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Estimation and Inference of the Forecast Error Variance Decomposition for Set-Identified SVARs

Lookup NU author(s): Dr Francesco FusariORCiD, Dr Joe MarlowORCiD

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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.

Publication metadata

Author(s): Fusari F, Marlow J, Volpicella A

Publication type: Article

Publication status: Published

Journal: Journal of Econometrics

Year: 2026

Volume: 255

Print publication date: 01/05/2026

Online publication date: 27/03/2026

Acceptance date: 10/03/2026

Date deposited: 27/07/2026

ISSN (print): 0304-4076

ISSN (electronic): 1872-6895

Publisher: Elsevier

URL: https://doi.org/10.1016/j.jeconom.2026.106233

DOI: 10.1016/j.jeconom.2026.106233

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