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Causal inference with imperfect instrumental variables

Author

Listed:
  • Miklin Nikolai

    (International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk, 80-308 Gdansk, Poland)

  • Gachechiladze Mariami

    (Department of Physics, Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany)

  • Moreno George

    (International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, P. O. Box 1613, Natal, Brazil)

  • Chaves Rafael

    (International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, P. O. Box 1613, Natal, Brazil)

Abstract

Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption, which states that the instrument and any confounding factor must be independent. However, if this independence condition is not met, can we still work with imperfect instrumental variables? Imperfect instruments can manifest themselves by violations of the instrumental inequalities that constrain the set of correlations in the scenario. In this article, we establish a quantitative relationship between such violations of instrumental inequalities and the minimal amount of measurement dependence required to explain them for the case of discrete observed variables. As a result, we provide adapted inequalities that are valid in the presence of a relaxed measurement dependence assumption in the instrumental scenario. This allows for the adaptation of existing and new lower bounds on the average causal effect for instrumental scenarios with binary outcomes. Finally, we discuss our findings in the context of quantum mechanics.

Suggested Citation

  • Miklin Nikolai & Gachechiladze Mariami & Moreno George & Chaves Rafael, 2022. "Causal inference with imperfect instrumental variables," Journal of Causal Inference, De Gruyter, vol. 10(1), pages 45-63, January.
    • Handle: RePEc:bpj:causin:v:10:y:2022:i:1:p:45-63:n:1
    DOI: 10.1515/jci-2021-0065
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    References listed on IDEAS

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    1. Matthew A. Masten & Alexandre Poirier & Linqi Zhang, 2024. "Assessing Sensitivity to Unconfoundedness: Estimation and Inference," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(1), pages 1-13, January.
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