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Simple Estimators for Binary Choice Models with Endogenous Regressors


  • Yingying Dong

    () (Department of Economics, University of California-Irvine)

  • Arthur Lewbel

    () (Department of Economics, Boston College)


This paper provides simple estimators for binary choice models with endogenous or mismeasured regressors. Unlike control function methods, which are generally only valid when endogenous regressors are continuous, the estimators proposed here can be used with limited, censored, continuous, or discrete endogenous regressors, and they also allow for latent errors having heteroskedasticity of unknown form, including random coefficients. The variants of special regressor based estimators we provide are numerically trivial to implement. We illustrate these methods with an empirical application estimating migration probabilities within the US.

Suggested Citation

  • Yingying Dong & Arthur Lewbel, 2012. "Simple Estimators for Binary Choice Models with Endogenous Regressors," Working Papers 111204, University of California-Irvine, Department of Economics.
  • Handle: RePEc:irv:wpaper:111204

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    1. Augusto Mendoza Calderón, 2017. "El Efecto del Empleo sobre la Violencia Doméstica: Evidencia para las Mujeres Peruanas," Working Papers 2017-99, Peruvian Economic Association.
    2. Frédéric Lesne, 2013. "School Fees, Parental Participation and Accountability: Evidence from Madagascar," Working Papers halshs-00825244, HAL.
    3. Giuseppe De Luca & Valeria Perotti, 2011. "Estimation of ordered response models with sample selection," Stata Journal, StataCorp LP, vol. 11(2), pages 213-239, June.
    4. repec:bla:jorssa:v:180:y:2017:i:3:p:793-816 is not listed on IDEAS
    5. Anna-Elisabeth Thum & Miroslav Beblavy, 2014. "Do Acquaintances and Friends Make Us Learn?: Social Capital and Lifelong Learning in Germany," SOEPpapers on Multidisciplinary Panel Data Research 673, DIW Berlin, The German Socio-Economic Panel (SOEP).
    6. Alexander Ahammer & G. Thomas Horvath & Rudolf Winter-Ebmer, 2017. "The effect of income on mortality—new evidence for the absence of a causal link," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 793-816, June.
    7. Carvalho, José Raimundo & Marinho, Emerson & Loria, Francesca, 2012. "Idleness, returns to education and child labor," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 66(4), December.
    8. repec:hal:wpaper:halshs-00825240 is not listed on IDEAS
    9. Lin, Wei & Wooldridge, Jeffrey M., 2015. "On different approaches to obtaining partial effects in binary response models with endogenous regressors," Economics Letters, Elsevier, vol. 134(C), pages 58-61.
    10. Dagsvik, John K, 2017. "Invariance Axioms and Functional Form Restrictions in Structural Models," Memorandum 08/2017, Oslo University, Department of Economics.
    11. Changhui Kang & Myoung-jae Lee, 2014. "Estimation of Binary Response Models With Endogenous Regressors," Pacific Economic Review, Wiley Blackwell, vol. 19(4), pages 502-530, October.
    12. repec:eee:foreco:v:26:y:2017:i:c:p:56-62 is not listed on IDEAS

    More about this item


    Binary choice; Binomial response; Endogeneity; Measurement error; Heteroskedasticity; Discrete endogenous regressor; Censored regressor; Random coefficients; Identification; Latent variable model;

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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