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An instrumental variable random‐coefficients model for binary outcomes

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  • Andrew Chesher
  • Adam M. Rosen

Abstract

In this paper, we study a random‐coefficients model for a binary outcome. We allow for the possibility that some or even all of the explanatory variables are arbitrarily correlated with the random coefficients, thus permitting endogeneity. We assume the existence of observed instrumental variables Z that are jointly independent with the random coefficients, although we place no structure on the joint determination of the endogenous variable X and instruments Z, as would be required for a control function approach. The model fits within the spectrum of generalized instrumental variable models, and we thus apply identification results from our previous studies of such models to the present context, demonstrating their use. Specifically, we characterize the identified set for the distribution of random coefficients in the binary response model with endogeneity via a collection of conditional moment inequalities, and we investigate the structure of these sets by way of numerical illustration.

Suggested Citation

  • Andrew Chesher & Adam M. Rosen, 2014. "An instrumental variable random‐coefficients model for binary outcomes," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 1-19, June.
  • Handle: RePEc:wly:emjrnl:v:17:y:2014:i:2:p:s1-s19
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    File URL: http://hdl.handle.net/10.1111/ectj.12018
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    References listed on IDEAS

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    1. Aviv Nevo, 2011. "Empirical Models of Consumer Behavior," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 51-75, September.
    2. Eric Gautier & Erwann Le Pennec, 2011. "Adaptive Estimation in the Nonparametric Random Coefficients Binary Choice Model by Needlet Thresholding," Working Papers 2011-20, Center for Research in Economics and Statistics.
    3. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    4. Ichimura, Hidehiko & Thompson, T. Scott, 1998. "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution," Journal of Econometrics, Elsevier, vol. 86(2), pages 269-295, June.
    5. repec:oup:restud:v:78:y::i:4:p:1264-1298 is not listed on IDEAS
    6. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    7. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    8. 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.
    9. Stefan Hoderlein, 2009. "Endogenous Semiparametric Binary Choice Models with Heteroscedasticity," Boston College Working Papers in Economics 747, Boston College Department of Economics, revised 29 Sep 2014.
    10. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
    11. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    12. Briesch, Richard A. & Chintagunta, Pradeep K. & Matzkin, Rosa L., 2010. "Nonparametric Discrete Choice Models With Unobserved Heterogeneity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 291-307.
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    Cited by:

    1. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.

    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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