Binary response model with many weak instruments

TL;DR

This paper introduces regularized estimators for endogenous binary response models with many weak instruments, improving estimation accuracy over existing methods, demonstrated through simulations and an application to family income's effect on college completion.

Contribution

It develops two novel regularized estimators, RCMLE and RNLSE, tailored for binary response models with many weak instruments, enhancing estimation reliability.

Findings

Proposed estimators outperform existing methods in simulations.

Estimators are consistent and asymptotically normal.

Application shows practical usefulness in social science research.

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.