The economic implications of oil price shocks have been extensively studied since the 1970s. Despite this huge literature, no dynamic stochastic general equilibrium model was available that captures two well-known stylized facts: (1) the stagflationary impact of an oil price shock, together with (2) the influence of the energy efficiency of capital on the depth and length of this impact. We build, estimate and simulate a New-Keynesian model with capital accumulation, which takes the case of an economy where oil is imported from abroad, and where these stylized facts can be accounted for. Moreover, the Bayesian estimation of the model on the US economy (1984–2007) suggests that the output elasticity of oil might have been above 10%, stressing the role of oil use in US growth at this time. Finally, our simulations confirm that an increase in energy efficiency significantly attenuates the effects of an oil shock—a possible explanation of why the third oil shock (1999–2008) did not have the same macro-economic impact as the first two ones. These results suggest that oil consumption and energy efficiency have been two major engines for US growth in the last three decades.