A note on bounding average treatment effects

Imposing the monotone treatment selection (MTS) assumption and the monotone instrumental variable (MIV) assumption implies bounds on average treatment effect that differ from those commonly reported in the applied literature. Instead, for the bounds to be correct, we should use an MTS assumption conditional on the value of a monotone instrument (cMTS). In this paper, we present an empirical example of bounding the effect of the mother's education on her children's education, in which the MTS and cMTS assumptions lead to considerably different bounds on the treatment effects.