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Robust Estimation of Probit Models with Endogeneity

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  • Naghi, Andrea A.
  • Váradi, Máté
  • Zhelonkin, Mikhail

Abstract

Probit models with endogenous regressors are commonly used models in economics and other social sciences. Yet, the robustness properties of parametric estimators in these models have not been formally studied. The influence functions of the endogenous probit model’s classical estimators (the maximum likelihood and the two-step estimator) are derived and their non-robustness to small but harmful deviations from distributional assumptions is proven. A procedure to obtain a robust alternative estimator is proposed, its asymptotic normality is proven and its asymptotic variance is provided. A simple robust test for endogeneity is also constructed. The performance of the robust and classical estimators is compared in Monte Carlo simulations with different types of contamination scenarios. The use of the robust estimator is illustrated in several empirical applications.

Suggested Citation

  • Naghi, Andrea A. & Váradi, Máté & Zhelonkin, Mikhail, 2025. "Robust Estimation of Probit Models with Endogeneity," Econometrics and Statistics, Elsevier, vol. 34(C), pages 78-90.
    • Handle: RePEc:eee:ecosta:v:34:y:2025:i:c:p:78-90
    DOI: 10.1016/j.ecosta.2022.05.001
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    1. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.
    2. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
    3. Pia M. Orrenius & Madeline Zavodny, 2015. "Does Immigration Affect Whether US Natives Major in Science and Engineering?," Journal of Labor Economics, University of Chicago Press, vol. 33(S1), pages 79-108.
    4. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    5. Stéphane Bonhomme & Martin Weidner, 2018. "Minimizing sensitivity to model misspecification," CeMMAP working papers CWP59/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Gerber, Alan S. & Green, Donald P., 2000. "The Effects of Canvassing, Telephone Calls, and Direct Mail on Voter Turnout: A Field Experiment," American Political Science Review, Cambridge University Press, vol. 94(3), pages 653-663, September.
    7. Duncan, Gregory M., 1987. "A simplified approach to M-estimation with application to two-stage estimators," Journal of Econometrics, Elsevier, vol. 34(3), pages 373-389, March.
    8. Giorgio Brunello & Daniele Fabbri & Margherita Fort, 2013. "The Causal Effect of Education on Body Mass: Evidence from Europe," Journal of Labor Economics, University of Chicago Press, vol. 31(1), pages 195-223.
    9. Horrace, William C. & Oaxaca, Ronald L., 2006. "Results on the bias and inconsistency of ordinary least squares for the linear probability model," Economics Letters, Elsevier, vol. 90(3), pages 321-327, March.
    10. Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2020. "On the Informativeness of Descriptive Statistics for Structural Estimates," Econometrica, Econometric Society, vol. 88(6), pages 2231-2258, November.
    11. Zhelonkin, Mikhail & Genton, Marc G. & Ronchetti, Elvezio, 2012. "On the robustness of two-stage estimators," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 726-732.
    12. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    13. Mikhail Zhelonkin & Marc G. Genton & Elvezio Ronchetti, 2016. "Robust inference in sample selection models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 805-827, September.
    14. Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2020. "Reply to: Comments on “On the Informativeness of Descriptive Statistics for Structural Estimates”," Econometrica, Econometric Society, vol. 88(6), pages 2277-2279, November.
    15. Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.
    16. Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2017. "Measuring the Sensitivity of Parameter Estimates to Estimation Moments," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1553-1592.
    17. Meer, Jonathan & Rosen, Harvey S., 2004. "Insurance and the utilization of medical services," Social Science & Medicine, Elsevier, vol. 58(9), pages 1623-1632, May.
    18. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    19. Gabriela V. Cohen Freue & Hernan Ortiz-Molina & Ruben H. Zamar, 2013. "A Natural Robustification of the Ordinary Instrumental Variables Estimator," Biometrics, The International Biometric Society, vol. 69(3), pages 641-650, September.
    20. Isaiah Andrews & James H. Stock & Liyang Sun, 2019. "Weak Instruments in Instrumental Variables Regression: Theory and Practice," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 727-753, August.
    21. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    22. Cantoni, Eva & de Luna, Xavier, 2020. "Semiparametric inference with missing data: Robustness to outliers and model misspecification," Econometrics and Statistics, Elsevier, vol. 16(C), pages 108-120.
    23. Marco Avella-Medina, 2021. "Privacy-Preserving Parametric Inference: A Case for Robust Statistics," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 969-983, April.
    24. Mark Grinblatt & Matti Keloharju & Juhani Linnainmaa, 2011. "IQ and Stock Market Participation," Journal of Finance, American Finance Association, vol. 66(6), pages 2121-2164, December.
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