Extension of HSVAR framework to more than two volatility regimes

Extend the heteroskedastic Structural Vector Autoregression (SVAR) framework developed for two volatility regimes with a known break date to accommodate more than two volatility regimes, and establish the associated identification conditions and inference procedures for structural parameters and impulse responses under potential eigenvalue multiplicity across multiple regimes.

Background

The paper develops identification and inference results for Structural Vector Autoregressions that exploit a single break in the variances of structural shocks, yielding two volatility regimes. Identification is characterized via an eigen-decomposition of reduced-form covariance matrices and can fail when eigenvalues are not distinct, in which case the authors propose combining heteroskedasticity with zero/sign restrictions and using robust Bayesian inference.

While the proposed theory and algorithms focus on two regimes (pre- and post-break), many empirical applications feature multiple volatility episodes. Extending the framework to more than two regimes would require generalizing the eigen-decomposition-based identification, characterizing the identified sets, and adapting the robust Bayesian procedures to multiple regime changes.