ICEF Job Market Seminar by Dakyung Seong (UC Davis)
Speaker: Dakyung Seong (UC Davis)Theme: "Binary Response Model with Many Weak Instrumental Variables"
Abstract: This paper considers an endogenous binary response model with many weak instruments. Unlike linear simultaneous equation models where asymptotic properties of (regularized) k-class estimators are well established even in the presence of such instrumental variables, the endogenous binary response model with many weak instruments has received very limited attention from econometricians in spite of its practical importance. In this paper, we provide two consistent and asymptotically normally distributed estimators based on first stage ridge-regularization, which are called a ridge-regularized conditional maximum likelihood estimator (RCMLE) and a ridge-regularized nonlinear least square estimator (RNLSE). Ridge-regularization is adopted in the first stage because other regularizations accompanying with variable selections may not be feasible due to a lack of signal in the first stage. We also provide consistent estimators of their asymptotic variances which make inference based on the RCMLE and the RNLSE feasible. Monte Carlo simulations show that the RCMLE and the RNLSE outperform existing estimators when many weak instruments are used in the first stage. We apply the proposed estimators to two empirical examples. In the first example, we examine the effect of education on being employed for a full calendar year. The second example illustrates the effect of children’s development on maternal employment status using various instrumental variables.