When treatment group assignments cannot be randomized due to ethical or practical reasons, the best we can do is to encourage compliance. However, encouragement does not guarantee compliance.

Compliance with the treatment assignment can be influenced by many factors, only some of which may be measurable. To account for unmeasured confounders of treatment compliance and the outcome, we could use IV estimation with treatment assignment as the instrument:

IV diagram where Treatment Compliance, Treatment Assignment, Outcome, and Confounders (both measured and unmeasured are represented. Treatment Assignment feeds Treatment Compliance. Treatment Compliance feeds the Outcome, and the Confounders feed both Treatment Compliance and the Outcome variables.

When the instrument AND treatment are both binary variables, we can define four types of “compliers”:

  1. Always takers: takes the treatment regardless of treatment assignment.
  2. Never takers: never takes the treatment regardless of treatment assignment.
  3. Compliers: takes the assigned treatment.
  4. Defiers: takes the opposite of the assigned treatment.

In the context of the recycling program example, the four types of compliers would be defined as follows:

Instrument Value
≤ 5 miles> 5 miles
Always takers RebateRebate
Never takers CurbsideCurbside

The issue of compliance is related to the fundamental problem of causal inference, which states that we can never observe both potential outcomes. In an IV estimation, we can never observe both potential treatments received for an individual. Thus, we cannot know with certainty what kind of complier an individual is.

Fortunately, we can get around this issue by making additional assumptions about our sample.


Take a look at the interactive flowchart in the learning environment. The flowchart has three levels: treatment assignment, treatment received, and type of compliance. For each treatment assignment, click on one treatment received. Depending on your selection of treatment received, the type of compliance will appear.

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