SVARs Identification Through Bounds on the Forecast Error Variance

Abstract

This article identifies structural vector autoregressions (SVARs) through bound restrictions on the forecast error variance decomposition (FEVD). First, the article shows FEVD bounds correspond to quadratic inequality restrictions on the columns of the rotation matrix transforming reduced-form residuals into structural shocks. Second, the article establishes theoretical conditions such that bounds on the FEVD lead to a reduction in the width of the impulse response identified set relative to only imposing sign restrictions. Third, this article proposes a robust Bayesian approach to inference. Fourth, the article shows that elicitation of the bounds could be based on DSGE models with alternative parameterizations. Finally, an empirical application illustrates the potential usefulness of FEVD restrictions for obtaining informative inference in set-identified monetary SVARs and remove unreasonable implications of models identified through sign restrictions.