Identifying Hedonic Models

Economic models for hedonic markets characterize the pricing of bundles of attributes and the demand and supply of these attributes under different assumptions about market structure, preferences, and technology (see Jan Tinbergen [1956], Sherwin Rosen [1974], and Dennis Epple [1987] for contributions to this literature). While the theory is well formulated and delivers some elegant analytical results, the empirical content of the model is under debate. It is widely believed that hedonic models Ž t in a single market are fundamentally underidentiŽ ed and that any empirical content obtained from them is a consequence of arbitrary functionalform assumptions. The problem of identiŽ cation in hedonic models is a prototype for the identiŽ cation problem in a variety of economic models in which agents sort on unobservable (to the economist) characteristics: models of monopoly pricing (Michael Mussa and Rosen, 1978; Robert Wilson, 1993) and models for taxes and labor supply (Heckman, 1974). Sorting is an essential feature of econometric models of social interactions (see William Brock and Steven Durlauf, 2001). In this paper we address the sorting problem in hedonic models. Nesheim (2001) extends this analysis to a model with peer effects. In this paper we note that commonly used linearization strategies made to simplify estimation and justify the application of instrumentalvariables methods, produce identiŽ cation problems. The hedonic model is generically nonlinear. It is the linearization of a fundamentally nonlinear model that produces the form of the identiŽ cation problem that dominates discussion in the applied literature. Linearity is an arbitrary and misleading functional form when applied to empirical hedonic models. Our research establishes that, even though sorting equilibrium in a single market implies no exclusion restrictions, the hedonicmodel is generically nonparametrically identiŽ ed. Instrumentalvariables and transformation-model methods identify economically relevant parameters even without exclusion restrictions. Multimarket data, widely viewed as the most powerful source of identiŽ cation, are no panacea and their identifying power depends on assumptions about why hedonic functions vary across markets.