SVARs Identification through Bounds on the Forecast Error Variance

Sign-restricted Structural Vector Autoregressions (SVARs) are increasingly common. However, they usually result in a set of structural parameters that have very different implications in terms of impulse responses, elasticities, historical decomposition and forecast error variance decomposition (FEVD). This makes it difficult to derive meaningful economic conclusions, and there is always the risk of retaining structural parameters with implausible implications. This paper imposes bounds on the FEVD as a way of sharpening set-identification induced by sign restrictions. Firstly, in a bivariate and trivariate setting, this paper analytically proves that bounds on the FEVD reduce the identified set. For higher dimensional SVARs, I establish the conditions in which the placing of bounds on the FEVD delivers a non-empty set and sharpens inference; algorithms to detect non-emptiness and reduction are also provided. Secondly, under a convexity criterion, a prior-robust approach is proposed to construct estimation and inference. Thirdly, this paper suggests a procedure to derive theory-driven bounds that are consistent with the implications of a variety of popular, but different, DSGE models, with real, nominal, and financial frictions, and with sufficiently wide ranges for their parameters. The methodology is generalized to incorporate uncertainty about the bounds themselves. Fourthly, a Monte-Carlo exercise verifies the effectiveness of those bounds in identifying the data-generating process relative to sign restrictions. Finally, a monetary policy application shows that bounds on the FEVD tend to remove unreasonable implications, increase estimation precision, sharpen and also alter the inference of models identified through sign restrictions.