Modeling Small Business Growth, Migration Behavior, Local Public Services and Household Income in Appalachia: A Spatial Simultaneous Equations Approach

In this paper, a spatial simultaneous growth equilibrium model of small business growth, migration behavior, median household income and local public expenditures is developed. The model is empirically estimated by Generalized Spatial Three-Stage Least Squares estimator using count-level data from Appalachia for 1990-2000. The results suggest the existence of interdependence among the growth rates of small business, gross in-and out-migration, median household income and local public services in the form of feedback simultaneities, spatial autoregressive lag and spatial cross-regressive lag simultaneities. The findings also suggest the existence of conditional convergence with respect to endogenous variables of the model. The speeds of adjustment towards the steady states, however, are very slow which would cover many generations. The growth rate of median household income with a half–life time of about 9 years is the fastest and the growth rate of gross in-migration with a half-life time of about 180 years is the slowest to adjust. The findings also indicate the clustering of counties on the bases of their growth rates of median household incomes which would require the need for development policy coordination at the regional level, a region being defined as a group of counties, or the whole Appalachia. Another key finding of the study is also that Appalachian counties with higher initial population sizes were both destinations and sources of migrants during the study period.