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Identifying causal effects with proxy variables of an unmeasured confounder

Author

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  • Wang Miao
  • Zhi Geng
  • Eric J Tchetgen Tchetgen

Abstract

SUMMARYWe consider a causal effect that is confounded by an unobserved variable, but for which observed proxy variables of the confounder are available. We show that with at least two independent proxy variables satisfying a certain rank condition, the causal effect can be nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the confounder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014), which rests on identification of the measurement error mechanism. When only one proxy for the confounder is available, or when the required rank condition is not met, we develop a strategy for testing the null hypothesis of no causal effect.

Suggested Citation

  • Wang Miao & Zhi Geng & Eric J Tchetgen Tchetgen, 2018. "Identifying causal effects with proxy variables of an unmeasured confounder," Biometrika, Biometrika Trust, vol. 105(4), pages 987-993.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:4:p:987-993.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy038
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    Citations

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    Cited by:

    1. AmirEmad Ghassami & Andrew Ying & Ilya Shpitser & Eric Tchetgen Tchetgen, 2021. "Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference," Papers 2104.02929, arXiv.org, revised Mar 2022.
    2. AmirEmad Ghassami & Alan Yang & David Richardson & Ilya Shpitser & Eric Tchetgen Tchetgen, 2022. "Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects," Papers 2201.10743, arXiv.org, revised Apr 2022.
    3. Crucinio, Francesca R. & De Bortoli, Valentin & Doucet, Arnaud & Johansen, Adam M., 2024. "Solving a class of Fredholm integral equations of the first kind via Wasserstein gradient flows," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    4. Rahul Singh, 2020. "Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments," Papers 2012.10315, arXiv.org, revised Mar 2023.
    5. Peña Jose M., 2020. "On the Monotonicity of a Nondifferentially Mismeasured Binary Confounder," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 150-163, January.
    6. Claudia Shi & Dhanya Sridhar & Vishal Misra & David M. Blei, 2021. "On the Assumptions of Synthetic Control Methods," Papers 2112.05671, arXiv.org, revised Dec 2021.
    7. Guido Imbens & Nathan Kallus & Xiaojie Mao, 2021. "Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models," Papers 2108.03849, arXiv.org.
    8. Pengzhou Wu & Kenji Fukumizu, 2021. "Towards Principled Causal Effect Estimation by Deep Identifiable Models," Papers 2109.15062, arXiv.org, revised Nov 2021.
    9. Ben Deaner, 2022. "Controlling for Latent Confounding with Triple Proxies," Papers 2204.13815, arXiv.org, revised May 2023.
    10. Rahul Singh, 2021. "Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimension," Papers 2102.11076, arXiv.org, revised Jul 2024.
    11. Andrew Bennett & Nathan Kallus & Xiaojie Mao & Whitney Newey & Vasilis Syrgkanis & Masatoshi Uehara, 2022. "Inference on Strongly Identified Functionals of Weakly Identified Functions," Papers 2208.08291, arXiv.org, revised Jun 2023.
    12. Ben Deaner, 2021. "Many Proxy Controls," Papers 2110.03973, arXiv.org.
    13. Zhang, Jeffrey & Li, Wei & Miao, Wang & Tchetgen Tchetgen, Eric, 2023. "Proximal causal inference without uniqueness assumptions," Statistics & Probability Letters, Elsevier, vol. 198(C).
    14. Liu, Lin & Mukherjee, Rajarshi & Robins, James M., 2024. "Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators," Journal of Econometrics, Elsevier, vol. 240(2).
    15. Peña Jose M., 2020. "On the Monotonicity of a Nondifferentially Mismeasured Binary Confounder," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 150-163, January.
    16. Ziyu Wang & Yucen Luo & Yueru Li & Jun Zhu & Bernhard Scholkopf, 2022. "Spectral Representation Learning for Conditional Moment Models," Papers 2210.16525, arXiv.org, revised Dec 2022.
    17. Yilin Li & Wang Miao & Ilya Shpitser & Eric J. Tchetgen Tchetgen, 2023. "A self‐censoring model for multivariate nonignorable nonmonotone missing data," Biometrics, The International Biometric Society, vol. 79(4), pages 3203-3214, December.
    18. Christian Tien, 2022. "Instrumented Common Confounding," Papers 2206.12919, arXiv.org, revised Sep 2022.
    19. Lan Liu & Eric Tchetgen Tchetgen, 2022. "Regression‐based negative control of homophily in dyadic peer effect analysis," Biometrics, The International Biometric Society, vol. 78(2), pages 668-678, June.
    20. Isaac Meza & Rahul Singh, 2021. "Nested Nonparametric Instrumental Variable Regression: Long Term, Mediated, and Time Varying Treatment Effects," Papers 2112.14249, arXiv.org, revised Mar 2024.

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