This paper surveys recent advances in drawing structural conclusions from vector autoregressions (VARs), providing a unified perspective on the role of prior knowledge. We describe the traditional approach to identification as a claim to have exact prior information about the structural model and propose Bayesian inference as a way to acknowledge that prior information is imperfect or subject to error. We raise concerns from both a frequentist and a Bayesian perspective about the way that results are typically reported for VARs that are set-identified using sign and other restrictions. We call attention to a common but previously unrecognized error in estimating structural elasticities and show how to correctly estimate elasticities even in the case when one only knows the effects of a single structural shock.

The substantial fluctuations in oil prices in the wake of the COVID-19 pandemic and the Russian invasion of Ukraine have highlighted the importance of tail events in the global market for crude oil which call for careful risk assessment. In this paper we focus on forecasting tail risks in the oil market by setting up a general empirical framework that allows for flexible predictive distributions of oil prices that can depart from normality. This model, based on Bayesian additive regression trees, remains agnostic on the functional form of the conditional mean relations and assumes that the shocks are driven by a stochastic volatility model. We show that our nonparametric approach improves in terms of tail forecasts upon three competing models: quantile regressions commonly used for studying tail events, the Bayesian VAR with stochastic volatility, and the simple random walk. We illustrate the practical relevance of our new approach by tracking the evolution of predictive densities during three recent economic and geopolitical crisis episodes, by developing consumer and producer distress indices that signal the build-up of upside and downside price risk, and by conducting a risk scenario analysis for 2024.