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A Model of Urbanization with Nonlinear Migration Flows

This paper seeks an appropriate specification of the migration exchange between rural and urban areas so that the implied evolution of the degree of urbanization agrees with its commonly observed S-shape. After demonstrating that the gross migration flows between rural and urban areas should be specified as nonlinear functions of the population in the origin sector, the paper introduces a model in which such flows are represented by gravity-type functional forms. When proper bounds are imposed on the parameters of these functional forms, the model yields an evolution of the degree of urbanization that is depicted by a logistic curve. It thus can be used to give insights into the time paths of three basic urbanization variables: the urban-rural growth rate differential, the rural net outmigration rate, and the urban net immigration rate. All take on a zero value at the two extremes of the urbanization process and evolve in between according to a bell-shaped curve. These findings are illustrated by applying the model to data from the United States for the period 1790-1980.