The Adaptive Lasso Method for Instrumental Variable Selection
نویسنده
چکیده
Adaptive lasso is a weighted `1 penalization method for simultaneous estimation and model selection. It has oracle properties of asymptotic normality with optimal convergence rate and model selection consistency. Instrumental variable selection has become the focus of much research in areas of application for which datasets with both strong and weak instruments are available. This paper develops an adaptive lasso method to select instrumental variables. We suggest standard two-stage least squares (TSLS) regression after the selection. Adaptive lasso is continuous and convex so that it can avoid the local optimization trap. In this paper we extend the technique of adaptive lasso to multivariate linear model framework and the situation in which we have weak instruments. Adaptive lasso estimates irrelevant instruments as 0 asymptotically as if it were known. In simulations we show adaptive lasso can select the strong instrumental variable consistently therefore improve the accuracy of the inference of TSLS.
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