Growth and Ergodicity: Has the World Converged?

One of the core issues in the economic growth literature is the degree to which economic activity is becoming ``similar'' across countries. This question has been addressed in a variety of manners, both theoretical and empirical. An implicit assumption within this literature is that the distribution of output per capita across countries is changing over time. This underlying assumption need not be true. This paper formally tests the hypothesis that the distribution of income across countries is changing using a simple representation of the data imposed by assuming that the relative income distribution of a large panel of countries evolves over time according to a simple convergent first order Markov chain. The Markov chain is defined using a finite number of income classifications. This allows us to characterise the behaviour of the data with respect to growth rates and income. In this framework we are able to construct a test of whether the world is in its ergodic state. We find evidence that the world has indeed reached its ergodic state thus contradicting the implicit assumption that the income distribution of countries is changing over time. We find that the nature of the ergodic distribution that is estimated in our study precludes both convergence in absolute income and convergence in growth rates. We also discuss income mobility issues and find evidence for a poverty trap in relative incomes. There is evidence to suggest that poorer countries are more mobile in the ergodic state while richer countries are less mobile.