Robust Estimation of Probit Models with Endogeneity

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. 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.

Corporate social responsibility and credit rating: evidence from French companies

“…This instrument is likely to be exogenous to the CSR score. We used the Probit models with endogenous regressors, which are commonly used in economics and other social sciences (Naghi et al , 2020). The advantage of this method lies in its ability to handle endogenous regressors more rigorously and accurately.…”