Is there evidence for unconditional convergence?

From Opalo's Weblog

When we look at the same question at the level of individual industries rather than countries a surprising finding emerges. Suppose we focus on, say, plastics, furniture, or the auto industry in developing countries. Does productivity in these (and other) industries experience automatic convergence with the technological frontier? Or is convergence once again conditional, depending on a host of country-level variables?

The interesting (and I think new) finding is that productivity convergence appears to be unconditional at the industry level – at least for manufacturing industries and for the period since the 1980s.

This addresses a very relevant question. Lets say, for example, that may be Guatemala's income per-capita is not converging with Germany's unconditional of education, investment, and population growth; but it might be the case that income of the Telecom sector is indeed converging to Germany's unconditional of those factors. What makes those sectors so especial?