reduction in poverty relative to a 1% increase in mean income. In particular, we find that post 2010, the median elasticity of poverty w.r.t. inequality is 5.19, while the median elasticity of poverty w.r.t. growth is only 2.78. Furthermore, we find substantial heterogeneity in these elasticities; in particular, the growth elasticity is decreasing sharply in initial inequality. However, despite these results, we also find that most of the observed changes in poverty over this time frame can be explained by changes in mean incomes. This is a consequence of average percentage changes in mean incomes being an order of magnitude larger than average percentage changes in inequality. Moreover, we find that 90% of the variation in changes in poverty can be explained by changes in mean incomes. Finally, to further illustrate our results, we project headcount poverty for 2030 under various hypothetical scenarios. We show that 1% per-annum declines in inequality over 2020-2030 lead to greater reductions in worldwide poverty compared to 1% increases in mean incomes.<sup>4</sup> These projections highlight the important role inequality can play in reducing future poverty even if prior poverty reductions have, in large part, been a consequence of economic growth.

To conclude, we discuss what our findings imply for policies aimed at reducing poverty. While our analysis shows that reductions in inequality can lead to meaningful reductions in poverty, we are cautious to offer guidance from this analysis alone for two reasons. First, our analysis abstracts from the possibility that inequality can have additional impacts on poverty through its effect on growth. The theoretical literature has developed many intricate theories about how inequality impacts growth; however, there are numerous competing effects, so ultimately this is an empirical question.<sup>5</sup> But the empirical literature has produced very mixed results.<sup>6</sup> It has been suggested that these mixed results reflect a gap between the intricacy of the relationship, as expressed in the theoretical literature, and the simple relations that are commonly estimated (Voitchovsky, 2009). In support of a more complex relationship, several papers provide empirical evidence of a non-linear, 4. Using a different model to predict headcount poverty, Lakner et al (2020) also find that reducing inequality by 1% per year leads to a greater reduction in 2030 headcount poverty than 1% increases in mean incomes.

5. Theoretically, the effect of inequality on growth is ambiguous: the conventional view is that higher inequality promotes stronger incentives, generates greater savings and investment, and endows the rich with the minimum capital needed to start economic activity, thereby stimulating growth (Aghion et al, 1999; Okun, 2015; Kaldor, 1957; Barro, 2000). Conversely, it has been argued that inequality hurts growth as it leads to redistributive pressure through taxes, social conflict, expropriation, or rent-seeking behavior (Alesina and Rodrik, 1994; Alesina, 1994; Benhabib and Rustichini, 1996; Benabou, 1996; Perotti, 1996; Persson and Tabellini, 1994; Glaeser et al, 2003); or in the presence of market failures, inequality prevents the talented poor from undertaking profitable investments, thereby limiting growth (Galor and Zeira, 1993; Banerjee and Newman, 1993).

6. Early papers, using a cross-section of countries, typically found negative effects of inequality on growth (Alesina and Rodrik, 1994; Persson and Tabellini, 1994). Then, with the introduction of the Deininger and Squire (1996) panel dataset, studies started to find positive effects (Li and Zou, 1998; Forbes, 2000). More recently, however, several papers find again a negative effect (Castell ́o-Climent, 2010; Halter et al, 2014; Ostry et al, 2014; and Dabla-Norris et al, 2015), although the validity of their estimation technique has been questioned (Kraay, 2015).

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