A second clue to the puzzle of why we do not see poverty convergence can be found in the literature on the effects of growth on poverty in developing countries. The consensus in that literature is that higher growth rates tend to yield more rapid rates of absolute poverty reduction.<sup>9</sup> There is also evidence that inequality matters to how much impact a given growth rate in the mean has on poverty.<sup>10</sup> Intuitively, in high inequality countries the poor will tend to have a lower share of the gains from growth in the mean. Ravallion (1997, 2007) examines this issue empirically using household surveys for multiple countries over time and finds evidence of a strong interaction effect between initial inequality and the growth rate in the mean when explaining the proportionate rate of poverty reduction. In the most parsimonious specification, which also fits the data for developing countries well, the expected value of the log difference in the poverty rate over time is directly proportional to the ―distribution-corrected‖ growth rate, given by the ordinary growth rate in the mean times one minus an index of inequality.

However, here too, one can question whether inequality is the only relevant parameter of the initial levels distribution. If consumption is log-normally distributed and inequality (the variance of consumption) is unchanged with growth in the mean then the (absolute) elasticity of the poverty rate to mean consumption will be strictly decreasing in the poverty rate as well as inequality.<sup>11</sup> This is of course as special case, but it at least suggests that poverty may be a relevant predictor of the elasticity, though this has never been tested to my knowledge.<sup>12</sup>

# **3. A model of aggregate growth with micro borrowing constraints**

Banerjee and Duflo (2003) provide a simple but insightful growth model with borrowing constraints. Someone who starts her productive life with sufficient wealth is able to invest her unconstrained optimal amount, equating the (declining) marginal product of her capital with the interest rate. But the ―wealth poor,‖ for whom the borrowing constraint is binding, are unable to do so. Banerjee and Duflo show that higher inequality in such an economy implies lower growth. However, they do not observe that their model also implies that higher current wealth poverty for

> 9 See World Bank (1990, 2000), Ravallion (1995, 2001, 2007), Fields (2001) and Kraay (2006). Also see the review of the arguments and evidence on this point in Ferreira and Ravallion (2009). (Relative poverty measures are less responsive to growth since the poverty lines rises with the mean.)

> 10 See Ravallion (1997, 2007); World Bank (2000, 2006); Bourguignon (2003) and Lopez and Servén (2006).

> 11 This claim can be readily verified from the results for the log-normal distribution in Bourguignon (2003).

> 12 This point is anticipated by Easterly (2009) who argues that countries with high poverty rates (with specific reference to Sub-Saharan Africa) will require higher growth rates to attain the same proportionate rate of poverty reduction (as required by the Millennium Development Goal of halving the 1990 poverty rate by 2015). Easterly does not present any evidence to support this view.

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