The Devil is in the Details: Growth, Polarization, and Poverty Reduction in Africa in the Past Two Decades

This paper investigates the distributional changes that limited pro-poor growth in the past two decades in Sub-Saharan Africa; these changes went undetected by standard inequality measures. By developing a new decomposition technique based on a nonparametric method -- the relative distribution -- the paper finds a clear distributional pattern affecting almost all the analyzed countries. Nineteen of 24 countries experienced a significant increase in polarization, particularly in the lower tail of the distribution, and this distributional change lowered the pro-poor impact of growth substantially. Without this change, poverty could have decreased an additional 5-6 percentage points during the past decade.


Policy Research Working Paper 8494
This paper is a product of the Poverty and Equity Global Practice. 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/research. The authors may be contacted at vmolini@worldbank.org. This paper investigates the distributional changes that limited pro-poor growth in the past two decades in Sub-Saharan Africa; these changes went undetected by standard inequality measures. By developing a new decomposition technique based on a nonparametric method-the relative distribution-the paper finds a clear distributional pattern affecting almost all the analyzed countries. Nineteen of 24 countries experienced a significant increase in polarization, particularly in the lower tail of the distribution, and this distributional change lowered the pro-poor impact of growth substantially. Without this change, poverty could have decreased an additional 5-6 percentage points during the past decade.

1 Introduction
Despite experiencing stable and sustained growth over almost two decades, several Sub-Saharan African (SSA) countries have not experienced a commensurate reduction in poverty.
The present paper identifies and interprets the distributional changes that occurred in most of these countries, which have offset the positive impact of growth in reducing poverty.
Recent estimates, based on an international poverty line of US$1.90 (in 2011 PPP U.S. dollars), suggest that poverty declined only by 23 percent between 1990 and 2012 (from 56 percent in to 43 percent) (Beegle et al., 2016). This rate is much lower than those experienced by countries with similar growth rates and similar poverty rates in other regions. World Bank (2018) calculates that in a typical non-African developing country where 50 percent of the population is living below the poverty line, a 1 percent yearly growth in GDP led to a reduction of 0.53 percentage points a year in the incidence of poverty. In contrast, the same 1 percent per capita GDP growth in a typical African country with the same poverty incidence reduced poverty by only 0.16 percentage point.
The explanations for this lower growth poverty-elasticity in Africa are generally two: one questioning the veracity of the recent African economic boom (the so-called African miracle) and another looking at the role of inequality. Jerven (2013,2015) has provided evidence on the problems afflicting GDP calculations in Africa and argued that for many SSA countries the recent high growth is merely statistical or, in other words, a feature of adding the informal sector that previously was not counted (Jerven, 2015). Since growth is overstated, it is thus not surprising that poverty did not fall so rapidly.
Although this argument has some validity, it does not completely solve the low elasticity puzzle. Figure 1 compares the average annual GDP per capita growth and average consumption 2 growth from available household surveys; consumption is the welfare measure typically used to calculate poverty rates and growth is the factor that really matters in poverty reduction (Adams, 2004;McKay, 2013). Indeed, the discrepancy between GDP per capita growth and household consumption growth is higher in SSA than in the rest of the developing world, yet SSA registers an average annual growth of household consumption of about 1.02 percent per year, not much lower than the South Asia Region (SAR) and slightly higher than Latin America. Therefore, household consumption increased in SSA not differently from other developing regions but still poverty declined slower. Regarding inequality, literature has debated its relation with growth and poverty. Dollar and Kray (2002) show that all income groups tend to benefit proportionally from increases in economic growth and that income distribution does not really matter for poverty reduction. Bourgignon (2003) and Ravallion (2007) find that inequality reduces the poverty-reducing effects of economic growth. Thorbecke (2013) argues that the combination of high endemic poverty and inequality is in general responsible for low growth elasticity of poverty. High initial poverty and inequality reduces directly the growth rate but also indirectly the poverty-reducing effect of this growth. Looking at SSA, Fosu (2009 finds that economic growth reduces poverty while growth elasticity is a decreasing function of initial inequality. Therefore, the low elasticity registered in SSA in the last two decades could potentially be attributed to an increase in inequality that limited the pro-poor content of growth. The central argument of this paper is that significant distributional changes against poverty reduction have, in fact, taken place in most of the SSA countries we analyze. These changes affected predominantly the lower part of the welfare distribution and went undetected by standard inequality measures. The reason is simple. Summary measures like the Gini do not assign a weight to the different percentiles; if a pro-inequality change in one part of the distribution is more than compensated by a pro-equality change in the rest of the distribution, the Gini will decline. The distributional changes that matter most for poverty reduction, however, are those localized in the lower part of the distribution but can be detected only if we are able to focus on this part only. To analyze these changes, this paper develops a novel yet simple decomposition based on the "relative distribution" method (Handcock andMorris, 1998, 1999). The strength of this decomposition consists of providing a non-parametric framework for taking into account all the distributional differences that could have affected the variation in the poverty rate and countered the pro poor effect of growth. In this way, it enables to summarize multiple features of the welfare distribution that a standard decomposition based on summary inequality measures would not have detected (Datt and Ravallion, 1992;Kolenikov and Shorrocks, 2005).
The paper is organized as follows Section 2 outlines the distinctive features of the relative distribution approach and presents the proposed decomposition. Section 3 discusses the data and provides summary statistics. Section 4 details the main findings of the study. Section 5 provides summary conclusions. 5 2 Methodology

Polarization and relative distribution
Over the last two decades, the issue of polarization has gained increasing importance in the analysis of income distribution (Foster and Wolfson, 1992;Levy and Murnane, 1992;Esteban and Ray, 1994;1994, 1997 and now it seems to be widely accepted that polarization is a distinct concept from inequality. A general notion of income polarization (Esteban and Ray, 1994) regards it as "clustering" of a population around two or more poles of the distribution, irrespective of where they are located along the income scale. The notion of income polarization in a multi-group context is an attempt at capturing the degree of potential conflict inherent in a given distribution (see Esteban and Ray, 1999, 2008. The idea is to consider society as an amalgamation of groups, where the individuals in a group share similar attributes with its members (i.e. have a mutual sense of "identification") but they are different from the members of the other groups (i.e. have a feeling of "alienation").
More formally, 3 let Y0 be the income variable for the reference population and Y the income variable for the comparison population. The relative distribution is defined as the ratio 6 of the density of the comparison population to the density of the reference population evaluated at the relative data r: where f (•) and f0 (•) denote the density functions of Y and Y0, respectively, and yr = is the quantile function of Y0. When no changes occur between the two distributions, g(r) has a uniform distribution; a value of g(r) higher (lower) than 1 means that the share of households in the comparison population is higher (lower) than the corresponding share in the reference population at the r th quantile of the latter.
One of the major advantages of this method is the possibility to decompose the relative distribution into changes in location and changes in shape. The decomposition can be written as: .
( 2) F0L (yr) is the median-adjusted density function: , where the value is the difference between the medians of the comparison and reference distributions-alternative indices like the mean and/or multiplicative location shift can also be considered.
The relative distribution approach also includes a median relative polarization index, which is a measurement of the degree to which the comparison distribution is more polarized than the reference one: The values of the MRP index range between -1 and 1: positive values represent more income polarization and negative values represent less polarization; a value of 0 indicates no difference in distributional shape. The MRP index can be additively decomposed into the lower relative polarization index and the upper relative polarization index, which behave similarly as the MRP. 7

Decomposition
The relative distribution is a well-established approach to distributional analysis, whereas novel is the polarization-poverty and growth decomposition we develop for showing how the distributional changes we observed in many SSA countries have effectively limited the impact of growth on poverty reduction.
In general terms, poverty , , is expressed in terms of poverty line, , mean income level, , and the Lorenz curve, , representing the structure of relative income inequalities.
Assuming the poverty line is fixed at a given level, poverty is given by , . The total change in poverty, ∆ , is then decomposed into two components. The first component is the growth component due to changes in the mean income while holding the Lorenz curve constant at some reference level, and the second is a redistribution component due to changes in the Lorenz curve while keeping the mean income constant at some reference level.
Following Heshmati (2007), one can compute growth and inequality decompositions in various ways. Kakwani and Subbarao (1990) introduced the following decomposition: where and are mean income and the Lorenz curve characterizing the distribution of income.
The subscripts 0 and 1 denote the two (consecutive or non-consecutive) initial and final periods of observation, and and are contributions from the growth and redistribution components. Jain and Tendulkar (1990) suggested an alternative formulation: which differs from the previous decomposition by the reference point (base year versus final year) that is initially chosen for computation of growth and redistribution components.
Kakwani (2000) suggested a simple averaging of both the growth and inequality components from Equations (5) and (6), which is: 8 Datt and Ravallion (1992) found the above decompositions of poverty changes as being time path dependent, arising through and dependent on the choice of reference levels. To make the changes path independent they proposed adding an extra residual as follows: The residual in (8) can be interpreted as the difference between the growth (redistribution) components evaluated at the terminal and initial Lorenz curves (mean incomes), respectively.
The above decompositions compute the growth and redistribution effects of poverty change through an analysis of mean incomes and relative inequalities. However, results would be different if the analysis is carried out through median incomes and absolute income gapsas it is in the spirit of the relative distribution approach. 4 In such an eventuality, the poverty change between two periods, and , into growth and redistribution components is decomposed as follows: 5 Variation , when is the period of reference, and: when is the period of reference. In the above: : poverty headcount ratio of the first period. 6  ∑ : poverty headcount ratio of the second period.

 Variation
: difference in poverty headcount ratio between and .
 : growth component when is the period of reference; is the poverty headcount ratio of the first period when all incomes of the first period 4 On the importance of paying more heed to absolute difference as well, rather than to relative difference only, see e.g. Atkinson and Brandolini (2010) and references therein. 5 Here, we assume that the headcount ratio is the poverty measure's precise functional form. In Section 5, we shall apply the decompositions to another common poverty measure, the poverty gap index, given by the aggregate income short-fall of the poor as a proportion of the poverty line and normalized by population size, i.e. ∑ , where is the number of poor people in the population. Taking the average of (9) and (10) yields the following decomposition of the variation in the poverty headcount between the two periods and : which is the one we shall use in the subsequent empirical analysis.

Data and summary statistics
The data used in the paper are obtained from national household surveys from as many countries We use (per capita) household expenditure as the main welfare indicator throughout the analysis. 9,10 In that, we depart from the literature using income as a measure of well-being. In economies where agriculture is an important and established sector, consumption has indeed proven preferable to income because the latter is more volatile and more highly affected by the harvest seasons, so that relying on income as an indicator of welfare might under-or overestimate living standards significantly (see, for instance, Deaton and Zaidi, 2002). On the theoretical ground, as consumption gives utility to individuals, the analysis of its distribution should be the most natural approach to study well-being. Income matters insofar as it gives access to consumption, which is the ultimate source of individual welfare. Consumption is a better measure of long-term welfare also because households can borrow, draw down on savings, or receive public and private transfers to smooth short-run fluctuations.
As the data show, for many of the countries studied average household consumption increased over time, following the significant economic growth Sub-Saharan Africa experienced over the last decades (e.g. Beegle et al., 2016). We can see this trend in Figure 2. Standard measures of inequality seem not to capture this widening gap between rich and poor. As shown in Figure 3, both the Gini and Theil indices declined for most of the analyzed countries, even though they start from a very high level. As for polarization, calculation of the Foster-Wolfson (FW) and Duclos-Esteban-Ray (DER) indices produced evidence that is mixed and thus hard to interpret. 11

Empirical results
In this section, we first provide an overview of the results of the standard relative distribution decomposition into growth effect and shape effect showing that in most analyzed countries, the consumption distribution polarized, in particular, in the lower tail of the distribution; in other words, these countries faced a significant process of lower polarization. In the second part, by decomposing the poverty variation into growth and shape effects, we show how this lower polarization offset the potential gains stemming from growth in consumption. to the median shift, is shown in the middle panels of Figure 4. Finally, the right panels of Figure   4 display the shape effect, which represents the relative distribution net of the median influence.  12 The analysis has been performed using the R package reldist (Handcock, 2016). The results for the remaining 34 countries are available upon request.

13
Looking at the shape effect graphs, we observe a clear concentration in the lowest decile.
Values above 1 indicate that, in relative terms, there are more households in that decile of the distribution at the end of the period than there were at the beginning, vice versa less than 1 means there are less, and equal to 1 means that things have not changed: 10 percent of households were in that decile at the beginning and 10 percent remained there. Therefore, relative to the initial period, households in the lowest percentiles of each country increased by 14 percentage points (+1.4 over 1) in Ethiopia, 20 (+2 over 1) in Ghana and 15 in South Africa (+1.5 over 1). In the three countries, this concentration in the lower tails (downgrading) is paralleled by a similar but smaller concentration in the upper tails (upgrading). Overall, the two effects produce a U-shaped relative density; households are concentrated in the tails of the distribution while the middle of the distribution hollows out.
For the sake of space, we analyze the performance of the remaining countries using the relative polarization indexes; these keep track of changes in the shape of the distribution and measure their direction and magnitude. Figure 5 plots the median, lower and upper polarization indexes for each country on a map. The null hypothesis of no change with respect to the reference distribution is tested for each index and in 21 of the 24 countries, the variation in the indexes is significant. 13 The type of distributional change observed for Ghana, Ethiopia and South Africa is closely replicated by 16 other countries; all of them experience a significant increase in polarization that is predominantly driven by a downgrading of the consumption distribution, the only notable exception being Nigeria where upgrading and downgrading are almost equivalent (see Clementi et al., 2017). Interestingly, the polarization phenomenon appears widespread in the region, while only in Madagascar and Zambia it decreased significantly. 13 Results are available upon request. Another common feature of the group of polarizing countries is that the Gini index either increased little or, as mentioned before, decreased. It is interesting to note that in the same period, economies more advanced than the SSA African ones, but equally reliant on commodities such as the Russian Federation and Brazil, experienced similar distributional changes. Nissanov and Pittau (2015) find that during the commodity boom of the 2000s, household net income restarted to grow after a long decline, Gini decreased while polarization increased, driven mainly by a downgrading in the income distribution. Likewise, Clementi and Schettino (2015) find that the decline in Gini experienced in Brazil between 2000-12 is accompanied by a hollowing out of the middle of the distribution and accentuated concentration of households in the lower tail.

Decomposition results
Once ascertained that there was a significant pro-polarization distributional change in the clear majority of SSA countries analyzed, we now proceed by linking this change to poverty reduction or lack thereof.  The question then arises as to why standard measures/decompositions did not capture this effect. Figures 7(a) and 7(b) compare our approach and the growth and distributive effects of a widely-used decomposition, that of Datt and Ravallion (1992). As it appears, the negative distributive effect (against poverty reduction) of this latter is always minimal or in many cases the distributional change is pro-poor. Our point is that the distributional change SSA countries went through could only be detected by the method we propose, and not by decompositions based on standard summary tools to measure distributional changes.  The reason is simple. Summary measure like Gini analyze the dispersion around the mean of the distribution and this, as shown in Figure 7, either did not change or sometimes improved in Africa. Also, most importantly, summary measures do not assign a weight to the different percentiles; therefore, if a pro-inequality change in one part of the distribution is more than compensated by a pro-equality change in the rest of the distribution, these measures will decline. Yet, the distributional changes that matter most for poverty reduction are those localized in the lower part of the distribution but can be detected only if one can look at changes at a very granular level. The type of decomposition we propose can shed light on this, whereas standard decompositions based on summary measures like Gini likely cannot.
The results of our analysis echo some recent findings from a recent World Bank (2018) report on structural transformation in Africa. While our analysis focuses on distributional changes, the report looks at changes in the labor markets and productivity that might explain the low growth-to-poverty elasticity in Africa. The low contribution of employment growth to poverty reduction, slow gains in agricultural productivity and a transition outside agriculture towards sectors characterized by equally low productivity all contributed to characterize SSA growth as little inclusive and consequently less able than other regions in the world in reducing poverty. From a distributional point of view, our paper complements this analysis by showing that this missed opportunity also translated into an increasing divide between the bottom 30-40 percent of the consumption distribution and the rest.

Summary conclusions
Since the end of the 1990s, two leading narratives prevailed when analyzing Sub-Saharan Africa. The first, predominant, painted a picture of a continent on track in reducing poverty, where middle classes were expanding, and prosperity was reaching large swaths of the population (African Development Bank, 2011;The Economist, 2011McKinsey, 2012).
The other narrative acknowledged the relatively robust growth, with a slow reduction in poverty, without however conclusive evidence on the mechanisms that hindered growth from trickling down.
This paper, to our knowledge, is the first attempt to provide a comprehensive explanation, from a distributive point of view, of this low growth elasticity to poverty that characterized SSA in a time when other regions in the world, growing as much as Africa, fared much better in terms of poverty reduction.
To show that important distributional changes took place in SSA and that these played against inclusive growth, this paper develops a novel yet simple decomposition based on the "relative distribution" method (Handcock andMorris, 1998, 1999). Whereas the standard "relative distribution" method enables to summarize multiple features of the welfare distribution, our small innovation links these changes to the poverty reduction process producing a poverty growth polarization decomposition.
In a nutshell, we find that the vast majority of SSA countries we analyze (about 80 percent) between the late 1990s and early 2010s experienced a very similar distributional change of lower polarization-that is the clustering of the poorest 30-40 percent around a local mean and an increasing divide between this group and the rest of the distribution. We also observe an upgrading in the distribution that is the fattening of the upper tail of the distribution (upper polarization), but only in the case of Nigeria this is commensurate to the lower polarization.
This low polarization process has important implications for poverty reduction. The proposed decomposition shows that polarization substantially reduces the positive effect of growth on poverty reduction: on average without downgrading, poverty could have been 5-6 percentage points lower in SSA. Standard decompositions of poverty into growth and inequality components fail to capture the impact of this distributional change on poverty also because there is hardly a common Gini pattern in SSA, whereas we show there is a clear downgrading pattern.
The potential policy implications are numerous. First, we show that the type of growth SSA experienced in the last decade was a sort of double-edged sword. It certainly reduced poverty but at the same time it increased the divide between the bottom 40 percent (World Bank, 2012) and the rest of the population. Therefore, since SSA's growth is not inclusive per se, more efforts should be put to expand the benefits of growth by diversifying economies into labor intensive sectors and reducing the divide between advanced and underdeveloped regions within each country. Second, it looks like this divide is a slow-motion process that accumulated over many years; evidence from Ghana and Nigeria for example (Bertoni et al., 2016;Clementi et al., 2017Clementi et al., , 2018 indicates that human capital, demography and basic infrastructures are the main drivers of the polarization process. Reversing this trend will require time and resources in a macroeconomic context that has substantially worsened after 2014; many SSA countries yet again experienced sluggish growth, high inflation rates and falling fiscal revenues.