Estimation of Binary Response Models With Endogenous Regressors

Abstract

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).

Instrument Residual Estimator for Any Response Variable with Endogenous Binary Treatment

“…Basu et al (2018) further obtained the same finding with binary D and Z, and noted that SUB is fine for E(Y 1 − Y 0 |complier), although biased for E(Y 1 − Y 0 ). In Kang and Lee (2014), both approaches performed comparably. Although ζ X can be estimated nonparametrically, to keep IRE practical, we use the probit of Z on X, which can be done in a 'standard' way, as propensity score estimation with probit/logit is widely practiced.…”