Twin peaks or three components?: analyzing the world's cross-country distribution of income

In this paper we analyze the world´s cross-national distribution of income and its evolution from 1970 to 2003. We argue that modeling this distribution by a finite mixture and investigating its number of components has advantages over nonparametric inference concerning the number of modes. In particular, the number of components of the distribution does not depend on the scale chosen (original or logarithmic), whereas the number of modes does. Instead of so-called twin-peaks, we find that the distribution appears to have only two components in 1970-1975, but consists of three components from 1976 onwards, a low, average and high mean-income group, with group means diverging over time. Here we apply recently developed modified likelihood ratio tests for the number of components in a finite mixture. The intra distributional dynamics are investigated in detail using posterior probability estimates.