In an interesting entry and comments, Dani Rodrik says this:
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.
I mostly agree with the commentator who had this to say:
The purpose of growth accounting is quite simple: ACCOUNTING --- NOT MODELING. Accounting requires a framework, and that's what the neoclassical 1957 Solow framework offers. ... Growth accounting serves the purpose of classifying growth into that part that can be traced to measured inputs and that part which cannot. The residual can be thought of as a "measure of our ignorance", that part for which we were not able to find measured or measurable inputs. The more sizable the residual, the more humble we ought to be about the accounting exercise.
Prof. Rodrik asks:
1) "Say you found it's 50% efficiency and 50% factor endowments. What conclusion do you draw from it?"
@ You can conclude that you've only done half the job. You may want to look into the work of Denison, Jorgenson, Mankiw, Romer, and Weil, Barro, and others who have seriously looked into expanding the range of measured inputs.
2) "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."
@ Sure, that's where you want to move away from accounting and towards modeling. Solow's 1956 model was a first shot, which typically explains about half of the growth. A lot more work has been done since. The new growth theories of Romer, Lucas, Aghion and Howitt, Grossman and Helpman, the barriers to riches theories of Prescott and Parente, and others, are one giant step in the right direction.
Countries that grow don't really care how or why they grow as long as they grow. Well, they really care because they would like to keep it up. Since economists are not able to tell them why they will continue to do the things that they've been doing.
1. Countries that grow continue to save, invest, educate their population since this works for them.
2. Countries that do not grow continue to engage in armed conflict, be corrupt and extract the wealth of their country for personal gain.
The more controversial issue was and still is the aggregate production function - its existence and how useful a construct it really is. Perhaps some sensitivity analyses on different functional forms may be illuminating.