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Inference with Many Weak Instruments

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  • Anna Mikusheva
  • Liyang Sun

Abstract

We develop a concept of weak identification in linear instrumental variable models in which the number of instruments can grow at the same rate or slower than the sample size. We propose a jackknifed version of the classical weak identification-robust Anderson–Rubin (AR) test statistic. Large-sample inference based on the jackknifed AR is valid under heteroscedasticity and weak identification. The feasible version of this statistic uses a novel variance estimator. The test has uniformly correct size and good power properties. We also develop a pre-test for weak identification that is related to the size property of a Wald test based on the Jackknife Instrumental Variable Estimator. This new pre-test is valid under heteroscedasticity and with many instruments.

Suggested Citation

  • Anna Mikusheva & Liyang Sun, 2022. "Inference with Many Weak Instruments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2663-2686.
    • Handle: RePEc:oup:restud:v:89:y:2022:i:5:p:2663-2686.
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    File URL: http://hdl.handle.net/10.1093/restud/rdab097
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