Traditional approaches to structural vector autoregressions can be viewed as special cases of Bayesian inference arising from very strong prior beliefs. These methods can be generalized with a less restrictive formulation that incorporates uncertainty about the identifying assumptions themselves. We use this approach to revisit the importance of shocks to oil supply and demand. Supply disruptions turn out to be a bigger factor in historical oil price movements and inventory accumulation a smaller factor than implied by earlier estimates. Supply shocks lead to a reduction in global economic activity after a significant lag, whereas shocks to oil demand do not.