Figure 5.

DGPs with noncompliance. Three possible scenarios involving encouragement $Z$, treatment $X$, and outcome $Y$. Panel (b) represents the true simulation DGP, where $Z\to X$ monotonicity is violated (indicated by absence of a +). Panel (a) depicts assumptions used by an “overcautious” analyst unwilling to assume away a direct $Z\to Y$ effect. Panel (c) corresponds to an “overconfident” analyst that incorrectly assumes monotonicity of $Z\to X$.