This study sets out to obtain values for the income elasticities and inequality of poverty in urban and rural areas of the Brazilian states. A panel data methodology capable of capturing spatial effects via a spatial lag model is used to identify whether there are spatial spillovers of poverty in the census situations studied. Changes in growth and inequality lead to spatial spillovers in the proportion of poor people in Brazil’s urban areas, but this does not happen at all in rural areas. By demonstrating the existence of spatial spillovers in urban areas, the study shows that anti-poverty measures for these areas should be applied at the national level. In rural areas, the absence of spatial spillovers in the proportion of poor people means that public policies to combat rural poverty can be implemented at both state and national levels.