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Revisiting the Many Instruments Problem using Random Matrix Theory

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  • Helmut Farbmacher
  • Rebecca Groh
  • Michael Muhlegger
  • Gabriel Vollert

Abstract

We use recent results from the theory of random matrices to improve instrumental variables estimation with many instruments. In settings where the first-stage parameters are dense, we show that Ridge lowers the implicit price of a bias adjustment. This comes along with improved (finite-sample) properties in the second stage regression. Our theoretical results nest existing results on bias approximation and bias adjustment. Moreover, it extends them to settings with more instruments than observations.

Suggested Citation

  • Helmut Farbmacher & Rebecca Groh & Michael Muhlegger & Gabriel Vollert, 2024. "Revisiting the Many Instruments Problem using Random Matrix Theory," Papers 2408.08580, arXiv.org.
    • Handle: RePEc:arx:papers:2408.08580
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    References listed on IDEAS

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    7. Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
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    9. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
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