The World Bank Economic Review, 36(3), 2022, 583–604 https://doi.org10.1093/wber/lhab026 Article Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 The Role of Income Inequality for Poverty Reduction Katy Bergstrom Abstract 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 examines the role of income inequality for poverty reduction. Under the assumption that income is log-normally distributed, we show that we can approximate this identity well. We find that the inequality elasticity of poverty reduction is larger, on average, compared to the growth elasticity of poverty reduction and that the growth elasticity declines steeply with a country’s initial level of inequality. However, we find that prior changes in poverty were, in large part, explained by changes in mean incomes. This is a consequence of changes in income inequality being an order of magnitude smaller than changes in mean incomes. Overall, our results highlight the important role income inequality can play in reducing poverty despite prior poverty changes being, in large part, a consequence of economic growth. JEL classification: I32, O10, O15 Keywords: income inequality, growth, poverty, inequality elasticity of poverty reduction, growth elasticity of poverty reduction 1. 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, absolute poverty reductions in a country can be decom- posed into growth in mean incomes, a reduction in inequality of incomes, or a combination of the two. Moreover, due to the nonlinear 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 reduction 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 income Katy Bergstrom is an economist in the Development Research Group, World Bank, Washington, DC, USA; her email address is kbergstrom@worldbank.org. The author thanks Samuel Freije-Rodriguez, Daniel Mahler, Christoph Lakner, Aart Kraay, Berk Özler, Marta Schoch, Judy Yang, Michael Woolcock, and two anonymous referees for their valuable comments and suggestions. This was originally 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. A supplementary online appendix is available with this article at The World Bank Economic Review website. 1 To be precise, the effect that initial inequality has on growth elasticity is theoretically ambiguous (Ravallion 2005). However, under certain assumptions it can be shown that the (absolute) growth elasticity of poverty is unambiguously decreasing with inequality (Bourguignon 2003; Ferreira 2010). © The Author(s) 2022. Published by Oxford University Press on behalf of the International Bank for Reconstruction and Development / THE WORLD BANK. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com 584 Bergstrom 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 Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 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 nonnegligible role both through the direct effect of inequality on poverty and the indirect effect inequality has on the growth elasticity of poverty reduction. Using the latest cross-country data, this paper seeks to update the empirical estimation of this identity and, in turn, reexamine the role of income inequality for poverty reduction. To begin, we rederive the identity that exists between changes in absolute poverty, changes in income 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 approxima- tion: our model is able to explain 94 percent of the variation in observed changes in headcount poverty. Under this assumption, 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 percent reduction in inequality, as measured by the standard deviation of log income, leads to a larger reduction in poverty relative to a 1 percent increase in mean income.3 In particular, we find that post 2010, the median inequality elas- ticity of poverty reduction is 5.19, while the median (absolute) growth elasticity of poverty reduction is only 2.78. Furthermore, we find substantial heterogeneity in these elasticities; in particular, the (absolute) 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 in- comes. 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 percent 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 percent per annum declines in inequality over 2020–2030 lead to greater reductions in worldwide poverty compared to 1 percent 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 own 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 2 See, for example, Bourguignon (2003), Kraay (2006), Lopez and Servén (2006), Kalwij and Verschoor (2007), Klasen and Misselhorn (2008), Bluhm, de Crombrugghe, and Szirmai (2018), and Fosu (2017). 3 Note, our measure of inequality is equal to the standard deviation of log income under the assumption that income is log-normally distributed. Under this assumption, the standard deviation of log income is simply an increasing function of the Gini coefficient. 4 Using a different model to predict headcount poverty, Lakner et al. (2020) also find that reducing inequality by 1 percent per year leads to a greater reduction in 2030 headcount poverty than 1 percent 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, Caroli, and Garcla-Pefialosa 1999; Okun 2015; Kaldor 1957; Barro 2000). Conversely, it has been argued that inequality hurts growth as it leads to redistributive pressure The World Bank Economic Review 585 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 nonlinear, context-specific relationship between inequality and growth Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 (Banerjee and Duflo 2003; Grigoli, Paredes, and Di Bella 2018; Grigoli and Robles 2019).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 policy makers to utilize case studies and tools that analyze the impacts of various policies on growth and inequality.9 These studies and tools, in conjunction with understanding the extent to which changes in inequality and growth are transformed into reductions in poverty, should guide policy makers in designing effective policies to combat poverty. Our paper is closely related to Bourguignon (2003) and Klasen and Misselhorn (2008) who also test whether the assumption that (per capita) incomes are log-normally distributed allows one to approxi- mate the poverty decomposition identity well. Like both of these papers, we too find that the log-normal assumption allows us to approximate the identity well; however, by using a more recent and compre- hensive data set and by estimating an approximation that allows for discrete changes in mean incomes and inequality, we find a much better fit of our approximation to the identity than both Bourguignon (2003) and Klasen and Misselhorn (2008). Moreover, in contrast to both of these papers, we place a much stronger focus on the role that income inequality plays in poverty reduction. In particular, we cal- culate the growth and inequality elasticities for all countries in our sample so that we can contrast the size of the inequality elasticity to the growth elasticity. Furthermore, we decompose observed changes in poverty into changes in mean incomes and changes in inequality so as to investigate the role that income inequality has played in prior poverty reductions. In this way, our paper is also closely related to Kraay (2006), Kalwij and Verschoor (2007), Bluhm, de Crombrugghe, and Szirmai (2018), and Fosu (2017), who also empirically approximate the poverty decomposition identity and, in turn, explore the role that changes in mean incomes and changes in the distribution of incomes have played in prior poverty changes. Our contribution relative to these papers is to use an alternative approximation to the identity and to use the latest cross-country data to reexamine the role that income inequality can play (and has played) in poverty reduction. through taxes, social conflict, expropriation, or rent-seeking behavior (Alesina and Rodrik 1994; Benhabib and Rusti- chini 1996; Benabou 1996; Perotti 1996; Persson and Tabellini 1994; Glaeser, Scheinkman, and Shleifer 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 data set, studies started to find positive effects (Li and Zou 1998; Forbes 2000). More recently, however, several papers find again a negative effect (Castelló-Climent 2010; Halter, Oechslin, and Zweimuller 2014; Ostry, Berg, and Tsangarides 2014; Dabla-Norris et al. 2015), although the validity of their estimation technique has been questioned (Kraay 2015). 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, Kleineberg, and Kraay (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. 9 For example, the CEQ Assessment tool (see Lustig 2018), which allows one to determine the extent to which fiscal policy reduces inequality and poverty in a particular country, would be very useful for this purpose. 586 Bergstrom The remainder of the paper is set up as follows: first we rederive the identity that links changes in mean incomes and inequality to changes in poverty. Guided by this identity, we then discuss the empirical specifications that we test and the data that we use. We then estimate these specifications and show that the assumption that income is log-normally distributed allows us to approximate the identity well. Using this Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 assumption, we then estimate the magnitudes of the growth and inequality elasticities. We then provide projections for 2030 headcount poverty under various scenarios. Finally we discuss our results in light of designing policies to reduce poverty. 2. Rederiving the Identity 2.1. Rederiving the Identity for a General Income Distribution In this section, following Bourguignon (2003), we rederive 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; t ) denote the CDF of per capita incomes yt in society in period t where t denotes the parameters governing the distribution; e.g., if incomes come from the log-normal distribution then t = {μt , σ t } where μt and σ t denote the mean and standard deviation of log income in period t, respectively. Let z denote the fixed poverty-line, let y ¯t denote mean incomes in period t, and let Ht = F(z; t ) 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 ˜ ( y ; θt ) denote the CDF of mean-normalized incomes yt in period t, where the PDF is given ¯t y ¯t y by f˜ ( ; θt ) = y ¯t y y ¯t f (y; t ), where f(y; t ) denotes the PDF of incomes in period t. Note, θ t denotes the parameters governing the distribution of mean-normalized incomes. For example, if log(y ) ∼ N (μt , σt2 ) y ˜ z ; θt ). ¯t ) ∼ N (−σ /2, σ ) meaning θ t = σ t . Trivially, Ht = F (z; t ) = F ( y 2 2 then log( y ¯t Using this notation, we can express the change in the poverty headcount from t to t using the expres- sion ˜ z ˜ z Ht − Ht = F ; θt −F ; θt ¯t y ¯t y ˜ z ˜ z ; θt ˜ z ˜ z = F ; θt − F + F ; θt −F ; θt , (1) ¯t y ¯t y ¯t y ¯t y growth component distribution component 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, θ t ).10 Dividing through by t − t and taking the limit as t − t → 0 we get dHt z z 1 dy¯t z 1 d θt = − f˜ ; θt + ˜θ F ; θt θt , dt ¯t y ¯t y ¯t dt y t ¯t y θt dt growth semi-elasticity inequality semi-elasticity t −Xt where dX dt t = limt −t →0 Xt −t , and where we have denoted the term multiplying the proportion change 1 dy ¯t in mean incomes, y ¯t dt , as the growth semi-elasticity, and we have denoted the term multiplying the 10 Technically our “distribution component” in equation (1) includes both the distribution component and a residual (as described in Datt and Ravallion 1992): ˜ z ˜ z ˜ z ˜ z F ; θt −F ; θt = F ; θt −F ; θt +R(t , t ; t ), ¯t y ¯t y ¯t y ¯t y distribution component distribution component, Datt and Ravallion where R(t, t ; t) denotes the residual term as described in Datt and Ravallion (1992). The World Bank Economic Review 587 1 d θt proportion change in the distribution of incomes, θt dt , as the inequality semi-elasticity. Dividing through by Ht = F˜ ( z ; θt ) everywhere we get y¯t 1 dHt f˜ ( y¯ ; θt )z 1 d y z ¯t ˜θ ( z ; θt )θt F t y ¯t 1 d θt = − zt + . (2) Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Ht dt ˜ F( y ¯t ; θt )yt ¯ ¯ y t dt F˜ ( z ; θt ) ¯t y θt dt growth elasticity inequality elasticity Equation (2) illustrates that the percentage change in headcount poverty can be broken down into the percentage change in mean incomes and the percentage change in the parameters governing the distribu- tion of relative incomes. Moreover, the extent to which a change in mean incomes and a change in the z distribution affect poverty will depend on the inverse level of development in period t, y ¯t , along with the parameters of the relative income distribution in period t, θ t . In other words, the growth and inequal- ity elasticities are not constant across countries with different initial conditions. From equation (2) it is clear that the growth elasticity is always negative: if there are no changes in the distribution or relative incomes, 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 distributional change. We can take our identity, equation (2), to the data in two ways. First, if we had microlevel data for all countries over time, we could nonparametrically identify the income distributions in each period t and thus nonparametrically 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 Servén 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 as- sumption 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, so proceed with analyzing the identity under the assumption of log-normality. 2.2. Log-Normal Distribution Let us assume that yt comes from a log-normal distribution, i.e., log(yt ) ∼ N (μt , σt2 ), where μt and σ t denote the mean and standard deviation of log (yt ), respectively. We know the identity σt2 y¯t = eμt + 2 , ¯t denotes mean income in period t. Rearranging we get remembering that y σt2 μt = log(y¯t ) − . 2 σ2 σt2 Thus, we get log(yt ) ∼ N (log(y¯t ) − 2 t , σt2 ). Hence, we get (log( y y¯t ) + t 2 )/σt ∼ N (0, 1), remembering that σ t denotes the standard deviation of log-income. Thus we get y y log( y¯t ) 1 ˜ F ; θt = + σt , (3) y¯t σt 2 588 Bergstrom where denotes the standard normal CDF. Taking the derivative with respect to y/y¯t we get y y log( y¯t ) 1 y¯t f˜ ; θt = φ + σt , y¯t σt 2 σt y Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 where φ denotes the standard normal PDF. Taking the derivative of equation (3) with respect to θ t = σ t we get ˜ ( y ; θt ) dF y log( y y y¯t ¯t ) 1 1 log( y¯t ) =φ + σt − . d θt σt 2 2 σt2 Hence, equation (2) becomes z z z dHt log( y¯t ) 1 1 1 dy ¯t log( y¯t ) 1 1 log( y¯t ) 1 d σt = −φ + σt +φ + σt σt − , (4) dt σt 2 σt y ¯t dt σt 2 2 σt σt dt growth semi-elasticity, κy ¯ inequality semi-elasticity, κσ where κy¯ denotes the growth semi-elasticity of poverty reduction when income is log-normally distributed and κ σ denotes the inequality semi-elasticity of poverty reduction when income is log-normally dis- tributed. Finally, equation (2) becomes log( yz ¯t ) log( yz ¯t ) log( yz ¯t ) φ σt +1 σ 2 t φ σt +1 σ 2 t 1 σ 2 t − σt 1 dHt 1 dy¯t 1 d σt =− + , (5) Ht dt log( yz ¯t ) ¯t dt y log( yz ¯t ) σt dt σt + 1 σ 2 t σt σt + 1 σ 2 t growth elasticity, ξy ¯ inequality elasticity, ξσ where ξy ¯ denotes the growth elasticity of poverty reduction when income is log-normally distributed, and ξ σ denotes the inequality elasticity of poverty reduction when income is log-normally distributed. Finally, we explore how our elasticities vary with mean incomes, y ¯ , and inequality, σ . Figure 1 shows how the absolute growth elasticity, |ξy ¯ and σ (on the left) and how the inequality elasticity, ¯ |, varies with y ξ σ , varies with y ¯ and σ (on the right). As shown in fig. 1 and as noted in Bluhm, de Crombrugghe, and Szirmai (2018), both elasticities are increasing in mean incomes. This is in part because the denominators of both |ξy ¯ | and ξ σ are equal to headcount poverty and headcount poverty approaches zero as mean incomes become sufficiently large—see fig. 2. Because of this somewhat misleading feature of these elas- ticities, one should focus most of one’s attention on comparisons of |ξy ¯ | and ξ σ within countries. Lastly, fig. 1 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 in mean incomes to generate greater percentage reductions in poverty (as shown by the absolute growth elasticity decreasing in initial inequality). 3. Empirical Specifications and Data 3.1. Empirical Specifications The empirical section of this paper will first be concerned with finding a specification that provides a reasonable approximation to the identity that exists between changes in poverty, changes in mean incomes, and changes in inequality. In this section we discuss the empirical specifications 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 empir- ical models: ¯ i,t + dHi,t = a0 + a1 y i,t , (6) ¯ i,t + b2 σi,t + dHi,t = b0 + b1 y i,t , (7) The World Bank Economic Review 589 Figure 1. How the Absolute Growth Elasticity and the Inequality Elasticity Vary with Mean Income and Inequality under the As- sumption That Income Is Log-Normally Distributed Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Source: Author’s calculations based on the assumption that income is log-normally distributed ¯ |, varies with mean income, y Note: The left-hand side of this figure shows how the absolute growth elasticity, |ξy ¯ , and the standard deviation of log income (inequality), σ , under the assumption that income is log-normally distribution. The right-hand side of this figure shows how the inequality elasticity, ξ σ , varies with mean income, ¯ , and the standard deviation of log income (inequality), σ , under the assumption that income is log-normally distributed. y ¯ , and Inequality, σ Figure 2. How Headcount Poverty Varies with Mean Income, y Source: Author’s calculations based on the assumption that income is log-normally distributed. ¯ , and the standard Note: This figure shows how headcount poverty (measured as the percentage of the population below the poverty line) varies with mean income, y deviation of log income (inequality), σ , under the assumption that income is log-normally distributed. 590 Bergstrom z ¯ i,t + c2 σi,t + c3 y dHi,t = c0 + c1 y ¯ i,t × ¯ i,t × σi,t −n + c4 y ¯ i,t −n y z + c5 σi,t × σi,t −n + c6 σi,t × + i,t , (8) Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 ¯ i,t −n y dHi,t = γ0 + γ1 κy ¯ i,t + γ2 κσ,i,t σi,t + ¯ ,i,t y i,t , (9) where dHi, t = (Hi, t − Hi,t−n ) × 100 denotes the percentage point change in headcount poverty from year t −Xi,t −n t − n to t for country i (where n can vary by country and year), where Xi,t = Xi,X i,t −n × 100 denotes the percentage change in variables X ∈ {y ¯ , σ } from year t − n to t for country i, and where σ i, t denotes our measure of income inequality and is calculated directly from the Gini coefficient, π i, t , as √ −1 πi,t + 1 σi,t = 2 . 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. Going forward, we will refer to σ as the standard deviation of log income (even though this is only true under log-normality) and as our measure of inequality. 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 percent change in σ , the Gini coefficient needs to change by <1 percent. For example, when σ = 0.68, to generate a 1 percent change in σ , the Gini coefficient must change by 0.93 percent.11 In equation (9), κy¯ ,i,t and κ σ ,i,t denote our theoretical values, under the assumption of log-normality, of the growth semielasticities of poverty reduction and the inequality semielasticities of poverty reduction, respectively: z 1 1 1 ¯ ,i,t = −φ log κy + σi,t −n , (10) ¯ i,t −n y σi,t −n 2 σi,t −n z 1 1 1 z 1 κσ,i,t = φ log + σi,t −n σi,t −n − log . (11) ¯ i,t −n y σi,t −n 2 2 ¯ i,t −n y σi,t −n ¯ , and inequal- If our assumption of log-normality is true, and provided that changes in mean incomes, y ity, σ , are small, we should find γ 0 = 0, γ 1 = 1, γ 2 = 1 and an R2 = 1 when estimating equation (9). However, when changes in mean incomes and inequality are not small, equation (9), even under the as- sumption 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 inequality—see equation (1)): z 1 1 z 1 1 dHi,t = ω0 + ω1 log + σi,t −n − log + σi,t −n × 100 ¯ i,t y σi,t −n 2 ¯ i,t −n y σi,t −n 2 z 1 1 z 1 1 + ω2 log + σi,t − log + σi,t −n × 100 + i,t . (12) ¯ i,t y σi,t 2 ¯ i,t y σi,t −n 2 11 In equations (7) and (8), Klasen and Misselhorn (2008) use the Gini coefficient as the measure of inequality as opposed to σ . In supplementary online appendix S1, we reestimate equations (7) and (8) replacing σ i, t with the Gini coefficient π i, t . Such a change has negligible effect on model fit. This is not surprising given that σ is an increasing function of π . The World Bank Economic Review 591 From equation (1), the term multiplying ω1 in equation (12) is the “growth component” while the term multiplying ω2 is the “distribution component” under the assumption that income is log-normally dis- tributed. Thus, if our assumption of log-normality is true, we should find ω0 = 0, ω1 = 1, ω2 = 1 and an R2 = 1.12 Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Finally, note that, 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 semielasticities 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 percent increase in headcount poverty as they moved from 0.0217 percent of their population below the poverty line to 0.396 percent of their population below the poverty line. It is desirable to place less weight on these countries given (a) we are primarily concerned with iden- tifying 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 to winsorize the data in some- what of an arbitrary fashion so as to remove observations where the percentage change in headcount poverty is enormous (e.g., Bourguignon 2003). To further illustrate this issue, in supplementary online appendix S3, we reestimate equations (6), (7), (8), and (9) using an elasticity framework as opposed to a semi-elasticity framework. We show how our results are very sensitive to including observations where headcount poverty is close to 0. 3.2. Data The data used to estimate equations (6), (7), (8), (9), and (12) are from PovcalNet.13 We include all countries that have at least two consecutive surveys where measurement of our three key variables (the headcount poverty rate, mean income, and the standard deviation of log income which is calculated directly from the Gini coefficient in PovcalNet) remain comparable.14 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 S4.1 in supplementary online appendix S4 for a list of all 135 countries with the range of survey years for each country and the number of growth-spells (observations) for each country. 12 Of course, a more direct test of log-normality is to simply regress observed headcount poverty Hi, t on predicted head- count poverty under the assumption of log-normality, H ˆ i,t = (log( z ) 1 + 1 σi,t ). Results from this regression are y¯ σ i,t 2i,t presented in supplementary online appendix S2 (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 good approximation (see Lopez and Servén (2006) for examples of alternative tests), we estimate specifications (9) and (12) 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 given by equations (6), (7), and (8). 13 PovcalNet is the publicly available online tool for poverty measurement developed by the World Bank; see http://iresearch.worldbank.org/PovcalNet/povOnDemand.aspx. 14 Atamanov et al. (2019, Section 4) discusses comparability of surveys within a country over time in PovcalNet. For instance, two surveys for a given country would not be comparable between years if the measurement of welfare switches from being consumption based to income based. 592 Bergstrom Table 1. Estimating Equations (6), (7), (8), (9), and (12) (1) (2) (3) (4) (5) (6) (7) ¯ y −0.206*** −0.213*** −0.00296 — — — — (0.007) (0.006) (0.020) Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 σ — 0.133*** −0.222*** — — — — (0.013) (0.042) ¯×σ y — — −0.199*** — — — — (0.025) ¯× y z ¯ y — — −0.135*** — — — — (0.009) σ ×σ — — 0.544*** — — — — (0.062) σ× z ¯ y — — −0.0598* — — — — (0.035) ¯ × κy y ¯ — — — 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 1,310 1,307 1,307 1,307 1,307 1,307 1,307 R-squared 0.425 0.463 0.584 0.893 0.951 0.876 0.942 Source: Author’s analysis using data from the World Bank’s PovcalNet Database. Note: In all columns the dependent variable is 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 percentage of the population under the $1.90 poverty line. Columns (1), (2), (3), (4), and (5) present regression results of equations (6), (7), (8), (9), and (12), respectively. Columns (6) and (7) reestimate equations (9) and (12) but restrict the coefficients in each regression to equal the coefficient values under the assumption that income is log-normally distributed. Standard errors presented in parentheses. *, **, *** denote significance at the 1, 5, and 10 percent levels, respectively. 4. Empirical Results In this section we present the results from our five empirical specifications (given by equations (6), (7), (8), (9), and (12) above) and, in turn, show that the assumption that incomes are log-normally distributed allows us to approximate the identity very well. First, using our entire sample of 135 countries over 1974– 2018, we estimate equations (6), (7), (8), (9), and (12). Results are presented in columns (1), (2), (3), (4), and (5) of table 1, respectively. It is clear from looking at the R2 in columns (1)–(5) of table 1 that equations (9) and (12) (columns (4) and (5), respectively) do a far superior job at explaining changes in poverty in our sample. Moreover, it appears that the assumption that incomes are log-normally distributed is reasonable: looking at column (4) of table 1, we see that both γ 1 and γ 2 are close in magnitude to 1, γ 0 is close in magnitude to 0, and the R2 is very close to 1. Moreover, in 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 (if income is truly log-normally distributed, we would expect equation (12) to fit better than equation (9) due to the discrete nature of the data).15 As a 15 We do, however, reject the null hypotheses that γ 1 = γ 2 = 1 − γ 0 = 1 and ω1 = ω2 = 1 − ω0 = 1, thus rejecting the null hypothesis that income distributions are truly log-normal. However, this is not the relevant test. We know income The World Bank Economic Review 593 Figure 3. Predicted vs. Actual Percentage Point Changes in Headcount Poverty under Assumption of Log-Normality Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Source: Author’s analysis using data from the World Bank’s PovcalNet Database. Note: This figure plots the predicted percentage point change in headcount poverty (under the assumption that income is log-normally distributed) for all growth-spells vs. the actual percentage point change in headcount poverty for all growth-spells. The dashed blue line plots the fitted values from the linear regression of the predicted changes in headcount poverty on the actual changes in headcount poverty. further test of whether the log-normality assumption is reasonable, we reestimate equations (9) and (12) imposing the log-normal restrictions on the coefficients (i.e., imposing γ 1 = γ 2 = 1 − γ 0 = 1 and imposing ω1 = ω2 = 1 − ω0 = 1). We find that under these restrictions, the models still fit the data extremely well; in particular, under our restricted version of equation (12), we get an R2 of 0.94 (see column (7) of table 1). Finally, we graphically illustrate how well we can approximate the identity under the assumption that incomes are log-normally distributed. In fig. 3 we plot the predicted percentage point change in headcount poverty under the assumption of log-normality for each growth-spell, d H ˆ i,t , vs. the actual percentage point change in headcount poverty, dHi, t , where the predicted change in headcount poverty is given by: ˆ i,t = z 1 1 z 1 1 dH log + σi,t −n − log + σi,t −n ¯ i,t y σi,t −n 2 ¯ i,t −n y σi,t −n 2 z 1 1 z 1 1 + log + σi,t − log + σi,t −n × 100. ¯ i,t y σi,t 2 ¯ i,t y σi,t −n 2 As can be seen in fig. 3, the points are closely centered around the 45-degree line, indicating that our approximation to the identity is reasonable. Finally, we explore by region how well our approximation fits the data: we reproduce fig. 3 for each region separately—see fig. 4. Figure 4 illustrates that the log- normality assumption provides us with a reasonable approximation to the identity for all regions with the exception of the OHI region (other high income region).16 For this region, our approximation predicts that the percentage point changes in headcount poverty are always 0, as our approximation predicts that, for these countries, headcount poverty is always at 0 percent. This is a consequence of mean incomes being so high for these countries. Notably, this is also the region where we expect measurement error distributions are not perfectly log-normal; what we really want to 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. 16 See http://iresearch.worldbank.org/PovcalNet/povOnDemand.aspx to obtain the list of countries in each region. 594 Bergstrom Figure 4. Predicted vs. Actual Percentage Point Changes in Headcount Poverty by Region under Assumption of Log-Normality Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Source: Author’s analysis using data from the World Bank’s PovcalNet Database. Note: This figure plots the predicted percentage point change in headcount poverty (under the assumption that income is log-normally distributed) for all growth-spells in a given region vs. the actual percentage point change in headcount poverty for all growth-spells in a given region. The dashed red lines denote the 45-degree lines. The regions are as follows: EAP denotes East Asia and Pacific, ECA denotes Europe and Central Asia, LAC denotes Latin America 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. in headcount poverty to be the worst given the reliance of observing incomes in the extreme left tails (thus, it may be the case that the log-normal assumption is also reasonable for these countries but that changes in poverty are measured with substantial error). Alternatively, it may be the case that the tails of the income distribution are not well approximated by a log-normal 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 very low and not changing in a substantial way seems entirely reasonable. 5. The Empirical Importance of Reductions in Income Inequality on Poverty Now that we have shown that the log-normal assumption allows us to approximate the identity well, we can use this assumption to gauge the importance of reductions in inequality on poverty. In particular, we will use this assumption to (a) calculate the magnitudes of the growth elasticities and the inequality elasticities so as to compare the reductions in poverty that will result from a 1 percent increase in mean incomes (all else equal) as opposed to a 1 percent decrease in inequality (all else equal), (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. The World Bank Economic Review 595 Figure 5. Absolute Growth Elasticity vs. Inequality Elasticity; Latest Survey Year Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Source: Author’s analysis using data from the World Bank’s PovcalNet Database. ¯ ,i,T |, vs. the inequality elasticity, ξ σ , i, T , for each country i in their latest survey year T under the Note: This figure plots the value of the absolute growth elasticity, |ξy assumption that income is log-normally distributed (we restrict to countries where the latest survey year is greater than or equal to 2010, i.e., T ≥ 2010). The shapes of the markers indicate the region that each country belongs to. The regions are as follows: EAP denotes East Asia and Pacific, ECA denotes Europe and Central Asia, LAC denotes Latin America 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. 5.1. The Growth Elasticity of Poverty Reduction vs. the Inequality Elasticity of Poverty Reduction First, we explore the magnitudes of the growth elasticities vs. the inequality elasticities of poverty reduction under the assumption that income is log-normally distributed. Under this assumption, the growth elasticity and inequality elasticity for country i in period t are given by the following two equations: −φ log( y ¯ i,t −n ) σi,t −n + 2 σi,t −n z 1 1 1 σi,t −n ¯ ,i,t = ξy , ¯ i,t −n ) σi,t −n + 2 σi,t −n z 1 1 log( y φ log( y ¯ i,t −n ) σi,t −n + 2 σi,t −n z 1 1 1 σ 2 i,t −n − log( y z 1 ¯ i,t −n ) σi,t −n ξσ,i,t = . ¯ i,t −n ) σi,t −n + 2 σi,t −n z 1 1 log( y As shown in fig. 1, 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 at least within region. Figure 5 plots the value of the absolute growth elasticity, ¯ ,i,T |, vs. the inequality elasticity, ξ σ , i, T , for each country i in their latest survey year T (conditional | ξy on the latest survey year being greater than or equal to 2010, i.e., T ≥ 2010), while table 2 provides summary statistics of these elasticities by region. As can be seen from fig. 5 and table 2, the inequality elasticity is comparable to, and often larger in magnitude than, the (absolute) growth elasticity. Thus, for many countries, a 1 percent reduction in inequality (as measured by the standard deviation of log income) generates a larger reduction in poverty than a 1 percent increase in mean incomes. Moreover, an interesting pattern emerges by mean income: for poorer countries (e.g., countries in Sub-Saharan Africa), the (absolute) growth elasticity is typically larger relative to the inequality elasticity, whereas the opposite appears to be true for relatively richer countries in our sample (e.g., countries in Europe and Central Asia). This is intuitive: reducing σ , all else equal, will reduce 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, ¯ < elog(z)−σ /2 , reducing σ will have detrimental effects on 2 for very low values of mean incomes, i.e., y 596 Bergstrom Table 2. 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 Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 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 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 Source: Author’s analysis using data from the World Bank’s PovcalNet Database. Note: Summary statistics are taken over each country i in their latest survey year by region (conditional on the latest survey year being greater than or equal to 2010). “All regions” excludes OHI (Other High Income) countries. Averages are not weighted by country population. The regions are as follows: EAP denotes East Asia and Pacific, ECA denotes Europe and Central Asia, LAC denotes Latin America 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. headcount poverty as it will result in bringing richer households below the poverty line). However, while this pattern may initially suggest that policies in the poorest countries should target growth (and, as countries get richer, policies may want to focus on both growth and equality), inequality has additional effects on poverty through its effect on the growth elasticity. We explore this next. 5.2. Initial Inequality and the Growth Elasticity Next we explore the extent to which initial (lagged) inequality affects the size of the growth elasticity. ¯ ,i,T |, vs. lagged Figure 6 plots the absolute growth elasticity for each country in their latest survey year, |ξy mean income, y ¯ i,T −n . In dashed gray lines, we overlay the value of the elasticity that would result for various values of initial (lagged) inequality, σ T−n . As can be seen, conditional on a value of (lagged) mean income, countries with lower initial inequality have substantially larger absolute growth elasticities. This is particularly apparent when comparing countries in LAC (Latin America and the Caribbean) with countries in ECA (Europe and Central Asia). While there is substantial overlap in (lagged) mean incomes for countries in these two regions, the growth elasticity is substantially smaller in LAC countries due to much higher inequality in these countries (average inequality across LAC countries in their latest survey year is 0.88 compared to 0.59 in ECA—see table 2).17 5.3. Which Has Been More Important: Changes in Mean Incomes or Changes in Inequality? While the above exercises highlight the effectiveness of reducing inequality on 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 subsection, 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 0, i.e., we shut the distribution component to 0: ˆ i,t | z 1 1 z 1 1 dH σ =0 = log + σi,t −n − log + σi,t −n × 100. ¯ i,t y σi,t −n 2 ¯ i,t −n y σi,t −n 2 17 However, as mentioned above, a misleading feature of the growth elasticity (and the inequality elasticity) is that it gets increasingly large as headcount poverty approaches 0. Thus, part of the reason |ξy ¯ ,t | increases as we decrease σ t − n is the fact that decreasing σ t − n decreases headcount poverty in period t − n, thus mechanically increasing |ξy ¯ ,t | (as the denominator of |ξy ¯ ,t | is headcount poverty in t − n). The World Bank Economic Review 597 Figure 6. Heterogeneity in the Absolute Growth Elasticity; Latest Survey Year Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Source: Author’s analysis using data from the World Bank’s PovcalNet Database. Note: This figure plots the absolute growth elasticity (under the assumption that income is log-normally distributed) for each country i in their latest survey year T, |ξy ¯ ,i,T |, vs. lagged mean income, y ¯ i,T −n . Note that (a) the length of the growth-spell, n, varies across countries and (b) we restrict to countries where the latest survey year is greater than or equal to 2010, i.e., T ≥ 2010. In gray lines, we overlay the value of the absolute elasticity that would result for various values of initial (lagged) inequality σ T−n . The shapes of the markers indicate the region that each country belongs to. The regions are as follows: EAP denotes East Asia and Pacific, ECA denotes Europe and Central Asia, LAC denotes Latin America 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. 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 fig. 7. Next, we repeat the same exercise, but this time we calculate the percentage point change in headcount poverty that would occur if the change in mean incomes were 0, i.e., we shut the growth component to 0: ˆ i,t | z 1 1 z 1 1 dH ¯ =0 y = log + σi,t − log + σi,t −n × 100. ¯ i,t −n y σi,t 2 ¯ i,t −n y σi,t −n 2 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 fig. 7. Here is how to interpret a point in Panel (a) of fig. 7. A point lying above the 45-degree line indicates that the increase (reduction) in poverty resulting from changes in mean incomes is higher (lower) than the observed increase (reduction) in poverty for a given growth-spell. Thus, these points are likely ac- companied by a reduction in inequality. Conversely, a point lying below the 45-degree line indicates that the increase in poverty resulting from changes in mean incomes is lower than the observed increase in poverty. Thus, these points are likely accompanied by an increase in inequality. Here is how to interpret a point in Panel (b) of fig. 7. A point lying above the 45-degree line indicates that the increase (reduction) in poverty resulting from changes in the inequality is higher than the observed increase (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-degree line indicates that the increase in poverty resulting from changes in inequality is lower than the observed increase in poverty. Thus, these point are likely accompanied by a reduction in mean incomes. We can see from fig. 7 that points are far more closely centered around the 45-degree line when changes in inequality are set to 0 (i.e., points in Panel (a) of fig. 7 are more closely scattered around the 45-degree 598 Bergstrom Figure 7. Decomposing Percentage Point Changes in Headcount Poverty Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Source: Author’s analysis using data from the World Bank’s PovcalNet Database. Note: Panel (a) plots the predicted percentage point change in headcount poverty for all growth-spells under the assumptions that (a) income is log-normally distributed and (b) changes in inequality for all growth-spells are 0 vs. the actual percentage point change in headcount poverty for all growth-spells. Panel (b) plots the predicted percentage point change in headcount poverty for all growth-spells under the assumptions that (a) income is log-normally distributed and (b) changes in mean incomes for all growth-spells are 0 vs. the actual percentage point change in headcount poverty for all growth-spells. line than points in Panel (b) of fig. 7). 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 the above subsections 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.18 This can be seen at the bottom of table 1, 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 to non-OHI countries, we find E[ y ¯ ] = 4.99 percent and E[ σ ] = −0.25 percent, so percentage changes in inequality are still an order of magnitude smaller than percentage changes in mean incomes). 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: ˆ i,t | Var(dH + Cov(dH σ =0 ) ˆ i,t | y ˆ ¯ =0 , dHi,t | σ =0 ) Share due to ¯= y , ˆ ˆ Var(dHi,t | σ =0 + dHi,t | y ¯ =0 ) ˆ i,t | Var(dH ¯ =0 ) y + Cov(dH ˆ i,t | y ˆ ¯ =0 , dHi,t | σ =0 ) Share due to σ = . ˆ i,t | σ =0 + dH Var(dH ˆ i,t | y¯ =0 ) 18 In semi-elasticity form, under the assumption of log-normality, we know to a first-order approximation that dHi,t = κy ¯ ,i,t , κ σ , i, t are given by equations (10) and (11). We saw above that the absolute growth ¯ i,t + κσ,i,t σi,t , where κy ¯ ,i,t y elasticity is similar in magnitude, although smaller on average, relative to the inequality elasticity, implying that |κy ¯ ,i,t | is similar to although smaller in magnitude than κ σ , i, t . Thus, since we find that the majority of changes in poverty are due to changes in mean incomes, it must be because y ¯ i,t is substantially larger in magnitude relative to σ i, t . The World Bank Economic Review 599 We find that for all growth-spells (excluding growth-spells from OHI countries), 89 percent of the variance in the predicted change in poverty is explained by changes in mean incomes, while only 11 percent 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, Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 when restricting to 2000 (2010) onward, the share due to changes in mean incomes is 90 percent (86 percent) while the share due to changes in inequality is 10 percent (14 percent). This differs from Bluhm, de Crombrugghe, and Szirmai (2018) 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 percent of the variance in the predicted change in poverty is explained by changes in mean incomes, while 29 percent is explained by changes in the distribution of incomes. For growth-spells of two years or more we find that 93 percent of the variance in the predicted change in poverty is explained by changes in mean incomes, while only 7 percent is explained by changes in the distribution of incomes. This is consistent with the findings of Kraay (2006) who also finds that 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 ¯ |) and the indirect effect (as seen by the sensitivity of |ξy value of ξ σ relative to |ξy ¯ ,t | to σ t − n ). However, for our data set, 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. 6. Poverty Projections We now proceed to generate poverty projections out to 2030 under various assumptions on changes in inequality and changes in mean income (maintaining the assumption that income is log-normally dis- tributed). Note, these are hypothetical scenarios constructed to highlight the contribution of changes in inequality vs. changes in 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 ˆ i,t = z 1 1 H log + σi,t ¯ i,t σi,t y 2 for each country i and for each year t = {T, T + 1, …, 2030}, where T denotes the latest survey year for each country (and will vary across countries). Then by region, we calculate average headcount poverty (weighted by country population): ˆ r,t = H ˆ i,t , ωi H i ∈r where r denotes region, and ωi denotes country i’s population relative to the total population in the region.19 To project headcount poverty, we need values for mean incomes and inequality out to 2030. As our baseline, we generate predictions for mean incomes using data on real GDP per capita from 1990–2022 from the World Bank’s Macro Poverty Outlook (MPO).20 In particular, we estimate the following MA(2) 19 For population measures, we use predicted country populations for 2022 taken from the World Bank’s Macro and Poverty Outlook. See https://www.worldbank.org/en/publication/macro-poverty-outlook#:˜:text=Next-,Overview, Group and International Monetary Fund. The predictions we use are from the vintage dated June 9, 2020. 20 Specifically, we use the vintage dated June 9, 2020. 600 Bergstrom Table 3. Poverty Projections for 2030 under Various Scenarios Region Baseline 1% ↓σ 1% ↑σ 1% ↑ y ¯ 1% ↓ y ¯ EAP 0.73 0.37 1.30 0.53 0.99 ECA 0.15 0.06 0.35 0.09 0.23 Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 LAC 2.74 1.30 5.13 2.11 3.52 MNA 4.40 3.60 5.63 3.57 5.41 OHI 0.00 0.00 0.00 0.00 0.00 SAS 3.66 1.90 6.26 2.56 5.13 SSA 32.32 28.69 36.33 28.54 36.37 World 5.69 4.52 7.29 4.78 6.78 Source: Author’s analysis using data from the World Bank’s PovcalNet Database and Macro Poverty Outlook. Note: This table shows projected headcount poverty by region in 2030 (measured in percentage terms), assuming income is log-normally distributed, under five different scenarios for changes in mean incomes and changes in inequality. Under the baseline scenario, mean incomes for each country are forecast using predicted growth rates in each country’s GDP per capita, while inequality is held constant at each country’s latest observed value in our PovcalNet data set. The four other scenarios are (a) decreasing inequality, σ , by 1 percent per year (over 2020–2030) relative to baseline, (b) increasing inequality by 1 percent per year (over 2020–2030) relative to baseline, (c) increasing mean incomes by 1 percent per year (over 2020–2030) relative to baseline, and (d) decreasing mean incomes by 1 percent per year (over 2020–2030) relative to baseline. Projected headcount poverty for a given region in 2030 is equal to weighted average projected headcount poverty across all countries in the region in 2030, where weights are equal to the country’s population relative to the total population in the region. The regions are as follows: EAP denotes East Asia and Pacific, ECA denotes Europe and Central Asia, LAC denotes Latin America 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. regression for each country i:21 log(gdp_pci,t ) = bi,0 + bi,1 yeart + ei,t + θi,1 ei,t −1 + θi,2 ei,t −2 , (13) where log(gdp_pci,t ) denotes the log of GDP per capita in country i in year t. Using the coefficients esti- mated 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 on mean income in each country from PovcalNet, y ¯ i,T , allow us to predict mean incomes out to 2030 for each country.22 Finally, to complete our baseline specification, we assume there is zero growth in σ so that σ i, 2030 = σ i, T (i.e., inequality is equal to the latest observed value for each country).23 Next we consider four counterfactual scenarios relative to our baseline scenario: (a) inequality declines by 1 percent per annum over 2020–2030 while mean incomes follow baseline trajectory, (b) inequality increases by 1 percent per annum over 2020–2030 while mean incomes follow baseline trajectory, (c) mean incomes increase by 1 percent per annum over 2020–2030 relative to their baseline trajectory while inequality remains constant at baseline value, and (d) mean incomes decrease by 1 percent per annum over 2020–2030 relative to their baseline trajectory while inequality remains constant at baseline value. Regional poverty rates for 2030 under our baseline and alternative scenarios are presented in table 3. Moreover, world headcount poverty rates for 2020–2030 are presented in fig. 8 under our baseline sce- nario and our counterfactual scenarios. Looking at table 3 and fig. 8 we see that, on average, a 1 percent reduction in inequality (per annum) leads to a greater reduction in projected headcount poverty relative to a 1 percent increase in mean incomes (per annum). Similarly, a 1 percent increase in inequality (per annum) is more harmful, on average, to 21 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. 22 ¯ , along For example, our latest observation of mean income for India is 2011; thus, we use the 2011 observation for y with per capita GDP growth rates for India for 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. 23 For example, because the latest observation for India is 2011, we assume σ India, 2030 = σ India, 2011 . The World Bank Economic Review 601 Figure 8. World Headcount Poverty Projections: Baseline and Counterfactual Scenarios Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Source: Author’s analysis using data from the World Bank’s PovcalNet Database and Macro Poverty Outlook. Note: This figure shows projected world headcount poverty (measured as the percentage of the population below the poverty line) assuming income is log-normally distributed under five different scenarios for changes in mean incomes and changes in inequality. Under the baseline scenario, mean incomes for each country are forecast using predicted growth rates in each country’s GDP per capita while inequality is held constant at each country’s latest observed value in our PovcalNet data set. The four other scenarios are (a) decreasing inequality, σ , by 1 percent per year (over 2020–2030) relative to baseline, (b) increasing inequality by 1 percent per year (over 2020–2030) relative to baseline, (c) increasing mean incomes by 1 percent per year (over 2020–2030) relative to baseline, and (d) decreasing mean incomes by 1 percent per year (over 2020–2030) relative to baseline. Projected world poverty in a given year is equal to weighted average headcount poverty across all countries in that year, where weights are equal to the country’s population relative to the world population. headcount poverty relative to a 1 percent 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. 7. 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 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 inequality elasticity of poverty reduction is on average greater in value than the (absolute) growth elasticity, one must also consider how difficult/costly it is to generate a 1 percent reduction in inequality as opposed to a 1 percent increase in mean incomes. In our data set, 602 Bergstrom Figure 9. Channels of Poverty Reduction Downloaded from https://academic.oup.com/wber/article/36/3/583/6500933 by Sectoral Library Rm MC-C3-220 user on 10 December 2023 Source: Author’s figure adapted from Bourguignon (2004). Note: This figure highlights the channels that lead to reductions in absolute poverty and the channels explored in this paper. 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 it is 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 ex- ample, 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, Kleineberg, and Kraay (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 suggest- ing 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, fig. 9 (adapted from Bourguignon (2004)’s Poverty-Growth-Inequality Triangle) high- lights 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 fig. 9), 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 fig. 9). To explore these additional channels, it will likely be useful for policy mak- ers to utilize case studies and tools that investigate the effect of various policies on both inequality and growth. References Aghion, P., E. Caroli, and C. 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