What makes a valid instrumental variable?
hardAnswer
- Z is a valid IV for T → Y if: (1) Relevance: Z affects T (Cov(Z, T) ≠ 0).
- (2) Exclusion: Z affects Y only through T (no direct Z → Y).
- (3) Exogeneity: Z ⊥ unobserved confounders.
- Estimand: LATE (Local Average Treatment Effect) = Cov(Z, Y) / Cov(Z, T) via 2SLS.
- Classic examples: judge leniency, distance to hospital, weather as an instrument for economic activity.
- Weak instruments (small Cov(Z, T)) → biased 2SLS with wide CIs.
Check yourself — multiple choice
- Random
- IV: relevant (Cov(Z,T)≠0) + exclusion (Z → Y only via T) + exogeneity (Z ⊥ confounders); estimator = 2SLS → LATE; weak instruments bias 2SLS
- Same as OLS
- Not real
IV: relevance + exclusion + exogeneity; 2SLS gives LATE.
#causal-inference
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