How sound are the foundations of the aggregate production function?

Abstract

The aggregate production function has been subject to a number of criticisms ever since its first empirical estimation by Cobb and Douglas in the 1920s, notably the problems raised by aggregation and the Cambridge Capital Theory Controversies. There is a further criticism due initially to Phelps Brown (and elaborated, in particular, by Simon and Shaikh) which is not so widely known. This critique is that because at the aggregate level only value data can be used to estimate production function, this means that the estimated parameters of the production function are merely capturing an underlying accounting identity. Hence, no reliance can be placed on estimates of, for example, the elasticity of substitution as reflecting technological parameters. The argument also explains why good statistical fits of the aggregate production functions are obtained, notwithstanding the difficulties posed by the aggregation problem and the Cambridge Capital Controversies noted above. 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