We conclude that the latter leave the central tenet unaffected.
The Cobb-Douglas Production Function and the Accounting Identity.
The problem that the accounting identity poses for the interpretation of the aggregate production function was first brought to the fore by Phelps Brown (1957) in his seminal paper "The Meaning of the Fitted Cobb-Douglas Function". (It had also been partly anticipated by Bronfenbrenner (1944).) It is one of the ironies of the history of economic thought that this article, which challenged the whole rationale for estimating aggregate production functions, was published in the same year as Solow's (1957) "Technical Change and the Aggregate Production Function". The latter, of course, was largely responsible for the beginning of the neoclassical approach to the empirical analysis of growth. .
Phelps Brown's critique was addressed to the fitting of production functions using cross-sectional data and was specifically directed at Douglas's various studies (see Douglas, 1944), and we consider this first, before considering the case of time-series data.
Cross-Section Data.
.
The fact that the crucial tenet of Phelps Brown's (1957) argument was presented rather obscurely and was buried in his paper did not help its reception, even though it was published in one of the US's leading economics journal. The following is the key passage:.
The same assumption would account for the observed agreement for the values obtained for ' [the output elasticity of labour], and the share of earnings given by the income statistics. For on this assumption the net products to which the Cobb-Douglas is fitted would be made up of just the same rates of return to productive factors, and quantities of those factors, as also make up the income statistics; and when we calculate ' by fitting the Cobb-Douglas function we are bound to arrive at the same value when we reckon up total earnings and compare them with the total net product.