# **I.  Introduction**

In recent years, poverty reduction has been formally enshrined as _the_ goal of development policy worldwide, and a rapidly expanding analytical and empirical literature has sought to clarify whether poverty changes are driven mainly by growth in aggregate income or by growth in the relative incomes of the poor. The question is of more than scholarly interest, because it has major implications for the roles of growthpromoting and inequality-reducing policies in the poverty reduction process. For example, if trends in relative incomes were found to account for the lion’s share of poverty changes, policy makers might face a tradeoff between fast growth and rapid poverty reduction.<sup>1</sup> In a recent contribution, Kraay (2005) decomposes poverty changes into three ingredients: (i) growth in average incomes; (ii) the sensitivity of poverty to growth; and (iii) changes in the distribution of income. In a large cross-country sample, he finds that growth in average incomes accounts for some 70 percent of the variation in (headcount) poverty changes in the short run, and over 95 percent in the medium to long run. In contrast, cross-country differences in the sensitivity of poverty to growth play a minimal role. Together, these results suggest that growth-oriented policies hold the key to poverty reduction.

In turn, Ravallion (1997, 2004) presents an empirical model relating poverty changes to the distribution-corrected rate of growth.<sup>2</sup> His estimates underscore the key role of initial inequality: depending on its level, a one-percent increase in income levels reduces poverty by as much as 4.3 percent (in very low inequality countries) or as little as 0.6 percent (in high inequality countries). This suggests that fast poverty reduction will be hard to achieve without declines in inequality, especially in very unequal countries.<sup>3</sup> This paper reassesses the roles of growth and inequality for poverty reduction from a different perspective, based on the use of a parametric approach to model the size distribution of income. Thus, the paper follows an abundant literature spanning over a century -- from Pareto (1897) to Gibrat (1931), Kalecki (1945), Rutherford (1955), Metcalf (1969), Singh and Maddala (1976) and Bourguignon (2003) -- that has attempted to approximate the distribution of income using a variety of functional forms. Specifically, the paper uses a large cross-country database including both industrial and developing countries and spanning almost 40 years to test the null hypothesis that the size distribution of per capita income can be described by a lognormal density.

> 1 This, of course, need not always be the case, since many policies are likely to be both growth-promoting and equality-enhancing. But some empirical evidence suggests that not all policies have this feature (Barro 2000, Lundberg and Squire 2003, Lopez 2004), and some may force policy makers to face a trade off between faster growth and increasing inequality.

> 2 Specifically, Ravallion (1997) interacts the growth rate with one minus the initial Gini coefficient, whereas Ravallion (2004) considers a distributional term of the form (1-Gini)<sup>θ</sup> with θ>1, to incorporate possible nonlinear interaction effects between the growth elasticity of poverty and initial inequality. 3 A similar point is made by Bourguignon (2004), who presents a simulation model calibrated on Mexican data. When no change takes place in the distribution of income, the model shows that a per capita growth rate of 3 percent per year over a 10-year period lowers the poverty rate by about 7 percentage points. When the same growth rate is accompanied by declining inequality (a reduction in the Gini coefficient by 10 percentage points), poverty falls twice as much -- over 15 percentage points.