What Impulse Response Do Instrumental Variables Identify?

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