Rich Country-Poor Country Convergence?: A New Approach to an Old Issue

Understanding whether the gap between rich and poor country’s GDP per capita has narrowed is really about the changing shapes of distributions of wellbeing and technology indicators. As limiting cases, convergence between rich and poor country groups can be brought about by countries within groups becoming less alike without any diminution of growth rate differentials between them, or it can be brought about by reductions in these differentials without any diminution of within group identity. A subject first theoretically explored by Esteban and Ray (1994). The empirical issue is about whether separate groups can be identified in the overall distribution, and whether they are tending toward common or distinct equilibria. This paper proposes two simple statistics for the problem, the Overlap measure and the Trapezoidal measure, which are capable of discerning changes in the underlying distributions which reflect a combination of increasing (decreasing) subgroup location differences and decreasing (increasing) subgroup spreads, which are the characteristics of polarization (convergence). Both statistics can be employed when country status is characterized in a multivariate framework. These techniques are applied to the examination of convergence in lifetime GDP per capita between rich and poor nations when growth is viewed either as a wellbeing index (population weighted) or a technology index (population unweighted). It turns out that such a distinction matters, since viewed technologically there is divergence, while in a wellbeing sense there is convergence. As a collection of countries, Africa is diverging from the rest of the world whatever the perspective of growth. JEL Code: C14, I32, O47