A researcher uses proximity to a hospital as an IV for whether patients receive a particular surgery. This IV is invalid if:
AProximity to a hospital is only weakly correlated with receiving surgery
BLiving near a hospital also improves health outcomes through better access to emergency care, preventive services, and specialists — independent of the surgery
CSome patients would always or never choose surgery regardless of proximity
DThe IV is too strongly correlated with the exposure, making the first-stage F-statistic too large
This violates the exclusion restriction: the IV must affect the outcome *only through the exposure*, not via any other pathway. If proximity to a hospital improves health through channels other than the specific surgery (better general care access), then the IV has a 'direct effect' on outcomes bypassing the exposure. This makes the IV estimate conflate the effect of surgery with the effect of broader hospital access. Option A describes a weak IV (problematic but a different failure); option C describes non-monotonicity (a separate assumption); option D is not a real problem.
Question 2 Multiple Choice
A lottery randomly assigns job-seekers to a training program. Not all winners attend (some 'always-takers' would have found training elsewhere; some 'never-takers' refuse). An IV analysis using lottery assignment estimates the causal effect of training for:
AThe entire population of job-seekers who could benefit from training
BEveryone assigned to training by the lottery, regardless of whether they attended
CCompliers — those who attend training when assigned but would not otherwise
DNever-takers, since their outcomes are unaffected by the lottery and serve as the control group
IV analysis identifies the Local Average Treatment Effect (LATE): the causal effect for compliers — those whose treatment status actually changes in response to the instrument. Always-takers (attend regardless) and never-takers (never attend regardless) do not contribute to the IV estimate because their behavior is unchanged by the instrument. This is a crucial distinction: the IV estimate may not generalize to the full population if compliers are systematically different from non-compliers.
Question 3 True / False
The exclusion restriction — that the IV affects the outcome primarily through the exposure — is empirically testable using standard statistical methods.
TTrue
FFalse
Answer: False
The exclusion restriction is fundamentally untestable from the data alone. It is an assumption about a counterfactual: what would happen to outcomes if the IV changed but the exposure did not? Since the exposure does change with the IV in the data, we cannot directly observe outcomes under the counterfactual condition. The assumption must be defended on subject-matter grounds — by arguing from theory and context that no direct pathway exists. Sensitivity analyses can probe how sensitive conclusions are to violations, but cannot verify the assumption itself.
Question 4 True / False
A weak instrumental variable (low first-stage F-statistic) produces IV estimates that are biased toward the OLS estimate and highly imprecise.
TTrue
FFalse
Answer: True
This is a critical practical limitation. A weak IV — one only loosely correlated with the exposure — isolates very little variation in the exposure. In finite samples, even small violations of the IV assumptions or chance correlations with confounders can dominate the estimate, pulling it toward the confounded OLS result. The first-stage F-statistic < 10 is a conventional warning sign. Strong relevance (high F-statistic) does not guarantee the IV is valid (exclusion restriction could still fail), but weakness guarantees problems.
Question 5 Short Answer
Why does IV analysis typically estimate the Local Average Treatment Effect (LATE) rather than the Average Treatment Effect (ATE), and why does this distinction matter for interpreting results?
Think about your answer, then reveal below.
Model answer: IV analysis estimates LATE because the instrument only creates variation in treatment for compliers — people whose exposure status changes in response to the instrument. Always-takers (who receive the treatment regardless) and never-takers (who never receive it regardless) are unaffected by the instrument, so their counterfactual outcomes are not identified. LATE is the effect among this specific subgroup. The distinction matters because compliers may be systematically different from the full population: if a schooling law IV only changes behavior for marginal students near the minimum age threshold, the estimated return to education applies to that group and may not generalize to students who would have stayed in school regardless.
The LATE vs. ATE distinction is one of the most important interpretive issues in IV analysis. Policy-makers often want the ATE — what would happen if we universally applied the treatment — but IV gives LATE, which applies only to those whose behavior the instrument actually shifts. The complier subgroup is often not directly observed and may be smaller or different from the broader population. Recognizing this limits the scope of causal claims from IV studies and motivates thinking carefully about external validity.