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An instrumental variable model of multiple discrete choice

Author

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  • Andrew Chesher

    (Institute for Fiscal Studies and University College London)

  • Adam Rosen

    (Institute for Fiscal Studies and Duke University)

  • Konrad Smolinski

    (Institute for Fiscal Studies)

Abstract

This paper studies identification of latent utility functions in multiple discrete choice models in which there may be endogenous explanatory variables, that is explanatory variables that are not restricted to be distributed independently of the unobserved determinants of latent utilities. The model does not employ large support, special regressor or control function restrictions, indeed it is silent about the process delivering values of endogenous explanatory variables and in this respect it is incomplete. Instead the model employs instrumental variable restrictions requiring the existence of instrumental variables which are excluded from latent utilities and distributed independently of the unobserved components of utilities. We show that the model delivers set, not point, identification of the latent utility functions and we characterize sharp bounds on those functions. We develop easy-to-compute outer regions which in parametric models require little more calculation than what is involved in a conventional maximum likelihood analysis. The results are illustrated using a model which is essentially the parametric conditional logit model of McFadden (1974) but with potentially endogenous explanatory variables and instrumental variable restrictions. The method employed has wide applicability and for the first time brings instrumental variable methods to bear on structural models in which there are multiple unobservables in a structural equation. This paper has now been revised and the new version is available as CWP39/11.

Suggested Citation

  • Andrew Chesher & Adam Rosen & Konrad Smolinski, 2011. "An instrumental variable model of multiple discrete choice," CeMMAP working papers CWP06/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:06/11
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    References listed on IDEAS

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    Cited by:

    1. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers CWP65/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    3. Laffers, Lukas, 2013. "Identification in Models with Discrete Variables," Discussion Paper Series in Economics 1/2013, Norwegian School of Economics, Department of Economics.
    4. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2019. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," NBER Working Papers 25827, National Bureau of Economic Research, Inc.
    5. 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.
    6. V. Chernozhukov & C. Hansen, 2013. "Quantile Models with Endogeneity," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 57-81, May.
    7. Jiaying Gu & Thomas M. Russell, 2021. "Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors," Papers 2101.01254, arXiv.org.
    8. Lukáš Lafférs, 2019. "Identification in Models with Discrete Variables," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 657-696, February.
    9. Marc Henry & Ismael Mourifié, 2012. "Sharp Bounds in the Binary Roy Model," CIRJE F-Series CIRJE-F-835, CIRJE, Faculty of Economics, University of Tokyo.
    10. Victor Chernozhukov & Christian Hansen & Kaspar Wuthrich, 2020. "Instrumental Variable Quantile Regression," Papers 2009.00436, arXiv.org.
    11. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    12. Guevara, C. Angelo, 2015. "Critical assessment of five methods to correct for endogeneity in discrete-choice models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 82(C), pages 240-254.
    13. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. 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.
    15. 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.
    16. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.

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