  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.
