Spatial growth with exogenous saving rates

Economic growth has traditionally been analyzed in the temporal domain, while the spatial dimension is captured by cross-country income differences. Data suggest great inequality in income per capita across countries, and a slight but noticeable increase in inequality across nations between 1960 and 2000. Seeking to explore the mechanism underlying the temporal evolution of the cross sectional distribution of economies, we develop a spatial growth model where saving rates are exogenous. Capital movements across locations are governed by a mechanism under which capital moves toward locations of relatively higher marginal productivity, with a velocity determined by the existing stock of capital. This augments the capital accumulation equation by a nonlinear diffusion term. Our results suggest that under diminishing returns, the growth process leads to a stable spatially nonhomogeneous distribution for per capita capital and income in the long run. Insufficient savings may lead to the emergence of persistent poverty cores where capital stock is depleted in some locations.