This study investigates changes in the relationship between oil prices and the US economy from a long-term perspective. Although neither of the two series (oil price and GDP growth rates) presents structural breaks in mean, we identify different volatility periods in both of them, separately. From a multivariate perspective, we do not observe a significant effect between changes in oil prices and GDP growth when considering the full period. However, we find a significant relationship in some subperiods by carrying out a rolling analysis and by investigating the presence of structural breaks in the multivariate framework. Finally, we obtain evidence, by means of a time-varying VAR, that the impact of the oil price shock on GDP growth has declined over time. We also observe that the negative effect is greater at the time of large oil price increases, supporting previous evidence of nonlinearity in the relationship.