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Identification of hedonic equilibrium and nonseparable simultaneous equations

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  • Victor Chernozhukov
  • Alfred Galichon
  • Marc Henry
  • Brendan Pass

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.

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  • Victor Chernozhukov & Alfred Galichon & Marc Henry & Brendan Pass, 2017. "Identification of hedonic equilibrium and nonseparable simultaneous equations," Papers 1709.09570, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:1709.09570
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    References listed on IDEAS

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    Cited by:

    1. William Torous & Florian Gunsilius & Philippe Rigollet, 2021. "An Optimal Transport Approach to Estimating Causal Effects via Nonlinear Difference-in-Differences," Papers 2108.05858, arXiv.org, revised Mar 2024.
    2. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    3. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," Working Papers hal-03936221, HAL.
    4. Gunsilius, Florian F., 2023. "A condition for the identification of multivariate models with binary instruments," Journal of Econometrics, Elsevier, vol. 235(1), pages 220-238.
    5. Tongseok Lim, 2023. "Replication of financial derivatives under extreme market models given marginals," Papers 2307.00807, arXiv.org.
    6. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," SciencePo Working papers Main hal-03936221, HAL.
    7. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.
    8. Bishop, Kelly C. & Timmins, Christopher, 2019. "Estimating the marginal willingness to pay function without instrumental variables," Journal of Urban Economics, Elsevier, vol. 109(C), pages 66-83.

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