This paper constructs a model of a supply chain to examine how demand volatility is passed upstream through the chain. In particular, we seek to determine how likely it is that the chain experiences a bullwhip effect, where the variance of the upstream firms’ production exceeds the variance of the upstream firm’s sales. We show that the bullwhip effect is more likely to occur and is greater in size in supply chains in which inventory control is centralized rather than decentralized, that is, exercised by the downstream firm.