Do production capabilities of countries evolve from existing capabilities or emerge de novo? The Product Space approach developed by Hidalgo, Klinger, Barabási and Hausmann postulates that a country's existing industrial structure largely determines its opportunities for industrial upgrading. However, this is difficult to reconcile with the export dynamism of many developing countries such as Thailand, Malaysia, Costa Rica and Vietnam that transformed from primary commodity dependence to exporters of dynamic manufactured products. In each of these cases, global production sharing facilitated industrial transition. In this article, we advance the Product Space approach to accommodate the role of global production sharing. Using a newly constructed multi-country data set of manufacturing exports that distinguishes between trade within global production networks and traditional horizontal trade, we find that that existing industrial structure has a smaller impact, but trade openness has a greater impact, on industrial upgrading within vertically integrated global industries.