Bayesian inference on fully and partially identified potentially non-Gaussian structural vector autoregressions

Abstract

We introduce a new approach to Bayesian inference in potentially non-Gaussian structural vector autoregressions. It relies on the result that the elements of the impact matrix are at least set-identified with narrow bounds under standard assumptions. As a result, an efficient simulation algorithm should be capable of exploring the parameter space, even if only some (or none) of the parameters are identified. We consider very efficient Hamiltonian Monte Carlo (HMC) methods. To exploit potential deviations from Gaussianity, we recommend using a versatile error distribution, which nests a Gaussian distribution as a special case. In this manner, we can infer from the data whether the structural shocks are Gaussian and assess the strength of identification by examining the properties of the estimated shock distributions. Simulations and an empirical application to US fiscal policy demonstrate that non-identification can be easily detected from the marginal posteriors of parameters governing the shapes of the distributions of the structural shocks, even when the data are Gaussian. They also highlight the importance of efficiently accounting for non-Gaussianity.