Robust Estimation of Probit Models with Endogeneity

Tinbergen Institute Discussion Paper 2021-004/III

29 Pages Posted: 10 Mar 2021

See all articles by Andrea Naghi

Andrea Naghi

Erasmus University Rotterdam (EUR)

Máté Váradi

Erasmus University Rotterdam (EUR)

Mikhail Zhelonkin

Erasmus University Rotterdam (EUR)

Date Written: December 20, 2020

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

JEL Classification: C26, C13, C18

Suggested Citation

Naghi, Andrea and Váradi, Máté and Zhelonkin, Mikhail, Robust Estimation of Probit Models with Endogeneity (December 20, 2020). Tinbergen Institute Discussion Paper 2021-004/III, Available at SSRN: https://ssrn.com/abstract=3766318 or http://dx.doi.org/10.2139/ssrn.3766318

Andrea Naghi (Contact Author)

Erasmus University Rotterdam (EUR) ( email )

Burgemeester Oudlaan 50
3000 DR Rotterdam, Zuid-Holland 3062PA
Netherlands

Máté Váradi

Erasmus University Rotterdam (EUR) ( email )

Burgemeester Oudlaan 50
3000 DR Rotterdam, Zuid-Holland 3062PA
Netherlands

Mikhail Zhelonkin

Erasmus University Rotterdam (EUR) ( email )

Burgemeester Oudlaan 50
3000 DR Rotterdam, Zuid-Holland 3062PA
Netherlands

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