Instrumental Variables & 2SLS
Causality from clever variation: instruments, relevance, exogeneity, and two-stage least squares.
Definition
Fixing endogeneity with an instrument: a variable that moves the endogenous regressor (relevance) but affects the outcome ONLY through it (exclusion).
Key equation
2SLS: regress x on z, then y on x̂; simple IV: β̂ = cov(z,y)/cov(z,x)
The intuition
Education and ability are tangled, but distance to college shifts education without (arguably) touching ability. The instrument isolates the clean variation. Everything rests on the exclusion restriction, which is untestable and must be argued.
Exam tip
Always report the first stage; weak instruments (F < 10 rule of thumb) make 2SLS worse than the disease.
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