= Solution
An <instrumental variable> $G$ supplies variation in an <exposure> $B$ that can be used for <causal inference> about its effect on $Y$. Its three core requirements are:
* \b[<Instrument relevance>:] $G$ changes the distribution of $B$; in a simple linear model this requires a nonzero first-stage association.
* \b[<Instrumental-variable independence>:] $G$ is independent of unmeasured common causes of $B$ and $Y$, or independent of the relevant <potential outcomes> conditional on specified measured covariates.
* \b[<Exclusion restriction>:] interventions on $G$ affect $Y$ only through $B$, with no other causal pathway. In <potential outcomes> notation, $Y(b,g)=Y(b)$.
\b[Relevance, independence, and exclusion are the core instrumental-variable assumptions.] They do not by themselves identify an arbitrary population-average effect. For a binary instrument and treatment, <instrumental-variable monotonicity> and the usual <consistency in causal inference> assumptions can identify a <local average treatment effect>; stronger effect-homogeneity or structural-model assumptions are needed for other effect interpretations.
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