Questions: Treatment Effects: ATE, CATE, and Heterogeneous Effects

Question 1

A researcher uses a draft lottery as an instrument to estimate the earnings effect of military service. The IV estimator identifies which estimand?

• A. ATE — the average effect across all men in the eligible population
• B. ATT — the effect on men who chose to serve voluntarily
• C. LATE — the effect on men who served because they were drafted but would not have enlisted voluntarily
• D. CATE — the effect conditional on observable characteristics like education and age

Answer: (C)

IV identifies LATE — the Local Average Treatment Effect — which is the treatment effect for compliers: people who comply with the instrument's assignment. In the draft lottery, compliers are men who served when drafted but would not have enlisted voluntarily. Always-takers (enlisted regardless) and never-takers (refused regardless) contribute no identifying variation. This LATE may differ substantially from ATE: men who served only because they were drafted may have had very different earnings trajectories than voluntary enlistees. Option A is ATE, which IV does not recover unless the instrument affects everyone.

Question 2

A policy analyst wants to evaluate whether a job training program benefited the workers who participated in it. Which estimand is most appropriate?

• A. ATE — the average effect if the program were extended to the entire eligible population
• B. ATT — the effect on treated units, i.e., those who actually enrolled in the program
• C. LATE — the effect on compliers with the assignment instrument
• D. CATE — the subgroup effects conditional on worker characteristics

Answer: (B)

ATT (Average Treatment Effect on the Treated) answers: 'was the program beneficial for participants?' — exactly what this analyst wants. ATE would answer a different question: 'would it benefit the full eligible population, including those who didn't enroll?' ATE and ATT differ when people self-select into treatment based on expected benefit — workers who chose to enroll may have higher expected returns from training than non-enrollees. If that selection exists, ATE ≠ ATT. Specifying ATT clarifies that the target is participants, not a hypothetical universal rollout.

Question 3

When a study uses an instrumental variable estimator and reports its main result, the estimate recovers the Average Treatment Effect (ATE) for the full population.

• T. True
• F. False

Answer: False

IV identifies LATE — the treatment effect specifically for compliers, the subgroup whose treatment status is actually changed by the instrument. Unless the instrument affects everyone in the population (full compliance), LATE ≠ ATE. LATE can be larger, smaller, or even opposite in sign to ATE if compliers are a selected subgroup. Reporting an IV estimate as if it were the population ATE is a common and consequential error — always ask: 'who are the compliers for this instrument, and how representative are they?'

Question 4

CATE can be thought of as a function from covariate values to local treatment effects, rather than as a single number.

• T. True
• F. False

Answer: True

CATE(x) = E[Y(1) − Y(0) | X = x] assigns a different expected treatment effect to each covariate vector x. Rather than averaging heterogeneous effects into one number (as ATE does), CATE preserves heterogeneity by conditioning on observable characteristics. For a drug, CATE might reveal the treatment works well for patients over 65 but has no effect for younger patients. This is why CATE estimation often uses machine learning methods (causal forests, meta-learners) that can flexibly model variation across the covariate space.

Question 5

Why do most empirical papers report ATT or LATE rather than ATE, even when the policy question seems to call for ATE?

Model answer: Most identification strategies — difference-in-differences, regression discontinuity, instrumental variables — only credibly identify treatment effects for a specific subpopulation, not the full population. DiD estimates the ATT for units that experienced the treatment. IV estimates LATE for compliers. RD estimates a local ATT near the cutoff. Estimating ATE would require identifying the counterfactual for everyone, including those who never received treatment and may be fundamentally different from treated units. Reporting ATT or LATE is honest about what the identification strategy actually delivers, even if ATE is the ultimately desired parameter.

The mismatch between the policy-relevant estimand (often ATE) and the identified estimand (often ATT or LATE) is one of the central tensions in applied econometrics. A drug approved based on a clinical trial's ATT may perform differently when given to the broader population — the people who enrolled in the trial (treated units) may be more motivated or healthier than the general public. Recognizing this gap, and being explicit about it, is what separates careful causal inference from naïve policy extrapolation.