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Monotone Confounding, Monotone Treatment Selection and Monotone Treatment Response

Author

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  • Jiang Zhichao

    (Peking University, Beijing, China)

  • Chiba Yasutaka

    (Division of Biostatistics, Clinical Research Center, Kinki University School of Medicine, Osaka, Japan)

  • VanderWeele Tyler J.

    (Departments of Epidemiology and Biostatistics, Harvard School of Public Health, Boston, MA, USA)

Abstract

Manski (Monotone treatment response. Econometrica 1997;65:1311–34) and Manski and Pepper (Monotone instrumental variables: with an application to the returns to schooling. Econometrica 2000;68:997–1010) gave sharp bounds on causal effects under the assumptions of monotone treatment response (MTR) and monotone treatment selection (MTS). VanderWeele (The sign of the bias of unmeasured confounding. Biometrics 2008;64:702–6) provided bounds for binary treatment under an assumption of monotone confounding (MC). We discuss the relation between MC and MTS and provide bounds under various combinations of these assumptions. We show that MC and MTS coincide for a binary treatment, but MC does not imply MTS for a treatment variable with more than two levels.

Suggested Citation

  • Jiang Zhichao & Chiba Yasutaka & VanderWeele Tyler J., 2014. "Monotone Confounding, Monotone Treatment Selection and Monotone Treatment Response," Journal of Causal Inference, De Gruyter, vol. 2(1), pages 1-12, March.
    • Handle: RePEc:bpj:causin:v:2:y:2014:i:1:p:12:n:1
    DOI: 10.1515/jci-2012-0006
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    References listed on IDEAS

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    1. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    2. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    3. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    4. Charles F. Manski & John V. Pepper, 2009. "More on monotone instrumental variables," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 200-216, January.
    5. Tyler J. VanderWeele, 2008. "The Sign of the Bias of Unmeasured Confounding," Biometrics, The International Biometric Society, vol. 64(3), pages 702-706, September.
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