Identification Verification for Structural Vector Autoregressions with Sparse Heterogeneous Markov Switching Heteroskedasticity

We propose a structural vector autoregressive model with a new and flexible specification of the volatility process which we call Sparse Heterogeneous Markov-Switching Heteroskedasticity. In this model, the conditional variance of each structural shock changes in time according to its own Markov process. Additionally, it features a sparse representation of Markov processes, in which the number of regimes is set to exceed that of the data-generating process, with some regimes allowed to have zero occurrences throughout the sample. We complement these developments with a definition of a new distribution for normalised conditional variances that facilitates Gibbs sampling and identification verification. In effect, our model: (i) normalises the system and estimates the structural parameters more precisely than popular alternatives; (ii) can be used to verify homoskedasticity reliably and, thus, inform identification through heteroskedasticity; and (iii) features excellent forecasting performance comparable with Stochastic Volatility. Finally, revisiting a prominent macro-financial structural system, we provide evidence for the identification of the US monetary policy shock via heteroskedasticity, with estimates consistent with those reported in the literature.