Identification of the outcome distribution and sensitivity analysis under weak confounder-instrument interaction

Recently, Wang and Tchetgen Tchetgen (2018) showed that the global average treatment effect is identifiable even in the presence of unmeasured confounders so long as they do not modify the instrument's additive effect on the treatment. We use a simple and direct method to show that this no-interaction assumption allows identification of the entire outcome distribution, which leads to multiply robust estimation procedures for nonlinear functionals like the quantile and Mann-Whitney treatment effects. Similarly, we can bound these causal estimands through the outcome distribution in sensitivity analysis against confounder-instrument interaction.