The effects of space and scale on unconditional beta convergence: test results from the United States, 1970–2004

Abstract

Beta convergence theorizes that regions with low levels of income will grow faster than regions with higher incomes as investment is moved to regions where returns can be maximized. The formal test for beta convergence is an OLS regression with income change as the dependent variable and initial income as the predictor. Beta convergence is present when the coefficient on initial income is negative. Empirical evidence of convergence is mixed, however. We contend that omission of spatial effects, and the confounding problem of geographic scale, help explain inconsistent empirical findings. We, therefore, examine the role of spatial effects on the standard convergence model at three spatial scales—states, Economic Areas, and counties—in the United States from 1970 to 2004. Our results indicate failure to account for spatial and scalar effects can lead to conflicting results. Convergence evidence is strongest at smaller levels of spatial aggregation, yet model fit is better at larger levels. In addition, accounting for spatial effects improves model diagnostic performance but weakens convergence evidence.