There has been a systematic increase in the volatility of the real price of crude oil since 1986, followed by a decline in the volatility of oil production since the early 1990s. We explore reasons for this evolution. We show that a likely explanation of this empirical fact is that both the short‐run price elasticities of oil demand and of oil supply have declined considerably since the second half of the 1980s. This implies that small disturbances on either side of the oil market can generate large price responses without large quantity movements, which helps explain the latest run‐up and subsequent collapse in the price of oil. Our analysis suggests that the variability of oil demand and supply shocks actually has decreased in the more recent past, preventing even larger oil price fluctuations than observed in the data. Copyright © 2012 John Wiley & Sons, Ltd.