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Policy Research Working Paper 9409
Development Economics Development Research GroupSeptember 2020
The Role of Inequality for Poverty ReductionKaty Bergstrom
Poverty and Shared Prosperity 2020
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Produced by the Research Support Team
Abstract
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Policy Research Working Paper 9409
Using World Bank PovcalNet data from 1974 –2018 for 135 countries, this paper approximates the identity that links growth in mean incomes and changes in the distribution of relative incomes to reductions in absolute poverty, and, in turn, examines the role of income inequality for pov-erty reduction. The analysis finds that the assumption that income is log-normally distributed allows one to approxi-mate the identity well. Using this approximation, both the growth and inequality elasticities of poverty reduction are calculated. The inequality elasticity of poverty reduction is larger, on average, compared to the (absolute) growth
elasticity of poverty reduction. Moreover, the (absolute) growth elasticity declines steeply with a country’s initial level of inequality. However, despite these results, most of the observed changes in poverty can be explained by changes in mean incomes. This is a consequence of changes in income inequality (as measured by percentage changes in the standard deviation of log-income) being an order of magnitude smaller than changes in mean incomes. Overall, the results highlight the important role income inequality can play in reducing poverty even if prior poverty changes have, in large part, been a consequence of economic growth.
This paper is a product of the Development Research Group, Development Economics. 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://www.worldbank.org/prwp. The author may be contacted at [email protected].
The Role of Inequality for Poverty Reduction
Katy Bergstrom∗
∗Development Research Group, World Bank. Email: [email protected]. Thanks to SamuelFreije-Rodriguez, Daniel Mahler, Christoph Lakner, Aart Kraay, Berk Ozler, Marta Schoch, Judy Yang,and Michael Woolcock for their valuable comments and suggestions. This is a background paper for thePoverty and Shared Prosperity 2020. The findings, interpretations, and conclusions expressed in thispaper are entirely those of the author. They do not necessarily represent the views of the World Bankand its affiliated organizations, or those of the Executive Directors of the World Bank or the governmentsthey represent.
I Introduction
It has long been established that an arithmetic identity exists between changes in
absolute poverty, changes in mean incomes, and changes in the distribution of relative
incomes (Datt and Ravallion, 1992; Kakwani 1993; Bourguignon, 2003). Generally speak-
ing, poverty reduction in a country can be decomposed into higher average growth, a
reduction in inequality of incomes, or a combination of the two. Moreover, due to the
non-linear nature of this identity, it has been shown that the sensitivity of poverty to
growth in mean incomes is dependent on a country’s initial level of inequality: in gen-
eral, the (absolute) growth elasticity of poverty is decreasing in a country’s initial level of
income inequality.1 The literature refers to this as the double-dividend effect of reducing
inequality today: a reduction in inequality today leads to a reduction in poverty today
and an acceleration of poverty reduction in the future (Bourguignon, 2004; Alvaredo and
Gasparini, 2015).
Several papers have sought to empirically approximate this identity, and, in turn,
quantify the role that growth in mean incomes and reductions in inequality play (and
have played) in poverty reduction.2 Despite the various specifications used to approximate
the identity, these papers offer similar conclusions: over the past few decades, growth in
mean incomes has been the primary driver of reductions in poverty, although changes in
inequality have played a non-negligible role both through the direct effect of inequality
on poverty and the indirect effect inequality has on the growth elasticity. Using the latest
cross-country data, this paper seeks to update the empirical estimation of this identity,
and, in turn, re-examine the role of income inequality for poverty reduction.
To begin, we re-derive the identity that exists between changes in poverty, changes
in inequality, and changes in mean incomes. Using World Bank PovcalNet data from
1974-2018 for 135 countries, we then search for an empirical model that allows us to
approximate the identity well. We find that the assumption that per-capita income is
log-normally distributed leads to a very decent approximation: our model is able to
explain 94% of the variation in observed changes in headcount poverty.3 Using this ap-
proximation, we empirically quantify the importance of changes in inequality on poverty
vs. changes in mean incomes on poverty. We find that for most countries, a 1% reduction
in inequality (as measured by the standard deviation of log-income) leads to a larger
1. To be precise, the effect that initial inequality has on the growth elasticity is theoretically ambiguous(Ravallion, 2007). However, under certain assumptions it can be shown that the (absolute) growthelasticity of poverty is unambiguously decreasing with inequality (Bourguignon, 2003; Ferriera, 2012).
2. See, for example, Bourguignon (2003), Kraay (2006), Lopez and Serven (2006), Kalwij and Ver-schoor (2007), Klasen and Misselhorn (2008), Bluhm et al (2016), and Fosu (2017).
3. This R2 is notably higher than that found in Bourguignon (2003) and Klasen and Misselhorn(2008) who also approximate the identity under the assumption that income is log-normally distributed.We believe our improved fit is due to two reasons: first, we use a much larger dataset, and second, weestimate a version of the identity that allows for discrete changes in mean incomes and inequality.
2
reduction in poverty relative to a 1% increase in mean income. In particular, we find that
post 2010, the median elasticity of poverty w.r.t. inequality is 5.19, while the median
elasticity of poverty w.r.t. growth is only 2.78. Furthermore, we find substantial hetero-
geneity in these elasticities; in particular, the growth elasticity is decreasing sharply in
initial inequality. However, despite these results, we also find that most of the observed
changes in poverty over this time frame can be explained by changes in mean incomes.
This is a consequence of average percentage changes in mean incomes being an order
of magnitude larger than average percentage changes in inequality. Moreover, we find
that 90% of the variation in changes in poverty can be explained by changes in mean
incomes. Finally, to further illustrate our results, we project headcount poverty for 2030
under various hypothetical scenarios. We show that 1% per-annum declines in inequality
over 2020-2030 lead to greater reductions in worldwide poverty compared to 1% increases
in mean incomes.4 These projections highlight the important role inequality can play
in reducing future poverty even if prior poverty reductions have, in large part, been a
consequence of economic growth.
To conclude, we discuss what our findings imply for policies aimed at reducing poverty.
While our analysis shows that reductions in inequality can lead to meaningful reductions
in poverty, we are cautious to offer guidance from this analysis alone for two reasons. First,
our analysis abstracts from the possibility that inequality can have additional impacts
on poverty through its effect on growth. The theoretical literature has developed many
intricate theories about how inequality impacts growth; however, there are numerous
competing effects, so ultimately this is an empirical question.5 But the empirical literature
has produced very mixed results.6 It has been suggested that these mixed results reflect
a gap between the intricacy of the relationship, as expressed in the theoretical literature,
and the simple relations that are commonly estimated (Voitchovsky, 2009). In support of
a more complex relationship, several papers provide empirical evidence of a non-linear,
4. Using a different model to predict headcount poverty, Lakner et al (2020) also find that reducinginequality by 1% per year leads to a greater reduction in 2030 headcount poverty than 1% increases inmean incomes.
5. Theoretically, the effect of inequality on growth is ambiguous: the conventional view is that higherinequality promotes stronger incentives, generates greater savings and investment, and endows the richwith the minimum capital needed to start economic activity, thereby stimulating growth (Aghion et al,1999; Okun, 2015; Kaldor, 1957; Barro, 2000). Conversely, it has been argued that inequality hurtsgrowth as it leads to redistributive pressure through taxes, social conflict, expropriation, or rent-seekingbehavior (Alesina and Rodrik, 1994; Alesina, 1994; Benhabib and Rustichini, 1996; Benabou, 1996;Perotti, 1996; Persson and Tabellini, 1994; Glaeser et al, 2003); or in the presence of market failures,inequality prevents the talented poor from undertaking profitable investments, thereby limiting growth(Galor and Zeira, 1993; Banerjee and Newman, 1993).
6. Early papers, using a cross-section of countries, typically found negative effects of inequality ongrowth (Alesina and Rodrik, 1994; Persson and Tabellini, 1994). Then, with the introduction of theDeininger and Squire (1996) panel dataset, studies started to find positive effects (Li and Zou, 1998;Forbes, 2000). More recently, however, several papers find again a negative effect (Castello-Climent,2010; Halter et al, 2014; Ostry et al, 2014; and Dabla-Norris et al, 2015), although the validity of theirestimation technique has been questioned (Kraay, 2015).
3
context specific relationship between inequality and growth (Duflo and Banerjee, 2003;
Grigoli et al, 2016; and Grigoli and Robles, 2017).7 Second, our analysis sheds no light
on how observed changes in inequality or growth came about, and, thus, sheds no light
on policy makers’ ability to influence these two variables. One potential concern is that
policy makers’ ability to influence inequality is limited (consistent with the finding that
percentage changes in inequality have been substantially smaller than percentage changes
in mean incomes; however, if prior policies were predominantly focused on enhancing
growth, this could also explain this finding).8 In light of these issues, it is likely worthwhile
for policymakers to utilize case-studies analyzing the impacts of various policies on growth
and inequality. These studies, in conjunction with understanding the extent to which
changes in inequality and growth are transformed into reductions in poverty, should
guide policymakers in designing effective policies to combat poverty.
Our paper is most closely related to Bourguignon (2003), Klasen and Misselhorn
(2008), and Lopez and Serven (2006) who also approximate the poverty decomposition
identity under the assumption that income is log-normally distributed. Moreover, our
paper is similar to Kraay (2006), Kalwij and Verschoor (2007), Bluhm et al (2016), and
Fosu (2017) who also empirically analyze the poverty decomposition identity but use
alternative specifications to do so. Ultimately, our primary contribution is to update the
estimation of this identity by using the latest cross-country data, and, in turn, re-examine
the role that inequality can play (and has played) in poverty reduction.
The remainder of the paper is set up as follows: Section II re-derives the identity
that links changes in mean incomes and inequality to changes in poverty; guided by this
identity, Section III discusses our empirical specifications to be tested and data to be
used, while Section IV estimates these specifications; Section V details the magnitudes of
the effects that reductions in inequality and growth have on poverty; Section VI provides
projections for 2030 headcount poverty under various scenarios; and Section VII discusses
our results in the light of designing policy to reduce poverty.
II Re-Deriving the Identity
In this section, following Bourguignon (2003), we re-derive the identity between
growth in mean incomes in a population, the change in the distribution of relative in-
comes, and the change in absolute poverty. First, let F (y; Ωt) denote the CDF of incomes
7. Another potential explanation for the mixed empirical results is that different forms of inequality,in particular, inequality of opportunity vs. inequality of effort, have differing effects on growth. Howeverempirical investigation of this question has not led to robust findings (see Ferreira et al (2014)).
8. Furthermore, Dollar et al (2016), using cross-country regressions, are unable to find correlates withchanges in inequality, potentially highlighting the difficulty of influencing inequality; alternatively, thiscould simply reflect a limitation of cross-country specifications.
4
yt in society in period t where Ωt denotes the parameters governing the distribution, e.g.,
if incomes come from the log-normal distribution then Ωt = µt, σt where µt and σt
denote the mean and standard deviation of log income in period t, respectively. Let z de-
note the fixed poverty-line, let yt denote mean incomes in period t, and let Ht = F (z; Ωt)
denote headcount poverty, i.e., the fraction of individuals with incomes less than the
poverty line in period t. Throughout the paper, we will set z = $1.90 per-capita, per-day.
Next, let F ( yyt
; θt) denote the CDF of mean-normalized incomes ytyt
in period t, where
the PDF is given by f( yyt
; θt) = ytf(y; Ωt), where f(y; Ωt) denotes the PDF of incomes in
period t. Note, θt denotes the parameters governing the distribution of mean-normalized
incomes. For example, if log(y) ∼ N(µt, σ2t ) then log(y/yt) ∼ N(−σ2/2, σ2) meaning
θt = σt. Trivially, Ht = F (z; Ωt) = F(zyt
; θt
).
Using this notation, we can express the change in the poverty headcount from t to t′
using the following expression:
Ht′ −Ht = F
(z
yt′; θt′
)− F
(z
yt; θt
)=
(F
(z
yt′; θt
)− F
(z
yt; θt
))︸ ︷︷ ︸
growth component
+
(F
(z
yt′; θt′
)− F
(z
yt′; θt
))︸ ︷︷ ︸
distribution component
(1)
where the growth component in Equation (1) captures the change in poverty due to
changes in mean income (i.e., due to growth), and the distribution component captures
the change in poverty due to changes in the distribution of relative incomes (captured by
changes in the parameters that govern the distribution, θt).9 Dividing through by t′ − t
and taking the limit as t′ − t→ 0 we get
dHt
dt= −f
(z
yt; θt
)z
yt︸ ︷︷ ︸semi-elasticity w.r.t. growth
1
yt
dytdt
+ Fθt
(z
yt; θt
)θt︸ ︷︷ ︸
semi-elasticity w.r.t. inequality
1
θt
dθtdt (2)
where dXtdt
= limt′−t→0Xt′−Xtt′−t , and where we have denoted the term multiplying the
proportion change in mean incomes, 1yt
dytdt
, as semi-elasticity of poverty w.r.t. growth,
9. Technically our “distribution component” in Equation (1) includes both the distribution componentand a residual (as described in Datt and Ravallion, 1992):(
F
(z
yt′; θt′
)− F
(z
yt′; θt
))︸ ︷︷ ︸
distribution component
=
(F
(z
yt; θt′
)− F
(z
yt; θt
))︸ ︷︷ ︸
distribution component, Datt and Ravallion
+R(t, t′; t)
where R(t, t′; t) denotes the residual term as described in Datt and Ravallion (1992). When doing povertydecompositions in Section V.C, we remove the residual term from the distribution component.
5
and we have denoted the term multiplying the proportion change in the distribution of
incomes, 1θtdθtdt
, as the semi-elasticity of poverty w.r.t. inequality. Dividing through by
Ht = F(zyt
; θt
)everywhere we get:
1
Ht
dHt
dt= −
f(zyt
; θt
)z
F(zyt
; θt
)yt︸ ︷︷ ︸
elasticity w.r.t. growth
1
yt
dytdt
+Fθt
(zyt
; θt
)θt
F(zyt
; θt
)︸ ︷︷ ︸
elasticity w.r.t. inequality
1
θt
dθtdt (3)
Equation (3) illustrates that the percentage change in headcount poverty can be bro-
ken down into the percentage change in mean incomes and a percentage change in the
parameters governing the distribution of relative incomes. Moreover, the extent to which
a change in mean incomes and a change in the distribution affect poverty will depend on
the inverse level of development in period t, zyt
, along with the parameters in the relative
income distribution in period t, θt. In other words, these elasticities are not constant
across countries with different initial conditions. From Equation (3), it is clear that the
growth elasticity is always negative: if there are no changes in the distribution, an in-
crease in mean incomes must be accompanied by a decline in headcount poverty. In other
words, growth must be accompanied by a decline in poverty unless it is accompanied by
a substantial distributional change.
We can take our identity, Equation (3), to the data in two ways. First, if we had
micro-level data for all countries over time, we could non-parametrically identify the
income distributions in each period t and thus non-parametrically estimate these elastici-
ties. Alternatively, if data are limited, one could assume a functional form on the income
distribution and estimate the elasticities under the given functional form assumption. In
particular, the log-normal distribution, which consists of only two parameters, has been
shown to fit the per-capita income distribution very well (Lopez and Serven, 2006). Con-
sistent with this finding, both Bourguignon (2003) and Klasen and Misselhorn (2008) find
that by assuming income is log-normally distributed, they are better able to approximate
the identity relative to alternative specifications. However, the log-normal assumption
is not without criticism. Both Bourguignon (2003) and Klasen and Misselhorn (2008)
find that the log normal approximation does not do well when approximating changes in
the poverty gap as opposed to changes in headcount poverty. Both conjecture that the
log-normal assumption is adequate for approximating a point in the income CDF, but
does poorly when approximating mean incomes below that point. We will focus only on
headcount poverty in this projection, so proceed with analyzing the identity under the
assumption of log-normality.
6
II.A Log Normal Distribution
Let µt, σt denote the mean and standard deviation of log(yt). Let’s assume yt comes
from a log normal distribution, i.e., log(yt) ∼ N(µt, σ2t ). We know the following identity:
yt = eµt+σ2t2
remembering that yt denotes mean income in period t. Rearranging we get:
µt = log(yt)−σ2t
2
Thus, we get log(yt) ∼ N(
log(yt)− σ2t
2, σ2
t
). Hence, we get
log(ytyt
)+σ2t2
σt∼ N (0, 1),
remembering that σt denotes the standard deviation of log income. Thus we get:
F
(y
yt; θt
)= Φ
log(yyt
)σt
+1
2σt
(4)
where Φ denotes the standard normal CDF. Taking the derivative w.r.t. y/yt we get:
f
(y
yt; θt
)= φ
log(yyt
)σt
+1
2σt
ytσty
where φ denotes the standard normal PDF. Taking the derivative of Equation (4)
w.r.t. θt = σt we get:
dF(yyt
; θt
)dθt
= φ
log(yyt
)σt
+1
2σt
1
2−
log(yyt
)σ2t
Hence, Equation (2) becomes:
dHt
dt= −φ
log(zyt
)σt
+1
2σt
1
σt︸ ︷︷ ︸semi-elasticity w.r.t. growth=κy
1
yt
dytdt
+ φ
log(zyt
)σt
+1
2σt
1
2σt −
log(zyt
)σt
︸ ︷︷ ︸
semi-elasticity w.r.t. inequality=κσ
1
σt
dσtdt
(5)
where κy denotes the semi-elasticity of poverty w.r.t. growth when income is log-
normally distributed and κσ denotes the semi-elasticity of poverty w.r.t. inequality when
income is log-normally distributed. Finally, Equation (3) becomes:
7
1
Ht
dHt
dt= −
φ
(log
(zyt
)σt
+ 12σt
)Φ
(log
(zyt
)σt
+ 12σt
)σt︸ ︷︷ ︸
elasticity w.r.t. growth=ξy
1
yt
dytdt
+
φ
(log
(zyt
)σt
+ 12σt
)(12σt −
log(zyt
)σt
)Φ
(log
(zyt
)σt
+ 12σt
)︸ ︷︷ ︸
elasticity w.r.t. inequality=ξσ
1
σt
dσtdt
(6)
where ξy denotes the elasticity of poverty w.r.t. growth when income is log-normally
distributed and ξσ denotes the elasticity of poverty w.r.t. inequality when income is
log-normally distributed.
Finally, we explore how our elasticities vary with mean incomes, y, and inequality, σ.
Figure I shows how |ξy| varies with y and σ (on the left) and how ξσ varies with y and σ
(on the right). As shown in Figure I and as noted in Bluhm et al (2016), both elasticities
are increasing in mean incomes. This is in part because the denominators of both ξy
and ξσ are equal to headcount poverty and headcount poverty approaches zero as mean
incomes become sufficiently large - see Figure II. Because of this somewhat misleading
feature of these elasticities, one should focus most of their attention on comparisons of
|ξy| and ξσ within countries (we will do this in Section V.A). Lastly, Figure I highlights
the double-dividend effect of decreasing inequality: first, it leads to a direct reduction
in poverty (as shown by the positive inequality elasticity); and, second, it leads to an
increase in the absolute growth elasticity thus allowing future growth to generate greater
percentage reductions in poverty (as shown by the absolute growth elasticity decreasing
in initial inequality).
Figure I: How ξy and ξσ vary with mean income, y, and inequality, σ
8
Figure II: How headcount poverty varies with mean income, y, andinequality, σ
III Empirical Specifications
The empirical section of this paper will first be concerned with finding a model that
allows us to approximate the identity well. In this section, we discuss the empirical
models we will test and the data we will use to estimate these models.
Guided by the specifications tested in Klasen and Misselhorn (2008), we test the
following four empirical models:10
dHi,t = a0+a1∆yi,t + εi,t (7)
dHi,t = b0+b1∆yi,t + b2∆σi,t + εi,t (8)
10. In specifications (8) and (9), Klasen and Misselhorn (2008) use the Gini coefficient as the measurefor inequality as opposed to σ. However, as we will soon discuss, σ is simply an increasing function ofthe Gini coefficient; hence, replacing one measure with the other will have minuscule effect on the modelfit.
9
dHi,t = c0+c1∆yi,t + c2∆σi,t + c3∆yi,t × σi,t−n + c4∆yi,t ×z
yi,t−n+
c5∆σi,t × σi,t−n + c6∆σi,t ×z
yi,t−n+ εi,t
(9)
dHi,t = γ0+γ1κy,i,t∆yi,t + γ2κσ,i,t∆σi,t + εi,t (10)
where dHi,t = (Hi,t−Hi,t−n)× 100 denotes the percentage point change in headcount
poverty from year t − n to t for country i (where n can vary by country and year), and
where ∆Xi,t =Xi,t−Xi,t−nXi,t−n
× 100 denotes our percentage change in variables X ∈ y, σfrom year t − n to t for country i. Our measure of income inequality, σi,t, is calculated
from the Gini coefficient, πi,t, as follows:
σi,t =√
2Φ−1
(πi,t + 1
2
)
Thus, σ is simply an increasing function of the Gini coefficient π. Moreover, σ will
be equal to the standard deviation of log income under the assumption that log income
is normally distributed. To understand how the values of σ relate to values of the Gini
coefficient, a Gini coefficient of π = 0.23 (the minimum observed value of π in our sample)
gives σ = 0.41, a Gini coefficient of π = 0.37 (the mean observed value of π in our sample)
gives σ = 0.68, and a Gini coefficient of π = 0.63 (the maximum observed value of π in
our sample) gives σ = 1.27. Moreover, to generate a 1% change in σ, the Gini coefficient
needs to change by < 1%. For example, when σ = 0.68, to generate a 1% change in σ,
the Gini coefficient must change by 0.93%.
In Equation (10), κy,i,t and κσ,i,t denote our theoretical values - under the assumption
of log-normality - of the semi-elasticities of poverty w.r.t. growth and the semi-elasticity
of poverty w.r.t. inequality, respectively:
κy,i,t = −φ(
log
(z
yi,t−n
)1
σi,t−n+
1
2σi,t−n
)1
σi,t−n(11)
κσ,i,t = φ
(log
(z
yi,t−n
)1
σi,t−n+
1
2σi,t−n
)(1
2σi,t−n − log
(z
yi,t−n
)1
σi,t−n
)(12)
If our assumption of log-normality is true, and provided changes in mean incomes and
σ are small, we should find γ0 = 0, γ1 = 1, γ2 = 1 and an R2 = 1 when estimating Equa-
10
tion (10). However, when changes in mean incomes and σ are not small, Equation (10),
even under the assumption of log-normality, only provides a first-order approximation for
the observed change in poverty. Thus, a better test for log-normality is to estimate the
following equation (which allows for discrete changes in both mean incomes and σ - see
Equation (1)):
dHi,t =ω0 + ω1
(Φ
(log
(z
yt
)1
σt−n+
1
2σt−n
)− Φ
(log
(z
yt−n
)1
σt−n+
1
2σt−n
))× 100+
ω2
(Φ
(log
(z
yt
)1
σt+
1
2σt
)− Φ
(log
(z
yt
)1
σt−n+
1
2σt−n
))× 100 + εi,t
(13)
From Equation (1), the term multiplying ω1 in Equation (13) is the “growth component”
while the term multiplying ω2 is the “distribution component” under the assumption
income is log-normal. Thus, if our assumption of log-normality is true, we should find
ω0 = 0, ω1 = 1, ω2 = 1 and an R2 = 1.11
Finally, note, when trying to find the best empirical specification to approximate the
identity, we focus on models that explain percentage point changes in the headcount
poverty as opposed to percentage changes in the headcount poverty. This is motivated
by Klasen and Misselhorn (2008) who discuss the empirical advantages in doing so. In
particular, by estimating semi-elasticities as opposed to elasticities, we place less weight
on countries with very low initial levels of headcount poverty who can easily see very, very
large percentage changes in headcount poverty. For example, in our sample of countries,
between 2005 and 2006 Ireland saw a 1, 726% increase in headcount poverty as they moved
from 0.0217% of their population below the poverty line to 0.396% of their population
below the poverty line. It is desirable to place less weight on these countries given (a) we
are primarily concerned with identifying the drivers of poverty reduction in settings with
substantial poverty to begin with (i.e., countries for which there is room to reduce poverty
substantially), and, (b) for these richer countries, percentage changes in poverty are
driven by changes in incomes in the very left-tails of the income distributions and, thus,
are more likely to be susceptible to measurement error. Consequently, because of these
issues, papers that estimate elasticity models as opposed to semi-elasticity models have
11. Of course, a more direct test of log-normality is to simply regress observed headcount poverty Hi,t
on predicted headcount poverty under the assumption of log-normality, Hi,t = Φ(
log(zyt
)1σt
+ 12σt
).
Results from this regression are presented in Appendix B (we find an extremely good fit: R2 = 0.99).Ultimately, while there are many specifications that can be run to test whether log-normality is a goodapproximation (see Lopez and Serven (2006) for examples of alternative tests), we estimate specifications(10) and (13) in the main text given that (a) our objective is to understand changes in headcount poverty,and (b) we want to be able to compare the fit of our log-normal specifications to the commonly estimatedregressions (7)-(9).
11
to winsorize the data in somewhat of an arbitrary fashion so as to remove observations
whereby the percentage change in headcount poverty is enormous (e.g., Bourguignon,
2003). To further illustrate this issue, in Appendix C, we re-estimate Equations (7)-(10)
using an elasticity framework as opposed to a semi-elasticity framework (i.e., we use ∆H
as our left-hand-side variable as opposed to dH). We show how are results are very
sensitive to including observations where headcount poverty is close to 0.
III.A Data
The data used to estimate Equations (7), (8), (9), (10), and (13) are taken from
PovcalNet for all countries that have at least two surveys where measurement of our key
variables (e.g., headcount poverty rate, Gini coefficient, mean income) remains compara-
ble across the two surveys.12 13This leaves us with a total of 135 countries with surveys
spanning 1974-2018. For each country, we calculate the difference in our key variables
across each pair of consecutive surveys for which measurement of these variables remained
comparable. This gives us a total of 1,307 observations on changes in our keys variables
or, equivalently, 1,307 “growth-spells”. See Table IV in Appendix A for a list of all 135
countries with the range of survey years for each country.
IV Empirical Results
In this section we present the results from our four empirical models, and, in turn,
explore in detail how well our preferred specification does at explaining observed changes
in headcount poverty. First, using our entire sample of 135 countries over 1974-2018, we
estimate Equations (7), (8), (9), (10), and (13). Results are presented in Columns (1)-(5)
12. PovcalNet is the on-line tool for poverty measurement developed by the Development ResearchGroup of the World Bank; see http://iresearch.worldbank.org/PovcalNet/povOnDemand.aspx
13. Section 4 of http://documents.worldbank.org/curated/en/344401569259571927/pdf/
September-2019-PovcalNet-Update-Whats-New.pdf discusses comparability of surveys within acountry over time. For instance, two surveys for a given country would not be comparable betweenyears if their measurement of welfare switches from being consumption based to income based.
12
of Table I, respectively.
TABLE I
(1) (2) (3) (4) (5) (6) (7)
∆y -0.206*** -0.213*** -0.00296
(0.007) (0.006) (0.020)
∆σ 0.133*** -0.222***
(0.013) (0.042)
∆y × σ -0.199***
(0.025)
∆y × zy -0.135***
(0.009)
∆σ × σ 0.544***
(0.062)
∆σ × zy -0.0598*
(0.035)
∆y × κy 0.942*** 1
(0.009)
∆σ × κσ 0.750*** 1
(0.022)
Growth Component 1.081*** 1
(0.007)
Distribution Component 0.882*** 1
(0.015)
Constant 0.103 0.156* 0.203*** 0.165*** 0.0129 0 0
(0.087) (0.083) (0.075) (0.036) (0.024)
E[dH] -0.826 -0.794 -0.794 -0.794 -0.794 -0.794 -0.794
E[∆y] 4.499 4.430 4.430 4.430 4.430 4.430 4.430
E[∆σ] -0.0626 -0.0626 -0.0626 -0.0626 -0.0626 -0.0626
Observations 1310 1307 1307 1307 1307 1307 1307
R-squared 0.425 0.463 0.584 0.893 0.951 0.876 0.942
Note: *,**,*** denote significance at the 1,5, and 10 percent level, respectively. Standard errors presented in paren-
theses. Dependent variable: percentage point change in the headcount poverty rate in country i from year t− n to t,
where the headcount poverty rate is calculated as the percent of the population under the $1.90 poverty line.
It is clear from looking at the R2 for each specification, that Equation (10) and (13)
(Columns 4 and 5, respectively) do a far superior job at explaining changes in poverty in
our sample. Moreover, it appears that our log-normality assumption provides us with a
very reasonable approximation to the arithmetic identity that exists between changes in
13
poverty, changes in inequality, and changes in mean incomes. First, looking at Column
(4) we see that both γ1 and γ2 are close in magnitude to 1, γ0 is close in magnitude to 0
and the R2 is very close to 1. And, looking at Column (5) we see that both ω1 and ω2 are
close in magnitude to 1, ω0 is close in magnitude to 0 and the R2 is even closer to 1 (under
the log-normal assumption, we would expect Equation (13) to fit better than Equation
(10) due to the discrete nature of the data).14 Second, we re-estimate Equations (10) and
(13) imposing the log-normal restrictions on the coefficients: see Columns (6) and (7) of
Table I respectively. We find that under these restrictions, the models still fit the data
extremely well - in particular under our restricted version of Equation (13), we get an R2
of 0.94.
Finally, we graphically illustrate how well the log-normal approximation fits the iden-
tity. In Figure III we plot predicted percentage point change in headcount poverty under
the assumption of log-normality (dHi,t) vs. the actual percentage point change in head-
count poverty (dHi,t), where the change in predicted headcount poverty is given by:
dHi,t =
(Φ
(log
(z
yi,t
)1
σi,t−n+
1
2σi,t−n
)− Φ
(log
(z
yi,t−n
)1
σi,t−n+
1
2σi,t−n
)+
Φ
(log
(z
yi,t
)1
σi,t+
1
2σi,t
)− Φ
(log
(z
yi,t
)1
σi,t−n+
1
2σi,t−n
))× 100
As can be seen, the points are closely centered around the 45 degree line indicating that
our approximation to the identity is decent.
14. We do, however, reject the null hypotheses that γ1 = γ2 = 1− γ0 = 1 and ω1 = ω2 = 1− ω0 = 1,thus rejecting the null hypothesis that income distributions perfectly follow a log-normal. However, thisis not the relevant test. We know income distributions are not perfectly log-normal; what we really wantto test is whether the log-normal assumption provides us with a reasonable approximation to reality.The arguments made in this section support that this is a reasonable approximation.
14
The dashed blue line plots the fitted values from the linear regression of dHi,t on dHi,t.
Figure III: Predicted vs. Actual Percentage Point Changes inHeadcount Poverty Under Assumption of Log-Normality
Finally, we explore by region how well our approximation fits the data: we repro-
duce Figure III for each region separately - see Figure IV. Note, EAP denotes East
Asia and Pacific, ECA denotes Europe and Central Asia, LAC denotes Latin Amer-
ica and the Caribbean, MNA denotes Middle East and North Africa, OHI denotes
Other High Income, SAS denotes South Asia, and SSA denotes Sub-Saharan Africa (see
http://iresearch.worldbank.org/PovcalNet/povOnDemand.aspx to obtain the list of
countries in each region). From these figures it is clear that log-normality seems like a
reasonable approximation. The one exception is the OHI region. For this region, our
model predicts that percentage point changes in headcount poverty are always 0 as our
model predicts that for these countries, headcount poverty is always at 0%. This is a
consequence of mean incomes being so high for these countries. Notably, this is also the
region where we expect measurement error in headcount poverty to be the worst given
the reliance of observing incomes in the very extreme left tails (thus, it may be that log-
normal is still a good fit for these countries, but that changes in poverty are measured with
substantial error). Alternatively, it could be the case that the log-normal approximation
to the income distribution is less appropriate for the tails of the distribution. Regardless,
we will omit OHI countries from our analysis; given we are interested in understanding
the drivers of changes in poverty, omitting countries where poverty is extremely low and
essentially not changing in a substantial way seems entirely reasonable.
15
EAP: East Asia and Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; MNA: Middle East
and North Africa; OHI: Other High Income; SAS: South Asia; SSA: Sub-Saharan Africa
Figure IV: Predicted vs. Actual Percentage Point Changes inHeadcount Poverty by Region Under Assumption of Log-Normality
V The Empirical Importance of Reductions in
Income Inequality on Poverty
Now that we have an empirical model to approximate our identity, we can use this
model to gauge the importance of reductions in inequality on poverty. In particular,
we will use this model to (a) investigate the magnitudes of the elasticities of poverty
w.r.t. growth and w.r.t. inequality so as to compare the reductions in poverty that will
result from a 1% increase in mean incomes as opposed to a 1% decrease in inequality;
(b) investigate the extent to which the growth elasticity is affected by initial inequality;
and (c) understand the extent to which changes in poverty have been driven by changes
in mean incomes as opposed to changes in inequality.
16
V.A The Elasticity of Poverty w.r.t. Inequality vs. The Elasticity of
Poverty w.r.t. Growth
First, we explore the magnitude of the two elasticities, ξy, ξσ, under our approximation
that income distributions are log-normal. Our elasticities are estimated via the following
equations:
ξy,i,t =−φ(
log(
zyi,t−n
)1
σi,t−n+ 1
2σi,t−n
)1
σi,t−n
Φ(
log(
zyi,t−n
)1
σi,t−n+ 1
2σi,t−n
)
ξσ,i,t =φ(
log(
zyi,t−n
)1
σi,t−n+ 1
2σi,t−n
)(12σi,t−n − log
(z
yi,t−n
)1
σi,t−n
)Φ(
log(
zyi,t−n
)1
σi,t−n+ 1
2σi,t−n
)As shown in Figure I, both elasticities will be increasing in absolute value with devel-
opment (as headcount poverty approaches 0). Thus, when comparing these elasticities,
the sensible comparison is to compare them within country or region. Figure V plots the
value of the absolute growth elasticity, |ξy,i,T |, vs. the inequality elasticity, ξσ,i,T for each
country i in their latest survey year T (conditional on the latest survey year being 2010
onward, T ≥ 2010), while Table II provides summary statistics of these elasticities by
region for the latest survey year. As can be seen, the inequality elasticity is comparable
to, and often larger in magnitude than the growth elasticity. Thus, for many countries,
a 1% reduction in inequality (as measured by the standard deviation of log-income) gen-
erates a larger reduction in poverty than a 1% increase in mean incomes. Moreover,
an interesting pattern emerges by mean income: for the poorest countries/regions, the
growth elasticity is typically larger relative to the inequality elasticity (e.g., for countries
in SAS and SSA), whereas the opposite appears to be true for relatively richer countries
in our sample. This is intuitive: reducing σ, all else equal, will reduce in the spread
of incomes around y; thus, if mean incomes are very low in a country, reducing σ will
have limited effects on poverty (and, in fact, for very low values of mean incomes, i.e.,
y < elog(z)−σ2/2, reducing σ will have detrimental effects on headcount poverty as it will
result in bringing richer households below the poverty line). However, while this pattern
may initially suggest that in the poorest countries policies should target growth (and, as
countries get richer, policies may want to shift to a combination of growth and equality
policies), inequality has additional effects on poverty through its effect on the growth
elasticity. We explore this next.
17
Figure V: Absolute Growth Elasticity vs. Inequality Elasticity; latestsurvey year
TABLE II: Summary Statistics of Poverty Elasticities; latest survey year
All Regions EAP ECA LAC MNA SAS SSA
Mean: latest survey year
|ξy| 3.41 3.03 6.53 2.73 3.70 2.50 1.21
ξσ 7.09 5.53 15.5 6.80 6.27 3.08 1.27
y 323.3 267.1 541.6 504.6 308.2 210.9 151.0
σ 0.73 0.68 0.59 0.88 0.63 0.64 0.83
All Regions EAP ECA LAC MNA SAS SSA
Median: latest survey year
|ξy| 2.78 2.71 6.34 2.74 3.80 2.71 1.02
ξσ 5.19 5.29 12.9 6.49 5.99 3.07 0.78
y 261.9 227.0 585.8 438.6 305.1 150.3 98.1
σ 0.71 0.69 0.60 0.87 0.62 0.61 0.80
Note: Summary statistics are taken over each country i in their latest survey year by region (con-
ditional on the latest survey year being 2010 onward). All regions excludes OHI. Averages are not
weighted by country population.
18
V.B Initial Inequality and the Growth Elasticity
Next we explore the extent to which initial (lagged) inequality affects the size of the
growth elasticity. Figure VI plots the absolute growth elasticity for each country in their
latest survey year, |ξy,i,T | vs. lagged mean income yi,T−n. In dashed grey lines, we overlay
the value of the elasticity that would result for various values of initial (lagged) inequality
σT−n. As can be seen, conditional on a value of (lagged) mean income, countries with
lower initial inequality have substantially larger growth elasticities. This is particularly
apparent when comparing countries in LAC with countries in ECA. While there is sub-
stantial overlap in mean incomes for countries in these two regions, the growth elasticity
is substantially smaller in LAC countries due to the much higher inequality (average
inequality in LAC countries is 0.88 compared to 0.59 in ECA countries - see Table II).15
Figure VI: Heterogeneity in the Growth Elasticity; latest survey year
15. However, as mentioned above, a misleading feature of the growth elasticity (and the inequalityelasticity) is that it gets increasingly large as headcount poverty approaches zero. Thus, part of thereason |ξy,t| increases as we decrease σt−n is due to the fact that decreasing σt−n decreases headcountpoverty in period t−n thus mechanically increasing |ξy,t| (the denominator of |ξy,t| is headcount povertyin t− n).
19
V.C Which Has Been More Important: Changes in Mean Incomes or
Changes in Inequality?
While the above exercises highlight how effective reducing inequality is at reducing
poverty, they do not shed any light on whether observed changes in poverty have been
primarily driven by changes in mean incomes, changes in inequality, or some combination
of the two. In this section, we seek to decompose changes in poverty into changes in mean
incomes and changes in inequality. We proceed as follows: first, for each growth-spell,
we calculate the percentage point change in poverty that would occur if the change in
inequality was zero, i.e., we shut the distribution component to zero:
dHi,t|∆σ=0=
(Φ
(log
(z
yi,t
)1
σi,t−n+
1
2σi,t−n
)− Φ
(log
(z
yi,t−n
)1
σi,t−n+
1
2σi,t−n
))×100
This allows us to calculate the change in poverty that would result from observed
changes in mean incomes only. Our results are presented in Panel (a) of Figure VII.
Next, we repeat the same exercise, however, this time we calculate the percentage point
change in headcount poverty that would occur if the change in mean incomes were zero,
i.e., we shut the growth component to zero:
dHi,t|∆y=0=
(Φ
(log
(z
yi,t−n
)1
σi,t+
1
2σi,t
)− Φ
(log
(z
yi,t−n
)1
σi,t−n+
1
2σi,t−n
))× 100
This allows us to calculate the change in poverty that would result from changes in
the distribution of income only (i.e., changes in σ only). Our results are presented in
Panel (b) of Figure VII.
Here is how to interpret a point in Panel (a) of Figure VII. A point lying above the
45 degree line indicates that the reduction in poverty resulting from changes in mean
incomes is lower than the observed reduction in poverty for a given growth-spell. Thus,
these points are likely accompanied by a reduction in inequality. Conversely, a point lying
below the 45 line indicates that the reduction in poverty resulting from changes in mean
incomes is higher than the observed reduction in poverty. Thus, these points are likely
accompanied by an increase in inequality.
Here is how to interpret a point in Panel (b) of Figure VII. A point lying above
the 45 degree line indicates that the reduction in poverty resulting from changes in the
inequality is lower than the observed reduction in poverty for a given growth-spell. Thus,
these points are likely accompanied by an increase in mean incomes. Conversely, a point
lying below the 45 line indicates that the reduction in poverty resulting from changes in
20
inequality is higher than the observed reduction in poverty. Thus, these point are likely
accompanied by a reduction in mean incomes.
Figure VII: Decomposing Percentage Point Changes in HeadcountPoverty
As we can see, points are far more closely centered around the 45 degree line when
changes in inequality are set to zero (i.e., points in Panel (a) of Figure VII are more
closely scattered around the 45 degree line than points in Panel (b) of Figure VII). This
suggests that changes in mean income have been more important in explaining changes in
poverty than changes in inequality. Note, this is not because changes in inequality have
a limited effect on poverty - our results in subsection V.A suggest the exact opposite.
Rather, average percentage changes in inequality have been much smaller than average
percentage changes in mean incomes over the past few decades.16 This can be seen
in the bottom Table I, where in the rows labeled E[∆y] and E[∆σ] we can see that
E[∆σ] has been orders of magnitude smaller than E[∆y] (note, when we restrict of non-
OHI countries, we find E[∆y] = 4.99% and E[∆σ] = −0.25%, so percentage changes
in inequality are still an order of magnitude smaller than percentage changes in mean
incomes).
16. In semi-elasticity form, under the assumption of log-normality, we know to a first order approxima-tion that dHi,t = κy,i,t∆yi,t+κσ,i,t∆σi,t where κy,i,t, κσ,i,t are given by Equations (11) and (12). We sawabove that the absolute growth elasticity is similar in magnitude, although smaller on average, relativeto the inequality elasticity, implying that |κy,i,t| is similar although smaller in magnitude to κσ,i,t. Thus,since we find that the majority of changes in poverty are due to changes in mean incomes, it must bebecause ∆yi,t is substantially larger in magnitude relative to ∆σi,t.
21
Finally, we calculate the share of the variance of predicted changes in poverty that
can be explained by changes in mean incomes and by changes in inequality, respectively:
Share due to ∆y =Var(dHi,t|∆σ=0) + Cov(dHi,t|∆y=0, dHi,t|∆σ=0)
Var(dHi,t|∆σ=0+dHi,t|∆y=0
)Share due to ∆σ =
Var(dHi,t|∆y=0) + Cov(dHi,t|∆y=0, dHi,t|∆σ=0)
Var(dHi,t|∆σ=0+dHi,t|∆y=0
)We find that for all growth-spells (excluding growth-spells from OHI countries), 89%
of the variance in predicted change in poverty is explained by changes in mean incomes,
while only 11% is explained by changes in the distribution of incomes. We repeat this
exercise for growth spells from 2000 onward and from 2010 onward and find that this
variance decomposition is fairly stable. In particular, when restricting to 2000 (2010)
onward, the share due to changes in mean incomes is 90% (86%) while the share due to
changes in inequality is 10% (14%). This differs from Bluhm et al (2016) who find that
the share due to inequality is substantially higher for 2000-2010 relative to 1981-2000
(although, regardless of time period, they too find that changes in mean incomes still
explain the majority of changes in headcount poverty). Finally, we repeat this exercise
for short growth-spells and longer growth-spells. For short growth-spells of one year
(the median growth-spell is one year in our sample), we find that 71% of the variance
in predicted change in poverty is explained by changes in mean incomes, while 29% is
explained by changes in the distribution of incomes. For growth-spells of 2 years or more
we find that 93% of the variance in predicted change in poverty is explained by changes in
mean incomes, while only 7% is explained by changes in the distribution of incomes. This
is consistent with the findings of Kraay (2006) who also finds the share of the variance
explained by changes in mean incomes increases with the length of the growth-spell.
Overall, the main takeaways from this section are as follows: reducing inequality, all
else equal, can have substantial effects on headcount poverty through both the direct
effect (as seen by the substantial value of ξσ relative to |ξy|) and the indirect effect (as
seen by the sensitivity of |ξy,t| to σt−n). However, for our dataset, because changes in σ
were substantially smaller than changes in y, most of the observed changes in poverty are
due to changes in mean incomes.
VI Poverty Projections
We now proceed to generate poverty projections out to 2030 under various assump-
tions on changes in inequality and changes in mean income. Note, these are hypothetical
22
scenarios constructed to highlight the contribution of changes in inequality vs. mean
incomes on poverty forecasts; thus, one should focus on the differences in projections
generated under the different scenarios as opposed to the actual forecast levels. We set
out to calculate:
Hi,t = Φ
(log
(z
yi,t
)1
σi,t+
1
2σi,t
)
for each country i, t = T, T + 1, ..., 2030, where T denotes the latest survey year
for each country. Then by region, we calculate average headcount poverty (weighted by
country population):
Hr,t =∑i∈r
ωiHi,t
where r denotes region, and ωi denotes country i′s population relative to the total
population in the region.17 Note, we could also project headcount poverty using an
elasticity approach, e.g., Hi,2030 = Hi,T +∑2030−T
s=1 (κy,i,s∆ys + κσ,i,s∆σs), but as discussed
earlier, the elasticity approach only provides a first-order approximation for headcount
poverty as changes in mean incomes and inequality are discrete.
To project headcount poverty, we need values for mean income and inequality out to
2030. As our baseline, we generate predictions for y using data on real GDP per-capita
from 1990-2022 from the Macro Poverty Outlook (MPO).18 In particular, we estimate
the following MA(2) regression for each country i:19
log(gdp pci,t) = bi,0 + bi,1yeart + ei,t + θi,1ei,t−1 + θi,2ei,t−2 (14)
where log(gdp pci,t) denotes the log of GDP per-capita in country i in year t. Using
the coefficients estimated from these regressions, we then predict real GDP per-capita for
2023-2030 for each country. Then, using this GDP per-capita series (the MPO series up
until 2022 plus our predicted series from 2023-2030), we calculate country specific growth
rates in GDP per-capita out to 2030. These growth rates, combined with the latest
observation of mean income in each country from PovcalNet, allow us to predict mean
17. For population measures, we use predicted country populations for 2022 generated bythe Macro and Poverty Outlook (MPO). See https://www.worldbank.org/en/publication/
macro-poverty-outlook#:~:text=Next-,Overview,Group%20and%20International%20Monetary%
20Fund.. The predictions we use are from the vintage dated June 9, 2020.18. Specifically, we use the vintage dated June 9, 2020.19. We estimate an MA(2) model as opposed to the simpler log-linear specification so as to smooth out
shocks when forecasting GDP per-capita. Note, the MPO projections take into account the anticipatedCOVID-19 shock.
23
incomes out to 2030 for each country.20 Finally, to complete our baseline specification,
we assume there is zero growth in σ so that σi,2030 = σi,T (i.e., inequality is equal to the
latest reported value for each country).21
Next, we consider four counterfactual scenarios relative to our baseline scenario: (1)
inequality declines by 1% per-annum over 2020-2030 while mean incomes follow baseline
trajectory; (2) inequality increases by 1% per-annum over 2020-2030 while mean incomes
follow baseline trajectory; (3) mean incomes increase by 1% per-annum over 2020-2030
relative to their baseline trajectory while inequality remains constant at baseline value;
and (4) mean incomes decrease by 1% per-annum over 2020-2030 relative to their baseline
trajectory while inequality remains constant at baseline value. World headcount poverty
rates by year are presented in Figure VIII under our baseline scenario and our coun-
terfactual scenarios. Moreover, regional poverty rates for 2030 under our baseline and
alternative scenarios are presented in Table III.
TABLE III: Poverty Projections for 2030 Under Various Scenarios
B (1) (2) (3) (4)Region Baseline 1% decr. σ 1% incr. σ 1% incr. y 1% decr. yEAP 0.73 0.37 1.30 0.53 0.99ECA 0.15 0.06 0.35 0.09 0.23LAC 2.74 1.30 5.13 2.11 3.52MNA 4.40 3.60 5.63 3.57 5.41OHI 0.00 0.00 0.00 0.00 0.00SAS 3.66 1.90 6.26 2.56 5.13SSA 32.32 28.69 36.33 28.54 36.37World 5.69 4.52 7.29 4.78 6.78
Note: Headcount poverty is multiplied by 100, i.e., we project 32.32% of the population in SSA tobe under the poverty line in 2030 under our baseline specification. World Headcount poverty is thesum of weighted regional poverty rates.
20. For example, our latest observation of mean income for India is 2011; thus, we use the 2011observation for y, along with per-capita GDP growth rates for India from 2012-2030 to calculate meanincome for 2012-2030. Note, we only include countries where the latest observation is from 2010 onward.For example, because our latest observation for mean income and inequality for Jamaica is 2004, Jamaicawould not be included in this projection exercise.
21. E.g., because the latest observation for India is 2011, we assume σIndia,2030 = σIndia,2011
24
Figure VIII: Poverty Projections: Baseline and CounterfactualScenarios
Looking at Table III and Figure VIII we see that, on average, a 1% reduction in in-
equality (per-annum) leads to a greater reduction in projected headcount poverty relative
to a 1% increase in mean incomes (per-annum). Similarly, a 1% increase in inequality
(per-annum) is more harmful, on average, to headcount poverty relative to a 1% decrease
(per-annum) in mean incomes. This is a consequence of the fact that the inequality
elasticity is larger on average relative to the growth elasticity. Thus, these projections
highlight the important role inequality can play in reducing future poverty even if prior
poverty reductions have, in large part, been a consequence of economic growth.
VII Discussion
The above empirical results highlight that reducing inequality, all else equal, is an
effective way to reduce poverty. Does this then mean policies aimed at reducing poverty
should focus on reducing inequality? Not necessarily. To answer this question, we need
to address three issues. First, we need to address the issue that in reality, changing
inequality likely affects growth, i.e., we cannot just consider the effect that changing
inequality has on poverty, all else equal. Thus, one needs to understand the relationship
between inequality and growth in order to fully determine how changing inequality will
affect poverty. For example, if reducing inequality causes a dramatic reduction in growth,
then reducing inequality is unlikely to be an effective way to reduce poverty. Alternatively,
if reducing inequality has little effect (or, even better, a positive effect) on growth, then
reducing inequality is likely an effective way to combat poverty. As discussed in the
introduction, a large body of theoretical and empirical literature examines the effect of
25
inequality on growth; theoretically, the relationship is complex, while empirically the
results are mixed.
Second, one must consider the ability of policy makers to influence inequality relative
to mean incomes. While this analysis highlighted that the elasticity of poverty w.r.t.
inequality is on average greater in value than the (absolute) elasticity of poverty w.r.t.
growth, one must also consider how difficult/costly it is to generate a 1% reduction
in inequality as opposed to a 1% increase in mean incomes. In our dataset, observed
changes in mean incomes are an order of magnitude larger than observed changes in
inequality. While we cannot draw any conclusions from this observation (as, for example,
prior policies may have focused far more heavily on enhancing growth as opposed to
tackling inequality), this observation should at least make one ask, how easy is it to
reduce inequality in a substantial way as opposed to increasing mean incomes?
Third, one must consider the effect of a policy not only on inequality, but also on
growth. In reality, it is unlikely that a policy will reduce inequality but leave growth
unchanged (or vice versa). For example, implementing a more progressive income tax
schedule will likely reduce inequality. But such a tax schedule may dampen growth as
richer individuals reduce their labor supply in response to higher tax rates. Dollar et al
(2016) find that changes in mean incomes, which have been, on average, positive over
the last few decades, are uncorrelated with changes in inequality, thus, suggesting that
some policies lead to increases in growth and reductions in inequality, while other policies
lead to increases in both growth and inequality. Similarly, Lopez (2004) finds that while
some pro-growth policies are accompanied by reductions in inequality, others have been
accompanied by increases in inequality.
To summarize, Figure IX (adapted from Bourguignon’s (2004) Poverty-Growth-Inequality
Triangle) highlights the channels which our paper investigates and the additional channels
one needs to understand in order to design the most effective policies to combat poverty.
Not only does one need to understand how changes in inequality and mean incomes are
transformed into reductions in poverty (as shown by the solid black arrows in Figure IX),
but one also needs to understand how growth and changes in inequality affect each other,
and how different policies affect both inequality and mean incomes (as shown by the blue
dashed lines in Figure IX). To explore these additional channels, it will likely be useful
for policy makers to utilize case studies which investigate the effect of various policies on
both inequality and growth.
26
Figure IX: The Channels of Poverty Reduction
27
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32
A Appendix: Data
TABLE IV: List of Countries
Country Min Year Max Year Obs. Country Min Year Max Year Obs.Albania 2002 2017 6 Liberia 2014 2016 1Angola 2008 2018 1 Lithuania 1998 2017 18Armenia 1999 2018 18 Luxembourg 1985 2017 18Australia 1989 2014 6 North Macedonia 2000 2017 14Austria 1987 2017 17 Madagascar 1997 2012 4Azerbaijan 2001 2005 4 Malawi 2004 2016 2Bangladesh 1983 2016 6 Malaysia 1984 2015 10Belarus 1993 2018 21 Mali 2006 2009 1Belgium 1985 2017 18 Malta 2006 2017 11Belize 1993 1999 4 Mauritania 2000 2014 3Benin 2011 2015 1 Mauritius 2006 2017 2Bhutan 2007 2017 2 Mexico 1989 2018 14Bolivia 1999 2018 15 Moldova 1997 2018 19Bosnia and Herzegovina 2001 2011 2 Mongolia 1995 2018 6Botswana 1985 2015 3 Montenegro 2005 2015 9Brazil 1981 2018 32 Morocco 1984 2013 4Bulgaria 1989 2017 12 Mozambique 1996 2014 3Burkina Faso 1998 2003 1 Myanmar 2015 2017 1Burundi 1998 2013 2 Namibia 2003 2015 2Cameroon 2001 2014 2 Nepal 1995 2003 1Canada 1971 2013 11 Netherlands 1983 2017 16Chad 2003 2011 1 Nicaragua 1993 2014 4Chile 1987 2017 12 Niger 2011 2014 1China 1981 2016 12 Nigeria 2003 2009 1Colombia 1992 2018 17 Norway 1979 2017 18Congo, Dem. Rep. 2004 2012 1 Pakistan 1987 2015 10Congo, Rep. 2005 2011 1 Panama 1995 2018 20Costa Rica 1981 2018 29 Paraguay 1990 2018 16Cote d’Ivoire 1985 2015 7 Peru 1985 2018 20Croatia 1998 2017 12 Philippines 1991 2015 5Cyprus 2004 2017 13 Poland 1987 2017 21Czech Republic 1996 2017 14 Portugal 2003 2017 14Denmark 1987 2017 17 Romania 1989 2017 20Dominican Republic 1996 2018 17 Russian Federation 1993 2018 22Ecuador 2000 2018 15 Rwanda 2000 2016 4Egypt, Arab Rep. 1990 2017 5 Samoa 2002 2013 2El Salvador 1991 2018 23 Senegal 2005 2011 1Estonia 1995 2017 17 Serbia 2012 2017 5Ethiopia 1995 2015 4 Sierra Leone 2003 2018 2Fiji 2002 2013 2 Slovak Republic 1992 2016 13Finland 1987 2017 17 Slovenia 1987 2017 17France 1978 2017 18 South Africa 2005 2014 2Georgia 1997 2018 21 Spain 1980 2017 17Germany 1991 2016 18 Sri Lanka 2002 2016 4Ghana 1987 2016 5 Eswatini 2000 2016 2Greece 1995 2017 15 Sweden 1975 2017 19Guatemala 1986 2014 3 Switzerland 2000 2017 12Guinea 2007 2012 1 Taiwan, China 1981 2016 10Honduras 1991 2018 25 Tajikistan 1999 2015 4Hungary 1987 2017 20 Tanzania 2000 2011 2Iceland 2003 2015 12 Thailand 1981 2018 20India 1993 2011 3 Timor-Leste 2001 2014 2Indonesia 1984 2018 20 Togo 2006 2015 2Iran, Islamic Rep. 1986 2017 10 Tonga 2009 2015 1Iraq 2006 2012 1 Tunisia 1985 2015 4Ireland 1994 2016 16 Turkey 1987 2018 17Israel 1979 2016 10 Uganda 1992 2016 6Italy 1986 2017 21 Ukraine 1992 2018 17Jamaica 1988 2004 5 United Kingdom 1969 2016 18Japan 2008 2013 2 United States 1974 2016 10Jordan 1986 2010 3 Uruguay 2006 2018 12Kazakhstan 2001 2017 15 Uzbekistan 1998 2003 3Kenya 2005 2015 1 Venezuela, RB 1981 2006 10Korea, Rep. 2006 2012 3 Vietnam 1992 2018 8Kosovo 2003 2017 10 West Bank and Gaza 2004 2016 7Kyrgyz Republic 1998 2018 18 Yemen, Rep. 2005 2014 1Lao PDR 1992 2012 4 Zambia 1998 2015 4Latvia 1993 2017 18 33
B Elasticity Regressions
We estimate the following regression:
Hi,t = a0+a1Hi,t + εi,t (15)
where Hi,t = Φ(
log(zyt
)1σt
+ 12σt
). Results are presented in Table V below. If the
assumption of log-normality is reasonable, we should (a) find that a1 ≈ 1, a0 ≈ 0 and (b)
R2 ≈ 1. The results in Table V confirm that the log-normal approximation is a reasonable
approximation. (Note, both Hi,t and Hi,t are measured as percent of the population under
the poverty line, meaning that a0 = 0.37 implies an intercept of 0.37%).
TABLE V: Regression Headcount Poverty on Predicted HeadcountPoverty Under Log-Normality
(1)
H 1.016***
(0.003)
Constant -0.373***
(0.056)
E[H] 10.26
Observations 1731
R-squared 0.987
Note: *,**,*** denote significance at the 1,5, and 10 percent level, respectively. Standard errors pre-
sented in parentheses. Dependent variable: headcount poverty rate (measured as the percent of the
population under the poverty line) in country i in year t, Hi,t.
C Elasticity Regressions
We estimate the following regressions:
∆Hi,t = a0+a1∆yi,t + εi,t (16)
∆Hi,t = b0+b1∆yi,t + b2∆σi,t + εi,t (17)
34
∆Hi,t = c0+c1∆yi,t + c2∆σi,t + c3∆yi,t × σi,t−n + c4∆yi,t ×z
yi,t−n+
c5∆σi,t × σi,t−n + c6∆σi,t ×z
yi,t−n+ εi,t
(18)
∆Hi,t = γ0+γ1ξy,i,t∆yi,t + γ2ξσ,i,t∆σi,t + εi,t (19)
where ξy and ξσ denote our theoretical values - under the assumption of log-normality -
of the elasticities of poverty w.r.t. growth and w.r.t. inequality, respectively. To highlight
sensitivity of these regressions to including countries with very low values of headcount
poverty, we estimate these regressions for (a) all observations - see Table VI, and (b)
observations where (lagged) headcount poverty is greater than 3% - see Table VII.22
Moving from Table VI to Table VII, we see that our coefficients change substantially,
and that our R2 for each regression increases substantially. Conversely, re-estimating
our semi-elasticity specifications, Equations (7) - (10), and restricting our sample to
observations where (lagged) headcount poverty is greater than 3%, we find that our
results far more stable. See Table VIII. It is for these reasons that in the text, we focus
on estimating semi-elasticity specifications in order to assess which functional form best
22. Note, we have slightly fewer observations in Tables VI and VII compared to Table I as for somecountries, headcount poverty in year t− n is 0 - hence, ∆H is undefined.
35
fits the data.
TABLE VI: Elasticity Specifications
(1) (2) (3) (4)
∆y -2.653*** -3.168*** -6.909***
(0.317) (0.313) (1.073)
∆σ 6.084*** 17.55***
(0.621) (2.480)
∆y × σ 4.100***
(1.370)
∆y × zy 1.588***
(0.483)
∆σ × σ -12.36***
(3.458)
∆σ × zy -7.242***
(1.870)
∆y × ξy 0.440***
(0.061)
∆σ × ξσ 0.283***
(0.042)
Constant 24.22*** 27.81*** 26.23*** 18.14***
(4.207) (4.074) (4.079) (4.047)
E[∆H] 12.11 12.22 12.22 12.22
Observations 1225 1222 1222 1222
R-squared 0.0540 0.123 0.161 0.0767
Note: *,**,*** denote significance at the 1,5, and 10 percent level, respectively. Standard errors
presented in parentheses. Dependent variable: percentage change in the headcount poverty rate in
country i from year t − n to t, ∆Hi,t. In column (4), we drop observations for which ξσ is greater
than 99th percentile - we do so as this theoretical elasticity can be extremely large when predicted
headcount poverty (under the assumption of log-normality) in t− n is essentially 0.
36
TABLE VII: Elasticity Specifications: Restricting to Observations whereHeadcount Poverty is Greater than 3%
(1) (2) (3) (4)
∆y -1.087*** -1.269*** -3.327***
(0.062) (0.057) (0.207)
∆σ 1.480*** 4.275***
(0.121) (0.579)
∆y × σ 1.592***
(0.218)
∆y × zy 0.933***
(0.065)
∆σ × σ -1.036*
(0.611)
∆σ × zy -3.131***
(0.296)
∆y × ξy 0.871***
(0.026)
∆σ × ξσ 0.815***
(0.036)
Constant -2.999*** -0.654 1.653** 1.881***
(1.032) (0.929) (0.749) (0.713)
E[∆H] -10.06 -9.918 -9.918 -9.918
Observations 501 498 498 498
R-squared 0.385 0.524 0.710 0.728
Note: *,**,*** denote significance at the 1,5, and 10 percent level, respectively. Standard errors
presented in parentheses. Dependent variable: percentage change in the headcount poverty rate in
country i from year t−n to t, ∆Hi,t. Sample restricted to observations where headcount poverty in
year t−n is greater than 3%. In column (4), we drop observations for which ξσ is greater than 99th
percentile - we do so as this theoretical elasticity can be extremely large when predicted headcount
poverty (under the assumption of log-normality) in t− n is essentially 0.
37
TABLE VIII: Semi-Elasticity Specifications: Restricting to Observationswhere Headcount Poverty is Greater than 3%
(1) (2) (3) (4)
∆y -0.303*** -0.330*** -0.626***
(0.011) (0.010) (0.043)
∆σ 0.248*** 0.180
(0.021) (0.119)
∆y × σ 0.348***
(0.045)
∆y × zy 0.00803
(0.013)
∆σ × σ 0.248**
(0.126)
∆σ × zy -0.204***
(0.061)
∆y × κy 0.951***
(0.014)
∆σ × κσ 0.780***
(0.033)
Constant -0.227 0.178 0.418*** 0.302***
(0.181) (0.164) (0.154) (0.090)
E[dH] -2.191 -2.116 -2.116 -2.116
Observations 501 498 498 498
R-squared 0.612 0.689 0.740 0.904
Note: *,**,*** denote significance at the 1,5, and 10 percent level, respectively. Standard errors pre-
sented in parentheses. Dependent variable: percentage point change in the headcount poverty rate
in country i from year t− n to t, dHi,t. Sample restricted to observations where headcount poverty
in year t− n is greater than 3%.
38
