1Many economists invoke the term “Cobb-Douglas” frequently, while knowing little of its history. In 1927, Paul H. Douglas presented his results on an estimated production function in a paper at the American Economic Association annual meeting. This was joint work with the mathematician Charles W. Cobb. What became known as the Cobb-Douglas production function was not new—Knut Wicksell had previously suggested it—but its estimation using time-series data marked the beginning of a new literature, with more at stake than one might think.

2Exactly twenty years later, Douglas gave the Presidential Address at the sixtieth annual meeting of the Association, having earned this accolade largely through his work on production functions. The two papers, which appeared as Cobb and Douglas (1928) and Douglas (1948), effectively book-ended Douglas’s work in the area. In 1949, he left academic research and served as a Senator for Illinois for eighteen years, while others developed the approach he and Cobb had initiated. They were intent on taking production functions out of the ivory tower, to cast light on diminishing returns to capital and labour, returns to scale in production, the extent of competition, and whether factors are paid their marginal products.

3In Progress through Regression, Jeff Biddle provides a forty-year history, over a period that roughly spans the late 1920s to the late 1960s. He makes a good case that estimating Cobb-Douglas relationships played a significant role in the development of applied econometrics and the study of economic growth. For the most part, Biddle is a well-informed and reliable guide. As may become clear from this review, the story is unexpectedly interesting, and the book should find a readership beyond historians of economic thought.

4Part I of the book gives a chronological account of the first few decades, extending Biddle (2011, 2012). After the 1928 paper, Cobb rarely worked in the area, but Douglas looked for new applications with a succession of co-authors. He seems to have been a resourceful and determined researcher: at one point, he answered some of his critics by constructing a three-dimensional physical model of the data and his regression estimates, using a tilted sheet of plexiglass to stand in for the regression surface (97). Appropriately, a photograph of this model appears on the cover of the book.

5Not all the details in the early chapters are equally diverting, and the discussion becomes a little hard to follow when it covers now obscure ideas like confluence analysis and bunch maps. The first part of the book might have worked better with shorter chapters, perhaps relegating less essential material to appendices. The intellectual level of the historical debate seems to advance markedly when Tinbergen, and then Marschak and Andrews, arrive on the scene. It took time for others working in the field to catch up, and Tinbergen’s 1942 paper was rather neglected at the time.

6Part II of the book is an easier read, partly through its greater familiarity. It traces a number of parallel developments: the appearance of the Cobb-Douglas production function in some of the first econometrics textbooks, a 1957 critique by Sir Henry Phelps Brown, the introduction of the CES production function, the estimation of production relations in agriculture—key to the early days of applied econometrics—and the use of Cobb-Douglas by those studying economic growth, notably Zvi Griliches and Robert Solow. Parts of this discussion overlap with two journal articles, Biddle (2011; 2020).

7Given the amount of work in the area, there is an inevitable tension between a properly historical account of the understanding of particular actors at a particular time, and the modified perspective achieved by later researchers. To give one example, the spectre of “multicollinearity” has been exorcised from nearly all modern econometrics textbooks—I think rightly—and Biddle could perhaps have done more to discuss the historical debate in the light of what we know now. Researchers at the time were concerned that high correlations among the explanatory variables would lead to imprecision or make the results too sensitive to the choice of sample. But then, recommending some form of robustness testing would have been better than invoking multicollinearity (or even worse, a vague notion of an associated “bias”) as somehow a clinching argument against the approach of Douglas and his co-authors.

8There are two other areas where Biddle could perhaps have gone further, armed with retrospective wisdom. One is aggregation: some early critics of Douglas took the view that production functions should be estimated only at the firm level, rather than using aggregate data. There are many economists, mainstream and heterodox, who would agree. The conditions needed to aggregate are known to be strict, as Franklin Fisher stressed, but his work on this—collected in Fisher (1993)—is not discussed. As with multicollinearity, Biddle covers the issue mainly through contributions made at the time, when occasionally it would have been useful to borrow the light of later understanding.

9Another vexed question is whether Cobb-Douglas estimates are spurious, reflecting only underlying identities. There are several versions of this claim, and Biddle sets out the argument made by Jan Tinbergen in a 1942 paper. Tinbergen argued that cross-section estimates of a common Cobb-Douglas function, across a set of industries with different production technologies, would generate regression estimates that looked falsely supportive. The industries face the same capital and labour costs but choose different points on an isocost line, because their technologies differ. These different points are then mistaken by the econometrician for those generated by a common production relation.

10Developing the argument further, Tinbergen showed that the world can look Cobb-Douglas even when it is not. Cross-section estimates of production functions across industries are not to be trusted. In the recent literature, there is more awareness that one should not impose a common production relation on a heterogeneous set of industries. That came to seem a bad idea even without Tinbergen’s critique, which was not well known at the time.

11Here is where things get more contentious. Tinbergen’s critique applied to estimates across industries, but a related argument is more general. In a two-factor world, the value-added identity says that value added generates income for capital and labour, and this implies that income traces out a plane as a function of capital and labour. This plane may appear to be well approximated by a constant-returns-to-scale Cobb-Douglas function when the underlying production function is rather different, or even when there is no well-defined production relation for the data at hand, perhaps because the output and input variables are aggregates.

12This argument has been rediscovered many times. One version appears in Phelps Brown (1957) as noted by Biddle (153). Another was briefly given by Simon and Levy (1963), and a more sophisticated time-series version by Shaikh (1974). The latter prompted a reply (Solow, 1974). A few years later Simon (1979) again raised concerns, in a paper with a gestation period of more than a decade. In an account of Douglas’s work, Samuelson (1979) also presented his own version of the argument, seemingly unaware of its history.

13Most of these arguments are less persuasive than Tinbergen’s. When factor prices vary—over time, say, or across countries—the value-added identity may not say much about the effects of mis-specifying a production relation. In the two-factor case, the plane represented by the identity will take a different angle each time that factor prices vary. Unlike a production surface, the value-added identity does not represent a surface on which a given economy can move around, as some critics seem to assume.

14Biddle discusses the issue several times and mentions some of the papers cited above; and I think he is right to give priority to Tinbergen’s account. Nevertheless, I would have liked to see him say more. The debate is part of the reception of the Cobb-Douglas regression, not least among Nobel laureates—Samuelson, Simon, Solow, Tinbergen. The ideas have been widely discussed, but some applied researchers remain unaware of them, and a definitive historical account would have been good to have.

15The generality of the argument has sometimes been overstated by heterodox economists, not least those who want to interpret the critique as somehow fatal to much of mainstream economics. In practice, the critique requires auxiliary assumptions, as Shaikh and Simon acknowledged. Nor can it explain why researchers estimating more general production relations will sometimes reject Cobb-Douglas. There are now many estimates of the elasticity of substitution between capital and labour in the United States that suggest a value well below unity. Nevertheless, the critics are right that an apparently good fit for a Cobb-Douglas function should be treated cautiously.

16Here the place of Robert Solow in the story is noteworthy. His view of the Cobb-Douglas production function has been ambivalent in interesting ways. Above all, he is uneasy about the possibilities it closes off, notably factor-biased technical change and time-varying factor shares. In a late-career retrospective, Solow has written of its “Santa Claus properties” (Solow, 2007, 13). His scepticism goes back a long way: his classic 1956 paper makes use of Cobb-Douglas, but also an early version of the CES production function, as Biddle notes (159). At other times, Solow defended Cobb-Douglas estimates against their critics; his personal correspondence with Herbert Simon has been published in Carter (2011). Perhaps Biddle could have provided a little more of this history.

17Solow’s views might prompt wider reflections. The Cobb-Douglas regression represented a step forward almost a century ago, but there is something a little absurd in its simplicity. Imagine explaining to a mathematician how this function has been routinely applied to so many different problems, often without much attention to alternatives. It is not clear why the elasticity of substitution between capital and labour should always be unity. One alternative, the CES function, is itself venerable—sixty years old as of 2021—and often a better choice. In some areas of modern economics, the use of simulation-based approaches means that adopting CES is straightforward. It is likely that Cobb-Douglas functions will be less central to the future of economics than to its past.

18In the meantime, it is useful to have a history. Dr Johnson said of Milton’s Paradise Lost that “None ever wished it longer than it is”. Faced with more than three hundred pages on the estimation of Cobb-Douglas production functions, I expected to say much the same. It is a tribute to the quality of Biddle’s scholarship and writing that I finished the book with a slight sense of regret, having found it an instructive and sometimes absorbing read. It will be a valuable reference not only for historians of economics and econometrics, but for anyone with an interest in estimating production relationships.