WPS6915


 Policy Research Working Paper                              6915




Inequality of Opportunity and Economic Growth
                        A Cross-Country Analysis

                                 Francisco H. G. Ferreira
                                    Christoph Lakner
                                    Maria Ana Lugo
                                       Berk Özler




 The World Bank
 Africa Region
 Office of the Chief Economist
   &
 Development Research Group
 Poverty and Inequality Team
 June 2014
Policy Research Working Paper 6915


  Abstract
  Income differences arise from many sources. While some                            inequality is generally negatively associated with growth
  kinds of inequality, caused by effort differences, might                          in the household survey sample, we find no evidence that
  be associated with faster economic growth, other kinds,                           this is due to the component associated with unequal
  arising from unequal opportunities for investment, might                          opportunities. In the Demographic and Health Surveys
  be detrimental to economic progress. This study uses two                          sample, both overall wealth inequality and inequality of
  new metadata sets, consisting of 118 household surveys                            opportunity have a negative effect on growth in some of
  and 134 Demographic and Health Surveys, to revisit                                the preferred specifications, but the results are not robust
  the question of whether inequality is associated with                             to relatively minor changes. On balance, although the
  economic growth and, in particular, to examine whether                            results are suggestive of a negative association between
  inequality of opportunity—driven by circumstances at                              inequality and growth, the data do not permit robust
  birth—has a negative effect on subsequent growth. The                             conclusions as to whether inequality of opportunity is
  results are suggestive but not robust: while overall income                       bad for growth.




  This paper is a product of the Office of the Chief Economist, Africa Region; and 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, clakner@worldbank.
  org, mlugo1@worldbank.org, or berk.ozler@otago.ac.nz.




         The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
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                  Inequality of Opportunity and Economic Growth:
                                A Cross-Country Analysis


                                            Francisco H. G. Ferreira
                                               Christoph Lakner
                                                Maria Ana Lugo
                                                  Berk Özler 1




Keywords: inequality, inequality of opportunity, economic growth

JEL codes: D31, D63, O40




1
  Ferreira is at the World Bank and the Institute for the Study of Labor (IZA). Lakner and Lugo are at the World
Bank. Özler is at the University of Otago and the World Bank. We are grateful to Manuel Fernandez-Sierra, Marina
Gindelsky, Christelle Sapata and Marc Smitz for excellent research assistance and to Claudio Montenegro for help
in assembling our data set. We are also thankful to Angus Deaton, Marc Fleurbaey, Peter Lanjouw, Leonardo
Santos de Oliveira and conference or seminar participants in Bari, Louvain-la-Neuve, Madrid, Rio de Janeiro, São
Paulo and Washington, DC, for comments on earlier versions. Support from the Knowledge for Change Program
(KCPII – TF012968) is gratefully acknowledged.
                                                       2

1.      Introduction

Although the question of whether inequality may have a detrimental effect on subsequent economic
growth has been asked many times, there is no consensus answer in the literature. Theory provides
ambiguous predictions: whereas higher inequality may lead to faster growth through some channels
(such as higher aggregate savings when a greater share of income accrues to the rich), it may have
negative effects through other channels (such as lower aggregate rates of investment in human capital if
credit constraints prevent the poor from financing an optimal amount of education).

The empirical evidence has been correspondingly mixed. The earliest crop of papers including measures
of income inequality in growth regressions, in the 1990s, tended to find a negative and statistically
significant coefficient, which was widely interpreted to suggest that the theoretical channels through
which inequality was bad for growth dominated those through which there might be positive effects.
But all of these studies relied on OLS or IV regressions on a single cross-section of countries. Using the
“high-quality” subset of the Deininger and Squire (1996) dataset, which permitted panel specifications,
Forbes (2000) and Li and Zou (1998) found positive effects of lagged inequality on growth, and
suggested that omitted (time-invariant) variables may have biased the OLS coefficients. Banerjee and
Duflo (2003) raised further questions about the credibility of the earlier results – whether drawing on
single cross-sections or on panel data – by showing that if the true underlying relationship between
inequality (or its changes) and growth was non-linear, this would suffice to explain why the previous
estimates were so unstable. The prevailing conclusion from these disparate results, as summarized by
Voitchovsky (2009), was that “recent empirical efforts to capture the overall effect of inequality on
growth using cross-country data have generally proven inconclusive”. (p. 549)

And yet, the question continues to motivate researchers and policymakers alike. Asking what might
explain the absence of poverty convergence in the developing world, Ravallion (2012) revisits the effects
of the initial distribution on subsequent growth, and claims that a higher initial level of poverty – not
inequality – is robustly associated with lower economic growth. In remarks delivered at the Center for
American Progress in 2012, Alan Krueger, Chairman of the Council of Economic Advisers to the US
president, claimed that “the rise in inequality in the United States over the last three decades has
reached the point that inequality in incomes is causing an unhealthy division in opportunities, and is a
threat to our economic growth” (Krueger, 2012). 2

The conjecture that an “unhealthy division of opportunities” might be bad for growth is consistent with
some of the theory: if production sets are non-convex and credit markets fail, the poor may be
prevented from choosing privately optimal levels of investment – in human or physical capital (Galor
and Zeira, 1993). Others have suggested that low levels of wealth are associated with reduced returns to
entrepreneurial effort as a result of the need to repay creditors. This moral hazard is anticipated by
lenders, leading to credit market failures and differences in the entrepreneurial opportunities available
to rich and poor agents (Aghion and Bolton, 1997).



2
 Voitchovsky (2009) also suggests that the link between income and wealth inequality and growth might operate
through the distribution of opportunities: “… income or asset inequality is considered to reflect inequities of
opportunity.”(p.550)
                                                      3

Drawing on the recent literature on the formal measurement of inequality of opportunity – as distinct
both from income or wealth inequality and from economic mobility – this paper seeks to address that
question directly. Is it possible that inequality – like cholesterol – comes in many varieties, and that
some are worse for the health and dynamism of an economy than others? In particular, is it possible
that the two broad categories of sources of inequality suggested by Roemer (1998) – opportunities and
efforts – have opposite effects on economic performance? If so, one reason for the ambiguity in past
empirical studies of the relationship between inequality and growth might have been the failure to
distinguish between the two types of inequality.

Unfortunately, measures of inequality of opportunity were not readily available for a large number of
countries, in the way that income inequality measures were in the Deininger and Squire (1996) dataset,
or the World Income Inequality Database of WIDER. We therefore constructed original measures of
inequality of opportunity from unit-record data from 118 income or expenditure household surveys (IES)
for 42 countries, and 134 Demographic and Health Surveys (DHS) for 42 countries. These indices were
combined with information on the other explanatory variables used by Forbes (2000), which are
illustrative of the set of regressors typically used in the literature. Although we use the same Difference
GMM specification as Forbes (2000) for comparison purposes, we also draw on more recent
developments in the estimation of Generalized Method of Moments models, including a number of
System GMM specifications which are designed to alleviate the weak instruments problem that plagues
Difference GMM with highly persistent data.

A preview of our results is as follows. In neither of the two country samples – one using the income or
expenditure surveys and the other using the DHS – do we find any support for the finding in Forbes
(2000) and Li and Zou (1998) of a positive coefficient on income inequality. Instead the coefficient on
income inequality is negative in most of our specifications (including Difference GMM) and often
significantly so, raising questions about the claim that the negative signs in earlier, OLS specifications
were entirely due to time-invariant omitted variables.

However, we do not find support on these data for the hypothesis that decomposing overall income
inequality into a component associated with inequality of opportunity and a residual component
(notionally related to inequality arising from effort differences) would help resolve the inconclusiveness
of empirical estimates of the relationship between inequality and growth. In the income or expenditure
survey sample, it is the residual inequality component (driven by efforts and omitted circumstances)
that maintains a statistically significant negative coefficient in most specifications, with the inequality of
opportunity component typically insignificant. In the DHS sample the coefficient on inequality of
opportunity is generally negative, but it is only significant (at the 10% level) in one of the four preferred
specifications.

The paper is organized as follows. The next section briefly reviews the literature on the relationship
between inequality and growth, with a focus on the main empirical papers. Section 3 introduces the
concept and measurement of inequality of opportunities. Section 4 describes the econometric
specification and the data used in the analysis. Section 5 describes the estimation procedures and
presents the results. Section 6 concludes.
                                                     4

2.         A brief review of the literature

Speculation that the distribution of incomes at a given point in time might affect the subsequent rate of
growth in aggregate income goes back at least to the 1950s, following the empirical finding that the
savings rate increased with income, albeit at a decreasing rate, in the Unites States (Kuznets, 1953).
Kaldor (1957) incorporated this feature into a growth model, by assuming that the marginal propensity
to save out of profits was higher than the propensity to save out of wages. Under that assumption, a
higher profit-to-wage ratio – which corresponded to higher income inequality in that model – would
lead to a faster equilibrium rate of economic growth. See also Pasinetti (1962).

But it was in the 1990s that a number of papers linking inequality to growth and the process of
development appeared, raising the profile of distributional issues not only within development
economics, but in the broader discipline as well.3 These papers came in two basic varieties: first, models
where the combination of an unequal initial distribution of wealth with imperfections in capital markets
led to inefficiencies in investment activities and, second, political economy models where inequality led
to taxation or spending decisions that deviated from those a benevolent social planner might make.

The first class of models is perhaps best illustrated by Galor and Zeira (1993), where agents have a
choice between investing in education and working as unskilled workers. An indivisibility in the
production function of human capital and the existence of monitoring or tracking costs in the credit
markets (as a result of information and enforcement costs) implies that there is a given, positive wealth
threshold (f) below which individuals choose not to invest in schooling. Above it, all agents choose to
acquire human capital. Wealth is transmitted across generations through bequests which, under certain
assumptions, render wealth dynamics a Markov process. The long-run limiting distribution depends on
initial conditions, and a higher mass of individuals below f leads to lower aggregate wealth in
equilibrium. 4

Other papers involving capital market imperfections rely on alternative mechanisms, but are essentially
variations on the same theme. Banerjee and Newman (1993) model a process of occupational choices
where, in the absence of credit markets, initial wealth determines whether individuals prefer to work in
self-employment, as employees, or as employers. A nice feature of the model is that the decision also
depends on aggregate factor prices, notably the wage rate, which is endogenous to the initial wealth
distribution, leading to multiple equilibria. In Aghion and Bolton (1997) borrowers suffer from an effort
supply disincentive arising from the need to repay their debts. The strength of this moral hazard effect
increases in the size of the loan required, and thus decreases in initial wealth, leading to higher interest
rates for the poorest borrowers. A related mechanism is the choice between investing in quantity and
quality of children: poorer agents experience a lower opportunity cost from having children, and thus a
higher fertility rate. However, credit market constraints prevent them from investing as much in each
child. In the aggregate, more unequal societies (i.e. those with greater numbers of poor people for a
given mean income level) tend to have a greater relative supply of unskilled workers, and hence a lower
unskilled wage rate leading, once again, to the possibility of multiple equilibria, with higher initial
inequality possibly causing lower subsequent growth.


3
    See Atkinson (1997).
4
    See Loury (1981) for a precursor.
                                                           5

The second group of models focuses on the effect of inequality on policy decisions – either through
voting or through lobbying. Alesina and Rodrik (1994) and Persson and Tabellini (1994) use standard
median voter models to predict that societies with a larger gap between median and mean incomes (a
plausible measure of inequality) would choose higher rates of redistributive taxation. If taxes distort
private investment decisions, then greater inequality might lead to lower growth rates through higher
distortive taxation. Bénabou (2000) proposes an alternative set up where inequality distorts public
policy by leading to inefficiently low – rather than high – taxes. This mechanism requires that voting
power increase with wealth, so that the pivotal voter has higher than median wealth. It also requires
that public investment (e.g. educational subsidies) have positive spillovers, so that taxes finance efficient
public expenditures. These conditions are not sufficient for, but may lead to, multiple equilibria that
depend on the initial distribution. 5

Inequality may also matter for political processes other than elections. Esteban and Ray (2000)
suggested that the rich might find it easier to lobby the government, and distort resource allocation
from the social optimal towards the kinds of expenditures they prefer. Campante and Ferreira (2007)
construct a model where the outcome of lobbying is generally not Pareto efficient: resource allocation
can be distorted away from the social optimal, and this may benefit poorer or richer groups, depending
on their relative productivity levels in economic and political activities. 6

These various predictions have been put to the test a number of times, typically by including a measure
of initial inequality in the standard cross-country growth regression of Barro (1991). In a first phase of
the literature, both Alesina and Rodrik (1994) and Persson and Tabellini (1994) reported results from
such an exercise. Alesina and Rodrik (1994) regressed the annual growth rate in per capita GDP on the
Gini coefficients (for income or land) in 1960, for different country samples, using both OLS and two-
stage least squares (TSLS) regressions. 7 Their inequality data come from secondary sources, namely
compilations of income Gini coefficients from Jain (1975) and Fields (1989), and of land coefficients from
Taylor and Hudson (1972). Both of these studies found a negative and statistically significant coefficient
for initial inequality in the growth regression. Alesina and Rodrik report a particularly robust correlation
between land inequality and subsequent growth, significant at the 1% level, and implying that an
increase of one standard deviation in land inequality would lead to a decline of 0.8 percentage points in
annual growth rates. Deininger and Squire (1998), using a larger (and arguably higher-quality) cross-
country inequality dataset they compiled, report the same basic finding of a negative effect of initial
inequality on growth.

This Deininger and Squire (1996) dataset, introduced in the late 1990s, contained inequality data points
for many more countries and, most importantly, at various points in time. This allowed Li and Zou (1998)
and Forbes (2000) to run the same growth regression as the earlier papers on a panel, rather than a
cross-section, of countries – ushering in “Phase 2” of the literature on inequality and growth. Forbes

5
  The mechanism proposed by Bénabou (2000) has the advantage that it is more consistent with the evidence that
high inequality countries tend to tax less, rather than more, than less unequal countries. See also Ferreira (2001).
6
  The theoretical literature on the links between inequality and growth has been extensively reviewed, and we do
not attempt to review it comprehensively here again. For some of the best surveys, see Aghion et al. (1999),
Bertola (2000) and Voitchovsky (2009).
7
  Literacy rates in 1960, infant mortality rates in 1965, secondary enrollment in 1960, fertility in 1965 and an Africa
dummy are used as instruments for inequality in the TSLS first-stage.
                                                         6

(2000) reported fixed effects, random effects, and GMM estimates for a panel of 45 countries where,
instead of regressing annualized growth over a long period on a single inequality observation at the
beginning of the period, growth rates for five-year intervals were regressed on inequality at the start of
each interval. In the difference-GMM estimates, lagged values of the independent variables were used
as instruments. The results from these panel specifications were strikingly different from single cross-
section results: the coefficient on inequality was generally positive and, in the preferred specifications,
statistically significant. Various interpretations were possible: perhaps the short-run effect of inequality
on growth was positive, but the long-term effect was negative. But another, equally if not more
plausible interpretation was that the OLS cross-section coefficients were biased by omitted variables
correlated with inequality. The fixed-effects and difference GMM estimates correct at least for time-
invariant omitted variables, and this correction would appear to invalidate the negative effect of
inequality on growth.

Other estimates are also available: Barro (2000) considered the possibility that the effect of inequality
on growth might differ between rich and poor countries. While no significant relationship is found for
the whole sample, he reports a significant negative relationship for the poorer countries and a positive
relationship among richer countries when the sample is split. Voitchovsky (2005) focuses on another
kind of heterogeneity: rather than asking whether the effect differs across the sample of countries, she
tests whether inequality “at the bottom” of the distribution had a different effect from inequality “at
the top”, claiming that this would be consistent with some of the theoretical mechanisms discussed
above. Indeed she finds that inequality measures more sensitive to the bottom of the distribution
appear to have a negative effect on growth, while those more sensitive to the top of distribution are
positively associated with growth. By the early to mid-2000s, however, the dominant conclusion that
appeared to be drawn from the existing evidence was that the cross-country association between
inequality and growth was simply not robust to variations in the data or econometric specification used
to investigate it. Banerjee and Duflo (2003), for example, argue that if the true relationship between the
two variables were non-linear, it may not be identified by the linear regressions described above.

Such skepticism has not prevented a recent revival in interest in the cross-country association between
inequality and growth. In what might be described as “Phase 3” of the literature, a number of recent
papers have suggested alternative tests of the same basic idea. Easterly (2007) sets out to test the
hypothesis that, over the long term, agricultural endowments predict inequality, and inequality in turn
affects institutional development and ultimately growth. 8 Using a new instrumental variable constructed
as the ratio of a country’s land endowment suitable for wheat production to the land suitable for
growing sugarcane, the author finds strong support for the endowments-inequality-growth link, with
higher inequality leading to lower subsequent growth. Berg, Ostry and Zettelmeyer (2012) look at a
different feature of growth processes – their sustainability, rather than intensity – and find that
inequality is a powerful (inverse) predictor of the duration of future growth spells.

Ravallion (2012) also finds that features of the initial distribution affect future growth, but suggests that
poverty - rather than inequality - provides the best distributional predictor of future growth. 9 Ostry et al.

8
 Engerman and Sokoloff (1997) originally formulated this hypothesis in these terms.
9
 “Phase 3” also saw the emergence of studies using variation in inequality within countries. For example,
consistent with the pivotal voter model of Bénabou (2000) and Ferreira (2001), Araujo et al. (2008) finds that more
                                                         7

(2014) investigate a recent data set – which, they claim, allows them to “calculate redistributive
transfers for a large number of country-year observations” (p.4) – and find that after-tax inequality is
robustly associated with lower rates of economic growth. 10 Taken together, this latest, third phase of
the empirical literature tends to replace the positive results of the second phase (“inequality is, if
anything, good for growth”) with the negative results that used to prevail in Phase 1: “inequality is bad
for growth, after all”. The pendulum would seem to have come full cycle.

Another possibility raised in this latest phase of research into the link between distribution and
economic performance is that scalar measures of income or expenditure inequality may be composite
indicators, the constituent elements of which affect economic performance in different ways. In
particular, it has been suggested that inequality of opportunity might have more adverse consequences
than the inequality which arises from differential rewards to effort (e.g. Bourguignon et al. 2007b). This
claim resonates with some of the theoretical mechanisms reviewed above, for example that low wealth
leads to forgone productive investment opportunities for part of the population. Such mechanisms
operate through differences in the opportunity sets faced by different agents, and are potentially still
consistent with differences in earnings that provide incentives for effort being good for growth.

If overall income inequality comprises both inequality of opportunity and inequality due to effort, and
these two components have different effects on economic growth, then the relationship that has
typically been estimated is mis-specified, and one ought to distinguish between the two kinds of
inequality. Marrero and Rodriguez (2013) do this for 26 states of the United States: they decompose a
Theil (L) index into a component associated with inequality of opportunity and another, which they
attribute to differences in efforts. When economic growth is regressed on income inequality and the
usual control variables in their sample of states, the coefficient on inequality is statistically insignificant.
But when the two components of inequality are entered separately, the coefficient on “effort
inequality” is generally positive, and that on inequality of opportunity is negative and strongly
significant.

To our knowledge, Marrero and Rodriguez (2013) is the only published paper that investigates whether
inequality of opportunity is the “active ingredient” in the relationship between inequality and growth. 11
Their findings suggest that this component of inequality was negatively associated with economic
growth in the United States in the 1970-2000 period. Is this a more general result? Can the same be said
of other places and contexts? In particular, can a decomposition of inequality into an opportunity and a
residual component help resolve the inconclusiveness of the cross-country literature on this subject? In
order to address this question, the next section briefly reviews the recent empirical literature on the
measurement of inequality of opportunity, and defines the indices we use in this paper.



unequal communities in Ecuador are less likely to receive Social Fund investment projects that provide private
goods to the poor – with the effect being strongest for expenditure shares at the top of the distribution.
10
   The data set used by Ostry et al. (2014) is the Standardized World Income Inequality Database (SWIID) – see Solt
(2009). Unfortunately, this database relies on a very large number of imputed inequality entries for country-year
cells for which no household surveys were conducted. Reliance on such “made-up data” makes the results in this
paper suspect, at least until considerable additional validation can be carried out.
11
   But see Teyssier (2013) for an attempt to replicate Marrero and Rodriguez’s approach to the case of Brazil,
finding opposite results: no effects of inequality of opportunity (or effort) on state-level growth rates.
                                                      8

3.      Inequality of opportunity

The concept of equality of opportunity has been widely discussed among philosophers since the seminal
papers by Dworkin (1981), Arneson (1989) and Cohen (1989). It is central to the school of thought that
believes that meaningful theories of distributive justice should take personal responsibility into account.
In essence, these “responsibility-sensitive” egalitarian perspectives propose that those inequalities for
which people can be held ethically responsible are normatively acceptable. Other inequalities,
presumably driven by factors over which individuals have no control, are unacceptable, and often
referred to as inequality of opportunity.

The concept was formalized and introduced to economists by Roemer (1993, 1998) and van de Gaer
(1993). Among economists, its usage was initially restricted to social choice theorists. Broader
applications in the field of public economics began with Roemer et al. (2003), who investigate the
effects of fiscal systems – broadly the size and incidence of taxes and transfers – on inequality of
opportunity in eleven (developed) countries. Actual empirical measures of inequality of opportunity
based on the definitions provided by Roemer (1998) and van de Gaer (1993) are more recent, and
include Bourguignon et al. (2007a), Lefranc et al. (2008), Checchi and Peragine (2010) and Ferreira and
Gignoux (2011).

In this paper, we follow the ex-ante approach independently proposed by Checchi and Peragine (2010)
and Ferreira and Gignoux (2011). Consider a population of agents indexed by ������ ∈ {1, … , ������}. Let yi denote
what is known in this literature as the “advantage” of individual i, which, in the present paper, will be a
measure of household income, consumption, or wealth. The N-dimensional vector y denotes the
distribution of incomes in this population. Let Ci be a vector of characteristics of individual i over which
she has no control, such as her gender, race or ethnic group, place of birth, and the education or
occupation of her parents. Let Ci have J elements, all of which are discrete with a finite number of
categories, xj, ������ = 1, … , ������. Following Roemer (1998), the elements of Ci are referred to as circumstance
variables.

Define a partition of the population Π = {T1 , T2 ,..., TK } , such that T1 ∪ T2 ∪ ... ∪ TK = {1,..., N } ,
Tl ∩ Tk = ∅, ∀l , k , and C i = C j , ∀i, j i ∈ Tk , j ∈ Tk , ∀k . Each element of Π, Tk, is a subset of the
population made up of individuals with identical circumstances. Following Roemer (1998), we call these
subgroups “types”. The maximum possible number of types is given by K = J x . 12
                                                                               ∏j =1
                                                                                       j




In simple terms, the ex-ante approach to measuring inequality of opportunity consists of agreeing on a
measure of the value of the opportunity set facing each type, assigning each individual the value of his
or her type’s opportunity set, and computing the inequality in that distribution. 13 Following van de Gaer
(1993) and Ooghe et al (2007), Ferreira and Gignoux (2011) choose the mean income in type k, ������������ , as a



12
   K < K if some cells in the partition are empty in the population.
13
  The ex-post approach to the measurement of inequality of opportunity requires computing the inequality among
individuals exerting the same degree of effort which, in turn, requires assumptions about how effort can be
measured. See Fleurbaey and Peragine (2012) for a discussion of both approaches.
                                                              9

measure of the value of the opportunity set faced by people in that type. In other words, a hypothetical
situation of equality of opportunity would require that:

                                      ������������ (������) = ������������ (������), ∀������, ������ |������������ ∈ Π, ������������ ∈ Π                    (1)

Using the superscript k to indicate the type to which individual i belongs, a typical element of the
income vector y is denoted ������������������ . The counterfactual distribution in which each individual is assigned the
value of his or her type’s opportunity set is then simply the smoothed distribution corresponding to the
vector y and the partition П, i.e the distribution obtained by replacing ������������������ with ������������ , ∀������ , ������. 14 Denoting that
                   ������
distribution as ������������� �, Ferreira and Gignoux propose a very simple measure of inequality of opportunity,
             ������
namely �������������������� ��, where I() is the mean logarithmic deviation, also known as the Theil (L) index. Among
inequality indices that use the arithmetic mean as the reference income, this measure is the only one
that satisfies the symmetry, transfer, scale invariance, population replication, additive decomposability
and path-independent decomposability axioms (Foster and Shneyerov, 2000). This is the empirical
measure of inequality of opportunity used in the income and expenditure survey sample in Section 5
below.

The mean log deviation is not, however, suitable for use in the Demographic and Health Survey sample.
As discussed in the next section, the DHS surveys do not contain credible measures of income or
consumption. It does however contain information on a number of assets and durable goods owned by
the household, as well as dwelling and access to service characteristics. Following Filmer and Pritchett
(2001), it has become standard practice to use a principal component of these variables as a proxy for
household wealth. As a principal component, this wealth index has negative values, and its mean is zero
by construction, so that the mean log deviation is not a suitable measure of its dispersion.

In our DHS sample, we therefore follow Ferreira et al. (2011) in using the variance of predicted wealth
from an OLS regression of the asset index on all observed circumstances in C as our measure of
inequality of opportunity. The essence of the rationale for this choice of measure is as follows. 15 We
tend to think of advantage (in this case the wealth index w) as a function of circumstances, efforts, and
possibly some random factor u:

                                              ������ = ������(������ , ������ , ������)                                         (2)

Although circumstances are exogenous by definition (i.e. they are factors beyond the control of the
individual and are hence determined outside the model), efforts can be influenced by circumstances:

                                              ������ = ������(������ , ������ )                                             (3)

For the purposes of simply measuring inequality of opportunity (as opposed to identifying individual
causal pathways), it suffices to estimate the reduced form of the system (2)-(3). Under the usual
linearity assumption, this is given by:

                                              ������ = ������������ + ������                                                (4)

14
  See Foster and Shneyerov (2000).
15
  This discussion draws heavily on Bourguignon et al. (2007a) and Ferreira and Gignoux (2011). Readers are
referred to those papers for detail.
                                                                      10

Under this linearity assumption, {������
                                  � } - where ������     � - is a parametric equivalent to the smoothed
                                              � = ������������
                ������
distribution ������������� � previously described. It is a distribution where individual values of the wealth index
have been replaced by the mean conditional on circumstances, much as before. Whereas a non-
parametric approach, using the cell means, is clearly preferable when data permits it, the parametric
approach based on estimating the reduced-form equation (4) may be preferable when K is large relative
to N, so that many cells are sparsely populated, and their means imprecisely estimated. Given the
properties of the distribution of w, we follow Ferreira et al. (2011) in measuring its inequality simply by
the variance: ������({������ � }).

An important caveat about these measures is that, in practice, not all relevant circumstance variables
may be observed in the data. If the vector of observed circumstances has dimension less than J, then
                                     ������
both the non-parametric index ��������������������                                     � }) are lower-bound estimates
                                        �� and the parametric measure ������({������
of true inequality of opportunity. See Ferreira and Gignoux (2011) for a formal proof. In addition, in the
presence of omitted circumstances, clearly neither the non-parametric decomposition nor the reduced-
form regression (4) can be used to identify the effect of individual circumstance variables. We do know
the direction of bias – downward – for the overall measures of inequality of opportunity, however,
which is why they are lower-bound estimators.

4.       Econometric specification and data sources

Our aim is to investigate whether decomposing inequality into inequality of opportunity and a residual
term (comprising inequality arising from efforts, as well as omitted circumstances) helps resolve the
inconclusiveness about the effects of inequality on subsequent growth in the empirical cross-country
literature. We first estimate the following equation, which is identical to the specification employed in
Forbes (2000):

         ������������������ = ������1 ������������,������−5 + ������2 ������(������)������,������−5 + ������3 ������������������,������−5 + ������4 ������������������,������−5 + ������5 ������������������������������,������−5 + ������������ + ������������ + ������������������   (5)

We estimate equation (5) (and equation (6), which replaces overall inequality with inequality of
opportunity and a residual component, described below) in two panel data sets: one consisting of
income and expenditure surveys (IES), and another comprised of DHS surveys. These data sets are
described in detail below. In both data sets, the dependent variable, ������������������ , is the average annual growth
rate of per capita gross national income in a five-year interval. The data comes from the World Bank’s
World Development Indicators data set, from which we also obtain the (five-year) lagged national
income per capita, ������������ ,������−5 , expressed in constant 2005 US dollars. 16 ������ (������)������,������−5 – our measure of overall
inequality – is the key variable that varies between the two samples 17: in the IES sample, it denotes the
mean logarithmic deviation of incomes (or expenditures) at the beginning of the five-year interval. In the
DHS sample, it denotes the (overall) variance of the asset index (������(������ )), also at the beginning of the five-


16
   With the exception of the Czech Republic, Estonia and Ireland in the case of the IES sample and of Haiti for the
DHS sample, where GDP is used instead of GNI.
17
   To be precise, we divide the survey years into five-year bins. For example, the value of inequality of opportunity
in 2005 may come from any year between 2001 and 2005. In a small number of cases, we have stretched the
boundaries slightly: in Romania, e.g., we use the 2002 survey for 1996-2000 and the 2006 survey for 2001-2005.
We only extend the boundaries forward and not backward (e.g. we do not use a 2000 survey for the 2001-2005
bin). Please see Tables A1 and A2 for details.
                                                                          11

year interval. Unlike in Forbes (2000) or most other studies in this literature, these inequality indices do
not come from a compilation of scalar measures from earlier studies, such as the Deininger and Squire
(1996) database, or the WIDER World Income Inequality Database. Instead, the inequality indices are
computed from the original microdata for all surveys in all countries. Details on the household-level
metadata set are provided below. Summary statistics for the growth and income variables, as well as the
total inequality variable, are reported in Table 1 (Income and Expenditure Surveys) and Table 2
(Demographic and Health Surveys).

Female and male education data (������������������,������−5 and ������������������,������−5 ) come from Lutz et al. (2007, 2010), and are
defined as the proportion of adult (male/female) population that attained at least one year of secondary
education. Lutz and co-authors produced estimates for 120 countries from 1970 to 2010, on a
quinquennial basis. 18 These data are in the spirit of Barro and Lee (2001), although the method used to
complete missing data differs slightly. 19 Finally, as in Forbes, market distortions are proxied by the price
level of investment from Penn World Tables (version 6.3), defined as the purchasing power parity of
investment/exchange rate (������������������������������,������−5). ������������ denotes country i’s fixed effect, ������������ is a period dummy, and ������������������
is the error term.

Equation (5) provides estimates for the effect of total inequality on growth à la Forbes (2000). However,
we are interested in whether the two components of overall inequality – namely inequality between
morally irrelevant groups and inequality within them, interpreted as proxies for inequality of
opportunity and inequality due to effort – have heterogeneous effects on growth. Therefore, in
equation (6), we re-estimate equation (5) but replacing ������ (������)������,������−5 with our measures of inequality of
                        ������
opportunity: ��������������������                                    � }) in the DHS sample. For simplicity, we denote both of
                           �� in the IES sample, and ������({������
these as ������������������������,������−5 in the generic specification. We also include the residual term, ������������������,������−5 = ������ (������)������,������−5 −
������������������������,������−5 , and estimate:

     ������������������ = ������1 ������������,������−5 + ������2 ������������������������,������−5 + ������3 ������������������,������−5 + ������4 ������������������,������−5 + ������5 ������������������,������−5 + ������6 ������������������������������,������−5 + ������������ + ������������ + ������������������ (6)

We estimate equations (5) and (6) using a variety of different techniques, which are discussed in the
next section before we present the results. All regressions for equation (6) include a quartic in the
number of types used to estimate inequality of opportunity. In the remainder of this section, we briefly
describe the microdata sets used to compute the inequality and inequality of opportunity variables.
Tables 1 and 2 also show the percentage of total inequality accounted for by inequality of opportunity.

The availability of household survey micro-data with information on both a reliable indicator of well-
being (income, consumption, or wealth) and circumstance variables – which are required for computing
inequality of opportunity measures – is the key factor constraining our sample(s) of countries. The
requirement is even more stringent since we need, for each country, at least two comparable surveys
five years apart to construct the panel of countries – three when using GMM estimators. As noted

18
   For the IES sample the five-year intervals align with the Lutz data. However, for the DHS sample, the five-year
intervals are one year later (e.g. the end-year is 1991 or 1996). Therefore, we move the Lutz data forward by one
year when matching to the DHS sample.
19
   While Barro and Lee used the perpetual inventory method to complete their data set, and transform flux into
stock of education, Lutz et al. used backward (2007) and forward (2010) projections from empirical observations
given by UNESCO and UN data on population structure.
                                                           12

earlier, we use two types of household surveys: income or expenditure households surveys (IES) such as
labor force surveys, household budget surveys or Living Standard Measurement Surveys, to construct
our first sample, and Demographic and Health Surveys (DHS) for the second sample.

The IES sample contains 42 countries, both developed and developing. 20 For a large proportion of the
countries, we use three harmonized meta-databases that allow for the construction of comparable
measures of household income or consumption. We use the Luxembourg Income Study (LIS) for 23
(mostly developed) countries, the Socioeconomic Database for Latin America and the Caribbean
(SEDLAC) for six Latin American countries, and the International Income Distribution Database from the
World Bank (I2D2) for another 10 developing economies. For the remaining three countries included in
the sample, we use the respective national household surveys. The advantage variable used to compute
total inequality and inequality of opportunity is always a measure of household wellbeing. For 32
countries, it is net household income per capita, while for another ten, where reliable income data are
not available, it is household expenditure per capita. Definitions are always consistent across periods
within countries and a dummy variable indicating whether the inequality measure is based on
expenditure or income is included in the estimation.

We use a number of circumstance variables, referring to the characteristics of the household head, to
partition the population into types. We classify circumstances into two sets. The first set is frequently
used in the literature, and it is generally agreed that these variables satisfy the exogeneity requirement
for circumstances. They include gender, race or ethnicity, the language spoken at home, religion, caste,
nationality of origin, immigration status and region of birth. 21 In the second set, we add the current
region of residence for those countries where the birth region was unavailable. While migration
decisions are obviously very important, region of residence is strongly correlated with birth region, and
might thus provide a proxy for the latter, which is unavailable in many surveys. Table A1 provides more
detailed information on the source and years of the household survey, the welfare and circumstance
variables and the number of types in the partition for each country. Once again, the circumstance
variables and the number of categories for each variable are unchanged over time within countries.

Unlike most studies of inequality of opportunity undertaken within specific countries, we were unable to
draw on a richer set of circumstance variables including father’s and/or mother’s education and
occupation and region of birth, in addition to race or language spoken at home. 22 Since these family
background variables have typically been found to account for a substantial share of the between-type
inequality in other studies, we anticipate the cost of having to rely on a “lowest common denominator”

20
   Note that we treat Germany before and after reunification as two separate countries to avoid any spurious
change in inequality of opportunity, so the result tables report 43 country observations.
21
   It is clear that not all of these characteristics satisfy the criteria to be considered ‘circumstances’. For example,
gender of the head of the household could be a choice or a circumstance. However, the gender of the head of
household does explain a non-negligible part of overall inequality in many countries and, hence, presents a trade-
off with respect to its exclusion. Given the limited number of circumstance variables available to us and to avoid
further underestimation of inequality of opportunity, we chose to include gender among our set of circumstance
variables. Immigration status is also clearly a choice variable, but its inclusion has little effect on our empirical
analysis, as this information is only available in a few IES data sets (see Table A1).
22
   When the advantage variable is individual earnings, rather than household income or expenditure, gender is
typically also included. The resulting partitions typically contain larger numbers of types: 72 in Checchi and
Peragine (2010) and Belhaj-Hassine (2012), 54 or 108 in Ferreira and Gignoux (2011), and so on.
                                                         13

circumstance vector in our panel cross-country analysis to be non-trivial. Naturally, a higher dimension
(J) for the circumstance vector (C) allows the analyst to better capture the possible sources of inequality
                                                        ������
of opportunity. Although the resulting measure, ��������������������   ��, is still a lower bound on actual inequality of
opportunity, as noted earlier, fewer omitted circumstances is likely to mean a smaller underestimation.

In an attempt to address this problem, we extended our analysis to an additional sample of countries
and household surveys, by drawing on the Demographic and Health Surveys (DHS), where additional
circumstance variables were available. The DHS sample contains 42 developing countries from Africa,
Asia and Latin America (see table A2 in the Appendix for details). The earliest survey used is from 1986
and the most recent from 2006. The DHS are designed to provide in-depth information on health,
nutrition, and fertility. In addition, the survey includes socioeconomic information of household
members and access to services. As noted earlier, the DHS does not typically contain estimates of
household income or expenditure, so we construct a wealth index as the first principal component of a
set of indicators on assets and durable goods owned, dwelling characteristics, and access to basic
services. The list of indicators included may vary somewhat from country to country, but we maintain
the same set of variables within countries across time.

For all women aged 15 to 49, the DHS collects relatively detailed information on circumstance variables.
We define the types based on the following indicators: region of birth, number of siblings, religion,
ethnicity, and mother tongue. Mother’s and father’s education are available in some countries for some
years, but never for all years, so this variable could not be included in our set of circumstances. Since not
all indicators are available in all surveys and the number of categories in each variable also varies, the
number of types differs from country to country (but, again, remains the same within countries across
time). Details of the DHS data set are also reported in Table A2.

5.       Estimation and Results

Equations (5) and (6) can be estimated using a variety of techniques. First, they can be estimated with
the classical OLS estimator. However, the OLS can suffer from biased coefficient estimates due to the
fact that the lagged outcome variable can be correlated with the fixed effect in the error term, especially
when T is small, violating the underlying consistency assumption for OLS. Therefore, a second technique
to estimate our model is by using a fixed effects (FE) estimator. The OLS and FE estimators are presented
in columns (1) and (2) in Tables 3-6. For comparison with other studies on inequality and growth, such as
Marrero and Rodríguez (2013), we also estimate a ten-year OLS, which regresses growth during the
latest 10-year period we have in each country on initial conditions at the beginning of that period,
excluding the time dummies. 23 These estimates are presented in column (3) of each regression table.

However, the FE estimator does not solve the endogeneity problem. Using the within-country variability,
the lagged dependent variable and the error term are still correlated, violating the assumption of
independence between the regressors and the error term. Whereas the OLS is biased in one direction,


23
  We would ideally like to run a long-run OLS, as in Marrero and Rodríguez (2013), examining growth over a long
period of time as a function of initial inequality. However, the durations of long-run periods vary widely in our data
sets. Hence, we chose to examine growth during the latest available 10-year period as a function of initial
inequality in our data set for consistency.
                                                       14

the FE estimator is biased in the other direction, meaning that theoretically superior estimates, such as
difference- or system-GMM estimators, should lie within or near the range of these estimates (Bond
2002; Roodman 2009a).

The obvious way to solve the endogeneity problem is to use instrumental variables. To avoid the
problem of finding suitable instruments in each case, difference- and system-GMM methods were
developed, with which the fixed effects are eliminated and where longer lags of the regressors are
available as instruments. Difference-GMM, the first difference transformation of equations (5) or (6),
does exactly this. However, considerable concern has been expressed, for example, that in a context
where the time series are persistent and the time dimension is small “the first-differenced GMM
estimator is poorly behaved” (Bond et al. 2001). In particular, under those circumstances - which
evidently apply to the data used in this paper, in Forbes (2000), and most of the cross-country growth
literature - the two-period lagged dependent-variable (in levels) used as instruments for the first-
differences in the second stage are weak instruments. When instruments are weak, large finite sample
biases can occur, and these problems have been documented in the context of first-difference GMM
models (Blundell and Bond, 1998; Bond et al. 2001).

To deal with these issues and increase efficiency, “system-GMM” models, using an additional set of
moment restrictions, combine the usual equation in first-differences using lagged levels as instruments,
with an additional equation in levels, using lagged first-differences as instruments. According to Blundell
and Bond (1998), Blundell et al. (2000) and Bond et al. (2001), this approach results in substantial
reductions in finite-sample biases in Monte-Carlo experiments. Although system GMM estimation is, for
these reasons, now generally preferred to difference GMMs, it is not problem-free. In particular,
Roodman (2009a) urges caution with the effect of instrument proliferation on the Hansen test of joint
validity of instruments. Although a significant Hansen statistic suggests that the instrument set is not
valid, Roodman points out that implausibly good p-values (of or very close to 1.0) are telltale signs of the
fact that the Hansen test has been weakened to the point of no longer being informative. To limit the
number of instruments in GMM estimation, two approaches have been proposed (and incorporated into
the Stata command xtabond2). First, one can collapse the instrument set, which makes the instrument
count linear in time periods T rather than quartic. 24 Second, one can apply principal component analysis
(pca) to the instruments and limit the number of instruments by retaining components of the
instruments with eigenvalues above a certain threshold. 25 This has the advantage of being purely data-
driven and, hence, a less arbitrary strategy for instrument reduction: Bontempi and Mammi (2012)
suggest that this method is a promising approach compared with lag truncation and collapsing the
instrument set.

To be transparent and thorough in checking the robustness of any finding in our empirical analysis, we
present four GMM estimates in each table: Difference-GMM in Column (4), system-GMM with the full
set of available instruments, the collapsed set of instruments, and instruments replaced with their

24
   The collapse option in Stata’s xtabond2 command performs this, and the resulting instrument matrix, according
to Roodman (2009a), “embodies the same expectation but conveys slightly less information” than the uncollapsed
instrument set. Roodman (2009b) suggests that collapsing the instrument set still retains more information than
limiting the use of only certain lags as instruments rather than the full set of available lags.
25
   For example, the pca option in Stata’s xtabond2 command retains components with eigenvalues greater than 1.
                                                         15

principal components in Columns (5)-(7). Table A3 reports the coefficient estimates for inequality, their
95% confidence intervals, and the associated Hansen J-test p-values for additional limits on the
instrument set. All estimates use the one-step System-GMM estimator. 26 As the first-difference
transform is affected by gaps in the panel data, orthogonal deviations transformation was used for
robustness checks in the DHS data set, which contains gaps in the panel for three countries. This issue
does not affect our findings. 27 We report standard errors clustered at the country level that are robust
to heteroskedasticity and autocorrelation. 28 For each GMM specification, we report the Hansen J-test of
instrument validity, and Arellano-Bond (1991) autocorrelation tests. We also report the numbers of
observations, countries, instruments, and, when relevant, principal components.

We start by discussing the relationship between total inequality and growth (equation 5), presented in
Table 3. This helps place our findings in the preceding literature by allowing comparisons with previous
findings before we proceed to examine the same relationship for the two distinct components of overall
inequality – namely inequality of opportunity and a residual term (a proxy for inequality due to effort).
As in Forbes (2000), whose empirical specification is identical to the one we use here, we find signs of
conditional convergence: the sign of the coefficient on initial income is always negative and significant at
the 95% level or confidence or above for three of the seven specifications. 29 The coefficient estimates
for male and female education and the price level of investment are also similar to those in Forbes
(2000). When it comes to the conditional correlation between inequality and growth, however, our
results diverge: whereas Forbes (2000) reports a coefficient on inequality that is always positive and
significant in four different specifications, our estimates are always negative and significant at the 90%
confidence level or above in five of the seven specifications. The difference-GMM specification in Forbes
(2000) (Table 3, column 4) implies a 1.3% increase in average growth over the next five-year period for a
10-point increase in the initial Gini coefficient, while the same estimate from our study is a 2.2%
decrease for a 10-point increase in initial mean log deviation (Table 3, column 4). A more conservative
estimate using system-GMM suggests a 1% decline in growth for the same change in initial inequality
(Table 3, column 5).

Two issues are worth additional discussion regarding the findings presented in Table 3. First, regression
diagnostics, particularly the Hansen J-test suggests that the validity of the instrument set is called into
question when we limit the number of instruments using the collapse or the pca options discussed
above (columns 6 & 7). 30 These p-values continue jumping around when we limit the number of

26
   While the two-step estimator is more efficient, it has been shown that any gains are small (Bond et al. 2001). The
two-step estimator converges relatively slowly to its asymptotic distribution. Furthermore, the one-step standard
errors are more robust for inference in finite samples (Blundell and Bond, 1998).
27
   Results are available from the authors upon request. The IES data set contains no gaps.
28
   Of course, for the long-run OLS, which uses a cross-section of countries, one cannot cluster at the country level
and we use robust standard errors.
29
   The only difference between our empirical specification and Forbes (2000) is the measure of inequality used: we
use mean log deviation while Forbes (2000) employs the Gini coefficient available in the Deininger and Squire
(1996) data set. Our findings are not qualitatively different if we use the Gini index instead of Theil (L). Readers
should note, however, that we are not trying to replicate Forbes (2000) here: Since the focus of our paper is as
much on inequality of opportunity as it is on overall inequality, the set of countries in our sample is restricted by
the availability of data on circumstances.
30
   The p-values that are less than 0.0001 for Hansen J-tests in columns 7 of Tables 3 and 5 seem to be due to the
presence of an outlier in the value of mean log deviation. Mean log deviation in Bolivia in 2000 is 0.978, which lies
                                                          16

components further by retaining the components with the largest eigenvalues (Table A3, panel A). The
p-values for the Hansen J-test are better for the difference-GMM and system-GMM specification using
the full set of available instruments, while the Arellano-Bond autocorrelation tests suggest no problems
with any of the GMM specifications. Nonetheless, the coefficient estimates of inequality from the four
GMM specifications are relatively stable – suggesting a negative conditional correlation between 1.0%
and 2.4%.

Second, while our findings are not robust enough to allow us to conclude that the conditional
correlation between initial inequality and growth is negative in this data set, we can nonetheless state
with some confidence that they are not consistent with the findings in Forbes (2000). This may reflect
differences in the country and period coverage of the two samples: we have 118 observations for 42
countries, whereas Forbes has 135 observations (in the GMM specification) for 45 countries. 24
countries are present in both Forbes’s and our IES sample. Periods also differ, with these ranging from
1961-65 to 1986-1990 in Forbes (2000), compared to 1981-1985 to 2001-2005 in our study. 31 In
addition, as noted earlier, not only the inequality measures used are different (Gini vs. Theil (L)), but also
our inequality measures arguably satisfy a higher standard of international comparability, since they
were all computed under exactly the same criteria and using the same routines directly from the
microdata, whereas Forbes (2000) relied on Gini coefficients available in the Deininger and Squire (1996)
data set. Whatever the reasons for the differences, it is fair to conclude that the relationship between
inequality and growth is not robust to changes in either data sources/periods or seemingly small
changes in empirical specifications.

As described in the previous section, the IES data set is comprised of 23 high-income countries and 19
low- and middle-income (LMIC) countries. In contrast, our DHS data set is comprised entirely of
developing countries from Africa, Asia, and Latin America. Although we constructed our DHS data set
because of its perceived advantage in containing more observed circumstance variables, it is still
interesting to examine the overall inequality-growth relationship in that data set, which we present in
Table 4. The findings here are much more equivocal than those presented in Table 3: while there are still
signs of conditional convergence, we find no statistically significant coefficient estimates for total
inequality (measured by the variance of the wealth index). For the difference-GMM and system-GMM
using the full set of instruments, signs of instrument proliferation are apparent: 52 and 73 instruments,
respectively, producing unusually high p-values of 0.965 and 0.999 for the Hansen J-test of instrument
validity (columns 4 & 5). The coefficient estimates, all of which are close to zero and about half of which
are negative, suggest no apparent relationship between inequality and growth in this data set.

Our main interest, however, lies in examining whether and how the association between inequality and
growth might change when we decompose overall inequality into the opportunity and residual

well to the right of the next highest value in our data set (0.829 in Panama in 2003). Excluding Bolivia (2000) from
our regression analysis brings the p-value to a much more reasonable 0.148 for the specification presented in
column 7 of Table 3, but makes little difference to the coefficient estimates for initial income and total inequality.
We present the findings for the full data set to avoid ad hoc exclusion of observations from our analysis.
31
   Clearly, neither sample of countries is representative of the world, since they are driven entirely by survey
availability, which is evidently non-random. Although our sample covers fewer countries, it has slightly broader
regional coverage, including two countries from Africa.
                                                        17

components, ������������������������,������−5 and ������������������,������−5 respectively, by estimating equation (6). Table 5 reports results from
this regression using the IES country sample. 32 We find no consistent relationship between growth and
either inequality between types or inequality within types (as proxies for inequality of opportunity and
inequality of effort, respectively): While 13 or the 14 estimates are negative, only one of them is
statistically significant at the 90% level of confidence (which happens to be in a specification where the
Hansen J-test strongly rejects the validity of the instruments). The coefficient estimates are more
scattered for both components of inequality using the DHS data set, but the conclusion is qualitatively
the same: one cannot detect any consistent pattern of a relationship between growth and inequality of
opportunity (Table 6). As in Tables 3 & 4, some of the GMM specifications suffer from instrument
proliferation while in others the validity of the instrument set is rejected. Table A3 confirms these null
findings when the instrument set is restricted further using the pca option. These findings are clearly not
supportive of the hypothesis that there might be a negative association between inequality of
opportunity and growth (and a positive one between the residual inequality and growth) à la Marrero
and Rodríguez (2013).

We considered the possibility that these findings might be driven by measurement error. As noted in
Section 4, the need for (rough) comparability of circumstance sets across countries led us to use a
measure of inequality of opportunity based on a very sparse partition of types. Like other examples of
this method, the measure used in the regressions reported in Tables 5 and 6 is a lower-bound indicator.
But given the paucity of types, it is arguably a very substantial underestimate of true inequality of
opportunity: On average across all the countries and years, our circumstances explain 11.6% of total
inequality in the IES and 15.7% in the DHS data sets (See Tables 1 and 2 for details). While it is obviously
not the only possible cause, this kind of measurement error would certainly be consistent with
substantial amounts of inequality of opportunity (due to omitted circumstances) contaminating the
residual component, leading to biased coefficients. The negative coefficient estimates for both the
within- and between-type inequality in Table 5 is suggestive of this possibility.

6.      Conclusions

In this study, our motivating hypothesis was that the lack of robust conclusions about the association
between initial inequality and economic growth in the previous literature might have been driven, at
least in part, by the conflation of two different kinds of inequality into the conventional income
inequality measure: inequality of opportunities and inequality driven by efforts. Because efforts are
notoriously difficult to measure, we have followed the recent literature on the measurement of ex-ante
inequality of opportunity, and decomposed overall income inequality into a component associated with
opportunities, and a residual component, driven by efforts as well as omitted circumstances.

These decompositions were carried out for the mean logarithmic deviation of household per capita
incomes (or expenditures) in 118 household income and expenditure surveys for 42 countries, and for
the variance of a wealth index obtained from Demographic and Household Surveys in 134 surveys for 42

32
  We use the sample that includes region of residence as a circumstance for our default data set. While region of
residence is not exogenous, region of birth is missing in many data sets, causing significant underestimation of
inequality of opportunity by excluding an important circumstance. Given this tradeoff between underestimation
and endogeneity, we report the findings using the data set that excludes region of residence and only utilizes
region of birth in Table A4.
                                                        18

countries. The resulting indices of inequality of opportunity and residual inequality were then included
as explanatory variables in growth regressions that also included measures of male and female human
capital investment and a measure of investment price distortion, following the specification in Forbes
(2000). The same regressions were run for the overall income inequality measure (with no
decomposition). The two country-level samples were unbalanced panels with a minimum time
dimension of three periods and we relied on OLS, fixed effects, long-run OLS, and various Generalized
Method of Moments specifications for estimation.

Our main findings are such that we cannot reject the null hypotheses that there is no relationship
between initial inequality and subsequent growth. Using a data set of income and expenditure surveys
and the mean log deviation of income (or expenditure) as our measure of overall inequality, there is
some suggestive evidence of a negative association between overall income inequality and subsequent
growth. While this weak finding is neither robust to changes in specification nor to switching to the DHS
data set, it is nonetheless inconsistent with a positive association such as the one found by Forbes
(2000) and Li and Zou (1998). Furthermore, we find no evidence in support of our original hypothesis,
which found some support in a data set of 26 U.S. states (Marrero and Rodríguez, 2013): there is no
apparent relationship between either component of inequality and growth in either of our two data
sets.

What can we take away from these null results, if anything? It would be hard to argue that the data we
use is much more problematic than other available data sets. Both the IES and the DHS data sets are the
most comprehensive cross-country data sets put together specifically for this purpose – products of
thousands of hours of very meticulous data work. 33 The only differences between our analysis and that
in Forbes (2000) are in the coverage of countries and time periods (and in the specific inequality
measure used as a dependent variable). As both studies are equally opportunistic in using the best data
available at the time, it is hard to argue that the findings in one should be preferred to the other. The
best explanation might be that any relationship between inequality and growth is not robust to the set
of countries and/or the time period included in the analysis.

It is harder to argue that our data are ideal for the construction of types needed to build a measure of
inequality of opportunity. While the numbers of variables we use to construct types in our data sets are
large (see Tables A1 and A2 for details), circumstance variables that are consistently available within a
country over time are limited. There is little doubt that the resulting estimates of inequality of
opportunity must be substantially lower than the actual measures that remain unobserved. This in turn
implies that the residual inequality term is contaminated with (unobserved) inequality of opportunity
rather than being purely a measure of inequality due to variation in effort within types.

It is again hard to argue that the resulting measure is inferior or superior to that used in other studies.
For example, in the only study examining the same question in the United States, Marrero and
Rodríguez (2013) use only two circumstances: father’s education and race, which explain approximately
5% of overall inequality in their sample of 26 states. Our data sets include these circumstances, along
with other circumstances, but not consistently for all countries in all years, causing them to be left out of
33
  In fact, one tangible thing that can be taken away from this endeavor is the public data set. Our aim is to make
these data sets available online as soon as possible, but interested researchers can request these data from the
authors in the meantime.
                                                    19

type definitions in many countries. There are many differences between these studies and all we can say
is that the hypothesis of heterogeneous effects of inequality on growth finds support in their study but
not here.

Another issue that needs to be highlighted here is the evident instability of coefficient estimates and
regression diagnostics to minor changes in the estimation procedures. It does appear, at least in our
data sets, that GMM methods in particular are very sensitive to the myriad of choices that need to be
made by the researcher. Simple changes not only move coefficient estimates around, but also render
instrument sets invalid or uninformative in many instances. Although we have diligently combed the
latest literature on GMM estimation techniques and closely adhered to the recommendations regarding
robustness checks and detailed reporting in Roodman (2009a), examining our results does not suggest
that these econometric techniques are reliable strategies in addressing the question at hand.

Similar (or more serious) data and econometric issues have also affected previous studies, and the
instability of results between the three “phases” of the empirical cross-country literature reviewed in
Section 2 smacks of the same lack of robustness that we have encountered in our two country samples.
A review of that literature suggests that, in retrospect, perhaps each individual researcher drew firmer
conclusions from his or her own particular study than later appears warranted. We are not confident
that the latest crop of papers - including Ostry et al. (2014), that relies on the SWIID data from Solt
(2000) - will prove to be immune from this trend. The lack of robustness in our own study may reflect
additional factors, such as unusually large measurement error in the inequality of opportunity variable,
but it also arises from data and methodological problems that have plagued the literature at large. One
conclusion we draw from our null results is that considerable circumspection is in order when
interpreting findings from any single cross-country study of the relationship between inequality and
growth.

If the best available cross-country data sets and the best available econometric techniques do not
appear suitable to answering this important question that has been the subject of considerable debate
recently, then what is? Taking advantage of case studies and natural experiments may be one such
promising avenue. Every time policymakers target certain interventions to disadvantaged groups, they
attempt to reduce future inequality of opportunity: anti-discrimination laws against minorities; early
childhood interventions for certain ethnic groups; schooling and mentoring programs for adolescent
girls; interventions that give voice and increase the participation of oppressed groups are all examples of
such interventions. To the extent that such interventions cause strong changes in measurable inequality
of opportunity (and satisfy exclusion restrictions), they can be used as instruments to study the
relationship between inequality of opportunity and subsequent growth. In cases where one country, or
one region/state/district within a country, implemented a novel policy or program with plausible effects
on reducing inequality of opportunity, recent causal inference methods, such as synthetic controls
(Abadie, Diamond, and Hainmueller, 2010), can be utilized. One could even imagine long-term
randomized controlled trials. Natural experiments and other causal inference methods relying on
interesting cases around the world may end up providing more fruitful avenues for studying this
important question than using cross-country regressions.
                                               20

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Table 1. Summary statistics for Income and Expenditure Surveys

                                                                                                                                              Ratio of inequality of opportunity(set
              Average annual growth rate of per capita GNI in   GNI per capita in constant 2005 USD
                                                                                                          Total inequality (set 1) (MLD)           2) to total inequality (set 2)
  Country                     next 5 years                             (in natural logarithm)
                                                                                                                                                            (in percent)
              1985      1990      1995      2000       2005     1985   1990    1995    2000    2005    1985   1990   1995     2000    2005   1985 1990 1995 2000 2005
Australia     0.0433   -0.0031    0.0014                        9.87   10.08   10.07                    0.2    0.2    0.21                   1.78     1.85    0.99
Austria                          -0.0282    0.0484     0.0279                  10.42   10.28   10.52                  0.27    0.15    0.15                    4.02      3.9    4.63
Belgium                          -0.0253    0.0496                             10.39   10.26                          0.19    0.24                            1.74     1.27
Bangladesh                        0.0179    0.0193     0.0577                   5.97    6.06    6.15                  0.13    0.19    0.18                    0.23     0.38    0.43
Bulgaria                          0.0185    0.1387                              7.41    7.51                          0.15    0.19                           18.77    34.01
Belize                            0.0388    0.0238                              8.16    8.35                          0.74    0.54                            9.42    10.85
Bolivia                                    -0.0192      0.094                              7    6.91                          0.98     0.7                            39.54   28.15
Brazil                           -0.0096   -0.0181     0.1563                   8.42    8.37    8.28                  0.71    0.71    0.64                   14.82    14.75   14.37
Canada        0.0491   -0.0228     0.001    0.0573     0.0343   9.98   10.23   10.12   10.12   10.41   0.24   0.17    0.17    0.21    0.21   5.99     4.37    3.79      3.1    4.68
Switzerland                      -0.0257    0.0472     0.0269                  10.87   10.74   10.98                  0.22    0.19    0.16                    7.73     3.37    4.86
Chile                                       0.0246     0.0888                           8.62    8.74                          0.54    0.54                             4.05    4.87
Colombia                                    0.0217     0.1054                           7.87    7.98                          0.58    0.59                            22.35   17.79
Czech
Republic                                    0.0408      0.021                           9.25    9.45                          0.12    0.12                             4.61     5.9
Germany                          -0.0407    0.0404     0.0247                  10.46   10.25   10.46                  0.15    0.14    0.16                    9.17     7.82    7.94
Denmark                0.0341    -0.0192    0.0613     0.0217          10.41   10.58   10.48   10.79          0.18     0.1     0.1    0.11             5.9    7.55     7.67       8
Spain                            -0.0049    0.0769      0.023                   9.78    9.76   10.14                  0.27    0.21    0.24                     7.5     9.65     6.2
Estonia                                     0.0726     0.0008                           8.88    9.24                          0.25    0.21                             11.2   12.88
Finland                           0.0186    0.0599     0.0211                  10.17   10.26   10.56                  0.09    0.12    0.13                    5.22     4.85    4.27
France                           -0.0234    0.0491     0.0195                  10.33   10.21   10.46                  0.18    0.16    0.17                    9.34     7.93    6.32
United
Kingdom                           0.0368    0.0598    -0.0241                  10.11   10.29   10.59                  0.22    0.23    0.24                    4.51     5.96    5.96
Ghana                            -0.0387    0.0415     0.1781                   6.14    5.95    6.15                  0.26     0.3    0.34                   15.75    29.19   25.54
Greece                           -0.0048    0.0849      0.023                   9.57    9.55    9.97                  0.32    0.24    0.21                    5.73    11.91    5.22
Guyana                            0.0209    0.0158                              6.79     6.9                          0.46    0.51                           12.31    13.96
Hungary                          -0.0001    0.1373     0.0279                   8.55    8.55    9.23                  0.21    0.15    0.17                    9.46    16.51   14.73
India                             0.0173    0.0762      0.092                   6.14    6.23    6.61                  0.18    0.17    0.22                   20.53    26.28   25.12
Ireland                           0.0449    0.1055    -0.0284                  10.04   10.27   10.79                  0.24    0.19    0.19                    4.78     5.11    6.58
Israel                  0.0277    0.0309    0.0015     0.0336           9.61    9.75     9.9    9.91          0.22    0.21    0.25     0.3            9.12   10.03    10.77   15.06
Italy                  -0.0036   -0.0049    0.0538     0.0089          10.11   10.09   10.07   10.34          0.18    0.25    0.35    0.25           19.35    19.7    24.04   17.99
Kyrgyzstan                                  0.0716     0.1057                           5.75    6.11                          0.24    0.13                            40.28   22.28
Luxembourg                       -0.0141    0.0688     -0.012                  10.87    10.8   11.14                  0.11    0.14    0.16                    4.75     3.47    6.97
Nicaragua                                   0.0146     0.0227                           6.98    7.06                          0.65    0.49                             8.13    6.54
Norway                                      0.0887     0.0459                           10.6   11.05                          0.15    0.18                             7.02    4.46
Panama                                       0.019     0.0856                           8.31     8.4                          0.81    0.83                            33.54   36.72
Peru                                        0.0318     0.0926                           7.74     7.9                           0.5    0.42                            15.83   16.63
                                                                                                       26

Poland                                              0.0683      0.0877                                   8.55       8.89                               0.18     0.22                                  12.1        11.16
Paraguay                                           -0.0452      0.1501                                   7.32        7.1                               0.57     0.47                                 24.39        18.53
Romania                                 0.0114       0.145      0.1238                          7.49     7.55       8.27                       0.3     0.14     0.13                       16.85     13.74         8.12
Russia                                 -0.1041      0.1685      0.1424                          8.08     7.56        8.4                       0.4     0.44     0.31                        2.08      1.17        11.94
Rwanda                                              0.0013      0.1156                                   5.55       5.56                               0.71      0.6                                 36.49        25.41
Sweden                                  0.0029      0.0518      0.0148                         10.39    10.41      10.67                     0.12      0.14     0.12                         3.96     4.24         4.24
United
States         0.0335       0.0135      0.0262      0.0268      -0.0081    10.24     10.41     10.48    10.61      10.74    0.25     0.26    0.28      0.32     0.35    10.43     10.4      9.26      8.83         8.72
Vietnam                                 0.0697      0.0829       0.1058                         5.76     6.11       6.52                     0.11      0.16     0.17                       19.55     26.07         26.1
West
Germany        0.1236       0.0409                                           9.64    10.25                                  0.15     0.14                                 3.83    4.81
Total          0.0624       0.0124      0.0004      0.0528      0.0569       9.93    10.16      9.08        8.68    8.99    0.21     0.19    0.25      0.32     0.29      5.51    7.97       8.95    13.91        12.31

The summary statistics correspond to the data used in the regressions. In every country, total inequality (set 1) is defined over the observations which have the set 1 circumstances. This is the more
comprehensive data set. The last five columns show the ratio of inequality of opportunity (set 2) to total inequality (set 2), which is defined over the observations with set 2 circumstances. Further summary
statistics are available from the authors.
                                                                                    27

Table 2. Summary statistics for Demographic and Health Surveys

                Average annual growth rate of per capita GNI in     GNI per capita in constant 2005                                             Ratio of inequality of opportunity to
                                                                                                          Total inequality (Variance)
   Country                      next 5 years                          USD (in natural logarithm)                                                    total inequality (in percent)
                1985      1990      1995       2000       2005    1985 1990 1995 2000 2005             1985   1990   1995   2000    2005       1985 1990 1995 2000 2005
Armenia                                        0.1783    0.0985                          6.66   7.55                         3.01       2.99                            1.61     0.2
Benin                                -0.006    0.0636    0.0333                 6.01     5.98    6.3                 4.97    5.42          5                    32.3   30.34   32.56
Burkina Faso                        -0.0256    0.0964    0.0517                  5.7     5.57   6.06                 4.42    4.06       4.51                    7.73    6.08    9.87
Bangladesh                0.0039     0.0048    0.0261    0.0735          5.99   6.01     6.03   6.16          3.67   3.66    3.47       3.07            0.28    0.85    0.03    0.11
Bolivia                             -0.0087    0.0048    0.1004                 6.98     6.94   6.96                    4    4.16       3.76                   38.56   35.63   30.98
Brazil          0.0611     0.067    -0.0783                       7.94   8.25   8.58                   2.96   3.12   2.41                      25.49   26.46   15.37
Cote d'Ivoire                       -0.0473    0.0584    0.0216                 6.76     6.52   6.82                 4.05    4.06       3.84                   11.21   14.99     7.4
Cameroon                  -0.0795               0.076    0.0192          7.06            6.46   6.84          4.56           4.27       4.25           28.48           26.47   26.25
Colombia        -0.0334    0.1247   -0.0347                       7.56   7.39   8.02                   4.49   4.06   4.36                      21.42    18.7   25.31
Dominican
Republic        -0.0294   0.1251     0.0249    0.0297    0.0657   7.36   7.21   7.84     7.96   8.11   3.09   3.05   2.66    2.52       2.26    9.27   11.91    9.43    5.74    5.12
Egypt           -0.0039   0.0515     0.0539    -0.033    0.1103    6.9   6.88   7.14     7.41   7.24   3.97   3.85   3.64    3.48       3.14   41.61   37.07    36.5   32.15   30.45
Ethiopia                                       0.0403    0.1103                          4.96   5.16                         5.88       6.16                            6.02    7.66
Ghana                     -0.0412   -0.0647    0.1171    0.1521          6.33   6.12      5.8   6.38          3.36   3.65    3.67       3.72           16.87   27.28   25.37    23.4
Guinea                                        -0.0498    0.0455                          5.92   5.67                         4.46       4.46                           10.98    8.22
Guatemala                 0.0606     0.0054    0.0322                    7.18   7.49     7.51                 4.13   3.94    3.78                      36.26   40.36   38.72
Haiti                               -0.0017    0.0265    0.0516                  6.1     6.09   6.22                 4.43    4.09       3.93                    0.55    1.22    0.47
Indonesia                 0.0953    -0.1154    0.1182    0.1322          6.72   7.19     6.62   7.21          2.88   2.78    2.25       2.45            2.13    1.51    2.19     2.1
India                                0.0056    0.0908    0.0971                  6.2     6.22   6.68                 5.67    5.32       5.07                   12.27   14.92   15.26
Jordan                    0.0381               0.0534    0.0783          7.34            7.61   7.88           2.4           2.18       1.83            2.01            1.37    0.89
Kazakhstan                          -0.0159    0.1853                           7.38      7.3                        2.73    3.03                               24.3   25.56
Kenya                      -0.027    0.0151     0.046    0.0533          6.14   6.01     6.09   6.32          3.22   3.44    3.55       3.52           12.74    13.3   18.91   16.52
Cambodia                                       0.0787    0.0692                          5.83   6.22                         5.35        4.8                            0.75    2.82
Madagascar                          -0.0014      -0.01   0.0642                 5.66     5.65    5.6                 3.64    3.43       3.77                   25.15   30.14   29.17
Mali                       -0.043   -0.0334    0.1096     0.054          5.96   5.74     5.57   6.12          3.45   3.77    3.94       3.69            2.41    3.75    2.27    2.15
Mozambique                                     0.0284    0.0642                          5.53   5.67                         4.23       4.63                           42.41   38.79
Malawi                              -0.0562    0.0656    0.0701                 5.32     5.04   5.36                 2.55    2.58       2.65                     6.4   10.52   13.87
Namibia                              -0.046    0.1191    0.0342                 7.87     7.64   8.23                 4.83    4.91       4.89                    3.41    2.62     3.1
Niger                               -0.0499    0.0677    0.0461                 5.48     5.23   5.57                 4.26    4.56       4.49                   19.03   18.82   20.17
Nigeria                   -0.0532              0.1746    0.0642          5.89            5.83    6.7          3.73           3.71       3.69           29.31           27.99    25.7
Nicaragua                            0.0043    0.0161                           6.95     6.97                         5.7    5.52                              33.57    32.6
Nepal                                     0    0.0507    0.0942                 5.57     5.57   5.83                    3    3.27       3.16                   13.24   13.92   17.91
Peru            -0.0072   0.1094    -0.0386     0.056    0.0983   7.36   7.33   7.87     7.68   7.96   3.94   3.93   3.51    3.48       3.22   34.51    32.1   34.73   34.89   35.91
Philippines                          -0.041    0.0198    0.0874                 7.25     7.04   7.14                 3.29    3.48        3.2                   13.34   16.41   14.92
                                                                                        28

Rwanda                               -0.0356     0.0465   0.1079                    5.62     5.44   5.67                   2.86     3.02   2.92                    3.57   11.67    6.87
Senegal          0.0368    -0.0759   -0.0368     0.0733   0.0336     6.67   6.85    6.47     6.29   6.65   3.51    3.33    3.52      3.4    3.3    2.65    7.11    4.76    3.64    6.21
Turkey                                0.0177     0.1291   0.0503                    8.16     8.25   8.89                   2.56     2.27   2.14                    18.5   20.98    14.1
Tanzania                   -0.0104    0.0805     0.0211   0.0481            5.48    5.43     5.83   5.94           3.22    3.47     3.41   3.77           12.24   17.59   16.82   17.29
Uganda                      0.0024    -0.041     0.0264   0.0663            5.77    5.78     5.57   5.71           2.92    2.87     2.95   3.13            0.52    0.57    1.12    2.21
Uzbekistan                           -0.0312     -0.011                             6.58     6.42                          2.56     2.65                          30.29   34.93
Vietnam                                0.048     0.0891   0.1038                    5.92     6.16    6.6                   4.01     3.84   3.67                   13.53   18.58   19.91
Zambia                     -0.0368   -0.0464     0.1075                     6.28    6.09     5.86                  4.23    4.53      4.6                   8.45    5.28    6.21
Zimbabwe                   -0.0688    -0.072    -0.0636    0.051            7.03    6.69     6.33   6.01           3.86    3.72     3.83      4            2.81    2.46    3.11    1.34
Total             0.004     0.0128   -0.0196     0.0589   0.0715      7.3   6.69    6.59     6.34   6.56   3.66    3.52    3.69     3.78   3.69   22.49   15.15   16.06   16.22      14

The summary statistics correspond to the data used in the regressions. Further summary statistics are available from the authors.
Table 3. Economic growth on total inequality
Income/expenditure survey sample

                                                         Long-run-   Difference              System-GMM
                                     OLS        FE
                                                            OLS        GMM           Full      Collapse        PCA
                                      (1)         (2)        (3)         (4)          (5)         (6)          (7)
Log initial GDP per capita        -0.005      -0.206***  -0.007      -0.190*** -0.016         -0.030      -0.037**
                                  (0.004)     (0.051)    (0.006)     (0.045)      (0.012)     (0.027)     (0.015)
Total inequality (set 1) (lagged) -0.037*     -0.174*    0.000       -0.219*      -0.102** -0.241*        -0.199
                                  (0.021)     (0.092)    (0.020)     (0.127)      (0.045)     (0.125)     (0.119)
Fem. second. educ. (lagged)       0.052       1.138**    -0.005      2.379**      0.137*      0.478       0.222
                                  (0.049)     (0.516)    (0.060)     (0.992)      (0.069)     (0.322)     (0.158)
Male second. educ. (lagged)       -0.021      -0.952     0.071       -2.272**     -0.099      -0.642      -0.236
                                  (0.056)     (0.579)    (0.068)     (1.087)      (0.100)     (0.428)     (0.229)
Price level of inv. (lagged)      -0.001*** 0.000        -0.000      -0.000       -0.001*     -0.001      -0.000
                                  (0.000)     (0.001)    (0.000)     (0.001)      (0.000)     (0.001)     (0.000)
Indicator of income data          -0.015                 -0.020                   0.010       0.051       0.057
                                  (0.010)                (0.015)                  (0.029)     (0.056)     (0.043)
Constant                          0.156*** 1.805***      0.112**                  0.251*** 0.492**        0.422***
                                  (0.037)     (0.429)    (0.043)                  (0.077)     (0.214)     (0.134)
Observations                      118         118        43          75           118         118         118
PCA                                                                                                       Yes
Collapse                                                                                      Yes
Countries                                     43                     43           43          43          43
Instruments                                                          37           56          28          24
Hansen                                                               0.840        0.930       0.142       0.0000214
Sargan                                                               0.0159       0.0189      0.000765 0.500
AR1                                                                  0.325        0.0585      0.133       0.0485
AR2                                                                  0.819        0.356       0.682       0.407
Components                                                                                                18
One-step GMM estimation method. Standard errors in parentheses. Period dummies not reported. LR-OLS omits period
dummies and uses average annual growth over the last decade a particular country is observed for. Education defined
as proportion of adult (fe)male population with some secondary education or above. Sources: Country-specific
household surveys, World Development Indicators, Penn World Tables, and Lutz et al. (2007, 2010). Inequality indices
are constructed using household income or expenditure data.
* p < 0.1, ** p<0.05, *** p < 0.01
                                                        30

Table 4. Economic growth on total inequality
Demographic and Health Survey sample

                                                      Long-run-    Difference           System-GMM
                                     OLS     FE
                                                          OLS        GMM          Full      Collapse      PCA
                                    (1)        (2)        (3)           (4)        (5)         (6)         (7)
Log initial GDP per capita       -0.001    -0.138***  -0.006        -0.166*** -0.006       -0.024      0.020
                                 (0.006)   (0.026)    (0.009)       (0.034)    (0.009)     (0.021)     (0.031)
Total inequality (lagged)        -0.001    0.016      -0.006        0.037      0.003       -0.022      0.034
                                 (0.004)   (0.022)    (0.005)       (0.025)    (0.009)     (0.045)     (0.049)
Fem. second. educ. (lagged)      0.053     0.284      -0.178        0.682      0.097       0.223       0.117
                                 (0.104)   (0.523)    (0.145)       (0.824)    (0.183)     (0.320)     (0.839)
Male second. educ. (lagged)      -0.003    -0.236     0.217*        -0.400     -0.027      -0.137      -0.278
                                 (0.083)   (0.468)    (0.118)       (0.753)    (0.166)     (0.360)     (0.883)
Price level of inv. (lagged)     -0.000    0.000      0.000         0.000      0.000       -0.000      0.001***
                                 (0.000)   (0.000)    (0.000)       (0.000)    (0.000)     (0.000)     (0.000)
Constant                         0.011     0.790***   0.085                    0.017       0.243       -0.287
                                 (0.057)   (0.202)    (0.061)                  (0.096)     (0.321)     (0.359)
Observations                     134       134        42            89         134         134         134
PCA                                                                                                    Yes
Collapse                                                                                   Yes
Countries                                  42                       42         42          42          42
Instruments                                                         52         73          29          22
Hansen                                                              0.965      0.999       0.359       0.214
Sargan                                                              0.0397     0.107       0.205       0.698
AR1                                                                 0.0665     0.000704 0.000923 0.00996
AR2                                                                 0.242      0.121       0.184       0.230
Components                                                                                             17
One-step GMM estimation method. Standard errors in parentheses. Period dummies not reported. LR-OLS omits
period dummies and uses average annual growth over the last decade a particular country is observed for.
Education defined as proportion of adult (fe)male population with some secondary education or above. Sources:
Country-specific household surveys, World Development Indicators, Penn World Tables, and Lutz et al. (2007,
2010). Inequality indices are constructed using data from the Demographic and Health Surveys.
* p < 0.1, ** p<0.05, *** p < 0.01
                                                            31



Table 5. Economic growth on inequality of opportunity and residual inequality
Income/expenditure survey sample

                                                         Long-                           System-GMM
                                                                  Difference
                                     OLS       FE         run-
                                                                    GMM          Full     Collapse     PCA
                                                          OLS
                                     (1)        (2)        (3)        (4)          (5)       (6)         (7)
Log initial GDP per capita       -0.003     -0.224***   -0.007    -0.219***    -0.016     -0.027     -0.036**
                                 (0.005)    (0.050)     (0.006)   (0.051)      (0.012)    (0.025)    (0.018)
Residual inequality (set 2)
(lagged)                         -0.036     -0.210      0.029     -0.228       -0.099     -0.114     -0.252*
                                 (0.035)    (0.145)     (0.075)   (0.211)      (0.079)    (0.239)    (0.128)
Inequality of Opportunity
(set 2) (lagged)                 -0.070     -0.050      -0.072    -0.088       -0.156     -0.679     -0.388
                                 (0.074)    (0.193)     (0.087)   (0.244)      (0.172)    (0.534)    (0.377)
Fem. second. educ.
(lagged)                         0.069      0.991*      -0.008    2.256**      0.102      0.380      0.194
                                 (0.046)    (0.497)     (0.081)   (0.993)      (0.070)    (0.364)    (0.150)
Male second. educ.
(lagged)                         -0.052     -0.819      0.080     -2.210**     -0.078     -0.613     -0.213
                                 (0.055)    (0.563)     (0.111)   (1.083)      (0.091)    (0.530)    (0.233)
Price level of inv. (lagged)     -0.001**   0.000       -0.000    -0.000       -0.000     0.000      -0.000
                                 (0.000)    (0.001)     (0.000)   (0.001)      (0.000)    (0.001)    (0.001)
Indicator of income data         -0.023*                -0.026                 0.007      0.015      0.054
                                 (0.011)                (0.016)                (0.032)    (0.090)    (0.059)
Constant                         0.143***   1.933***    0.102*                 0.243***   0.441*     0.441***
                                 (0.041)    (0.445)     (0.058)                (0.087)    (0.221)    (0.114)
Observations                     118        118         43     75              118        118        118
PCA                                                                                                  Yes
Collapse                                                                              Yes
Countries                                 43                   43          43         43         43
Instruments                                                    44          65         35         29
Hansen                                                         0.761       0.949      0.273      0.00145
Sargan                                                         0.0160      0.0268     0.00479 0.0403
AR1                                                            0.296       0.0420     0.131      0.101
AR2                                                            0.721       0.398      0.719      0.445
Components                                                                                       19
One-step GMM estimation method. Standard errors in parentheses. Period dummies not reported. LR-OLS
omits period dummies and uses average annual growth over the last decade a particular country is
observed for. Quartic polynomial in the number of types included throughout. Education defined as
proportion of adult (fe)male population with some secondary education or above. Sources: Country-specific
household surveys, World Development Indicators, Penn World Tables, and Lutz et al. (2007, 2010).
Inequality indices are constructed using household income or expenditure data.
* p < 0.1, ** p<0.05, *** p < 0.01
                                                          32



Table 6. Economic growth on inequality of opportunity and residual inequality
Demographic and Health Survey sample

                                                          Long-run-   Difference
                                      OLS         FE                                         System-GMM
                                                             OLS        GMM
                                                                                      Full      Collapse     PCA
                                       (1)        (2)         (3)         (4)          (5)        (6)         (7)
Log initial GDP per capita           -0.003    -0.005     -0.137***   -0.158***    -0.017*     -0.022      0.003
                                     (0.007)   (0.010)    (0.028)     (0.033)      (0.010)     (0.020)     (0.018)
Residual inequality (lagged)         -0.001    -0.001     0.022       0.014        -0.006      0.009       0.019
                                     (0.006)   (0.007)    (0.031)     (0.037)      (0.012)     (0.039)     (0.048)
Inequality of Opportunity (lagged)   0.006     -0.017**   0.005       0.040        0.015       0.050       0.012
                                     (0.007)   (0.008)    (0.040)     (0.035)      (0.011)     (0.048)     (0.038)
Fem. second. educ. (lagged)          0.047     -0.176     0.365       0.753        0.170       0.115       0.222
                                     (0.106)   (0.150)    (0.621)     (0.865)      (0.159)     (0.286)     (0.538)
Male second. educ. (lagged)          0.001     0.232*     -0.350      -0.632       -0.104      -0.063      -0.233
                                     (0.098)   (0.133)    (0.546)     (0.769)      (0.136)     (0.318)     (0.403)
Price level of inv. (lagged)         -0.000    0.000      0.000       -0.000       -0.000      -0.000      0.001**
                                     (0.000)   (0.000)    (0.000)     (0.000)      (0.000)     (0.000)     (0.000)
Constant                             0.025     0.061      0.808***                 0.128       0.093       -0.119
                                     (0.061)   (0.070)    (0.238)                  (0.097)     (0.260)     (0.227)
Observations                         134       42         134         89           134         134         134
PCA                                                                                                        Yes
Collapse                                                                                       Yes
Countries                                                 42          42           42          42          42
Instruments                                                           63           88          37          30
Hansen                                                                0.985        1.000       0.363       0.468
Sargan                                                                0.0357       0.149       0.268       0.605
AR1                                                                                                        0.0016
                                                                     0.0234       0.000605 0.000757 3
AR2                                                                  0.117        0.102        0.203       0.136
Components                                                                                                 21
One-step GMM estimation method. Standard errors in parentheses. Period dummies not reported. LR-OLS omits
period dummies and uses average annual growth over the last decade a particular country is observed for. Quartic
polynomial in the number of types included throughout. Education defined as proportion of adult (fe)male
population with some secondary education or above. Sources: Country-specific household surveys, World
Development Indicators, Penn World Tables, and Lutz et al. (2007, 2010). Inequality indices are constructed using
data from the Demographic and Health Surveys.
* p < 0.1, ** p<0.05, *** p < 0.01
                                                                                                                   33


Table A1. List of countries included in the Income and Expenditure Surveys sample

                                     Welfare                                                                                                                                                                          Number
Country          Source                                                                     Circumstance variable                                                                                                                                 Survey years
                                     Variable                                                                                                                                                                         of Types




                                                 gender

                                                          ethnicity

                                                                      language

                                                                                 religion

                                                                                             citizen

                                                                                                       immigrant

                                                                                                                        country born

                                                                                                                                       disability

                                                                                                                                                    father educ

                                                                                                                                                                  mother educ

                                                                                                                                                                                birth region

                                                                                                                                                                                               region of residence
                                                                                                                                                                                                                     Set           1981-   1986-     1991-   1996-   2001-
                                                                                                                                                                                                                           Set 2
                                                                                                                                                                                                                      1            1985    1990      1995    2000    2005




Australia        LIS               Income        1                                                                      1                                                                      1                     10    70      1985    1989      1995
Austria          LIS               Income        1                                           1                                                                                                 1                     8     44                        1995    2000    2004
Bangladesh       I2D2              Expenditure   1                               1                                                                                                                                   10    10                        1991    2000    2005
Belgium          LIS               Income        1                                           1                                                                                                 1                     11    25                        1995    2000
Belize           I2D2              Income        1        1                                                                                                                                    1                     10    92                        1994    1999
Bolivia          SEDLAC            Income        1        1           1                                                                                                                        1                     50    325                               2000    2005
Brazil           SEDLAC            Income        1        1                                                                                                                     1                                    259   259                       1995    1999    2005
Bulgaria         I2D2              Expenditure   1        1                                                                                                                                    1                     66    120                       1995    2001
Canada           LIS               Income        1                                                     1                               1                                                       1                     8     22      1981    1987      1991    2000    2004
Chile            SEDLAC            Income        1        1           1                                                                                                                        1                     30    427                               2000    2003
                 National
                 Quality of Life
Colombia         Survey            Expenditure   1                                                                                                  1             1             1                                    994   994                               1997    2003
Czech Republic   LIS               Income        1                                           1                                         1                                                       1                     18    182                               1996    2004
Denmark          LIS               Income        1                                                     1                               1                                                       1                     8     213             1987      1995    2000    2004
Estonia          LIS               Income        1        1                                  1                                         1                                                       1                     43    418                               2000    2004
Finland          LIS               Income        1                    1                                                                1                                                       1                     67    506                       1995    2000    2004
France           LIS               Income        1                                           1                                                                                                 1                     10    209                       1994    2000    2005
Germany          LIS               Income        1                                                                      1              1                                                       1                     108   1025                      1994    2000    2004
Ghana            I2D2              Expenditure   1        1                                                                                                                                    1                     10    85                        1991    1998    2005
Greece           LIS               Income        1                                           1                                         1                                                       1                     12    45                        1995    2000    2004
Guyana           I2D2              Income        1        1                                                                                                                                    1                     12    113                       1992    1999
Hungary          LIS               Income        1        1                                                                                                                                    1                     4     16                        1994    1999    2005
India            I2D2              Expenditure   1        1                      1                                                                                                             1                     38    1224                      1993    1999    2004
                                                                                  34


Ireland          LIS             Income           1                                    1   1                    1     15    90                        1995      2000    2004
Israel           LIS             Income           1    1                                                              8     8                 1986    1992      1997    2005
Italy            LIS             Income           1                                    1   1                    1     16    271               1989    1995      2000    2004
Kyrgyzstan       I2D2            Expenditure      1                                    1                        1     16    136                                 1997    2002
Luxembourg       LIS             Income           1                     1                                             6     6                         1994      2000    2004
Nicaragua        SEDLAC          Income           1    1     1                                            1           139   139                                 2001    2005
Norway           LIS             Income           1                           1        1   1                    1     83    255                                 2000    2004
                 Living
                 Standard
                 Household
Panama           Survey          Expenditure      1          1                         1       1     1                499   499                                 1997    2003
Paraguay         SEDLAC          Income           1          1                                            1           109   109                                 1999    2005
Peru             SEDLAC          Income           1    1                                                  1           246   246                                 2001    2005
Poland           LIS             Income           1                                        1                    1     4     289                                 1999    2004
Romania          I2D2            Expenditure      1                                    1                        1     10    394                       1994      2002    2006
                 Longitudinal
                 Monitoring
Russia           Survey          Income           1                     1              1                        1     42    103                       1994      2000    2005
Rwanda           I2D2            Expenditure      1                1                                            1     8     144                                 2000    2005
Spain            LIS             Income           1                     1                  1                    1     8     50                        1995      2000    2004
Sweden           LIS             Income           1                     1                  1                    1     21    113                       1995      2000    2005
Switzerland      LIS             Income           1          1          1                                       1     18    53                        1992      2000    2004
United Kingdom   LIS             Income           1    1                                   1                    1     24    292                       1994      1999    2004
United States    LIS             Income           1    1                                   1                    1     16    64       1986     1991    1994      2000    2004
Vietnam          I2D2            Expenditure      1    1                                                        1     20    124                       1993      1998    2006
West Germany     LIS             Income           1                                    1                        1     10    211      1984     1989
Number of observations (Total and per year)                                                                                 118      4        7       29        41      37
Number of countries                                                                                                         43

Notes: Income refers to per capita household income (net). Expenditure refers to per capita household expenditure. The circumstances birth region and region of residence may
contain more than one variable (e.g. administrative region and rural/urban). The number of types is the average across the years for a given country, rounded to the nearest
integer. The number of types may differ across years for a given country if some categories are unobserved in a particular year.
LIS: Luxemburg Income Study
SEDLAC: Socioeconomic Database for Latin America and the Caribbean (CEDLAS-World Bank)
I2D2: International Income Distribution Database
                                                                            35


Table A2. List of countries included in the Demographic and Health Survey sample.

                                                       Circumstance variables
                            Welfare                                                        Number     1982-   1987-   1992-   1997-   2002-
       Country                           Region      No. of              Ethnic   Mother
                            variable                          Religion                     of types   1986    1991    1996    2001    2006
                                         of birth   siblings              group   tongue
Armenia                 Wealth Index                                              1        3                                  2000    2005
Bangladesh              Wealth Index                         1                             4                  1993    1996    1999    2004
Benin                   Wealth Index    1                    1          1                  213                        1996    2001    2006
Bolivia                 Wealth Index    1                                                  4                          1994    1998    2003
Brazil                  Wealth Index    1                    1                             16         1986    1991    1996
Burkina Faso            Wealth Index                         1          1                  38                         1992    1998    2003
Cambodia                Wealth Index    1                    1                             20                                 2000    2005
Cameroon                Wealth Index    1                    1          1                  30                 1991            1998    2004
Colombia                Wealth Index    1                                                  3          1986    1990    1995
Cote d'Ivoire           Wealth Index                         1          1                  24                         1994    1998    2005
Dominican Republic      Wealth Index    1                                                  2          1986    1991    1996    1999    2002
Egypt                   Wealth Index    1                                                  2          1988    1992    1995    2000    2003
Ethiopia                Wealth Index    1                    1                    1        93                                 2000    2005
Ghana                   Wealth Index    1                    1          1                  83                 1988    1993    1998    2003
Guatemala               Wealth Index    1                               1                  6                  1987    1995    1998
Guinea                  Wealth Index    1                    1          1         1        175                                1999    2005
Haiti                   Wealth Index                         1                             4                          1994    2000    2005
India                   Wealth Index                         1          1         1        166                        1992    1998    2005
Indonesia               Wealth Index                         1                             6                  1991    1994    1997    2002
Jordan                  Wealth Index                         1                             2                  1990            1997    2002
Kazakhstan              Wealth Index    1                    1          1                  65                         1995    1999
Kenya                   Wealth Index    1                    1          1                  105                1989    1993    1998    2003
Madagascar              Wealth Index    1           1        1                             63                         1992    1997    2003
Malawi                  Wealth Index    1           1                                      15                         1992    2000    2004
Mali                    Wealth Index                         1          1                  21                 1987    1995    2001    2006
Mozambique              Wealth Index    1           1                             1        279                                1997    2003
Namibia                 Wealth Index    1                    1                             19                         1992    2000    2006
Nepal                   Wealth Index                         1          1         1        87                         1996    2001    2006
Nicaragua               Wealth Index    1                                                  4                          1997    2001
Niger                   Wealth Index    1                    1          1                  29                         1992    1998    2006
                                                                                   36


Nigeria                    Wealth Index       1                    1                                12                   1990              1999    2003
Peru                       Wealth Index       1                                                     3           1986     1992     1996     2000    2004
Philippines                Wealth Index                            1           1          1         148                           1993     1998    2003
Rwanda                     Wealth Index       1                                                     2                             1992     2000    2005
Senegal                    Wealth Index                                        1                    6           1986     1992     1997     1999    2005
Tanzania                   Wealth Index       1                    1                                10                   1992     1996     1999    2004
Turkey                     Wealth Index       1                                           1         9                             1993     1998    2003
Uganda                     Wealth Index                            1                                3                    1988     1995     2000    2006
Uzbekistan                 Wealth Index       1                    1           1          1         55                            1996     2002
Vietnam                    Wealth Index                            1           1                    27                            1997     2002    2005
Zambia                     Wealth Index                            1           1          1         107                  1992     1996     2001
Zimbabwe                   Wealth Index                            1                                3                    1988     1994     1999    2005
Number of observations (Total and per year)                                                         134         6        19       34       40      35
Number of countries                                                                                 42

The number of types is the average across the years for a given country, rounded to the nearest integer. The number of types may differ across years for a
given country if some categories are unobserved in a particular year.
                                                      37

Table A3. Robustness checks on the System-GMM
Only coefficients on inequality are reported

                                                                                      PCA + Restricted number of
                                                                                             components
                                                       Full         Full PCA
                                                                                     15          10         6 or 7
                                                       (1)            (2)            (3)         (4)          (5)
A. Total inequality - Income and Expenditure Surveys (Table 3)
Total inequality (lagged)                          -0.102**      -0.199           -0.117     -0.184       -0.871*
                                                   (0.045)       (0.119)          (0.101)    (0.173)      (0.505)
Hansen p-value                                     0.930         0.0000214        0.305      0.135        0.857
Instrument count                                   56            24               21         16           12
Component count                                                  18               15         10           6
B. Total inequality - Demographic and Health Surveys (Table 4)
Total inequality (lagged)                         0.003          0.034            0.001      0.042        -0.016
                                                    (0.009)      (0.049)          (0.052)    (0.115)      (0.467)
Hansen p-value                                      0.999        0.214            0.700      0.985        0.419
Instrument count                                    73           22               20         15           11
Component count                                                  17               15         10           6
C. Inequality of opportunity (set 2) - Income and Expenditure Surveys (Table 5)
Residual inequality (lagged)                        -0.099       -0.252*          -0.149     -0.803**     -0.923
                                                   (0.079)       (0.128)          (0.241)    (0.357)      (0.588)
Inequality of Opportunity inequality (lagged)      -0.156        -0.388           -0.483     0.688        1.236
                                                   (0.172)       (0.377)          (0.543)    (1.131)      (2.120)
Hansen p-value                                     0.949         0.00145          0.427      0.325        0.179
Instrument count                                   65            29               25         20           17
Component count                                                  19               15         10           7
D. Inequality of opportunity - Demographic and Health Surveys (Table 6)
Residual inequality (lagged)                      -0.006        0.019              0.010       -0.038    0.123
                                                   (0.012)        (0.048)          (0.082)     (0.178)   (0.432)
Inequality of Opportunity inequality (lagged)      0.015          0.012            0.057       0.088     0.455
                                                   (0.011)        (0.038)          (0.057)     (0.127)   (0.567)
Hansen p-value                                     1.000          0.468            0.611       0.948     0.878
Instrument count                                   88             30               24          19        16
Component count                                                   21               15          10        7
One-step GMM estimation method. Standard errors in parentheses. Specifications as in the main tables. The smallest
number of components considered is 6 for total inequality and 7 for inequality of opportunity.
Columns (1) and (2) are reproduced from the main tables.
                                                 38

 Table A4. Economic growth on inequality decomposed into residual and between inequality
Income/expenditure survey sample

                                           Long-run-             Difference
                                  OLS                    FE                              System-GMM
                                              OLS                  GMM
                                                                                 Full     Collapse    PCA
                                   (1)         (2)       (3)       (4)            (5)        (6)      (7)
Log initial GDP per capita     -0.007      -0.216***   -0.004 -0.216***       -0.025      -0.053* -0.076***
                               (0.006)     (0.065)     (0.010) (0.054)        (0.015)     (0.030) (0.022)
Residual inequality (set 1)
(lagged)                       -0.042      -0.271*     0.033   -0.329         -0.150*     -0.384*   -0.603***
                               (0.033)     (0.143)     (0.048) (0.214)        (0.080)     (0.196)   (0.205)
Inequality of Opportunity
(set 1) (lagged)               -0.136      0.228       -0.128    0.327        -0.177      -0.189    0.005
                               (0.088)     (0.472)     (0.172)   (0.584)      (0.264)     (0.953)   (0.832)
Fem. second. educ. (lagged)    0.043       1.226**     -0.034    2.312**      0.178**     0.496     0.361
                               (0.049)     (0.497)     (0.081)   (0.878)      (0.086)     (0.350)   (0.247)
Male second. educ. (lagged)    -0.009      -1.059*     0.112     -2.223**     -0.128      -0.624    -0.426
                               (0.058)     (0.549)     (0.100)   (0.941)      (0.105)     (0.439)   (0.335)
Price level of inv. (lagged)   -0.001***   0.000       -0.000    -0.000       -0.001      -0.000    -0.000
                               (0.000)     (0.001)     (0.000)   (0.001)      (0.000)     (0.001)   (0.001)
Indicator of income data       -0.010                  -0.030                 0.040       0.119     0.203***
                               (0.016)                 (0.032)                (0.039)     (0.074)   (0.068)
Constant                       0.168***    1.830***    0.083                  0.314***    0.625**   0.784***
                               (0.049)     (0.555)     (0.069)                (0.106)     (0.238)   (0.164)
Observations                   118         118         43       75            118         118       118
PCA                                                                                                 Yes
Collapse                                                                                 Yes
Countries                                  43                   43           43          43         43
Instruments                                                     44           65          35         31
Hansen                                                          0.677        0.975       0.265      0.771
Sargan                                                          0.0123       0.0355      0.00697 0.509
AR1                                                             0.195        0.0618      0.0934     0.0890
AR2                                                             0.622        0.396       0.562      0.364
Components                                                                                          21
One-step GMM estimation method. Standard errors in parentheses. Period dummies not reported. LR-OLS
omits period dummies and uses average annual growth over the last decade a particular country is observed
for. Quartic polynomial in the number of types included throughout. Education defined as proportion of adult
(fe)male population with some secondary education or above. Sources: Country-specific household surveys,
World Development Indicators, Penn World Tables, and Lutz et al. (2007, 2010). Inequality indices are
constructed using household income or expenditure data.
* p < 0.1, ** p<0.05, *** p < 0.01