Heterogeneity within Communities: A Stochastic Model with Tenure Choice

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.