Instrumental Variables

Card (1995): IV estimate of returns to education +7.5% vs biased OLS +10%. The 2.5 pp gap is the eliminated IQ confounding via instrument 'college proximity'.

• **Labor economics:** IV is used in half of top-journal studies: Card (education), Angrist (draft lottery), Borjas (immigration).
• **Pharmaceuticals:** distance to specialist as IV -- standard FDA approach without RCT.
• **Tech:** A/B tests with imperfect compliance require IV for Intent-to-Treat analysis.

Instrumental Variables: Identification

Card (1995) used proximity to a college as an instrumental variable to estimate the return to education: the random placement of a college eliminates confounding between IQ and wages, yielding a causal effect of +7.5% income per year of schooling.

Local Average Treatment Effect (LATE)

Angrist and Imbens (Nobel Prize 2021) showed: IV estimates not the ATE but the LATE -- the average effect for 'compliers', those whose behavior changes in response to the instrument. In the Vietnam War lottery study, LATE is the effect of military service on earnings for those who served because of their draft number.

Key ideas

• **Wald estimator:** beta_IV=Cov(Z,Y)/Cov(Z,X). Instrument Z eliminates endogeneity when F>10 and exclusive.
• **2SLS:** stage 1 -- X_hat from Z; stage 2 -- Y on X_hat. Extends IV to the multivariate case.
• **LATE:** IV estimates the effect for compliers, not ATE. Critical with heterogeneous treatment effects.