Estimation of Binary Response Models With Endogenous Regressors

This paper reviews six approaches to binary response (y₁) structural forms with an endogenous regressor y₂: (i) the two-stage least squares estimator-like substitution approach, (ii) the control function approach, (iii) the system reduced-form approach, (iv) the artificial instrumental regressor approach, (v) the transformed-response instrumental variable estimator approach and (vi) the classical maximum likelihood estimator approach. The applicability of the six methods differs greatly, depending on whether y₂ is a continuously distributed random variable or a discrete transformation of a latent y 2 *. We conduct a real-data-based simulation study, and provide an empirical illustration. Our overall recommendation is using (i) and (ii), as the others have undesirable features such as analytic complexity in (iii), computational difficulty in (iv) and (vi), and poor finite-sample performance in (v).