The Millennium Peak in Club Convergence - What the Critical Bandwidth Can Say About Distributional Changes in the Wealth of Nations

The convergence debate of whether poorer countries are catching up with richer ones has recently focused on the concept of club convergence, hence convergence within groups of countries. Formally detecting club convergence in the distribution of countries' income per capita over time has, however, proved difficult. I suggest a nonparametric measure that captures intradistributional changes in one number: When two clusters are involved, changes in Silverman s (1981) critical bandwidth for unimodality reflect modes becoming more or less pronounced, which, respectively, is evidence for club convergence or de-clubbing. Significance of the change can be determined in a bootstrap procedure, while working with standardized densities removes the influence of time-varying variance. This paper seems to be the first one not only to take the critical bandwidth to a dynamic context but also to relate it to the club convergence literature. Furthermore, a conceptual comparison shows parallels and differences to polarization measures. In the empirical section with the distribution of income per capita of 123 countries, my method provides evidence of club convergence in the 1980s and 1990s, peaking at the turn of the millennium and followed by a de-clubbing movement in the 2000s.