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 (Acemoglu 2009). 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 towards locations of relatively higher marginal productivity, with a velocity determined by the existing stock of capital. This mechanism leads to a capital accumulation equation augmented by a nonlinear diffusion term, which characterizes spatial movements. Our results suggest that under diminishing returns the growth process leads to a stable spatially non-homogenous 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.