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. In this paper, we derive the influence functions of the endogenous probit model's classical estimators (the maximum likelihood and the two-step estimator) and prove their non-robustness to small but harmful deviations from distributional assumptions. We propose a procedure to obtain a robust alternative estimator, prove its asymptotic normality and provide its asymptotic variance. A simple robust test for endogeneity is also constructed. We compare the performance of the robust and classical estimators in Monte Carlo simulations with different types of contamination scenarios. The use of our estimator is illustrated in several empirical applications.
A new and rapidly growing econometric literature is making advances in the problem of using machine learning methods for causal inference questions. Yet, the empirical economics literature has not started to fully exploit the strengths of these modern methods. We revisit influential empirical studies with causal machine learning methods and identify several advantages of using these techniques. We show that these advantages and their implications are empirically relevant and that the use of these methods can improve the credibility of causal analysis.
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