This chapter first looks at important theoretical and statistical critiques of Douglas’s production function research that appeared during WWII. A theoretical line of criticism used neoclassical models to infer what relationship, if any, would exist between parameters of firm production functions and the coefficients estimated by Douglas. A critique from the perspective of the Cowles Commission econometric research program was provided by Marschak and Andrews. The Marschak and Andrews article can be read as a devastating criticism of Douglas’s work, a list of problems that fatally marred the program, but their tone suggested a different conclusion: that Douglas’s pioneering vision of statistically estimating the key relationships of neoclassical value and distribution theory could be realized, given better data and the methods of the Cowles econometricians. The chapter also analyzes Douglas’s 1947 AEA presidential address, which reveals his own understanding (as opposed to that of his coauthors and those who reacted to his work) of what he had accomplished with his 20-year research program.

This chapter presents speculation regarding factors that contributed to the success of the Cobb–Douglas regression. I discuss in particular four factors that helped facilitate the widespread adoption of the regression approach to production function estimation. (i) Douglas’s decision to link his procedure to fundamental concepts of the neoclassical approach to economics, which was destined to grow in influence over the course of the twentieth century. (ii) the flexibility and adaptability of the technique. (iii) Douglas’s rhetoric of persuasion, and (iv) the emergence of prominent advocates for the technique, such as Earl Heady and Zvi Griliches who communicated, by words and example, the attitude that despite its weaknesses, the technique was potentially very valuable, that the best way to realize that potential was to continue using the technique while working to address the weaknesses, and that even while this process of improvement was going on, the technique was still able to contribute to knowledge. The question of why such allies emerge is explored.

The chapter puts the orignal Cobb–Douglas paper in the context of Douglas’s previous research and the theoretical frameworks and empirical practices employed by economists in the 1920s. Douglas’s early research with the time series version of the regression is described. During this period, Douglas linked his procedure to the marginal productivity theory of distribution, and presented his research as part of a broader effort to build a quantitative account of economic activity on the “valuable theoretical scaffolding” of neoclassical theory. Several friendly critics saw Douglas’s research program as complementary to their own neoclassical-econometric program, but judged Douglas's methods and results based on what they revealed about the characteristics of firm-level production functions. This issue was never crucial for Douglas, who considered an aggregate production function to be an important theoretical entity worth estimating. However, Douglas regarded these economists as potential allies in his effort to promote his new research technique. It was they who had first labeled the relationship that Douglas was attempting to estimate a “production function”, and after 1935 Douglas adopted this label.

Between 1937 and 1943, Douglas and several younger coauthors developed an approach to estimating the Cobb–Douglas regression with cross section data, applying it to industry-level data from the US, Australia, and Canada. This research is described in detail. Over this period claims made by the Douglas team about the meaning of an estimated Cobb–Douglas regression and its relationship to neoclassical theory evolved and never really reached a settled state. During this period, Douglas and his coauthors also responded to Horst Mendershausen's forceful critique of Douglas's work with the regression. Mendershausen pointed to a number of problems in Douglas’s data and methods, concluding that his results did not represent a stable, causal relationship between inputs and output and that his regression method was an unreliable tool for estimation of a production function. Douglas and his associates developed detailed responses to Mendershausen’s critique, and after going back and forth with Mendershausen for a few years, Douglas essentially declared victory and moved on. This debate is analyzed, and possible reasons that Mendershausen’s criticisms did not have more influence are offered.