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Bounds on direct and indirect effects under treatment/mediator endogeneity and outcome attrition

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Document pages: 34 pages

Abstract: Causal mediation analysis aims at disentangling a treatment effect into anindirect mechanism operating through an intermediate outcome or mediator, aswell as the direct effect of the treatment on the outcome of interest. However,the evaluation of direct and indirect effects is frequently complicated bynon-ignorable selection into the treatment and or mediator, even aftercontrolling for observables, as well as sample selection outcome attrition. Wepropose a method for bounding direct and indirect effects in the presence ofsuch complications using a method that is based on a sequence of linearprogramming problems. Considering inverse probability weighting by propensityscores, we compute the weights that would yield identification in the absenceof complications and perturb them by an entropy parameter reflecting a specificamount of propensity score misspecification to set-identify the effects ofinterest. We apply our method to data from the National Longitudinal Survey ofYouth 1979 to derive bounds on the explained and unexplained components of agender wage gap decomposition that is likely prone to non-ignorable mediatorselection and outcome attrition.

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