Income convergence and the catch-up index

Defining a catch-up index that measures rich-poor country income convergence and comparing it to within group convergence (β-convergence), defining relative convergence as decrease in rich-poor country income ratio and absolute convergence as decrease in rich-poor country income gap, we derive an equation for years for income equality to the frontier (full convergence). Focusing on relatively homogeneous countries of Sub-Saharan Africa and South Asia, we show neither region has achieved either within group convergence or significant catching-up since 1951, and 21 of the 28 countries exhibiting catching-up in the most recent 21-years period, using US as the frontier, show falling behind over the longer period. We show years for full convergence depend also on the initial conditions; the neo-classical hypothesis that poorer countries grow faster means relative convergence, relative convergence is a necessary but not sufficient condition for absolute convergence; “Iron law of convergence” does not hold; and within group convergence is consistent with poorer countries in the group diverging absolutely while richer countries converge.