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Semiparametric structural models of binary response: shape restrictions and partial identification

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  • Andrew Chesher

    () (Institute for Fiscal Studies and University College London)

Abstract

The paper studies the partial identifying power of structural single equation threshold crossing models for binary responses when explanatory variables may be endogenous. The paper derives the sharp identified set of threshold functions for the case in which explanatory variables are discrete and provides 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. It is shown that the restriction brings great computational benefits, allowing direct 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 mis-measured explanatory variables. This is a further revised version (Oct 7th 2011) of CWP23/09 "Single equation endogenous binary response models"

Suggested Citation

  • Andrew Chesher, 2011. "Semiparametric structural models of binary response: shape restrictions and partial identification," CeMMAP working papers CWP31/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:31/11
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    References listed on IDEAS

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    1. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 655-679.
    2. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, September.
    3. Chesher, Andrew & Smolinski, Konrad, 2012. "IV models of ordered choice," Journal of Econometrics, Elsevier, vol. 166(1), pages 33-48.
    4. Richard Blundell & Rosa Matzkin, 2010. "Conditions for the existence of control functions in nonseparable simultaneous equations models," CeMMAP working papers CWP28/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    6. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    7. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
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    9. Richard Blundell & James L. Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, March.
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    13. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    14. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
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    18. Andrew Chesher & Adam Rosen, 2012. "Simultaneous equations for discrete outcomes: coherence, completeness, and identification," CeMMAP working papers CWP21/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, May.
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