  This paper derives conditions under which preferences and technology are
nonparametrically identified in hedonic equilibrium models, where products are
differentiated along more than one dimension and agents are characterized by
several dimensions of unobserved heterogeneity. 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 Ekeland, Heckman and Nesheim (2004) and Heckman,
Matzkin and Nesheim (2010). We develop similar shape restrictions in the
multi-attribute case. These shape restrictions, which are 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 nonparametric identification results for
nonseparable simultaneous equations and multi-attribute 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.
