Identification of hedonic equilibrium and nonseparable simultaneous equations

This paper derives conditions under which preferences and technology are nonparametrically identified in hedonic equilibrium models. With products differentiated along a quality index and agents characterized by scalar unobserved heterogeneity, single-crossing conditions on preferences and technology provide identifying restrictions in previous work. We develop similar shape restrictions in the multiattribute case. These shape restrictions, based on optimal transport theory and generalized convexity, allow us to identify preferences for goods differentiated along multiple dimensions from the observation of a single market. We thereby derive identification results for nonseparable simultaneous equations and multiattribute hedonic equilibrium models with (possibly) multiple dimensions of unobserved heterogeneity. One of our results is a proof of absolute continuity of the distribution of endogenously traded qualities, which is of independent interest.