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Point-identification in multivariate nonseparable triangular models

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  • Florian Gunsilius

Abstract

In this article we introduce a general nonparametric point-identification result for nonseparable triangular models with a multivariate first- and second stage. Based on this we prove point-identification of Hedonic models with multivariate heterogeneity and endogenous observable characteristics, extending and complementing identification results from the literature which all require exogeneity. As an additional application of our theoretical result, we show that the BLP model (Berry et al. 1995) can also be identified without index restrictions.

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  • Florian Gunsilius, 2018. "Point-identification in multivariate nonseparable triangular models," Papers 1806.09680, arXiv.org.
    • Handle: RePEc:arx:papers:1806.09680
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    1. Lee, Sokbae & Lewbel, Arthur, 2013. "Nonparametric Identification Of Accelerated Failure Time Competing Risks Models," Econometric Theory, Cambridge University Press, vol. 29(5), pages 905-919, October.
    2. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    3. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    4. Susanne Schennach & Halbert White & Karim Chalak, 2007. "Local Indirect Least Squares and Average Marginal Effects in Nonseparable Structural Systems," Boston College Working Papers in Economics 680, Boston College Department of Economics, revised 26 Dec 2009.
    5. repec:cwl:cwldpp:1787rr is not listed on IDEAS
    6. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    7. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.
    8. repec:hal:spmain:info:hdl:2441/4kovgv3hs883bok2tvdkibejb6 is not listed on IDEAS
    9. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    10. Maximilian Kasy, 2014. "Instrumental Variables with Unrestricted Heterogeneity and Continuous Treatment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1614-1636.
    11. Xavier D'Haultfoeuille & Stefan Hoderlein & Yuya Sasaki, 2013. "Nonlinear Difference-in-Differences in Repeated Cross Sections with Continuous Treatments," Boston College Working Papers in Economics 839, Boston College Department of Economics.
    12. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    13. Victor Chernozhukov & Alfred Galichon & Marc Henry & Brendan Pass, 2018. "Single Market Nonparametric Identification of Multi-Attribute Hedonic Equilibrium Models," SciencePo Working papers Main hal-01169655, HAL.
    14. Ivar Ekeland, 2010. "Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 275-315, February.
    15. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
    16. Ivana Komunjer & Andres Santos, 2010. "Semi-parametric estimation of non-separable models: a minimum distance from independence approach," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 28-55, October.
    17. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    18. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    19. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    20. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    21. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    22. Steven T. Berry & Philip A. Haile, 2011. "Identification in a Class of Nonparametric Simultaneous Equations Models," Cowles Foundation Discussion Papers 1787, Cowles Foundation for Research in Economics, Yale University.
    23. Schennach, Susanne & White, Halbert & Chalak, Karim, 2012. "Local indirect least squares and average marginal effects in nonseparable structural systems," Journal of Econometrics, Elsevier, vol. 166(2), pages 282-302.
    24. repec:spo:wpmain:info:hdl:2441/4kovgv3hs883bok2tvdkibejb6 is not listed on IDEAS
    25. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, March.
    26. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    27. Torgovitsky, Alexander, 2017. "Minimum distance from independence estimation of nonseparable instrumental variables models," Journal of Econometrics, Elsevier, vol. 199(1), pages 35-48.
    28. Alexander Torgovitsky, 2015. "Identification of Nonseparable Models Using Instruments With Small Support," Econometrica, Econometric Society, vol. 83(3), pages 1185-1197, May.
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    Cited by:

    1. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).

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