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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. 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.

Suggested Citation

  • Victor Chernozhukov & Alfred Galichon & Marc Henry & Brendan Pass, 2021. "Identification of Hedonic Equilibrium and Nonseparable Simultaneous Equations," Journal of Political Economy, University of Chicago Press, vol. 129(3), pages 842-870.
    • Handle: RePEc:ucp:jpolec:doi:10.1086/712447
    DOI: 10.1086/712447
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    Cited by:

    1. 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.
    2. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," Sciences Po Economics Publications (main) hal-03936221, HAL.
    3. Florian F Gunsilius, 2025. "A primer on optimal transport for causal inference with observational data," Papers 2503.07811, arXiv.org, revised Mar 2025.
    4. Paula Calvo & Ilse Lindenlaub & Ana Reynoso, 2024. "Marriage Market and Labour Market Sorting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(6), pages 3316-3361.
    5. Tongseok Lim, 2023. "Replication of financial derivatives under extreme market models given marginals," Papers 2307.00807, arXiv.org.
    6. 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.
    7. Steven C. Bourassa & Martijn I. Dröes & Martin Hoesli, 2024. "Housing Market Segmentation: A Finite Mixture Approach," De Economist, Springer, vol. 172(4), pages 291-337, December.
    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.
    9. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," Working Papers hal-03936221, HAL.
    10. Tianyun Zhu & Hui Luo, 2026. "Auto ownership rationing and willingness to pay for subway proximity: a hedonic analysis," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 75(1), pages 1-23, March.
    11. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    12. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.

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