A simple test for convergence of metropolitan income in the United States

The prevalent test for income convergence used in many recent studies of convergence across spatial economic units in the United States is to use a regression equation in which income growth is regressed against the initial level of income (this is known as β convergence). That method, however, has been crtiticized as an instance of Galton's fallacy of regression. We devise a simple test for the income β-convergence hypothesis which does not suffer from "Galton's fallacy" and apply it to all of the metropolitan areas of the United States for the period 1969-1995. For the test we use two income measures: per capita personal income and average wages. Our results conclusively support convergence of per capita personal income and of wage per worker for metropolitan areas in the United States. We also test for σ convergence, the hypothesis of diminishing dispersion in income among places over time, and find no support for the hypothesis.