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A Regularization Approach to Biased Two-Stage Least Squares Estimation

Nam-Hyun Kim () and Winfried Pohlmeier ()
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Nam-Hyun Kim: Department of Economics, University of Konstanz, Germany

Working Paper series from Rimini Centre for Economic Analysis

Abstract: We propose to apply –norm regularization to address the problem of weak and/or many instruments. We observe that the presence of weak instruments, or weak and many instruments is translated into a nearly singular problem in a control function representation. Hence, we show that mean squares error-optimal -norm regularization with a small sample size reduces the bias and variance of the regularized 2SLS estimators with the presence of weak and/or many instruments. A number of different strategies for choosing a regularization parameter are introduced and compared in a Monte Carlo study.

Date: 2015-06
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