Identification of hedonic equilibrium and nonseparable simultaneous equations

TL;DR

This paper establishes nonparametric identification conditions for multi-attribute hedonic equilibrium models with unobserved heterogeneity using shape restrictions derived from optimal transport theory.

Contribution

It extends identification results to multi-attribute models with multiple unobserved heterogeneity dimensions, employing shape restrictions based on optimal transport.

Findings

Identification of preferences and technology in multi-attribute models.

Proof of absolute continuity of the distribution of traded qualities.

Development of shape restrictions for nonseparable simultaneous equations.

Abstract

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.