I am teaching this stuff this week, and while I enjoy doing it and think it is important for students to know--no World Bank country economic memorandum is apparently complete without a sources-of-growth exercise--I wonder what purpose it really serves.
These accounting exercises come in two flavors. A levels-exercise which decomposes differences in GDP per worker across countries into factor endowments and efficiency (or TFP). For the state of the art on this, see this paper by Francesco Caselli. The more traditional kind decomposes growth within a country into components having to do with physical and human capital deepening and a residual (TFP growth). A comprehensive source on the latter is the 2003 paper by Barry Bosworth and Susan Collins.
Aside from all kind of measurement problems, these accounting exercises say nothing about causality, and so are very hard to interpret. Say you found it's 50% efficiency and 50% factor endowments. What conclusion do you draw from it? You could imagine a story where the underlying cause of growth is factor accumulation, with technological upgrading or enhanced allocative efficiency as the by-product. Or you could imagine a story whereby technological change is the driver behind increased accumulation. Both are compatible with the result from accounting decomposition. Indeed, I have yet to see a sources-of-growth decomposition which answers a useful and relevant economic or policy question.
Caselli says that these accounting exercises are just a diagnostic tool--but he does not say how they help us diagnose anything in particular. Sure, they tell us that accumulation alone cannot be the whole story, but is that a surprise to anyone?
Perhaps the best known paper on sources of growth was the Alwyn Young exercise on East Asia, which showed that most of growth was "accounted" for by accumulation rather than productivity growth. In other words, the East Asian miracle was mostly perspiration, and not much inspiration. Yet surely it was a miracle for these countries to have engineered jumps in their investment rates of the order of 20 or more percentage points, and even if the Young decomposition is right (it has been challenged by Chang-Tai Hsieh among others), I am not sure the result teaches us anything of importance. Do you suddenly think less of East Asians because the residual is lower than what you may have anticipated?
So here is a contest for economist (or wannabe economist) readers of this blog: can you come up with an interesting question to which a sources-of-growth decomposition is the answer?