Revisiting convergence: A research note

• Income distributions are biased against extreme levels of (in)equality.
• I apply this principle to trends in GDP PC across 127 countries between 1980 and 2010.
• Convergence in GDP PC is primarily a function of large income gaps between countries.

A number of recent studies show that income inequality is declining between countries. In this research note, I question the significance of this trend by examining the role of initial conditions in producing convergence. An important (but neglected) property of inequality dynamics is the tendency for extreme distributions to become more moderate. When income disparities are large, the subsequent trend is biased toward convergence. Conversely, when initial conditions approach parity, divergence becomes the more likely long-term outcome. I apply this principle to trends in GDP PC across 127 countries during the 1980–2010 period. Using counterfactual analysis, I manipulate the initial level of inequality in GDP PC while holding constant each country’s observed growth rate during the sample period. I find that the growth dynamics of GDP PC produce either convergence or divergence based simply on the initial distribution of income. The point of transition occurs at a moderate level of inequality, whether using population weights (Gini = .365) or not (Gini = .377). I conclude that the recent convergence observed in GDP PC is primarily a function of large income gaps between countries and would not have materialized at more moderate levels of initial inequality. By contrast, an examination of the pre-1950 period reveals divergent growth patterns that are not sensitive to initial conditions.