According to the guidelines of the Intergovernmental Panel on Climate Change, carbon emissions are attributed to the producers of goods and services. This approach has been challenged by recent literature, advocating an attribution criterion based on consumers, i.e. accounting for the carbon embedded into the goods imported by each country. Quantifying the effectiveness of such a consumption-based accounting requires understanding the complex structure of the graph induced by the flows of emissions between world countries. To this aim, we have considered a balanced panel of a hundred of countries and constructed the corresponding Carbon Trade Network for each of the past twenty years. Our analysis highlights the tendency of each country to behave either as a ‘net producer’—or ‘net exporter’—of emissions or as a ‘net consumer’—or ‘net importer’—of emissions; besides, it reveals the presence of an unexpected, positive feedback: despite individual exchanges having become less carbon-intensive, the increasing trade activity has ultimately risen the amount of emissions directed from ‘net exporters’ towards ‘net importers’. Adopting a consumption-aware accounting would re-distribute responsibility between these two groups, possibly reducing disparities.