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 initiid level coefficient is interpreted as convergence.These tests turn out to be plagued by Francis Gahon's classical fallacy of regression towards the mean.Using a dynamic version of Gallon's fallacy, we establish that, in fact, coefficients of arbi- trary signs in such regressions are consistent with an unchanging cross-section distribution of incomes.Feathers bit the ground before their weight can leave the air.