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Structural modeling of simultaneous discrete choice

Author

Listed:
  • Andrew Chesher

    (Institute for Fiscal Studies and University College London)

  • Adam Rosen

    (Institute for Fiscal Studies and Duke University)

Abstract
Models of simultaneous discrete choice may be incomplete, delivering multiple values of outcomes at certain values of the latent variables and covariates, and incoherent, delivering no values. Alternative approaches to accommodating incompleteness and incoherence are considered in a unifying framework afforded by the Generalized Instrumental Variable models introduced in Chesher and Rosen (2017). Sharp identification regions for parameters and functions of interest defined by systems of conditional moment equalities and inequalities are provided. Almost all empirical analysis of simultaneous discrete choice uses models that include parametric specifications of the distribution of unobserved variables. The paper provides characterizations of identified sets and outer regions for structural functions and parameters allowing for any distribution of unobservables independent of exogenous variables. The methods are applied to the models and data of Mazzeo (2002) and Kline and Tamer (2016) in order to study the sensitivity of empirical results to restrictions on equilibrium selection and the distribution of unobservable payoff shifters, respectively. Confidence intervals for individual parameter components are provided using a recently developed inference approach from Belloni, Bugni, and Chernozhukov (2018). The relaxation of equilibrium selection and distributional restrictions in these applications is found to greatly increase the width of resulting confidence intervals, but nonetheless the models continue to sign strategic interaction parameters.

Suggested Citation

  • Andrew Chesher & Adam Rosen, 2020. "Structural modeling of simultaneous discrete choice," CeMMAP working papers CWP9/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:9/20
    as

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    References listed on IDEAS

    as
    1. 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.
    2. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
    3. Amemiya, Takeshi, 1974. "Multivariate Regression and Simultaneous Equation Models when the Dependent Variables Are Truncated Normal," Econometrica, Econometric Society, vol. 42(6), pages 999-1012, November.
    4. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
    5. 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.
    6. 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.
    7. Blundell, Richard & Smith, Richard J., 1994. "Coherency and estimation in simultaneous models with censored or qualitative dependent variables," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 355-373.
    8. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Hoshino, Tadao & Yanagi, Takahide, 2023. "Treatment effect models with strategic interaction in treatment decisions," Journal of Econometrics, Elsevier, vol. 236(2).
    2. Tadao Hoshino, 2020. "A Pairwise Strategic Network Formation Model with Group Heterogeneity: With an Application to International Travel," Papers 2012.14886, arXiv.org, revised Feb 2021.
    3. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    4. Bei, Xinyue, 2024. "Local linearization based subvector inference in moment inequality models," Journal of Econometrics, Elsevier, vol. 238(1).

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