the Cobb-Douglas production function

The current issue of the Journal of Economic Perspectives (open access) has a 14-page essay on the Cobb-Douglas regression, a popular form of aggregate production function. About time, I thought, that someone writing in a popular journal exposed this work-horse of econometrics for the fraud that it is. I accessed the essay with great anticipation, only to find it full of praise, with very light – almost non-existent – criticism. Here are the essay’s two concluding sentences:

There remain open questions about the scientific value of this procedure in each of the contexts in which it is applied, some of which are variations of the friendly and unfriendly questions raised by Douglas’s initial critics. However, measured by the extent to which it has been embraced, applied, and elaborated upon by subsequent economists, Douglas’s innovative 1927 idea that one could use statistical analysis to uncover meaningful empirical relationships between inputs and outputs, as well as his specific implementation of that idea using the Cobb–Douglas functional form and least squares regression, was an overwhelming success.

Jeff Biddle, “The Introduction of the Cobb–Douglas Regression“, Journal of Economic Perspectives 26:2 (Spring 2012), pp. 223-236.

Michigan State University economist Jeff Biddle took to heart this advice of MIT economist Franklin Fisher:

[A]ttempts to explain the impossibility of using aggregate production functions in practice are often met with great hostility, even outright anger. To that I say … that the moral is: “Don’t interfere with fairytales if you want to live happily ever after.”

Franklin M. Fisher, “Aggregate Production Functions – A Pervasive, but Unpersuasive, Fairytale“, Eastern Economic Journal 31:3 (Winter 2005), pp. 489-491.

Nowhere does Professor Biddle mention the most damning criticism of aggregate production functions (including the Cobb-Douglas variant): their good fit to empirical data is a statistical artifact – a result of the fact that the functions reflect  the accounting identity between the values of inputs and outputs. In other words, aggregate production functions are almost tautologies – true by definition! This was pointed out independently by two Nobel laureates – Paul Samuelson and Herbert Simon – in articles that were published in 1979, and subsequently ignored by virtually everyone. Here are short quotes from each article:

It is a late hour to raise these doubts about the Emperor’s clothes, but ….

Why use the words “production function” for such an accounting-tautology … ?

Paul A. Samuelson, “Paul Douglas’s Measurement of Production Functions and Marginal Productivities“, Journal of Political Economy 87:5, Part 1 (October 1979), pp. 923-939.


Empirical data on the Cobb-Douglas and ACMS [Arrow, Chenery, Minhas and Solow] production functions have been alleged to provide substantial support for the classical theory of the firm–so substantial that further testing of that theory, as distinguished from elaboration of its detail, was no longer necessary. An examination of the evidence suggests instead that the observed good fit of these functions to data … are very likely all statistical artifacts. The data say no more than that the value of the product is approximately equal to the wage bill plus the cost of capital services. This interpretation of the statistical findings is plausible for both interindustry cross-sectional studies and time-series studies, the latter for either a single industry or a whole economy. (p. 469)

Herbert A. Simon, “On parsimonious explanations of production relations“, Scandinavian Journal of Economics 81:4 (1979), pp. 459-474.

Professor Biddle cites Samuelson’s article, but fails to mention Samuelson’s criticism of the Cobb-Douglas function. Biddle does not even cite Herbert Simon in his essay.

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