As Simon (1979a) pointed out in his Nobel Memorial lecture, the good fits to the Cobb-Douglas production function "cannot be taken as strong evidence for the classical theory, for the identical results can readily be produced by mistakenly fitting a Cobb-Douglas function to data that were in fact generated by a linear accounting identity (value of output equals labor cost plus capital cost)"
Specifications of aggregate production functions, using value data, may be nothing more than approximations to an accounting identity, and hence can convey no information, per se, about the underlying technology of the "representative firm". This is not a new critique, but first came to prominence in Phelps Brown's (1957) criticism (later formalised by Simon and Levy (1963)) of Douglas's cross-industry results. Shaikh (1974, 1980, 1987) generalised it to time-series estimation of production functions and Simon (1979b) also considered the criticism in the context of both cross-section and time-series data. The criticism was re-examined and extended by Felipe and McCombie (2000, 2001 a&b, 2002 a&b), Felipe (2001a and 2001b), McCombie (1987, 1998, 2000, 2000-2001, 2001), McCombie and Dixon (1991) and McCombie and Thirlwall (1994).
Once it is recognised that all that is being estimated is an underlying identity, it can be shown how it is always possible, with a little ingenuity, to obtain a perfect statistical fit to a putative production function, which exhibits constant returns to scale and where the estimated "output elasticities" equal the factor shares. It can also shown how the results of estimation of production functions which find increasing returns to scale and externalities are simply due to misspecification of the underlying identity and the estimated biased coefficients may actually be predicted in advance (McCombie, 2000-2001, Felipe, 2001a). .
The purpose of this paper is to provide a survey of the main elements of this critique and also to consider some counter-criticisms which have been made.