Semiparametric IV Estimation and Model Selection with Weak Instruments and Heteroskedasticity

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. The adaptive LASSO is constructed to allow the possibility of either a nonparametric or parametric model. The second stage uses an OLS regression with the fitted values of the first stage. The methodology exploits the model selection benefits of the adaptive LASSO, reduces its post-selection bias, and is the first time a nonparametric adaptive LASSO is analyzed in the presence of instrument weakness.