We assess the extent to which the great US macroeconomic stability since the mid-1980s can be accounted for by changes in oil shocks and the oil share in GDP. To do this we estimate a DSGE model with an oil-producing sector before and after 1984 and perform counterfactual simulations. We nest two popular explanations for the Great Moderation: (1) smaller (non-oil) real shocks; and (2) better monetary policy. We find that the reduced oil share accounted for as much as one-third of the inflation moderation, and 13% of the growth moderation, while smaller oil shocks accounted for 11% of the inflation moderation and 7% of the growth moderation. This notwithstanding, better monetary policy explains the bulk of the inflation moderation, while most of the growth moderation is explained by smaller TFP shocks.