Sensitivity of Policy‐Relevant Treatment Parameters to Violations of Monotonicity

ABSTRACT This paper proposes a method to bound policy‐relevant treatment parameters (PRTPs) when the monotonicity assumption that the IV affects individuals' treatment response in the same direction is weakened. 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 method is illustrated in an empirical application where the same‐sex instrument was used to calculate the effect of having a third child on labor force participation. I find that bounds are informative only for small violations in monotonicity.