Assessing the convergence and mobility of nations without artificially specified class boundaries

There is a long-established practice in the empirical growth and convergence literature of classifying countries into groups or clubs by arbitrarily specifying group boundaries. A problem with this approach is that determining boundaries in a particular fashion also determines the nature of the group in a way that is often prejudicial for analysis ultimately affecting the way transition and class mobility behavior is evaluated. Here a semi-parametric technique for class categorization without resort to arbitrarily specified frontiers is proposed and the convergence of classes and mobility between them is studied in the context of the size distribution of per capita GDP of nations. Category membership is partially determined by the commonality of observed behavior of category members: partial in the sense that only the probability of category membership in each category is determined for each country. Such an approach does not inhibit the size of classes or the nature of transitions between them. A study of the world distribution over the 40 years preceding 2010 reveals substantial changes in class sizes and mobility patterns between them which are very different from those observed in a fixed class size analysis.