Studies of the crude oil market based on structural vector autoregressive (VAR) models typically assume a time-invariant model and transmission of shocks and possibly allow for heteroskedasticity by using robust inference procedures. We assume a heteroskedastic reduced-form VAR model with time-invariant slope coefficients and explicitly consider the possibility of time-varying shock transmission due to heteroskedasticity. We study a model for the global crude oil market that includes key world and U.S. macroeconomic variables and find evidence for changes in the transmission of shocks to oil price expectations during the last decades which can be attributed to heteroskedasticity.