Income divergence in the face of faster technology adoption

We live in an increasingly global world. As production moves to where capital and labor are the cheapest, we should be expecting a convergence of incomes across the world. Know-how and technology also flow more rapidly from leaders to followers, which should reinforce this convergence. Thus, unless something is really messed up with other factors of production (institutions, climate, ...), we should observe convergence. Yet it has not happened as much as one would have expected, quite to the contrary. What is wrong with my reasoning above?

Diego Comin and Martí Mestieri focus on the diffusion of 25 technologies across 132 countries over two centuries. They conclude that the adoption speed of new technologies has indeed increased faster in poor countries, but not the penetration rates (once diffusion is completed). That means that while countries first use new technology earlier than before, especially developing ones, the later use the technology relatively less throughout the economy. This has an ambiguous impact on convergence, but with a simple model Comin and Mestieri show that the latter effect is predominant, and how. With their numbers they can justify a multiplication by 3.2 of the income gap between rich and poor countries over the last two centuries, that is, almost all of the fourfold increase in that gap observed in the data. One more reason to wean the poorest countries off the illusion that they must grow a healthy agricultural sector, which uses little technology on land that is not well suited for agriculture in the first place (more). They need to jump to stronger manufacturing and adopt more technology throughout the economy.