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Identification in a Generalization of Bivariate Probit Models with Endogenous Regressors

Author

Listed:
  • Sukjin Han

    (Department of Economics, University of Texas at Austin)

  • Edward J. Vytlacil

    (Department of Economics, New York University)

Abstract

This paper provides identification results for a class of models specified by a triangular system of two equations with binary endogenous variables. The joint distribution of the latent error terms is specified through a parametric copula structure, including the normal copula as a special case, while the marginal distributions of the latent error terms are allowed to be arbitrary but known. This class of models includes bivariate probit models as a special case. The paper demonstrates that an exclusion restriction is necessary and sufficient for globally identification of the model parameters with the excluded variable allowed to be binary. Based on this result, identification is achieved in a full model where common exogenous regressors that are present in both equations and excluded instruments are possibly more general than discretely distributed.

Suggested Citation

  • Sukjin Han & Edward J. Vytlacil, 2013. "Identification in a Generalization of Bivariate Probit Models with Endogenous Regressors," Department of Economics Working Papers 130908, The University of Texas at Austin, Department of Economics.
    • Handle: RePEc:tex:wpaper:130908
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    References listed on IDEAS

    as
    1. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    2. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-512, March.
    3. Wilde, Joachim, 2000. "Identification of multiple equation probit models with endogenous dummy regressors," Economics Letters, Elsevier, vol. 69(3), pages 309-312, December.
    4. Freedman, David A. & Sekhon, Jasjeet S., 2010. "Endogeneity in Probit Response Models," Political Analysis, Cambridge University Press, vol. 18(2), pages 138-150, April.
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    Cited by:

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    4. Sengupta, Reshmi & Rooj, Debasis, 2019. "The effect of health insurance on hospitalization: Identification of adverse selection, moral hazard and the vulnerable population in the Indian healthcare market," World Development, Elsevier, vol. 122(C), pages 110-129.

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    More about this item

    Keywords

    Identification; triangular threshold crossing model; bivariate probit model; endogenous variables; binary response; copula; exclusion restriction;
    All these keywords.

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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