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Growth and Inequality:
Issues and Policy Implications
CESifo Conference Centre, Munich
18-20 May 2001
The Pace of Economic Growth and Poverty Reduction
by
François Bourguignon
The pace of economic growth and poverty reduction1
François Bourguignon
(TheWorld Bank and Delta, Paris)
First draft
December 2000
1
A preliminary vesrion of this paper was presented at the conference "World Poverty : a Challenge for the Private
Sector", organized by the Amsterdam Institute for International Development, Amsterdam, October 3-4, 2000. I am
indebted to Martin Ravallion for making the data set used in this paper available to me.
1
Abstract
There is a very precise relationship among economic growth, poverty reduction and changes in
the distribution of income during some time period in a given country. Based on that
relationship, this paper fully characterizes the way the elasticity of poverty with respect to the
mean income of the population depends on the initial level of development and the initial degree
of income inequality when the distribution is assumed to be Log-normal. Any discrepancy
between observed elasticities and this theoretical value can only be explained by changes in the
distribution of income during the period of observation or the inadequacy of the Log-normal
approximation. The second part of the paper analyzes the size and direction of that discrepancy
in a sample of actual growth spells in developing countries. It turns out that the discrepancy
amounts to less than 50 per cent of observed changes in poverty and is mostly explained by
distributional changes. The paper finally draws several implications of this simple exercise for
the analysis of the relationship between economic growth and the evolution of poverty.
2
Introduction
Part of the ongoing debate on poverty reduction strategies bear on the issue of the actual
contribution of economic growth to the goal of poverty reduction. There is no doubt that faster
economic growth is associated with faster poverty reduction. Ravallion and Chen (1997) have
estimated that, on average, the corresponding elasticity of poverty incidence with respect to the
mean income of a population is around 3 -i.e. a one per cent increase in mean income or
consumption expenditures reduces the proportion of people living below the poverty line by 3
per cent. As emphasized in the recent World Development Report on "Attacking Poverty",
however, there seems to be some pronounced heterogeneity across countries in the way
economic growth actually translates into reduced poverty. If reducing poverty is seriously taken
as a world policy objective, understanding the causes of that heterogeneity is important.
Clarifying what are these causes is the goal of this paper.
There is something like an identity that links the growth of the mean income in a given
population, the change in the distribution of relative incomes, and the reduction of poverty.
Formally, the relationship between poverty and growth may be obtained from that identity in the
case where there would be no change whatsoever in the distribution of relative individual
incomes , or, in other words, in the case income growth would proceed at the same pace in all
segments of society. Even in that case, however, it is shown in this paper that the growth-poverty
relationship is not simple and the corresponding elasticity is certainly not constant across
countries and across the various ways of measuring poverty. In effect, the growth-elasticity of
poverty is a decreasing function of the aggregate development level of a country and a
decreasing function of the degree of inequality of the distribution of relative incomes, these
functions depending themselves on the poverty index that is being used. For all indices, however,
1
a first source of heterogeneity in the way growth affects poverty in various countries must be
found in their initial level of development and degree of inequality. The main point made in this
paper is that this heterogeneity may be very precisely taken into account.
The second source of heterogeneity is of course the change in the distribution of relative incomes
over time. Measuring the actual contribution of that source to the observed evolution of poverty
is of utmost importance since this should give an indication of the practical relevance of
distributional concerns in comparison with pure growth concerns in poverty reduction policies.
Because the actual contribution of growth to poverty reduction is not precisely identified by the
current practice that consists of assuming some constant elasticity, it follows that the
contribution of the distributional component is also imprecisely estimated. The methodology
proposed in this short paper should permit to correct for that imprecision and has implications for
the interpretation of available evidence on the growth-poverty relationship.
Several recent papers focused on the statistical relationship between economic growth and
poverty reduction across spells of economic growth in various countries and at various points of
time - see in particular Ravallion and Chen (1997), de Janvry and Sadoulet (1998), Dollar and
Kraay (2000). All these papers are based on linear regressions where the evolution of some
measure of poverty between two points of time is explained by the growth of income or GDP per
capita and a host of other variables, the main issue being the importance of GDP and these other
variables in determining poverty reduction. The present paper draws on previous work by
Ravallion and Huppi (1991), Datt and Ravallion (1992) and Kakwani (1993). It suggests that the
specification of that econometric model may not be satisfactory. Depending on what poverty
measure is on the left hand-side of the regression, GDP growth should be combined in some nonlinear way with the initial level of GDP per capita and some characteristics of the distribution of
2
income for this estimation exercise to make full sense. 1 Interestingly enough, however, if the
specification used in this kind of analysis were correct, there should be no logical difference
between trying to explain the pace of poverty reduction and finding the determinants of observed
changes in the distribution of relative incomes.
The paper is organized as follows. The first section introduces and discusses the analytical
identity that links poverty, growth and distribution. It also analyzes in some detail the theoretical
relationship it implies between poverty reduction, the level of development and the inequality of
the distribution when the distribution of income is remaining constant over time. Empirical
evidence on the relationship between growth and poverty reduction is analyzed in the second
section in the light of the preceding identity. Finally, the concluding section draws several
implications of the main argument in the paper for the empirical analysis of the relationship
between growth and poverty and for poverty reduction policy.
1. The arithmetics of distributional and poverty changes
A poverty index may be seen as some mean characteristic of all individuals in a population
whose standard of living lies below some predetermined limit. In what follows, we shall assume
that there is no ambiguity on the definition of that 'poverty line' , that is whether it is defined in
terms of income or consumption, the kind of equivalence scale being used to account for
heterogeneity in household composition, and indeed the level of that poverty line. We shall also
assume this line is defined in 'absolute' terms, or in other words that it is constant over time - or
at least during all the period being analyzed. Since the argument will implicitly refer to
international comparisons, it makes also sense to assume that this absolute poverty line is the
1
The importance of the initial level of inequality in the relationship betwxeen growth and poverty reduction is
stressed by Ravallion (1997).
3
same across countries, for instance the familiar 1$ or 2$ a day after correction for purchasing
power parity.
Given this definition of poverty, let y be a measure of individual living standard - say income per
adult equivalent - and let z be the poverty line. In a given country, the distribution of income at
some point of time, t, is represented by the cumulative function Ft(Y), which stands for the
proportion of individuals in the population with living standard, or income, less than Y. The
most widely used poverty index is simply the proportion of individuals in the population below
the poverty line, z. This index is generally refereed to as the 'headcount'. With the preceding
notations, it may be formally defined by :
Ht = Ft (z)
(1)
For the sake of simplicity, the analysis will be momentarily restricted to that single poverty
index.
The definition of the headcount poverty index implies the following tautological definition of
'change' in poverty between the two points of time t and t' :
∆ H = Ht' - Ht = Ft'(z) - Ft(z)
To put into evidence the contribution of growth in this identity, it is convenient to define the
distribution of relative income at time t as the distribution of incomes after normalizing by the
income mean. This is equivalent to defining the distribution of income in a way that is
~
independent from the scale of income. Let denote Ft ( X ) that distribution of relative incomes.
Given that definition, any change in the distribution of income may then be decomposed into the
change into the mean income of the population and the change in the distribution of relative
income, or the 'true' distributional change. In other words any change in the full distribution of
4
income may be represented by two successive operations : a) a proportional change in all
incomes that leaves the distribution of relative income unchanged ; b) a change in the
distribution of relative incomes, which, by definition, leaves the mean income unchanged. For
obvious reasons the first change will be referred to as the 'growth' effect whereas the second one
will be termed the 'distributional' effect.
This decomposition, already discussed in some detail by Datt and Ravallion (1992) and Kakwani
(1993) is illustrated in figure 1. This figure shows the density of the distribution of income, that
is the number of individuals at each level of income represented on a logarithmic scale on the
horizontal axis. In that figure the function F( ) does not appear as such but indirectly as the area
under the density curves, starting from the left. The move from the initial to the new distribution
passes by an intermediate step, which is the density curve derived from the initial one by a
simple horizontal translation to curve (I). Because of the logarithmic scale, this change
corresponds to the same proportional increase of all incomes in the population and thus stands
for the 'growth effect'. Then moving from curve (I) to the new distribution curve occurs at
constant mean income. This movement thus corresponds to the change in the distribution of
'relative' income and the 'distribution' effect. Of course, there is some path dependence in that
decomposition. Instead of moving first right and then up and down as in figure 1, it would have
been possible to move first up and down and to have the distribution effect based on the mean
income observed in the initial period, and then right. Presumably these two paths are not
necessarily equivalent except for infinitesimal changes.
Figure 1 illustrates the natural decomposition of the change in the distribution of income
between two points of time. However, if the focus is on poverty, as measured by the headcount,
things are much simpler. In figure 1, the poverty headcount is simply the area under the density
curve at the left of the poverty line arbitrarily set at 1$ a day. The move from the initial curve to
5
the intermediate curve (I) and then from that curve to the new distribution curve have natural
counterparts in terms of changes in this area. More formally this decomposition may be written
as :
~ z
~ z  ~ z
~ z 
∆H = H t ' − H t =  Ft ( ) − Ft ( )  +  Ft ' ( ) − Ft ( ) 
yt '
yt  
y t'
yt' 

(2)
This expression is the direct application in the case of the headcount poverty index of the general
formula proposed by Datt and Ravallion (1992) and applied to Brazilian and Indian distribution
data. The first term in square bracket in the right hand side corresponds to the growth effect at
~
'constant 'relative income distribution', Ft ( X ) , that is the translation of the density curve along
the horizontal axis in figure 1, whereas the second one formalizes the distribution effect, that is
~
~
the change in the relative income distribution, Ft ' ( X ) − Ft ( X ) , at the new level of the 'relative'
poverty line, that is the ratio of the absolute poverty line and the mean income. Shifting to
elasticity concepts, the growth-elasticity of poverty may thus be defined as :
ε = Lim t '→t
~ z
~ z  ~ z
 Ft ( ) − Ft ( )  / Ft ( )
yt
yt 
yt '

( yt ' − yt ) / yt
(3)
The distribution effect is more difficult to translate in terms of elasticity because it cannot be
represented by a scalar.
The terms entering the decomposition identity (2) may be evaluated as long as one observes
some continuous approximation of the distribution functions F( ) at the two points of time t and
t'. This is necessary because one has to evaluate what would be the poverty headcount in period t
if all incomes had been multiplied by the same factor as mean income between the two periods.
Continuous kernel approximations of the density and cumulative relative distribution functions
6
may be computed from available microeconomic data sets or the points of time and evaluating
the decomposition identity for any growth spell on which distribution data are available should
not be difficult. However, in a cross-country analysis, this might require manipulating a large
number of micro-economic data sets and may be found to be cumbersome. Fortunately, a very
simple approximation of (2) may be obtained in the case where the distributions may be assumed
to be close to the Log-normal distribution. Indeed, in that case it is easy to see that :
~
 Log( X ) 1 
Ft ( X ) = Π 
+ σ
2 
 σ
where Π( ) is the cumulative function of the standard normal and σ is the standard deviation of
the logarithm of income. Substituting this expression in (2) shows that the change in poverty
headcount between time t and t' depends on the level of mean income at these two dates,
expressed as a proportion of the poverty line, and on the standard deviation of the distribution of
income at the two dates.
Allowing t' to be very close to t in (2) and taking limits as in (3) then leads to :
 Log( z / y t ) 1   ∆Log( y ) 1 Log( z / y t )

∆H
= λ
+ σ .  −
+( −
)∆σ 
2
Ht
2
2
σ
σ
σ



(4)
where λ( ) stands for the ratio of the density to the cumulative function - or hazard rate- of the
standard normal, ∆Log (y ) is the growth rate of the economy and ∆σ is the variation in the
standard deviation of the logarithm of income. Based on that expression and following (3), the
growth-elasticity of poverty, ε, may be defined as the relative change in the poverty headcount
for one percent growth in mean income for constant relative inequality, σ :
ε =−
∆H
1  Log( z / y t ) 1 
= λ
+ σ .
∆Log ( y )H t σ 
σ
2 
(5)
7
In that expression, it appears clearly that the growth elasticity of poverty, as measured by the
headcount, is an increasing function of the level of development, as measured by the inverse of
the ratio z / y t , and a decreasing function of the degree of relative income inequality as measured
by the standard deviation of the logarithm of income, σ.
The preceding relationship is represented in figure 2 through curves in the
development/inequality space along which the growth elasticity of poverty is constant. As in (5)
the inverse of development is measured along the horizontal axis by the ratio of the poverty line
and the mean income of the population. However, inequality is measured along the vertical axis
by the Gini coefficient of the distribution of relative income rather than the standard deviation of
logarithm. This measure of inequality is more familiar than σ but may be shown to be an
increasing function of it. 2
Figure 2 is useful to get some direct and quick estimate of the growth-elasticity of poverty.
Consider for instance the case of a poor country where the mean income is only twice the
poverty line at the extreme right of the figure. Reading the figure, it may be seen that the growthelasticity is around 3 if inequality is low - i.e. a Gini coefficient around .3 - but it is only 2 if the
Gini coefficient is at the more common value, .4. If the economy gets richer, then the elasticity
increases. But at the same time it becomes more sensitive to the level of inequality. For instance
when the mean income of the population is four times the poverty line, the growth-elasticity of
poverty is 5 for low income inequality - i.e. a Gini equal to .3 - but 2 again if inequality is high i.e. a Gini coefficient equal to .5. These various combinations are illustrated by the example of a
few countries in the mid 1980s. The ratio of the poverty line to the mean income is taken to be
2
In the case of a Log-Normal distribution, it is known that both magnitudes are related by the following relationship
– see Atcheson and Brown (1966) : G = 2 Π(σ/21/2)-1
8
the 1$ a day line related to GDP per capita whereas the Gini coefficients are taken from the
Deininger and Squire (1996) data base. Growth-elasticities of poverty reduction consistent with
the Log-normal assumption vary between 5 for a country like Indonesia to 3 for India and Cote
d'Ivoire which were poorer but had a higher level of inequality - in the case of Cote d'Ivoire. The
elasticity is around 2 for Brazil despite the fact that it is considerably richer than the other
countries. Income inequality makes the difference. Finally, the elasticity is much below 2 in the
case of Senegal and Zambia which cumulate the inconvenience of being poor and unequal.
Figure 2 and the underlying Log-normal approximation to the growth-elasticity of poverty in (5)
refers to the headcount as the poverty index. Similar expressions and curves may be obtained
using alternative indices. For instance, the poverty gap is a measure of poverty obtained by
multiplying the headcount by the average relative distance at which the poor are from the
poverty line. The advantage of that measure over the headcount is obviously that it takes into
account the depth of poverty on top of the proportion of people being poor. Under the Lognormal assumption, it may be shown that the growth-elasticity of the poverty gap is given by the
following formula :
ε =−
Π[Log (z / y t ) / σ − σ / 2 ]* ( y t / z )
Π[Log (z / y t ) / σ + σ / 2 ] − Π[Log (z / y t ) / σ − σ / 2 ]* ( y t / z )
(6)
where, as before, Π( ) is the cumulative distribution function of the standard normal variable. As
before, the growth-elasticity depends on the level of development as measured by the ratio z / yt
and the inequality of the distribution of income as given by the standard deviation of the
logarithm of income. Function (6) is represented in figure 3, the format of which is the same as
that of figure 2. It may be seen that the curves along which the growth-elasticity of poverty
reduction is constant have the same decreasing and convex shape.
9
As for the headcount, an exact expression can be obtained for the growth-elasticity of the
poverty gap. This would be the equivalent of (3) above but with another function at the
numerator. Although this is still to be done, equivalent formulas may be derived for other
poverty measures, in particular those belonging to the well-known P α family – see Foster, Greer
and Thorbecke (1984).
2. Revisiting the evidence on the growth-poverty relationship
If there is something like an identity linking growth, poverty reduction and distributional
changes, it must show up very clearly in the data. This section shows that this is indeed the case
and that the preceding Log-Normal approximation proves to be practically useful.
The data being used are drawn from pairs of household surveys taken at two points of time in
several developing countries. Each pair of household surveys corresponds to a 'growth spell'.
The comparison of the two household surveys in a growth spell yields a measure of the poverty
reduction during that growth spell - and poverty increase in case of negative growth. This
information may then be combined with the observed increase in mean income from the first to
the second survey, after correcting for price changes, and with observed changes in the
distribution of relative income to test the identity analyzed in the previous section. The data set
used here was made available by Chen and Ravallion. It covers 116 growth spells in a total of 52
countries, that is a little more than two spells in each country on average. The sample includes
mostly developing countries but a few transition economies are also present. No modification
whatsoever has been made to the original data, except eliminating all spells where the percentage
change of in the poverty headcount was abnormally large in absolute value. Cases left aside
essentially correspond to situations where the poverty headcount went from 0 or an almost
10
negligible figure to some positive value, or the opposite, in a few years. The mean growth in
mean income over all these spells is 2.7 per cent, the mean relative change in the poverty
headcount - with a 1 $ a day poverty line - is close to zero and the mean change in the Gini
coefficient is -.0022.
Based on this data set, four different models are compared against each other. The first
corresponds to the naive view that there is some constant elasticity between poverty reduction
and growth. It consists of regressing observed changes in the poverty headcount on observed
changes in mean income. The second model, which is termed 'standard' model in table1
comprises the observed change in income inequality, as measured by the Gini coefficient as an
additional explanatory variable. It is thus consistent with a decomposition of type (2) above,
except for the fact that both the growth-elasticity and the Gini-elasticity of poverty reduction are
taken to be constant. The third model improves on the previous one by allowing the growth
elasticity to depend on the inverse level of development, as measured by the poverty-line/meanincome ratio, and on the initial degree of inequality as measured by the Gini coefficient. Nothing
is imposed a priori on that relationship, though, and finding its shape is left to econometrics. To
do so, two additional variables are introduced in the regression : the interaction between growth
and the preceding two variables. The final model relies on the Log-normal approximation
discussed above. The explanatory variables are the theoretical elasticity defined in (5) times the
observed growth rate of mean income 3 and the change in the Gini coefficient. If the identity
argument is correct and if the Log-normal approximation is not too bad, then one should find that
the coefficient of the theoretical elasticity in the regression is not significantly different from
3
Expression (5) relies on the standard deviation of the logarithm of income whereas inequality is measured by the
Gini coefficient in the data set. However, it is well-known that there is a one to one relationship between these two
magnitudes when the underlying distribution is Log-normal. We used that relationship to derive σ from the
observed value of the Gini.
11
unity.
The estimation of these four models is reported in Table1. Results fully confirm the identity
relationship discussed in this paper. First, one can see that the naive model suggests a significant
negative elasticity of poverty with respect to growth but its explanatory power is very low.
Things improve quite substantially when shifting to the standard model by adding the change in
the Gini coefficient. Practically, the R² coefficient is multiplied by two, suggesting that the
heterogeneity in distributional changes is as much responsible for variation in poverty reduction
across growth spells as the heterogeneity in growth itself.
Interacting growth with the initial poverty-line/mean-income ratio and the initial Gini coefficient
in the 'improved standard model' yields still another significant improvement in explanatory
power. The two interaction terms are very significant and go in the right direction. Both a lesser
level of development and a higher level of inequality reduce the growth-elasticity of poverty. As
expected, both effects are significant and sizable. At the mean point of the sample - i.e. for a
growth spell leading to a 2.7 per cent rise in mean income - an increase of the initial level of
development by one standard deviation of the poverty-line/mean-income variable increases
poverty reduction by some 3 percentage points. In the same conditions, an increase in the initial
Gini coefficient by one standard deviation reduces poverty reduction by a little less than one
percentage point.
No assumption is made in the preceding regression on the way income growth, the development
level and the initial degree of inequality interact to determine poverty reduction. In the last
column of table1, on the contrary, it is assumed that the joint effect of these three variables is in
accordance with the theoretical elasticity derived in the preceding section under the assumption
that the underlying distribution of relative income is Log-Normal. The resulting explanatory
12
variable in the poverty reduction regression thus is this theoretical elasticity times the observed
growth of the mean income. This test of the identity that links poverty reduction and growth is
fully successful. On the one hand, the R² coefficient proves to be substantially higher than when
the various explanatory variables are entered without functional restriction as in the preceding
regression. On the other hand, the coefficient of the theoretical value of the elasticity proves to
be not significantly from unity. Overall, it must then be concluded that the best simple
explanation of observed poverty reduction in a sample of growth spells is indeed provided by the
identity that logically links poverty and growth under the Log-normality assumption.
Despite the fact that it is supposed to represent some identity linking poverty reduction, growth
and distributional changes, it must be stressed that this last model explains only half of the total
variance observed in the available sample of growth spells. What phenomenon is behind the
remaining half ? According to the argument in the preceding section, the answer must be found
in the Log-normal assumption and, predominantly, in the fact that the change in the distribution
between the initial and terminal year of the growth spell is represented by a single summary
measure. If a more detailed representation of the actual distributional change were used, this
last model would then become much closer to the original identity.
3. Some implications
This identity relationship between poverty reduction, growth and distributional change has
several implications for policy making and economic analysis in the field of poverty.
On the policy side, it was shown in this paper that this identity permits to identify precisely the
potential contribution of growth and distributional change to poverty reduction. However, it
13
also introduces in the debate of growth vs. redistribution as a poverty reduction strategy an
element that is often overlooked, although it had been stressed by Ravallion (1997). To the
extent that growth is sustainable in the long-run whereas there is a natural limit to redistribution,
it may reasonably be argued that an effective long-run policy of poverty reduction should rely
primarily on sustained growth. According to the basic identity analyzed in this paper, however,
income redistribution has essentially two role in poverty reduction. Of course, a permanent
redistribution of income reduces poverty instantaneously through what was identified as the
‘distribution effect’. But, in addition it also contributes to a permanent increase in the elasticity
of poverty reduction with respect to growth and therefore to an acceleration of poverty
reduction for a given rate of economic growth. This is independent from the phenomenon
emphasized in the recent growth-inequality literature according to which growth would tend to
be faster in a less inegalitarian environment. 4 If this were true, there would be a kind of ‘double
dividend’ to a redistribution policy since it would at the same time accelerate growth and
accelerate the speed at which growth spills over onto poverty reduction.
From the point of view of economic analysis, the basic argument in this paper has clear
implications for the understanding of poverty reduction. The common practice of trying to
explain the evolution of some poverty measure over time, possibly across various countries, as a
function of a host of variables including economic growth has something tautological. The
preceding section has shown that even when considering actual data the actual growth-elasticity
of poverty reduction had the value predicted by theory, even under the Log-normality
assumption. Running a regression like the ‘standard model’ above where growth appears among
the regressors would make sense only in the case where one does not observe the actual
4
On this see the survey by Aghion et al. (1999).
14
determinant of that theoretical value, that is the level of development and inequality. This would
be surprising, though, since poverty estimates are generally derived from surveys where both the
mean income of the population and the degree of inequality are directly observed. In this case,
the way poverty reduction depends on growth is perfectly known. According to the basic identity
analyzed in this paper, the only thing left for explanation in poverty reduction thus is the pure
‘distribution’ effect. Somehow all the variables that may be added in the regression after the
growth effect has been rigorously taken into account can only explain the effect of the change in
distribution over poverty. If growth has been improperly taken into account, however, these
variables may also simply be correlated to the bias due to not using the proper specification for
the growth-elasticity of poverty. This kind of problem may be present in an analysis like that of
de Janvry and Sadoulet (1998). It is not present in the recent paper by Dollar and Kraay (2000)
because that paper does not use a conventional poverty measure. By focusing on the mean
income of the bottom 20 per cent of the population, rather than the income of people below a
constant poverty line, this paper really is about pure distributional changes rather than the effect
of growth on poverty.
15
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16
Table 1. Explaining the evolution of poverty across growth spellsa
Dependent variable = Percentage change in poverty headcount during growth spell
Naive model
Standard model
Improved
standard model
Identity check
Intercept
0.0546
0.0457
0.0727
0.0387
0.0596
0.0383
0.0505
0.0359
Y = Percentage change in mean income
-1.4650
0.2705
-1.8664
0.2362
-5.5100
1.3612
4.9309
0.7233
5.4315
0.7220
Explanatory variables
Variation in Gini coefficient
Y * poverty Line/mean income
3.3130
1.2786
Y * Initial Gini coefficient
5.9349
2.7073
Y * Theoretical value of growth-elasticity
under Log-Normal assumption
Number of observations
R²
a
5.2799
0.6814
-1.1393
0.1215
116
116
116
116
0.2046
0.4364
0.4793
0.5078
Ordinary least squares estimates, standard errors in italics. All coefficients are significantly different from zero at the 1% probability level except the
intercept
Figure 1. Decomposition of change in distribution and poverty into growth and distributional effects
0.6
Growth effect
Distribution effect
0.5
New distribution
Density ( share of population)
Growth effect
on poverty
Distribution effect
on poverty
(I)
0.4
Initial distribution
0.3
0.2
(I)
0.1
(I)
0
0.1
Poverty line
1
10
Income ($ a day, logarithmic scale)
100
Figure 2. Poverty (headcount)/growth elasticity as a function of mean income and income
inequality, under the assumption of constant (Lognormal) distribution
0.7
0.65
0.6
Inequality = Gini coefficient
* Brazil
0.55
* Senegal
elasticity =2
0.5
* Zambia
0.45
elasticity = 3
elasticity = 4
0.4
* Cote d'Ivoire
0.35
elasticity = 6
* Indonesia
0.3
* India
elasticity=10
0.25
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
poverty line as a proportion of mean income
0.4
0.45
0.5
Figure 3. Poverty (poverty gap)/growth elasticity as a function of mean income and income
inequality, under the assumption of constant (Lognormal) distribution
0.582116841
0.541670017
0.498874718
Elasticity = 2
0.453832946
0.406677639
Elasticity = 4
0.357571468
Elasticity = 6
0.306704931
Poverty line as a proportion of mean income
0.5
0.47
0.44
0.41
0.38
0.35
0.32
0.29
0.26
0.23
0.2
0.17
0.14
0.11
0.08
0.05
0.02
0.254293848
Gini coefficient