Identifying Shocks in Structural VAR models via heteroskedasticity: a Bayesian approach

This paper contributes to the literature on statistical identification of macroeconomic shocks by proposing a Bayesian VAR with time varying volatility of the residuals that depends on a hidden Markov process, referred to as an MS-SVAR. With sufficient statistical information in the data and certain identifying conditions on the variance�covariance structure of the innovations, distinct volatility regimes of the reduced form residuals allow all structural SVAR matrices and impulse response functions to be estimated without the need for conventional a priori identifying restrictions. We give mathematical identification conditions and propose a novel combination of the Gibbs sampler and a Bayesian clustering algorithm for the posterior inference on MS-SVAR parameters. The new methodology is applied to US macroeconomic data on output, inflation, real money and policy rates, where the effects of two real and two nominal shocks are clearly identified