Traditional studies of the Dutch disease do not typically account for productivity spillovers between the booming energy sector and non-oil sectors. This study identifies and quantifies these spillovers using a Bayesian Dynamic Factor Model (BDFM). The model allows for resource movements and spending effects through a large panel of variables at the sectoral level, while also identifying disturbances to the real oil price, global demand and non-oil activity. Using Norway as a representative case study, we find that a booming energy sector has substantial spillover effects on the non-oil sectors. Furthermore, windfall gains due to changes in the real oil price also stimulates the economy, but primarily if the oil price increase is caused by global demand. Oil price increases due to, say, supply disruptions, while stimulating activity in the technologically intense service sectors and boosting government spending, have small spillover effects on the rest of the economy, primarily because of reduced cost competitiveness. Yet, there is no evidence of Dutch disease. Instead, we find evidence of a two-speed economy, with non-tradables growing at a much faster pace than tradables. Our results suggest that traditional Dutch disease models with a fixed capital stock and exogenous labor supply do not provide a convincing explanation for how petroleum wealth affects a resource rich economy when there are productivity spillovers between sectors.