Acknowledged as a key reference in empirical literature, the contribution of Barro and Sala-i-Martin (1995) strongly supports what the Solow model with exogenous technological progress in a closed economy predicts in terms of convergence. Barro and Sala-i-Martin used both gross state product and per capita personal income 12 , exclusive of all transfers, for 47 U.S. states or territories from 1880 to 198813, and found a β-convergence rate of about 2 percent a year. According to the authors, factors of production indeed flowed from low- to high-income states, leading the economies further below the steady-state position to grow faster. The evidence of convergence within the United States tends to support more the neoclassical model of growth than the evidence of convergence over large samples of many countries. The main reason is that one country’s features usually contrast more with another country’s than regions within the same country.
Note that the β-convergence, here tested within the United States, does not imply convergence across states, as Olivier Blanchard14 pointed out. Indeed, cross-sectional means that fluctuate within an interval shrinking over time can still display increasing standard-deviations. Blanchard highlighted this nuance to better argue against it. He showed that the temporal dimension of Barro and Sala-i-Martin’s data can be used to test the hypothesis of convergence in broader terms. Considering 1) dispersion over time, and 2) convergence coefficient over time, “both [ways] strongly suggest convergence [across the U.S. states]”. In other words, Blanchard generalized Barro and Sala-i-Martin’s conclusions on β-convergence to overall convergence across U.S. states. Such results are now taken for granted in the economic literature, and this is exactly what I think can be improved, and this for two reasons.
First, Barro and Sala-i-Martin tested the neo-classical equation using arithmetic means as a proxy for the distribution of income. How to measure income discrepancies is an issue debated carefully in the income inequality literature, and the arithmetic mean hardly belongs to the set of the best statistical tools. A response to this problem is to resort to dispersion indicators, such a quartiles, deciles, or percentiles, revealing, at least partially, the income distribution itself.
Second, the later trends of increasing income inequalities observed recently in the United States question the neoclassical theory in that respect. The issue is controversial also in regard to the decade when income inequality started to widen: the mid-1970s, versus the mid-1980s. Such an argument carries much weight in the academic circles of human geography.
Barro and Sala-i-Martin (1995, p. 383) distinguish two definitions of convergence: β-convergence and σ-convergence. “In one view (…), convergence applies if a poor economy tends to grow faster than a rich one, so that the poor country tends to catch up with the rich one in terms of the level of per capita income or product. This property corresponds to our concept of β convergence. (This phenomenon is sometimes described as “regression toward the mean”.) The second concept (…) concerns cross-sectional dispersion. In this context, convergence occurs if the dispersion _measured, for example, by the standard deviation of the logarithm of per capita income or product across a group of countries or regions_ declines over time. We call this process σ convergence.”
BEA’s quote: “Personal income is the income that is received by persons from all sources. It is calculated as the sum of wage and salary disbursements, supplements to wages and salaries, proprietors' income with inventory valuation and capital consumption adjustments, rental income of persons with capital consumption adjustment, personal dividend income, personal interest income, and personal current transfer receipts, less contributions for government social insurance. This measure of income is calculated as the personal income of the residents of a given area divided by the resident population of the area. In computing per capita personal income, BEA uses the Census Bureau's annual midyear population estimates.”
For 1880, 1900, 1920, and annually from 1929 to 1988, as regards BEA Personal State Income data.
See “Comments and Discussion” in Barro, Sala-i-Martin, Blanchard & Hall (1991, p. 159-174).