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...

Abstract Standard causal mediation analysis decomposes the total effect into a direct effect and an indirect effect in settings with only one single mediator. Under the settings with multiple mediators, all mediators are often treated as one single block of mediators. The effect mediated by a...