Sensitivity of Policy Relevant Treatment Parameters to Violations of Monotonicity
This paper proposes a method in an environment with heterogeneous treatment eﬀects to bound policy relevant treatment parameters (PRTP) without the monotonicity assumption that the instrumental variable works in the same direction for all individuals. While the procedure applies to all PRTP objects, this paper provides a detailed analysis for local average treatment eﬀects in counterfactual environments (LATE*) that does not yet have a procedure for sensitivity analysis to monotonicity violations. The bounding framework uses the proportion of deﬁers relative to compliers as a sensitivity parameter and yields an identiﬁed set that is an interval. The bounds are sharp for binary outcomes. The method is illustrated in an example where the same sex instrument is used to ﬁnd the eﬀect of having a third child on labor force participation. I ﬁnd that bounds are informative only for small violations in monotonicity.
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