I have a new paper out by this title, which you can download here. It shows that unconditional convergence is alive and well, but that we need to look for it within manufacturing industries rather than the economy as a whole. Industries that start at lower levels of labor productivity grow faster, regardless of the quality of policies or institutions in their home economies.
Here are four illustrative cases:
The initial level of labor productivity is on the horizontal axis, while subsequent growth rates (net of a constant term) are shown on the vertical axis.
Similar scatter plots never show convergence at the aggregate (country) level. Hence what seems to matter for growth is the ability to pull resources into the economies' "convergence industries," manufacturing in particular. What high-growth countries have in common is their ability to deploy policies that compensate for the market and government failures that block such structural transformation. Countries that manage to affect the requisite structural change grow rapidly while those that fail don't