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Assessing the strength of many instruments with the first-stage F and Cragg-Donald statistics

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  • Zhenhong Huang
  • Chen Wang
  • Jianfeng Yao

Abstract

This paper investigates the behavior of Stock and Yogo (2005)'s first-stage F statistic and the Cragg-Donald statistic (Cragg and Donald, 1993) when the number of instruments and the sample size go to infinity in a comparable magnitude. Our theory shows that the first-stage F test is oversized for detecting many weak instruments. We next propose an asymptotically valid correction of the F statistic for testing weakness of instruments. The theory is also used to construct confidence intervals for the strength of instruments. As for the Cragg-Donald statistic, we obtain an asymptotically valid correction in the case of two endogenous variables. Monte Carlo experiments demonstrate the satisfactory performance of the proposed methods in both situations of a single and multiple endogenous variables. The usefulness of the proposed tests is illustrated by an analysis of the returns to education data in Angrist and Keueger (1991).

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  • Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "Assessing the strength of many instruments with the first-stage F and Cragg-Donald statistics," Papers 2302.14423, arXiv.org.
    • Handle: RePEc:arx:papers:2302.14423
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