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Macro shocks are often composites, yet overlooked in the impulse responseanalysis. When an instrumental variable (IV) is used to identify a compositeshock, it violates the common IV exclusion restriction. We show that the LocalProjection-IV estimand is represented as a weighted average of component-wiseimpulse responses but with possibly negative weights, which occur when the IVand shock components have opposite correlations. We further develop alternative(set-) identification strategies for the LP-IV based on sign restrictions oradditional granular information. Our applications confirm the composite natureof monetary policy shocks and reveal a non-defense spending multiplierexceeding one.

What Impulse Response Do Instrumental Variables Identify?