This paper proposes a new two stage least squares (2SLS) estimator which is consistent and asymptotically normal in the presence of many weak instruments and heteroskedasticity. The first stage of the estimator consists of two components: first, an adaptive absolute shrinkage and selection operator (LASSO) that selects the instruments; and second, an OLS regression with the selected regressors....

Two-stage least squares (2SLS) is commonly used to obtain consistent structural parameter inferences and asymptotically-valid inference results where one or more explanatory variables is – due to endogeneity, measurement error, etc.– correlated with the model error term. But the validity of 2SLS rests on an assumption that each of the instruments used is itself is unflawed – i.e., uncorrelated ...