The paper Appropriate Technology and Growth by Basu and Weil presents a model whose outcomes seem to describe two of the main behaviours of country growth in the world economy. The first is that growth can be highly non-linear and subject to sudden accelerations and slowdown. The second is that countries can form into different convergence clubs, meaning that incomes or growth rates tend to converge for separate groups of countries, and that the rates in separate groups may not coincide.
The paper assumes that technology is specific to a particular ratio of national capital to national income, and that a country produces improved technology for a band around its ratio. So a late-coming country could save a great deal, reach the band of innovation for the world's technological and wealth leaders, and then surf along in their wake receiving all their technological benefits, even enjoying a higher level of consumption than them.
The paper is clean in its equations and logic, visually appealing, and reflects observed behaviour. Since I like it, here are some unsolicited comments about its scope.
The capital to income ratio could measure many things. In theoretical works, the assumption of capital to income ratios being the key determinant is tolerable; in empirics it could become a real headache.
The paper is retrospective, and it is easier to produce perfect models of past events than future ones. The original work proposing the importance of capital to labour ratios for technology was prospective and earned major prizes, I believe.
I am sure a limiting distribution could be found when large numbers of countries are used in the model, and this distribution could be used as an approximation for smaller numbers. I haven't produced it.
The assumption of effortless technological catch-up for countries free-riding on an innovator seems too optimistic - which would be acknowledged, I think - but also could give misleading theoretical predictions. Followers have to do work to adopt technology, which probably means high level of research and development, and in some circumstances any follower will fall behind a leading innovator no matter what are their own efforts at copying. The adjustment for imperfect transfers could be readily included in the model.