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A Regularization Approach to Biased Two-Stage Least Squares Estimation

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  • Nam-Hyun Kim

    (Department of Economics, University of Konstanz, Germany)

  • Winfried Pohlmeier

    (Department of Economics, University of Konstanz, Germany; The Rimini Centre for Economic Analysis, Italy)

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.

Suggested Citation

  • Nam-Hyun Kim & Winfried Pohlmeier, 2015. "A Regularization Approach to Biased Two-Stage Least Squares Estimation," Working Paper series 15-22, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:15-22
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    References listed on IDEAS

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