To assess this issue, we run a linear regression of the headcount poverty rate (using a poverty line of US$2) on (log) average income and the Gini coefficient. The non-linear effect of the regressors is then included in the residual term. Consistent with the empirical model (12), we include fixed effects in the specification and run Within-Group (WG) regressions. The estimated equation is (robust _t_ statistics in parentheses):

***: significant at 1%.

Thus, poverty is negatively correlated with (log) average per capita income, and positively correlated with inequality.<sup>18</sup> The coefficient estimates are strongly significant. However, the linear specification accounts for just 42% of the sample variation of poverty.<sup>19</sup> Put differently, the nonlinear effects of income and/or inequality could account for up to 58% of the variation of poverty. Thus, we conclude that collinearity does not prevent identification of  in (12), because poverty is far from being a linear function of average income and inequality.<sup>20</sup> To conclude this section, we turn to the set of controls included in _x_ . Rather than adding to the already huge variety of growth models contributing yet another idiosyncratic set of regressors, we opt for considering alternative growth specifications found in the literature, in order to explore the sensitivity of our results to the specific choice of control variables.

First, we consider a skeleton model of growth (M1), which includes only lagged income, poverty and the Gini coefficient as regressors in (12) (i.e., _x_ =0). In this parsimonious setting, the estimated parameters capture the direct impacts of poverty and inequality on growth, as well as potential indirect effects due to other variables excluded from the model (Galor, 2009). Our second model (M2) is taken from the empirical literature on inequality and growth.<sup>21</sup> It comprises a measure of market distortions, given by the domestic price of investment goods relative to that of the U.S., and a measure of human capital, which includes the average years of secondary education of the male

> 18  However, the simulations in Figure 1 suggest that the correlation between poverty and inequality may depend on the prevailing level of poverty: it may turn negative at very high levels of poverty, and vanish at very low levels of poverty. We return to the role of the prevailing level of poverty in Section V.

> 19 Using alternative poverty lines (US$1.25 and US$ 4.00) or definitions ( _P1_ and _P2_ , as defined in the Appendix), estimation results are qualitatively similar: positive and significant coefficients for per capita income, negative and significant for the Gini coefficient. Quantitatively, the parameter estimates differ as expected: for per capita income, they range from -0.021 for _P2_ (US$ 1.25) to -0.211 for _P0_ (US$ 4); for the Gini coefficient, they range from 0.1929 for _P2_ (US$ 1.25) to 0.390 for _P0_ (US$ 1.25). The regression _R_<sup>_2_</sup> ranges from 0.255 for _P2_ (US$ 1.25) to 0.575 for _P0_ (US$ 4).

> 20 This of course follows from the construction of the poverty data. See footnote 38 in the Appendix for details.

> 21 See Perotti (1996), Forbes (2000), Knowles (2005), López and Servén (2009), and Berg et al. (2018), among others.

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