Robust Estimation of Probit Models with Endogeneity

Andrea A. Naghi, Máté Váradi and Mikhail Zhelonkin
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Andrea A. Naghi: Erasmus University Rotterdam
Máté Váradi: Erasmus University Rotterdam
Mikhail Zhelonkin: Erasmus University Rotterdam

No 21-004/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Binary outcomes; Probit model; Endogenous variable; Instrumental variable; Robust Estimation (search for similar items in EconPapers)
JEL-codes: C13 C18 C26 (search for similar items in EconPapers)
Date: 2021-01-14
New Economics Papers: this item is included in nep-dcm, nep-ecm and nep-ore
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