Mixture models and convergence clubs

In this paper we argue that modeling the cross-country distribution of per capita income as a mixture distribution provides a natural framework for the detection of convergence clubs. The framework yields tests for the number of component distributions that are likely to have more power than "bump hunting" tests and includes a natural method of assessing the cross-component immobility necessary to imply a correspondence between components and convergence clubs. Applying the mixture approach to cross-country per capita income data for the period 1960 to 2000 we find evidence of three component densities in each of the nine years that we examine. We find little cross-component mobility and so interpret the multiple mixture components as representing convergence clubs. We document a pronounced tendency for the strength of the bonds between countries and clubs to increase. We show that the well-known "hollowing out" of the middle of the distribution is largely attributable to the increased concentration of the rich countries around their component means. This increased concentration as well as that of the poor countries around their component mean produces a rise in polarization in the distribution over the sample period.
N.B.: This article is the preprint for the following:
"Mixture Models, Convergence Clubs and Polarization," 2010, Paul Johnson, Maria Grazia Pittau and Roberto Zelli, <em>Review of Income and Wealth</em>, 56:102-22.