Ridge regularization for Mean Squared Error Reduction in Regression with Weak Instruments

Karthik Rajkumar

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arXiv · 1904.08580

Ridge regularization for Mean Squared Error Reduction in Regression with Weak Instruments

Karthik Rajkumar

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Abstract

In this paper, I show that classic two-stage least squares (2SLS) estimates are highly unstable with weak instruments. I propose a ridge estimator (ridge IV) and show that it is asymptotically normal even with weak instruments, whereas 2SLS is severely distorted and un-bounded. I motivate the ridge IV estimator as a convex optimization problem with a GMM objective function and an L2 penalty. I show that ridge IV leads to sizable mean squared error reductions theoretically and validate these results in a simulation study inspired by data designs of papers published in the American Economic Review.

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BibTeX RIS

Karthik Rajkumar. 2019-04-18. Ridge regularization for Mean Squared Error Reduction in Regression with Weak Instruments. https://arxiv.org/abs/1904.08580

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