Compliance with the treatment assignment influences which causal estimand we calculate:

- When compliance is perfect, the treatment assignment and treatment received can be used interchangeably to get an accurate estimate of the causal effect.
- When compliance is NOT perfect, we cannot estimate the average treatment effect (ATE) because treatment assignment and treatment compliance are NOT interchangeable. Instead, the average effect of treatment assignment can be thought of as the effect of the
*intention to treat*, or ITT effect.

IV estimation allows us to approximate the ATE by estimating a local average treatment effect (LATE) just among the compliers. This is known as the *compliers’ average causal effect* (CACE). To estimate the CACE, we must make four assumptions about the sample:

*Relevance*: the instrument has a causal effect on the treatment received.*Exclusion*: the instrument affects the outcome ONLY indirectly through the treatment received.*Exchangeability*: there are no confounders that influence both the instrument AND the outcome.*Monotonicity*: there are no “defiers” in the sample.

The relevance assumption implies that there are no “never-takers” and “always-takers” in the sample. In these subgroups, the treatment received doesn’t depend on the value of the assigned treatment. And in order to estimate the treatment effect among the “compliers,” we must also assume that there are no “defiers” in the sample.

### Instructions

The learning environment contains four pausable slides — one for each IV assumption. Check each slide for additional information about the assumptions, including diagrams showing violations of these assumptions.