Confounder-instrument interaction
= Confounder-instrument interaction
A confounder-instrument interaction occurs when an instrument's effect on treatment varies with a variable that also affects the outcome. If the conditional first-stage effect is $\delta(U)=\mathbb E[A\mid Z=1,U]-\mathbb E[A\mid Z=0,U]$, absence of this interaction means that $\delta(U)$ is constant.