Misclassification-robust semiparametric estimation of single-index binary-choice models

In this paper, a new class of semiparametric estimators for single-index binary-choice models is introduced. The proposed estimators are based on the semiparametric indirect inference that identifies and estimates the parameters of the model via possibly misspecified auxiliary criteria. A large class of considered auxiliary criteria includes the ordinary least squares, nonlinear least squares, and nonlinear least absolute deviations estimators. Besides deriving the consistency and asymptotic normality of the proposed methods, we demonstrate that the proposed indirect inference methodology—at least for selected auxiliary criteria—combines weak distributional assumptions, good estimation precision, and robustness to misclassification of responses. We conduct Monte Carlo experiments and an application study to compare the finite-sample performance of the proposed and existing estimators.