 3.84 0.44 14.59 43.54 1.70 22.62
Malawi 2010 90.24 1.67 2.51 0.26 24.10 57.17 1.48 29.32
Mali 2006 39.32 3.17 6.14 1.08 10.85 25.09 3.47 14.28
Mexico 2008 92.50 80.30 98.30 72.00 86.70 89.60 83.53 86.57
Mozambique 2003 69.91 1.45 3.00 0.47 5.81 37.86 1.64 19.75
Namibia 2006-07 92.66 25.70 15.48 11.58 53.46 73.06 17.59 45.32
Nicaragua 2005 84.60 14.80 52.50 36.50 33.50 59.05 34.60 46.83
Niger 2006 29.98 1.03 2.54 0.17 5.88 17.93 1.25 9.59
Nigeria 2008 63.00 1.80 29.31 4.20 42.35 52.68 11.77 32.22
Panama 2003 90.80 50.20 60.20 31.40 70.60 80.70 47.27 63.98
Paraguay 2008 92.00 67.20 94.70 48.40 56.30 74.15 70.10 72.13
Peru 2008 95.00 42.60 64.40 54.40 74.10 84.55 53.80 69.18
Rwanda 2010 93.33 0.95 2.90 0.06 8.73 51.03 1.30 26.17
Senegal 2010-11 55.33 36.52 32.28 13.89 24.68 40.00 27.57 33.78
Sierra Leone 2008 65.73 2.37 3.24 0.61 24.41 45.07 2.07 23.57
South Africa 2010 98.72 20.57 78.82 24.95 50.74 74.73 41.44 58.09
Tanzania 2010 81.52 2.84 2.89 0.33 45.72 63.62 2.02 32.82
Uganda 2006 90.64 0.56 1.62 0.10 15.95 53.30 0.76 27.03
Uruguay 2008 94.80 89.30 98.20 96.60 78.40 86.60 94.70 90.65
Venezuela, R. B. de 2005 94.60 88.10 98.50 83.70 73.40 84.00 90.10 87.05
Zambia 2007 87.97 4.69 6.44 3.56 29.81 58.89 4.90 31.89
Zimbabwe 2010-11 92.05 8.48 12.63 7.58 78.00 85.03 9.56 47.30
Note: HOI Education is the simple average of HOI for school attendance and HOI for finishing primary school on time. HOI
Housing Conditions is the simple average of the other three individual HOIs. The last column is the simple average of the two
preceding sub-aggregates. This follows the authors in the sources below.
Source: Molinas Vega et al. (2011) and World Bank (2012a)
Figure 1: An illustration: inverse advantage distribution for three types
y k ( pk ) F3âˆ’1
Âµ3
F2âˆ’1
Âµ2
F1âˆ’1
Âµ 1
1 pk = F k ( y )
Figure 2: inequality of economic opportunity: lower-bound estimates
Inequality of economic opportunity index (IEO-R)
26
Figure 3: Inequality of economic opportunity and the level of development
Figure 4: Inequality of opportunity and income inequality
Income Inequality (mean logarithmic deviation)
27
Figure 5: Inequality of opportunity and intergenerational mobility
Figure 6: Inequality of opportunity and the intergenerational correlation of education
28
Figure 7: The Human Opportunity Index in Africa and Latin America
Figure 8: The Human Opportunity and Development Indices
29
Figure 9: IEO-R and the Dissimilarity Index in the common subsample
30