Dynamic housing market equilibrium with taste heterogeneity, idiosyncratic perfect foresight, and stock conversions

A discrete-time, nonstationary dynamic equilibrium model of the housing market is developed in which consumers exhibit taste heterogeneity and investors act with perfect foresight subject to idiosyncratic uncertainty in costs. Housing is treated as a discrete, durable, and differentiated good which is indivisible in consumption and a convertible asset in investment. The dynamic market equilibrium determines the allocation of each consumer type among the housing types, the rent and vacancies of each housing type, the asset prices of housing and land, and the conversions between land and housing and among the stocks of housing of each type. The model relies on probabilistic discrete choice theory, whereby the investor's and consumer's choice probabilities are given the multinomial logit specification. An algorithm is developed which solves for dynamic equilibrium by assuming a relationship between rents and asset prices in the terminal period. The computable model is used to examine the "filtering hypothesis": that technological progress or government subsidies targeted to the construction of high-quality housing eventually benefit the poor. While this hypothesis is correct when subsidies do not induce stock conversions, it is false if investors demolish sufficient numbers of low-quality housing units in order to construct high-quality housing.