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Ortalo-Magné, François and Rady, Sven (2005): Heterogeneity within Communities: A Stochastic Model with Tenure Choice. Discussion Papers in Economics 2005-8
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Abstract

Standard explanations for the income heterogeneity within neighborhoods rely on differences of preferences across households and heterogeneity of the housing stock. We propose an alternative and complementary explanation. We construct a stochastic equilibrium sorting model where (1) income is the sole dimension of household heterogeneity, (2) households form state-contingent housing location plans that may involve moves over their lifetimes, (3) households choose whether to own or rent depending on the housing expenditure risk associated with each tenure mode, and (4) there is a probability that newcomer households move in and compete for homes with native households. Income mixing within neighborhood arises for two reasons. First, allowing natives to form state-contingent housing location plans breaks the indivisibility of housing consumption implicit in the literature where households choose their location once and for all. Second, natives can insure themselves against rent fluctuations by buying their home prior to the realization of the population shock; newcomers cannot. As a result, poorer natives stay in the more desirable communities and only richer newcomers move in these communities. Evidence from U.S. metropolitan areas supports the effects predicted by the model.