The decoupling of energy-related carbon emissions from economic growth has been mostly driven by reductions of the energy intensity of GDP, which can be attributed either to changes in countries’ economic structure or within-sector energy-efficiency improvements. One question is whether observed reductions in energy intensity may stem from shifts to less energy-intensive sectors without equivalent changes in consumption patterns, raising uncertainty on their true impact on global decarbonization. This paper aims to empirically investigate this mechanism in a panel of 15 OECD countries. First, using an Index Decomposition Analysis (IDA) including an offshoring factor, we show that structural changes in the production side have generally been unmatched with similar changes in consumption patterns. We then proxy a “demand-invariant structural change” in a Bayesian Structural Panel VAR model, by exploiting a novel measure given by the divergence between consumption-based and production-based carbon emissions. We find that shocks in this divergence measure are efficiently associated with demand-invariant structural changes and persistently and significantly reduce national energy intensity. Taken together, our results support the thought that caution should be taken when using production-based indicators to assess a country’s contribution to global carbon mitigation.