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A note on the identification in two equations probit model with dummy endogenous regressor

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  • Romuald Meango
  • Ismael Mourifie

Abstract

This paper deals with the question whether exclusion restrictions on the exogenous regressors are necessary to identify two equation probit models with endogenous dummy regressor. Contradictory opinions have been exposed in the literature on the necessity of an exclusion restriction. Wilde (2000) argued that an exclusion restriction is not necessary, and proposed a simple criterion for identi fication in this model. We contradict his result, and show how the inherent incompleteness of the model leads to failure of (point) identi cation. We provide an exact identification proof when an exclusion restriction is available.

Suggested Citation

  • Romuald Meango & Ismael Mourifie, 2013. "A note on the identification in two equations probit model with dummy endogenous regressor," Working Papers tecipa-503, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-503
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    References listed on IDEAS

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    1. Wilde, Joachim, 2000. "Identification of multiple equation probit models with endogenous dummy regressors," Economics Letters, Elsevier, vol. 69(3), pages 309-312, December.
    2. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    3. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. 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.
    5. Sartori, Anne E., 2003. "An Estimator for Some Binary-Outcome Selection Models Without Exclusion Restrictions," Political Analysis, Cambridge University Press, vol. 11(2), pages 111-138, April.
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    2. Filippini, Massimo & Greene, William H. & Kumar, Nilkanth & Martinez-Cruz, Adan L., 2018. "A note on the different interpretation of the correlation parameters in the Bivariate Probit and the Recursive Bivariate Probit," Economics Letters, Elsevier, vol. 167(C), pages 104-107.
    3. Santiago Acerenza & Otávio Bartalotti & Désiré Kédagni, 2023. "Testing identifying assumptions in bivariate probit models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 407-422, April.
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    6. Marlon R. Tracey & Chanita C. Holmes & Marvin G. Powell, 2024. "Parental limit-setting decisions and adolescent subject grades," Review of Economics of the Household, Springer, vol. 22(1), pages 143-171, March.
    7. Sukjin Han & Sungwon Lee, 2019. "Estimation in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 994-1015, September.
    8. Zhe Chen & Apurbo Sarkar & Md. Shakhawat Hossain & Xiaojing Li & Xianli Xia, 2021. "Household Labour Migration and Farmers’ Access to Productive Agricultural Services: A Case Study from Chinese Provinces," Agriculture, MDPI, vol. 11(10), pages 1-20, October.
    9. Lina Zhang & David T. Frazier & D. S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Papers 2009.02642, arXiv.org, revised Sep 2022.
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    13. Craig E. Landry & Dylan Turner & Daniel Petrolia, 2021. "Flood Insurance Market Penetration and Expectations of Disaster Assistance," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 79(2), pages 357-386, June.
    14. Böckerman, Petri & Ilmakunnas, Pekka, 2020. "Do good working conditions make you work longer? Analyzing retirement decisions using linked survey and register data," The Journal of the Economics of Ageing, Elsevier, vol. 17(C).
    15. Li, Chuhui & Poskitt, D.S. & Zhao, Xueyan, 2019. "The bivariate probit model, maximum likelihood estimation, pseudo true parameters and partial identification," Journal of Econometrics, Elsevier, vol. 209(1), pages 94-113.
    16. Zhou Xun, 2015. "Preference for Redistribution and Inequality Perception in China: Evidence from the CGSS 2006," AMSE Working Papers 1518, Aix-Marseille School of Economics, France.
    17. Giampiero Marra & Rosalba Radice & David M. Zimmer, 2020. "Estimating the binary endogenous effect of insurance on doctor visits by copula‐based regression additive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 953-971, August.
    18. Massimo Filippini & Suchita Srinivasan, 2020. "Voluntary adoption of environmental standards and limited attention: Evidence from the food and beverage industry in Vietnam," CER-ETH Economics working paper series 20/338, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    19. Han, Sukjin & Vytlacil, Edward J., 2017. "Identification in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Econometrics, Elsevier, vol. 199(1), pages 63-73.

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    More about this item

    Keywords

    Probit model; Endogenous dummy regressor; Partial identification;
    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

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