Xinyi Xu, Xiangjie Li, Jingxiao Zhang

【Abstract】

Traditional penalty-based methods might not achieve variable selection consistency when endogeneity exists in high-dimensional data. In this article we construct a regularization framework based on the two-stage control function model, so called the regularized control function (RCF) method, to estimate important covariate effects, select key instruments, and replace the CF-based hypothesis test with variable selection to identify truly endogenous predictors. Under appropriate conditions, we establish theoretical properties of the RCF estimators, including the consistency of coefficient estimation and model selection. Simulation results confirm that the RCF method is effective and superior to its main competitor, the penalized least squares (PLS) method. The proposed method also provides insightful and interpretable results on a real data analysis.

【Keywords】

endogeneity, regularization, control function, consistency of estimation, model selection, penalized least squares