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

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

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KIM, Namhyun, Winfried POHLMEIER, 2016. A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments. In: Oxford Bulletin of Economics and Statistics. 78(6), pp. 915-924. ISSN 0305-9049. eISSN 1468-0084

@article{Kim2016-07-23Regul-36281, title={A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments}, year={2016}, doi={10.1111/obes.12144}, number={6}, volume={78}, issn={0305-9049}, journal={Oxford Bulletin of Economics and Statistics}, pages={915--924}, author={Kim, Namhyun and Pohlmeier, Winfried} }

eng Kim, Namhyun The presence of weak instruments is translated into a nearly singular problem in a control function representation. Therefore, the L<sub>2</sub>-norm type of regularization is proposed to implement the 2SLS estimation for addressing the weak instrument problem. The L<sub>2</sub>-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 L<sub>2</sub>-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. Kim, Namhyun 2016-12-13T12:29:06Z 2016-12-13T12:29:06Z 2016-07-23 Pohlmeier, Winfried A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments Pohlmeier, Winfried

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