Estimating Hedonic Models

In this paper we consider the conditions under which instrumental variables methods are required in estimating a hedonic price function and its accompanying demand and supply relations. We assume simple functional forms that permit an explicit solution for the equilibrium hedonic price function. The principles are the same for models in which no analytic solution exists, but having the solutions makes the issues far more transparent. The need for instrumental variables estimation is directly analogous for the classical demand and supply model with undifferentiated products and for the hedonic model with differentiated products. In estimating individual demand and supply functions, instrumental variables estimation is required if the consumer and firm unobservables, which give rise to the error terms in the demand and supply functions, are correlated across consumers/firms within a community. In estimating inverse demand/supply functions, which are referred to as bid/offer functions in the hedonic model, instrumental variables estimation is required even if the unobservables are not correlated across agents within a community. If the unobservables are not correlated across agents within a community, then community binaries or the means of observable consumer and firm characteristics can be used as instruments. If the unobservables are correlated then only the latter can be used. The error term in the hedonic price function is often assumed to be uncorrelated with the chosen attributes. This assumption may be reasonable if consumers have quasilinear preferences. If not, then the error term in the price function may affect the utility-maximizing amounts of the attributes. The feasible instruments again depend upon whether the error term is correlated for agents within a community. If not, then community binaries or observed individual characteristics may be used as instruments. If so, then the community binaries are correlated with the error terms and cannot serve as instruments.