title: Monotone Confounding, Monotone Treatment Selection and Monotone Treatment Response.
abstract: Manski (1997) and Manski and Pepper (2000) gave sharp bounds on causal effects under the assumptions of monotone treatment response (MTR) and monotone treatment selection (MTS). VanderWeele (2008) 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.
authors.affiliation: Departments of Epidemiology and biostatistics, Harvard School of Public Health, Boston, MA, USA, tvanderw@hsph.harvard.edu.
authors.forename: Tyler J
authors.initials: TJ
authors.lastname: VanderWeele
authors.affiliation: Peking University, Beijing, China.
authors.forename: Zhichao
authors.initials: Z
authors.lastname: Jiang
authors.affiliation: Division of Biostatistics, Clinical Research Center, Kinki University School of Medicine, Osaka, Japan, chibay@med.kindai.ac.jp.
authors.forename: Yasutaka
authors.initials: Y
authors.lastname: Chiba
keywords: bias; endogeneity; nonparametric bounds; partial identification