What is the Price Elasticity of Housing Demand?

DISAGREEMENT about the responsiveness of housing demand to variations in relative prices persists, despite extensive empirical analyses. Two factors underlie this disagreement: the multidimensional character of housing makes direct observation of prices (as distinct from expenditures) impossible; and, the significant search, transactions, and moving costs associated with changing dwellings imply that, at any instant, a given household's consumption may deviate significantly from its utility maximizing level in a static equilibrium. While a number of ingenious attempts have been made to circumvent these problems, each is quite indirect and relies upon strong, and untestable, assumptions (cf. Mayo (1978)). This paper provides direct estimates of price elasticities, based upon an explicit model of housing consumption dynamics and utilizing the experimental manipulations of housing prices incorporated in the Housing Allowance Demand Experiments.1 While the data are limited to two years of longitudinal data and pertain only to low income renters, they nevertheless permit the direct estimation of this key parameter of housing demand. This analysis focuses on the price responsiveness of households, but clearly other changes in household circumstances (such as in income or family size) affect desired housing consumption. In fact, given the limited longitudinal data, information about other demand adjustments provides valuable insights into consumption dynamics. Price changes can be viewed as but one of a variety of exogenous influences on housing demand. A complete structural model of housing demand would consider the joint influence of household preferences, relocation costs, and prices on search and moving behavior and, conditional on this, their subsequent influence on housing consumption. However, both household preferences and relocation costs are generally unobserved, and estimation of such a complete model is simply beyond our current capabilities. We concentrate upon the more modest goal of modelling the reduced form relationship between housing consumption and housing stock disequilibrium (defined below). Consumption dynamics are represented by variants of a linearized stock adjustment process . This formulation is based on the simple observation that adjustments will generally be a monotonic function of the magnitude of disequilibrium in housing consumption. As indicated by past work (Hanushek and Quigley, 1979), this is both a convenient and powerful characterization of short run dynamics. Two basic formulations of consumption dynamics are considered. Let Htd represent the desired, or static equilibrium, quantity of housing demanded by a given household, and let Ht be the actual (observed) housing consumption at time t. In the simplest form, households are assumed, on average, to close the gap between desired and equilibrium housing consumption at a constant rate a, so that