Long-run income convergence is investigated in the US context. We employ a novel pair-wise econometric procedure based on a probabilistic definition of convergence. The time-series properties of all the possible regional income pairs are examined by means of unit root and non-cointegration tests where inference is based on the fraction of rejections. We distinguish between the cases of strong convergence, where the implied cointegrating vector is [1,-1], and weak convergence, where long-run homogeneity is relaxed. To address cross-sectional dependence, we employ a bootstrap methodology to derive the empirical distribution of the fraction of rejections. We find supporting evidence of US states sharing a common stochastic trend consistent with a definition of convergence based on long-run forecasts of state incomes being proportional rather than equal. We find that the strength of convergence between states decreases with distance and initial income disparity. Using Metropolitan Statistical Areas data, evidence for convergence is stronger.
