Distribution Dynamics and Cross‐Country Convergence: A New Approach

Distribution dynamics is a method for studying the evolution in time of an entire cross‐section distribution and has been initially employed to assess cross‐country convergence of per capita incomes. It has subsequently seen a widespread application in many different economic areas. When describing the law of motion of the distribution as a Markovian stochastic process, working in a discrete state‐space set up has several advantages, but the arbitrary discretisation of a continuous state‐space process has the undesired effect of removing the Markov property. This paper outlines a rigorous method for discretising a continuous state‐space Markov chain. The method is then applied to the distribution of per capita income across countries to reassess the (non‐) convergence phenomenon. It is found that the long run polarisation of per capita incomes across countries emerges even more dramatically than in previous studies.