An Almost Ideal Demand System for Housing Attributes

In recent articles, Mendelsohn [16] and Palmquist [20] use restricted versions of Rosen's [22] model of household behavior to consistently estimate demand functions for attributes of a differentiated product. Rosen's [22] model is of a single market for such a product, and he proposes a two-step technique to estimate attribute demand functions. First, a single hedonic price function is estimated for the differentiated product. Attribute prices are the first derivatives of the fitted hedonic price function with respect to the relevant attributes. Second, demand functions for attributes are estimated using the prices imputed in the first step.' If the hedonic price function estimated in the first step is linear, then there is no price variation for attributes, and demand functions cannot be estimated. If the hedonic price function is nonlinear, then there is price variation. But, it is endogenous to households, since in a single market, price and attribute quantity are chosen jointly.2 Indeed, within market price variation will always be endogenous. In either case, without sufficient restriction on the model, the parameters of the demand functions for attributes cannot be consistently estimated using Rosen's [22] method.3 Mendelsohn [16] and Palmquist [20] assume that there are many markets for the differentiated product and that households with like preferences may be observed in the different markets. By this restriction households face price variation across markets that is exogenous, whether hedonic price functions are linear or nonlinear. If so, demand functions can be consistently estimated.4