(In)stability in the Dynamics of the Cross-Country Distribution of Income Per Capita

Using a panel of 102 countries from PWT 10.0 covering 1970-2019, we examine the veracity of the assumption that a time-homogeneous, first-order process describes the evolution of the cross-country distribution of per capita output, an assumption often made in studies of the convergence hypothesis employing the distribution dynamics approach pioneered by Quah (1993). To test homogeneity, we compare transition kernels estimated for different time periods and, for those periods exhibiting evidence of homogeneity, we test the first-order assumption using an implication of such a process's Chapman-Kolmogorov equations. Both tests require measurement of the distance between probability distributions which we do with several different metrics, employing bootstrap methods to assess the statistical significance of the observed distances. We find that the process was time-homogeneous and first-order in the 1970-1995 period during which the distribution dynamics imply a bimodal long-run distribution, consistent with convergence clubs. Following the apparent break in the process in the late 1990s, the 2000-2010 distribution dynamics imply a unimodal long-run distribution suggestive of a single convergence club, consistent with recent claims of short-term beta-convergence from the late 1990s and beyond made by Patel et al. (2021) and Kremer et al (2022). After 2010, there is some evidence of a return to non-convergent dynamics similar to those of the 1970-1995 period.