Monotone Confounding, Monotone Treatment Selection and Monotone Treatment Response

Jiang Zhichao, Chiba Yasutaka () and VanderWeele Tyler J. ()
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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

Journal of Causal Inference, 2014, vol. 2, issue 1, 1-12

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.

Keywords: bias; endogeneity; nonparametric bounds; partial identification (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:2:y:2014:i:1:p:12:n:1

DOI: 10.1515/jci-2012-0006

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