A Regularization Approach to Biased Two-Stage Least Squares Estimation
We propose to apply â€“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 of creation:||Jun 2015|
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- Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
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- Bun, Maurice J.G. & Windmeijer, Frank, 2011. "A comparison of bias approximations for the two-stage least squares (2SLS) estimator," Economics Letters, Elsevier, vol. 113(1), pages 76-79, October.
- Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May. Full references (including those not matched with items on IDEAS)
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