# I Introduction

It has long been established that an arithmetic identity exists between changes in absolute poverty, changes in mean incomes, and changes in the distribution of relative incomes (Datt and Ravallion, 1992; Kakwani 1993; Bourguignon, 2003). Generally speaking, poverty reduction in a country can be decomposed into higher average growth, a reduction in inequality of incomes, or a combination of the two. Moreover, due to the non-linear nature of this identity, it has been shown that the sensitivity of poverty to growth in mean incomes is dependent on a country’s initial level of inequality: in general, the (absolute) growth elasticity of poverty is decreasing in a country’s initial level of income inequality.<sup>1</sup> The literature refers to this as the double-dividend effect of reducing inequality today: a reduction in inequality today leads to a reduction in poverty today and an acceleration of poverty reduction in the future (Bourguignon, 2004; Alvaredo and Gasparini, 2015).

Several papers have sought to empirically approximate this identity, and, in turn, quantify the role that growth in mean incomes and reductions in inequality play (and have played) in poverty reduction.<sup>2</sup> Despite the various specifications used to approximate the identity, these papers offer similar conclusions: over the past few decades, growth in mean incomes has been the primary driver of reductions in poverty, although changes in inequality have played a non-negligible role both through the direct effect of inequality on poverty and the indirect effect inequality has on the growth elasticity. Using the latest cross-country data, this paper seeks to update the empirical estimation of this identity, and, in turn, re-examine the role of income inequality for poverty reduction.

To begin, we re-derive the identity that exists between changes in poverty, changes in inequality, and changes in mean incomes. Using World Bank PovcalNet data from 1974-2018 for 135 countries, we then search for an empirical model that allows us to approximate the identity well. We find that the assumption that per-capita income is log-normally distributed leads to a very decent approximation: our model is able to explain 94% of the variation in observed changes in headcount poverty.<sup>3</sup> Using this approximation, we empirically quantify the importance of changes in inequality on poverty vs. changes in mean incomes on poverty. We find that for most countries, a 1% reduction in inequality (as measured by the standard deviation of log-income) leads to a larger

> 1. To be precise, the effect that initial inequality has on the growth elasticity is theoretically ambiguous (Ravallion, 2007). However, under certain assumptions it can be shown that the (absolute) growth elasticity of poverty is unambiguously decreasing with inequality (Bourguignon, 2003; Ferriera, 2012). 2. See, for example, Bourguignon (2003), Kraay (2006), Lopez and Serv ́en (2006), Kalwij and Verschoor (2007), Klasen and Misselhorn (2008), Bluhm et al (2016), and Fosu (2017).

> 3. This _R_<sup>2</sup> is notably higher than that found in Bourguignon (2003) and Klasen and Misselhorn (2008) who also approximate the identity under the assumption that income is log-normally distributed. We believe our improved fit is due to two reasons: first, we use a much larger dataset, and second, we estimate a version of the identity that allows for discrete changes in mean incomes and inequality.

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