Instrumental Variable

An instrumental variable (IV) is a third variable that nudges the treatment but affects the outcome only through the treatment, never directly. It acts like a natural lottery that shuffles treatment around for reasons unrelated to the outcome, letting you estimate an effect even when confounders are present.

Because the instrument's only route to the outcome is via the treatment, the part of the outcome that moves with the instrument can be credited to the treatment. The catch is that the key assumptions — relevance and the exclusion restriction (no direct path) — are largely untestable, so a weak or invalid instrument can give badly misleading answers.