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This paper presents new evidence on urbanization using sub-county data for the United States from the period 1880-2000 and municipality data for Brazil from the period 1970-2000. They show that the two central stylized features of population growth for cities - Gibrat's Law and a stable population distribution - are strongly rejected when both rural and urban areas are considered. Population growth exhibits a U-shaped relationship with initial population density, and only becomes uncorrelated with initial population density at the high densities found in predominantly urban areas.
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