This paper examines the growth and dispersion of personal income in U.S. states and regions since 1880, relating the patterns for individual states to the behavior of regions. It analyzes the interplay between net migration and economic growth, studying the evolution of gross state product since 1963 and relating it to productivity in eight major sectors. The evidence strongly supports convergence, with poor states tending to grow faster in terms of per capita income and product, both within sectors and for state aggregates. The rate of convergence is approximately 2% per year. The same framework is applied to patterns of convergence across 73 regions of seven European countries since 1950, showing a similar process of convergence. The findings suggest that the convergence process will occur, but at a slow pace, as seen in the historical context of the American South becoming nearly as well off as the North. The paper also discusses the role of net migration in speeding up convergence, finding that while migration can account for up to a third of the estimated speed of convergence if migrants have no human capital, it cannot explain more than 10% if migrants have reasonable human capital.This paper examines the growth and dispersion of personal income in U.S. states and regions since 1880, relating the patterns for individual states to the behavior of regions. It analyzes the interplay between net migration and economic growth, studying the evolution of gross state product since 1963 and relating it to productivity in eight major sectors. The evidence strongly supports convergence, with poor states tending to grow faster in terms of per capita income and product, both within sectors and for state aggregates. The rate of convergence is approximately 2% per year. The same framework is applied to patterns of convergence across 73 regions of seven European countries since 1950, showing a similar process of convergence. The findings suggest that the convergence process will occur, but at a slow pace, as seen in the historical context of the American South becoming nearly as well off as the North. The paper also discusses the role of net migration in speeding up convergence, finding that while migration can account for up to a third of the estimated speed of convergence if migrants have no human capital, it cannot explain more than 10% if migrants have reasonable human capital.