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

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  • Karthik Rajkumar

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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  • Karthik Rajkumar, 2019. "Ridge regularization for Mean Squared Error Reduction in Regression with Weak Instruments," Papers 1904.08580, arXiv.org.
    • Handle: RePEc:arx:papers:1904.08580
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    References listed on IDEAS

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    1. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
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