Galton’s Fallacy and Tests of the Convergence Hypothesis

Recent tests for the convergence hypothesis derive from regressing average growth rates on initial levels: a negative initial level coefficient is interpreted as convergence. These tests turn out to be plagued by Galton’s classical fallacy of regression towards the mean. Using a dynamic version of Galton’s fallacy, I establish that coefficients of arbitrary signs in such regressions are consistent with an unchanging cross-section distribution of incomes. Alternative, more direct empirics used here show a tendency for divergence, rather than convergence, of cross-country incomes. Communications to: D. T. Quah, LSE, Houghton Street, London WC2A 2AE. [Tel: +44-171-955-7535, Email: [email protected]] [(URL) http://econ.lse.ac.uk/~dquah/] Nontechnical Summary What causes some countries to grow rapidly, others only slowly? Do some regions stagnate while others boom? Is there a tendency for poorer countries to catch up with richer ones? (That the last might be true is also known as the “convergence hypothesis”.) Questions such as these have motivated both the new growth theory and recent empirical studies of cross-country growth. This paper shows that the usual interpretations given in those empirical studies suffer from a classical fallacy in regression theory. Finding that the countries initially poorer also happen to grow faster—using standard regression techniques—turns out to be uninformative on the convergence hypothesis. The paper then also presents new empirical evidence showing that in the post War era rich countries tend to become richer, poor countries poorer, while the middle-income group of countries appears to be an (eventually) vanishing class.