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

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  • Chesher, Andrew

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 revised version of CWP23/09 "Single equation endogenous binary response models"

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 29 (2013)
Issue (Month): 02 (April)
Pages: 231-266

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Handle: RePEc:cup:etheor:v:29:y:2013:i:02:p:231-266_00

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  1. Andrew Chesher & Adam Rosen & Konrad Smolinski, 2011. "An instrumental variable model of multiple discrete choice," CeMMAP working papers CWP39/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-85, May.
  3. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
  4. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106, April.
  5. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, 03.
  6. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 835-864.
  7. Andrew Chesher & Konrad Smolinski, 2009. "IV models of ordered choice," CeMMAP working papers CWP37/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Richard Blundell & James Powell, 2001. "Endogeneity in semiparametric binary response models," CeMMAP working papers CWP05/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. Magnac, Thierry & Maurin, Eric, 2003. "Identification and Information in Monotone Binary Models," IDEI Working Papers 180, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2004.
  10. 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, 05.
  11. Mathias Dewatripont & Lars Peter Hansen & Stephen Turnovsky, 2003. "Advances in economics and econometrics: the eighth world congress," ULB Institutional Repository 2013/9557, ULB -- Universite Libre de Bruxelles.
  12. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
  13. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-59, July.
  14. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, 03.
  15. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532, April.
  16. Jean-Pierre Florens & James J. Heckman & Costas Meghir & Edward J. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous Treatment and Heterogeneous Effects," NBER Working Papers 14002, National Bureau of Economic Research, Inc.
  17. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090, April.
  18. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
  19. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549, April.
  20. 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.
  21. 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.
  22. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, 05.
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