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An instrumental variable random coefficients model for binary outcomes

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  • Andrew Chesher

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

  • Adam Rosen

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

Abstract

In this paper we study a random coefficient model for a binary outcome. We allow for the possibility that some or even all of the regressors 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 generalised instrumental variable models studied in Chesher and Rosen (2012a), and we thus apply identification results from that and related studies 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.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP34/12.

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Date of creation: Oct 2012
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Handle: RePEc:ifs:cemmap:34/12

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Related research

Keywords: random coefficients; instrumental variables; endogeneity; incomplete models; set identification; partial identification; random sets;

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References

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  1. Aviv Nevo, 2010. "Empirical Models of Consumer Behavior," NBER Working Papers 16511, National Bureau of Economic Research, Inc.
  2. 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.
  3. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2010. "Sharp identification regions in models with convex moment predictions," CeMMAP working papers CWP25/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Eric Gautier & Erwan Le Pennec, 2011. "Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding," Working Papers inria-00601274, HAL.
  5. 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 403-26, March.
  6. repec:oup:restud:v:78:y::i:4:p:1264-1298 is not listed on IDEAS
  7. Stefan Hoderlein, 2009. "Endogenous Semiparametric Binary Choice Models with Heteroscedasticity," Boston College Working Papers in Economics 747, Boston College Department of Economics.
  8. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, 03.
  9. Eric Gautier & Yuichi Kitamura, 2011. "Nonparamatric estimation in random coefficients binary choice models," Working Papers hal-00403939, HAL.
  10. 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.
  11. 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.
  12. Patrick Bajari & Jeremy Fox & Kyoo il Kim & Stephen P. Ryan, 2009. "The Random Coefficients Logit Model Is Identified," NBER Working Papers 14934, National Bureau of Economic Research, Inc.
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