Abstract
We study estimation and inference of the Forecast Error Variance Decomposition (FEVD) in Structural Vector Autoregressions (SVARs) that are set-identified by internal and external (proxy) restrictions. The FEVD measures the importance of shocks for macroeconomic fluctuations and is thus key to business cycle analysis. We deliver three practitioner-oriented results. First, we characterize the endpoints of the FEVD as the extreme eigenvalues of a symmetric reduced-form matrix, and propose a consistent plug-in estimator. Second, we use perturbation theory and establish differentiability of the FEVD bounds with respect to reduced-form parameters. Third, we construct a set-length-adjusted delta-method confidence interval that ensures the nominal point-wise coverage. Monte-Carlo exercises based on macroeconomic sample sizes show that it effectively balances validity and tightness relative to conventional alternatives. Two applications illustrate the practical advantages of our approach, including substantial speed-ups relative to robust Bayesian procedures.