We study the identification of oil shocks in a structural vector autoregressive (SVAR) model of the oil market. First, we show that the cross-equation restrictions of a SVAR impose a nonlinear relation between the short-run price elasticities of oil supply and oil demand. This relation implies that seemingly plausible restrictions on oil supply elasticity may map into implausible values of the oil demand elasticity, and vice versa. Second, we propose an identification scheme that restricts these elasticities by minimizing the distance between the elasticities allowed by the SVAR and target values that we construct from a survey of relevant studies. Third, we use the identified SVAR to analyze sources and consequences of movements in oil prices. We find that (1) oil supply shocks and global demand shocks explain 50 and 35 percent of oil price fluctuations, respectively; (2) a drop in oil prices driven by supply shocks boosts economic activity in advanced economies, whereas it depresses economic activity in emerging economies; and (3) the selection of oil market elasticities is essential for understanding the source of oil price movements and to measuring the multipliers of oil prices on economic activity.