metadata: authors: 0: author: Bergstrom,Katy Ann
count: World
docna: 0: docna: The Role of Inequality for Poverty Reduction
docty: Policy Research Working Paper
subtopic: Inequality,Poverty Reduction Strategies,Industrial Economics,Economic Theory & Research,Economic Growth,Crime and Society
teratopic: Poverty Reduction,Industry,Macroeconomics and Economic Growth,Social Development
abstracts: cdata!: 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 poverty reduction. The analysis finds that
            the assumption that income is log-normally distributed
            allows one to approximate 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.
repnme: repnme: The Role of Inequality for Poverty Reduction
display_title: The Role of Inequality for Poverty Reduction
listing_relative_url: /research/2020/09/32422044/role-inequality-poverty-reduction
topicv3: Economic Growth m1326241 471,Poverty m1326687 695,Criminal Justice m1326993 1014,Growth, Poverty and Inequality m1327633 1091,Income Inequality m1503891 2668
publishtoextweb_dt: 2020-09-21T00:00:00Z
historic_topic: Poverty Reduction,Industry,Macroeconomics and Economic Growth,Social Development
origu: DECRG: Poverty & Inequality (DECPI)
no_of_pages: 40
author_keys: 0: author_key: 1811674
model_extractions: Policy Research Working Paper 9409 Poverty and Shared Prosperity 2020 _Background Paper_ The Role of Inequality for Poverty Reduction _Katy Bergstrom_ Development Economics Development Research Group September 2020
Policy Research Working Paper 9409

# **Abstract**

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 poverty reduction. The analysis finds that the assumption that income is log-normally distributed allows one to approximate 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 kbergstrom@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# The Role of Inequality for Poverty Reduction

Katy Bergstrom<sup>_∗_</sup>

> _∗_ Development Research Group, World Bank. Email: kbergstrom@worldbank.org. Thanks to Samuel Freije-Rodriguez, Daniel Mahler, Christoph Lakner, Aart Kraay, Berk Ozler,<sup> ̈</sup> Marta Schoch, Judy Yang, and Michael Woolcock for their valuable comments and suggestions. This is a background paper for the Poverty and Shared Prosperity 2020. The findings, interpretations, and conclusions expressed in this paper are entirely those of the author. They do not necessarily represent the views of the World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they 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 speaking, 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 general, the (absolute) growth elasticity of poverty is decreasing in a country’s initial level of income inequality.<sup>1</sup> 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.<sup>2</sup> 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.<sup>3</sup> Using this approximation, 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) growth elasticity of poverty is unambiguously decreasing with inequality (Bourguignon, 2003; Ferriera, 2012). 2. See, for example, Bourguignon (2003), Kraay (2006), Lopez and Serv ́en (2006), Kalwij and Verschoor (2007), Klasen and Misselhorn (2008), Bluhm et al (2016), and Fosu (2017).

> 3. This _R_<sup>2</sup> 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, we estimate 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 heterogeneity 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.<sup>4</sup> 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.<sup>5</sup> But the empirical literature has produced very mixed results.<sup>6</sup> 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 reducing inequality by 1% per year leads to a greater reduction in 2030 headcount poverty than 1% increases in mean incomes.

5. Theoretically, the effect of inequality on growth is ambiguous: the conventional view is that higher inequality promotes stronger incentives, generates greater savings and investment, and endows the rich with 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 hurts growth as it leads to redistributive pressure through taxes, social conflict, expropriation, or rent-seeking behavior (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 on growth (Alesina and Rodrik, 1994; Persson and Tabellini, 1994). Then, with the introduction of the Deininger 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 (Castell ́o-Climent, 2010; Halter et al, 2014; Ostry et al, 2014; and Dabla-Norris et al, 2015), although the validity of their estimation 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).<sup>7</sup> 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).<sup>8</sup> 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 Serv ́en (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 incomes, and the change in absolute poverty. First, let _F_ ( _y_ ; Ω _t_ ) 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. However empirical 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 with changes in inequality, _potentially_ highlighting the difficulty of influencing inequality; alternatively, this could simply reflect a limitation of cross-country specifications.

4
<!-- Start of picture text --> (- )<br>- ) 6 )<br>( CE ) © ) ( 6 ) 6 )<br>- ()- ) +<br>( FE ) & ) C e ) © )<br><!-- End of picture text -->
and we have denoted the term multiplying the proportion change in the distribution of incomes, _θ_ <u>1</u> _t_ _<u>dθdtt</u>_<sup>,asthesemi-elasticityofpovertyw.r.t.inequality.Dividingthroughby</sup> _Ht_ = _F_<sup> ̃</sup> � _y_ ̄ _<u>zt</u>_<sup>;</sup><sup>_θt_</sup> � everywhere we get: Equation (3) illustrates that the percentage change in headcount poverty can be broken 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 _<u>z</u>_ the inverse level of development in period _t_ , _y_ ̄ _t_<sup>,alongwiththeparametersintherelative</sup> 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 increase 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 elasticities. 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 Serv ́en, 2006). Consistent 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
<!-- Start of picture text --> ( - ) —_l_<br>(_ ) _&) .<br>(_ ) 6)<br>—F)OO. ._&)<br>— OF . ©.. ©)<br><!-- End of picture text -->
<!-- Start of picture text --> ee ——_____— _ SS<br><!-- End of picture text --> <!-- Start of picture text --> 2 8 ‘<br>y of 7<br>7 7<br>Lo2&go 7Yo aN3{=} /FA<br><: 7 & /<br>3 o<br>(o) / w /<br>2 / . 8 / a“<br>3 / _— 8 / 7<br>3go / - = =2 / Z<br>< / o / oa oo<br>l/7 oaweoor weet_. I A oferr oo"een.<br>[Serra n nnn Mord nine<br>fo) Y SadSe Loi Tiateneee fo) aeoee<br>ie} 100 200 300 400 500 0 100 200 300 400 500<br>Mean Income (monthly, per-capita) Mean Income (monthly, per-capita)<br>—_=—= sigma=0.4 =—='— sigma=0.6 —=-—= sigma=0.4 =—='— sigma=0.6<br>=== sigma=0.8 = '='= sigma=1.0 === sigma=0.8 = '= = sigma=1.0<br>seeee=) sigma=1.2 seeee= sigma=1.2<br><!-- End of picture text -->
<!-- Start of picture text --> ~\<br>\<br>ee)<br>G S%<br>a©c3 Ws\\sv"*,LAS v0,Soyfo,<br>84 \ SN fee,<br>3 VSS an “tee,<br>x= \ XN a ey ~ eee,<br>N \ NK ssa = =m . oa eeeseesenas<br>AN ~~ Sse ll oon<br>Oo Sm na = oe oe om en =<br>0 100 200 300 400 500<br>Mean Income (monthly, per-capita)<br>=== sigma=0.4 “= '=—'* sigma=0.6<br>===== sigma=0.8 === '= sigma=1<br>eueeeeeee sigma=1.2<br><!-- End of picture text -->
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_ =<sup>_Xi,_</sup> _X_<sup>_t−_</sup> _i,t_<sup>_X_</sup> _−_<sup>_i_</sup> _n_<sup>_<u>,t−n</u>_</sup> _×_ 100 denotes our percentage change in variables _X ∈{y, σ_ ̄ _}_ from 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: 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: If our assumption of log-normality is true, and provided changes in mean incomes and _σ_ are small, we should find _γ_ 0 = 0, _γ_ 1 = 1, _γ_ 2 = 1 and an _R_<sup>2</sup> = 1 when estimating Equa10
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)): From Equation (1), the term multiplying _ω_ 1 in Equation (13) is the “growth component” while the term multiplying _ω_ 2 is the “distribution component” under the assumption income is log-normal. Thus, if our assumption of log-normality is true, we should find _ω_ 0 = 0, _ω_ 1 = 1, _ω_ 2 = 1 and an _R_<sup>2</sup> = 1.<sup>11</sup> 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, _H_<sup>ˆ</sup> _i,t_ = Φ �log � _yz_  ̄ _t_ � _σ_ <u>1</u> _t_<sup>+</sup><sup><u>1</u></sup> 2<sup>_σt_</sup> �. Results from this regression are presented in Appendix B (we find an extremely good fit: _R_<sup>2</sup> = 0 _._ 99). Ultimately, while there are many specifications that can be run to test whether log-normality is a good approximation (see Lopez and Serv ́en (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 estimated regressions (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 comparable across the two surveys.<sup>1213</sup> This 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 Research Group 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 a country over time. For instance, two surveys for a given country would not be comparable between years 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***<br>(0.025)|||||
|∆ ̄_y ×_ <sup>_z_</sup><br> ̄_y_|||-0.135***<br>(0.009)|||||
|∆_σ × σ_|||0.544***<br>(0.062)|||||
|∆_σ ×_ <sup>_z_</sup><br> ̄_y_|||-0.0598*<br>(0.035)|||||
|∆ ̄_y × κ_ ̄_y_||||0.942***<br>(0.009)||1||
|∆_σ × κσ_||||0.750***<br>(0.022)||1||
|Growth Component|||||1.081***<br>(0.007)||1|
|Distribution Component|||||0.882***<br>(0.015)||1|
|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 parentheses. 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 _R_<sup>2</sup> 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
(C ~~(—-~~ ) ~~CE)~~ C ~~O) -~~ ) ~~CO)~~ )
<!-- Start of picture text --> eS<br>@.-"<br>eo ° 2<br>° oe, are<br>@ of ®<br>Do e bd<br>5e<br>5ef<br>no} o*%, je<br>RS}2 0?e rdsA ee<br>Bo2 e Pte“3<br>ay oo<br>e id e @<br>o ioe e e<br>lo)<br>%<br>-20 -10 0 10<br>Actual Change<br>ssress="= 45 degree line --------- Fitted Values (slope=0.88)<br><!-- End of picture text -->
<!-- Start of picture text --> ° EAP ° ECA ° LAC<br>Do DO Do<br>oN -® oN “7 oN -7<br>se ee Be se Bs o~<br>[S) -@ (Ss) (S)<br>BeBe Ta BSSe a 3SSe at<br>oN oN oN<br>a! a! a!<br>-20 -10 0 10 20 -20 -10 0 10 20 -20 = -10 0 10 20<br>Actual Change Actual Change Actual Change<br>°Do MNA °Do OHI °Do SAS<br>on id cn id on oe<br>Bo oe Bo ee Bo<br>otnone) ee otnone) oo oFme] wo<br>a! a! a!<br>-20 -10 0 10 20 -20 -10 0 10 20 -20 = -10 0 10 20<br>Actual Change Actual Change Actual Change<br>° SSA<br>2a cS<br>£o a<br>3=OoO<br>BeSafewe<br>aoh + Se<br>-20 -10 0 10 20<br>Actual Change<br><!-- End of picture text -->
_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: As shown in Figure I, both elasticities will be increasing in absolute value with development (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) generates 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_ ̄ _< e_<sup>log(</sup><sup>_z_)</sup><sup>_−σ_2</sup><sup>_/_2</sup> , 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
<!-- Start of picture text --> w<br>— a= -<br>=<br>> a7<br>8 oo<br>2 =<br>WSnomOo Uo<br>= ao<br>QO =~ A An<br>rs aaa<br>aSs oe fe) Gh A fe) A 4A<br>22 ace bia, 4+ 14 A oO<br>Pal Were) @°o;+,F +<br>x x XxX<br>oO x.<br>0) 5 10 15<br>Inequality Elasticity<br>fe) EAP 4 ECA<br>+ LAC O MNA<br>° SAS x SSA<br>—-—-— 465 degree line<br><!-- End of picture text -->
<!-- Start of picture text --> (o)<br>N<br>2<br>S<br>mo<br>& vv<br>mT<br>ao<br>Zo A A<br>oOo A<br>0)2 aA _ a* ee<br>=) _<br>[one ofa. oo A<br>3 Bo a Broa x A 4 o A A, .<br>* fp O88 Pt eet a<br>oO<br>0 200 400 600 800<br>Lagged Mean Income (monthly, per-capita)<br>oO EAP A ECA<br>+ LAC o MNA<br>° SAS x SSA<br>——— sigma=0.4 —-—-— sigma=0.6<br>------- sigma=1.0 - - - -- sigma=1.2<br><!-- End of picture text -->
# _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: 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: 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
<!-- Start of picture text --> Panel (a) Panel (b)<br>e ’<br>2.427<br>e<br>eo ° %rtjvee ° =$s e e e ° oera<br>s eo %’ee o ee eo”<br>= ee © Pe i=a © e. Mee 9 oe,’ 7 @4e e<br>3 % Se < od . 74° °<br>6 e ‘@ 3° wo ts @<br>2o e° ° 2° @ e Zoe od i PS ¢<br>3 e e ee 5 ee e iy a e e<br>2 eo eo ° 2 Cd wv oe eo<br>g og | -e S @ of” fe e<br>a © of asee Ne ee<br>ry ) of ee 2 eo. e<br>2s eo 8 ay vv<br>g Cao © &<br>oO & e ,- C) e ©> //<br>C%@ ° g ye<br>“ (6) vo<br>o| “e ol ”<br>~ ~<br>-20 -10 0 10 -20 -10 0 10<br>Change in Poverty Change in Poverty<br>------- 465 degree line ------- 465 degree line<br><!-- End of picture text -->
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: 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 assumptions 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: 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): where _r_ denotes region, and _ωi_ denotes country _i_<sup>_′_</sup> _s_ population relative to the total population in the region.<sup>17</sup> Note, we could also project headcount poverty using an elasticity approach, e.g., _Hi,_ 2030 = _Hi,T_ +<sup>�2030</sup> _s_ =1<sup>_−T_</sup> ( _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).<sup>18</sup> In particular, we estimate the following MA(2) regression for each country _i_ :<sup>19</sup> where log( _gdp_ _~~p~~ ci,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 by the 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 anticipated COVID-19 shock.

23
incomes out to 2030 for each country.<sup>20</sup> 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).<sup>21</sup> 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 counterfactual 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)<br>(4)|
|---|---|---|---|---|
|Region|Baseline|1% decr. _σ_|1% incr. _σ_|1% incr. ̄_y_<br>1% decr. ̄_y_|
|EAP|0.73|0.37|1.30|0.53<br>0.99|
|ECA|0.15|0.06|0.35|0.09<br>0.23|
|LAC|2.74|1.30|5.13|2.11<br>3.52|
|MNA|4.40|3.60|5.63|3.57<br>5.41|
|OHI|0.00|0.00|0.00|0.00<br>0.00|
|SAS|3.66|1.90|6.26|2.56<br>5.13|
|SSA|32.32|28.69|36.33|28.54<br>36.37|
|World|5.69|4.52|7.29|4.78<br>6.78|

_Note:_ Headcount poverty is multiplied by 100, i.e., we project 32.32% of the population in SSA to be under the poverty line in 2030 under our baseline specification. World Headcount poverty is the sum of weighted regional poverty rates.

20. For example, our latest observation of mean income for India is 2011; thus, we use the 2011 observation for _y_ ̄, along with per-capita GDP growth rates for India from 2012-2030 to calculate mean income 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, Jamaica would not be included in this projection exercise.

21. E.g., because the latest observation for India is 2011, we assume _σ_ India _,_ 2030 = _σ_ India _,_ 2011 24
<!-- Start of picture text --> lo)<br>=<br>> oPwe<br>xSOSAZa Som ES_ so<br>> ON NN<br>= ~ NN<br>oO ~ \F--<br>>0 : 7 m-~_<br>S zx ~A_T--y<br>ao~ aN TAS —-A LT --4<br>c3 » NS ~~ TALL<br>8 ‘~ ~~<br>ne}fog ~l om ~<br>Lo “Bla<br>S Wor~a_<br>5 Ba ~ a<br>= 74>~~<br>~/7<br>+<br>2020 2025 2030<br>year<br>——®— baseline ——-m-—- 1% decr. in sigma<br>——-m-—- 1% incr. in sigma ——-4-—- 1% incr. in mean inc<br>—-4&-—- 1% decr. in mean income<br><!-- End of picture text -->
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
<!-- Start of picture text --> This Paper: _<br>Changes in. Absolute Poverty Additional Channels: = = = =<br>Changes in Inequality #+--------»>» Changes in Mean Incomes<br>y<br>x w<br>4<br>\<br>\4<br>\4<br>\4<br>N7<br>N4<br>N4<br>N4<br>Polices<br><!-- End of picture text -->