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Measurement errors in the binary instrumental variable model

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  • Zhichao Jiang
  • Peng Ding

Abstract

Summary Instrumental variable methods can identify causal effects even when the treatment and outcome are confounded. We study the problem of imperfect measurements of the binary instrumental variable, treatment and outcome. We first consider nondifferential measurement errors, that is, the mismeasured variable does not depend on other variables given its true value. We show that the measurement error of the instrumental variable does not bias the estimate, that the measurement error of the treatment biases the estimate away from zero, and that the measurement error of the outcome biases the estimate toward zero. Moreover, we derive sharp bounds on the causal effects without additional assumptions. These bounds are informative because they exclude zero. We then consider differential measurement errors, and focus on sensitivity analyses in those settings.

Suggested Citation

  • Zhichao Jiang & Peng Ding, 2020. "Measurement errors in the binary instrumental variable model," Biometrika, Biometrika Trust, vol. 107(1), pages 238-245.
    • Handle: RePEc:oup:biomet:v:107:y:2020:i:1:p:238-245.
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    File URL: http://hdl.handle.net/10.1093/biomet/asz060
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    Cited by:

    1. Santiago Acerenza & Kyunghoon Ban & D'esir'e K'edagni, 2021. "Marginal Treatment Effects with a Misclassified Treatment," Papers 2105.00358, arXiv.org, revised Apr 2023.
    2. Kruse, Herman & Myhre, Andreas, 2021. "Early Retirement Provision for Elderly Displaced Workers," MPRA Paper 118689, University Library of Munich, Germany, revised 21 Sep 2023.
    3. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.
    4. Kruse, Herman & Myhre, Andreas, 2021. "Early Retirement Provision for Elderly Displaced Workers," MPRA Paper 109431, University Library of Munich, Germany.
    5. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.

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