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 Francis 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.