σ-convergence in the presence of spatial effects

This paper explores the implications that spatial effects can hold for the application of measures of σ-convergence. The bias of a common indicator of σ-convergence is examined for a family of spatial process models including: [a] spatial lag, [b] spatial error, and [c] spatial moving average. We show that the measure of σ-convergence is sensitive to a number of distinct influences including global dispersion, spatial dependence, and a variety of forms of spatial heterogeneity. We suggest a decomposition of the convergence indicator into two components: one reflecting global dispersion, and one reflecting the influence of spatial effects. We then illustrate this approach with a case study of the U.S. states over the 1929-2000 period.