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This work provides a new empirical assessment of global economic hierarchies and the associated unequal distribution of value between core and peripheral economies. This is accomplished by looking at the functional division of labour induced by the international fragmentation of production and the related value capture dynamics in global value chains (GVCs). To this aim, we introduce and compute an indicator of 'functional specialization' of economies based on their ability to attract Foreign Direct Investment, which allows us to detect the value adding activities in which more than 100 countries have specialized from 2003 to 2018. We show that the most intangible-intensive activities are concentrated in core capitalist economies, while production operations at the lower end of the value chain are mainly the prerogative of low- and middle-income countries. Although China and India have emerged as partial but significant outliers, a substantial persistence of this functional division of labour across world macro-regions is also observed over the period. Most notably, we find that a higher specialization in the most intangible-intensive functions allows countries to capture a greater amount of value from trade in GVCs, thus providing novel empirical support to the 'Smile curve' hypotheses and the underlying 'intellectual monopoly' perspective. [ABSTRACT FROM AUTHOR] more...