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. Copyright 2001 by Scottish Economic Society.
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