Covariance structure drives SVAR impulse response asymmetry
A Federal Reserve Bank of Philadelphia working paper by Arias, Rubio-Ramírez, and Waggoner demonstrates that asymmetry in structural vector autoregression impulse responses stems from reduced-form covariance structures rather than Bayesian priors over orthogonal matrices.
Challenging the Baumeister-Hamilton critique
Baumeister and Hamilton (2018) previously argued that unexpected distributional asymmetry in structural vector autoregressions under a uniform prior resulted from an implicit Bayesian prior over orthogonal matrices.
Arias, Rubio-Ramírez, and Waggoner show that this concern is actually driven by an unacknowledged sign restriction combined with the reduced-form covariance structure.
Analyzing a three-variable U.S. economy model featuring the output gap, inflation, and the fed funds rate, the authors prove that a uniform prior over orthogonal matrices implies symmetric marginal prior and posterior distributions about the origin in the absence of sign restrictions.
Decomposing restrictions into scale, label, and economics
To resolve methodological pitfalls in Bayesian SVAR analysis, the authors provide a foundational proposition establishing that any identifying restriction can be decomposed into three distinct types: scale, label, and economic.
Using this theoretical framework, they develop a robust algorithm for inference based on unit modulus normalization.
Their mathematical proofs demonstrate that when sign restrictions are introduced, any resulting asymmetry in impulse responses depends entirely on expected residual correlations, such as the covariance between fed funds rate and output gap innovations.
Methodological clarity for empirical macro
This study delivers a crucial methodological correction for applied macroeconomists.
By separating scale, label, and economic restrictions, the authors dismantle a prominent critique.
Researchers can now utilize conventional priors with renewed confidence.