Binary response model with many weak instruments

Abstract: This paper considers an endogenous binary response model with many weak instruments. We employ a control function approach and a regularization scheme to obtain better estimation results for the endogenous binary response model in the presence of many weak instruments. Two consistent and asymptotically normally distributed estimators are provided, each of which is called a regularized conditional maximum likelihood estimator (RCMLE) and a regularized nonlinear least squares estimator (RNLSE). Monte Carlo simulations show that the proposed estimators outperform the existing ones when there are many weak instruments. We use the proposed estimation method to examine the effect of family income on college completion.