A two-stage Bridge estimator for regression models with endogeneity based on control function method.

In this study, we investigate a penalty-based two-stage least square estimator in regression models when the exploratory variables are correlated with the error term. We propose a two-stage Bridge estimator to overcome this endogeneity problem in high-dimensional data. Our proposed estimator enjoys remarkable statistical properties such as consistency and asymptotic normality. As special cases, this method deals some ill-condition situations such as the multicollinearity as well as the sparsity. Performance of the proposed estimators is demonstrated by simulation studies and it is compared to the existing estimators. An application in real data set is presented for illustration. [ABSTRACT FROM AUTHOR]