This paper analyzes how global economic activity reacts to shocks in the crude oil market, allowing that such reactions may change over time by using a Time-Varying Parameter Vector Autoregression model. Our findings show that an unanticipated disruption in oil supply leads to a relevant decline in global economic activity at any period of time considered (1973:08–2019:06) and at any response horizon, with impacts being relatively similar over time. An unexpected expansion in aggregate demand meaningfully boots global economic activity at any period of time and at any response horizon. In contrast, an unexpected oil-specific demand increase only has a short-lived substantial effect on global economic activity for the shocks produced in the early 2000s, the global financial crisis and the shocks occurred in the last years of the 2010s. These findings are in line with those of Baumeister and Hamilton (2019) who, using a time-invariant model, found that oil supply shocks reduce global economic activity, but oil consumption-demand shocks do not.