Large Bayesian SVARs with linear restrictions

This paper develops a Markov Chain Monte Carlo (MCMC) algorithm for Bayesian inference in large structural vector autoregressions (SVARs) with linear restrictions. Our proposed method is based on a novel parameter transformation scheme, which aims to facilitate sampling from the posterior distribution of model parameters when linear equality and inequality restrictions are imposed on contemporaneous impulse responses. A prominent feature of the proposed methodology is its applicability for inference in SVARs with over-identifying restrictions. In our empirical application, we demonstrate the usefulness of our method by employing a large Proxy-SVAR with multiple proxy variables to simultaneously identify multiple macroeconomic shocks and investigate their contributions to the 2007–09 Recession.