Instrumental variables (IV)

Instrumental variables estimation addresses a situation where treatment and outcome are both driven by some unmeasured confounder, so a direct comparison would be biased, by finding a third variable, the instrument, that affects who gets treated but has no direct effect on the outcome except through treatment. The classic textbook instrument is distance to a facility: it plausibly influences whether someone uses a service without directly affecting the outcome that service is meant to change.

The effect is estimated using only the variation in treatment that the instrument itself explains, filtering out the variation driven by the confounder. This only works if the instrument satisfies two conditions that cannot both be fully verified statistically: relevance, it must genuinely move treatment, and exclusion, it must affect the outcome only through treatment, never directly. A weak or invalid instrument can produce an estimate more biased than the naive comparison it was meant to fix.

IV is used when neither randomization nor a credible matching strategy is available and unmeasured confounding is suspected. In practice, finding an instrument that plausibly satisfies the exclusion restriction is the hardest and most debated part of applying the method, and analysts are expected to argue for its validity explicitly rather than assume it.