Robust Estimation of Probit Models with Endogeneity

Andrea A. Naghi, Máté Váradi, Mikhail Zhelonkin*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)


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.

Original languageEnglish
JournalEconometrics and Statistics
Publication statusPublished - 11 May 2022

Bibliographical note

Funding Information:
The authors thank the Editor, the Associate Editor and two anonymous referees for very constructive and helpful comments which improved the original version of the manuscript. Naghi acknowledges partial support of EU Horizon 2020, Marie Skłodowska-Curie individual grant (No. 797286).

Publisher Copyright:
© 2022 The Author(s)


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