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Abstract
In an article in the 2006 volume of this journal, Jonathan Temple presented a defence of the use of the aggregate production function in growth theory in the light of various criticisms that have been levelled at it. These criticisms include the Cambridge Capital Theory Controversies, various aggregation problems, and the problems posed by the use of value data and the underlying accounting identity. We show that Temple has underestimated the seriousness of these criticisms, especially the last one, which vitiates the concept of the aggregate production function. Because of the identity, estimates of putative aggregate production functions, such as the aggregate elasticity of substitution, cannot be interpreted as reflecting the underlying technology, and hence the use of the aggregate production function is extremely problematical.
Acknowledgements
We are grateful to Jonathan Temple for his helpful detailed comments on an earlier version of this paper and for clarifying some of his arguments – he has convinced us that there are greater areas of agreement between us than we had previously thought, although, as can be seen, substantial differences of opinion remain. We also benefited from the comments of two anonymous referees.
Notes
1. We somewhat unconventionally define an aggregate production function as one that uses value data. Consequently, estimating production functions using value data at, for example, the four‐digit SIC level is equally subject to the problems posed by the identity as estimating an aggregate production function for the whole economy or for manufacturing.
2. A notable exception is Temple (Citation1999, 150) who states that ‘arguably the aggregate production function is the least satisfactory element of macroeconomics, yet many economists seem to regard this clumsy device as essential to an understanding of national income levels and growth rates’. However, apart from noting the problems that structural change poses for the concept, he does not elaborate further.
3. For expositional ease, we shall confine our discussion to value added, although the same arguments hold when gross output is used and the inputs include intermediate goods and materials.
4. Land may be included as another factor of production without affecting the conclusions of the argument. Land is not included in any estimations of production functions for industry or the whole economy (as opposed to the agricultural sector) due to the unavailability of separate data in the national accounts.
5. Indeed, Kaldor (Citation1961) who first put forward the ‘stylised facts’ of economic growth was dismissive of the neoclassical aggregate production function.
6. Felipe and McCombie (Citation2009) demonstrate that neoclassical labour demand functions are also merely capturing the identity.
7. See also Shaikh (Citation1974, Citation1980) for the case of the Humbug production function, and Felipe and Adams (Citation2005), who subjected the original data of Cobb and Douglas (Citation1928) to the accounting identity critique. McCombie (Citation2000‐2001) showed that Solow’s (Citation1957) original data gave a statistically insignificant fit when estimated as a Cobb‐Douglas relationship with a linear time‐trend.
8. This problem is more serious than may be gathered from Temple. The Diamond‐McFadden impossibility theorem has shown that with labour‐ and capital‐augmenting technical change growing at different rates over time, it is not possible to identify the technological parameters of the aggregate production function, even when the latter exists (Diamond, McFadden, and Rodriguez Citation1978).
9. It is also straightforward to show that the interpretation of the dual derived from the cost function suffers from the same problem, namely, that it is determined solely by that the accounting identity. The proof is available on request from the authors.
10. In fact, the criticism can be traced back to the 1940s (see McCombie Citation1998b, for a discussion of the history of the aggregate production function).
11. Alternatively, we can assume a continuum of firms, totally differentiate the accounting identity and then integrate the result. If factor shares are constant we will obtain a Cobb‐Douglas relationship.