A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments

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Oxford Bulletin of Economics and Statistics. 2016, 78(6), pp. 915-924. ISSN 0305-9049. eISSN 1468-0084. Available under: doi: 10.1111/obes.12144
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The presence of weak instruments is translated into a nearly singular problem in a control function representation. Therefore, the L2-norm type of regularization is proposed to implement the 2SLS estimation for addressing the weak instrument problem. The L2-norm regularization with a regularized parameter O(n) allows us to obtain the Rothenberg (1984) type of higher-order approximation of the 2SLS estimator in the weak instrument asymptotic framework. The proposed regularized parameter yields the regularized concentration parameter O(n), which is used as a standardized factor in the higher-order approximation. We also show that the proposed L2-norm regularization consequently reduces the finite sample bias. A number of existing estimators that address finite sample bias in the presence of weak instruments, especially Fuller's limited information maximum likelihood estimator, are compared with our proposed estimator in a simple Monte Carlo exercise.

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ISO 690KIM, Namhyun, Winfried POHLMEIER, 2016. A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments. In: Oxford Bulletin of Economics and Statistics. 2016, 78(6), pp. 915-924. ISSN 0305-9049. eISSN 1468-0084. Available under: doi: 10.1111/obes.12144
BibTex
@article{Kim2016-07-23Regul-36281,
  year={2016},
  doi={10.1111/obes.12144},
  title={A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments},
  number={6},
  volume={78},
  issn={0305-9049},
  journal={Oxford Bulletin of Economics and Statistics},
  pages={915--924},
  author={Kim, Namhyun and Pohlmeier, Winfried}
}
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