"Decoding One-Sided Compliance in Experiments"

One-sided compliance in field experiments occurs when only the treatment group has the option to adhere to an intervention, requiring researchers to account for compliance variation to accurately estimate causal effects using methods like instrumental variable analysis.

Concept

Description

One-Sided Compliance in Field Experiments

One-sided compliance in the context of field experiments refers to a scenario where only one group, typically the treatment group, has the option or opportunity to comply with the intervention or treatment being studied. Participants in the treatment group may choose to adhere to the intervention (compliers) or not (non-compliers), whereas the control group is never exposed to the intervention and thus has no opportunity to comply or deviate. This concept is particularly important for analyzing the impact of interventions, as researchers must account for the variation in compliance within the treatment group to accurately estimate the causal effect. Statistical methods such as instrumental variable analysis are often used to isolate the treatment effect among compliers, ensuring robust and meaningful conclusions.

Infographic: One-Sided Noncompliance

THE REALITY OF IMPERFECT EXPERIMENTS

In ideal experiments, everyone follows instructions. In the real world, they don't. This gap between who is **assigned** a treatment and who actually **receives** it is called noncompliance. Here’s how we draw valid conclusions anyway.

Who's Who in the Experiment?

To understand noncompliance, we classify people into four hidden groups based on how they would behave. This is **Principal Stratification**.

✓

Compliers

Take the treatment if, and only if, they are assigned to it. They follow the rules.

✗

Never-Takers

Will not take the treatment, no matter what group they're in.

Always-Takers

Will get the treatment, no matter what group they're in.

Defiers

Do the opposite of their assignment. These are rare and usually assumed away.

The Key Simplification: In **one-sided noncompliance**, the control group can't get the treatment. This means Always-Takers and Defiers are impossible, leaving us with just Compliers and Never-Takers!

What Are We Actually Measuring?

With noncompliance, we can't just compare treated vs. untreated. We must choose the right causal question.

Intention-to-Treat (ITT)

The effect of OFFERING the treatment.

This compares everyone assigned to treatment vs. everyone assigned to control. It's a real-world policy effect, but it's "diluted" because many people in the treatment group don't actually get treated.

Complier Average Causal Effect (CACE)

The effect of RECEIVING the treatment.

This measures the true effect of the treatment, but only for the sub-group of Compliers. It adjusts for the dilution to estimate the treatment's true efficacy on those who use it.

Case Study: Vitamin A & Child Mortality

A classic study in Indonesia assigned villages to receive Vitamin A supplements. Not everyone took them, creating a one-sided noncompliance problem. Let's see the data.

Comparing Mortality Rates (The Outcome)

Comparing the two randomly assigned groups shows the raw effect of the program offer (ITT).

Comparing Take-Up Rates (Compliance)

The difference in who actually received the supplement tells us the share of the population who are Compliers.

The CACE Formula: A Simple Ratio

The logic to find the true effect on Compliers (CACE) is surprisingly simple. We just "inflate" the diluted ITT effect by the compliance rate.

Effect of Program Offer (ITT)

(Difference in mortality rates)

÷ Compliance Rate

(Difference in take-up rates)

= Effect for Compliers (CACE)

(True effect of the treatment)

The Final Results

Plugging in the numbers from the Vitamin A study reveals the program's impact.

Intention-to-Treat (ITT) Effect

-0.26%

Offering Vitamin A reduced mortality by 0.26 percentage points across the whole group.

Complier Average Causal Effect (CACE)

-0.32%

For those who took it, Vitamin A reduced mortality by 0.32 percentage points. The effect is larger once "dilution" from non-compliers is removed.

2-causal-inference 3-hypothesis-testing 4-covariates 5-one-sided-compliance

Topic

Home

2-causal-inference

3-hypothesis-testing

4-covariates

5-one-sided-compliance