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Semiparametric Structural Models Of Binary Response: Shape Restrictions And Partial Identification

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  • Chesher, Andrew

Abstract

I study the partial identifying power of structural single-equation threshold-crossing models for binary responses when explanatory variables may be endogenous. The sharp identified set of threshold functions is derived for the case in which explanatory variables are discrete, and I provide a constructive proof of sharpness. There is special attention to a widely employed semiparametric shape restriction, which requires the threshold-crossing function to be a monotone function of a linear index involving the observable explanatory variables. The restriction brings great computational benefits, allowing calculation of the identified set of index coefficients without calculating the nonparametrically specified threshold function. With the restriction in place, the methods of the paper can be applied to produce identified sets in a class of binary response models with mismeasured explanatory variables.

Suggested Citation

  • Chesher, Andrew, 2013. "Semiparametric Structural Models Of Binary Response: Shape Restrictions And Partial Identification," Econometric Theory, Cambridge University Press, vol. 29(2), pages 231-266, April.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:02:p:231-266_00
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    Cited by:

    1. Matthew Gentry & Tong Li, 2014. "Identification in Auctions With Selective Entry," Econometrica, Econometric Society, vol. 82(1), pages 315-344, January.
    2. Gu, Jiaying & Russell, Thomas M., 2023. "Partial identification in nonseparable binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 528-562.
    3. Matthew Gentry & Tong Li, 2012. "Identification in auctions with selective entry," CeMMAP working papers 38/12, Institute for Fiscal Studies.
    4. Xiaohong Chen & Matthew Gentry & Tong Li & Jingfeng Lu, 2020. "Identification and Inference in First-Price Auctions with Risk Averse Bidders and Selective Entry," Cowles Foundation Discussion Papers 2257, Cowles Foundation for Research in Economics, Yale University.
    5. Alexander Torgovitsky, 2019. "Partial identification by extending subdistributions," Quantitative Economics, Econometric Society, vol. 10(1), pages 105-144, January.
    6. Jiaying Gu & Thomas M. Russell, 2021. "Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors," Papers 2101.01254, arXiv.org, revised Jul 2022.
    7. Chesher, Andrew & Rosen, Adam M., 2020. "Generalized instrumental variable models, methods, and applications," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 1-110, Elsevier.
    8. Schennach, Susanne M., 2020. "Mismeasured and unobserved variables," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 487-565, Elsevier.

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