This work applies the empirical mode decomposition (EMD) method to data on real quarterly oil price (West Texas Intermediate - WTI) and U.S. gross domestic product (GDP). This relatively new method is adaptive and capable of handling non-linear and non-stationary data. Correlation analysis of the decomposition results was performed and examined for insights into the oil-macroeconomy relationship. Several components of this relationship were identified. However, the principal one is that the medium-run cyclical component of the oil price exerts a negative and exogenous influence on the main cyclical component of the GDP. This can be interpreted as the supply-driven or supply-shock component of the oil price-GDP relationship. In addition, weak correlations suggesting a lagging demand-driven, an expectations-driven, and a long-run supply-driven component of the relationship were also identified. Comparisons of these findings with significant oil supply disruption and recession dates were supportive. The study identified a number of lessons applicable to recent oil market events, including the eventuality of persistent economic and price declines following a long oil price run-up. In addition, it was found that oil-market related exogenous events are associated with short- to medium-run price implications regardless of whether they lead to actual supply disruptions.