Empirical macroeconomists often estimate impulse response functions using external instruments (proxy variables) for the shocks of interest. However, existing methods do not answer the key question of how important the shocks are in driving macro aggregates, unless the researcher is willing to assume either a Structural Vector Autoregressive representation or that the shocks are directly observed. We provide tools for doing inference on forecast variance decompositions in a general semiparametric moving average model, disciplined only through the availability of valid external instruments. We show that the share of the forecast variance that can be attributed to a shock is partially identified, albeit with informative bounds. Point identification can be achieved under a shock recoverability assumption that is restrictive but weaker than invertibility (i.e., the SVAR model assumption). The degree of invertibility is also set-identified; hence, the invertibility assumption is testable. To perform inference, we construct easily computable, partial identification robust confidence intervals. Finally, we interpret our results through the lens of a workhorse structural macro model.

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