Identification of structural shocks in Bayesian VEC models with two-state Markov-switching heteroskedasticity

TL;DR

This paper introduces a Bayesian approach for identifying structural shocks in cointegrated VAR models with two-state Markov-switching heteroskedasticity, ensuring global identification and enabling posterior inference.

Contribution

It develops a novel Bayesian framework for SVEC models with Markov-switching heteroskedasticity, including identification conditions and an MCMC inference procedure.

Findings

Successfully applied to simulated data

Effectively analyzed real-world economic data

Ensures unique global identification of shocks

Abstract

We develop a Bayesian framework for cointegrated structural VAR models identified by two-state Markovian breaks in conditional covariances. The resulting structural VEC specification with Markov-switching heteroskedasticity (SVEC-MSH) is formulated in the so-called B-parameterization, in which the prior distribution is specified directly for the matrix of the instantaneous reactions of the endogenous variables to structural innovations. We discuss some caveats pertaining to the identification conditions presented earlier in the literature on stationary structural VAR-MSH models, and revise the restrictions to actually ensure the unique global identification through the two-state heteroskedasticity. To enable the posterior inference in the proposed model, we design an MCMC procedure, combining the Gibbs sampler and the Metropolis-Hastings algorithm. The methodology is illustrated both with a simulated as well as real-world data examples.