Production and Distribution Theory in the 1920s

Both Douglas’s decisions about how and why to pursue the research program that began with “A Theory of Production” and the reactions of other economists to his work with the Cobb–Douglas regression reflected certain theoretical and conceptual frameworks important to economic researchers working in the early twentieth century, some of which had their roots in the “classical economics” of the nineteenth century. Central to classical economics was a desire to discover the “laws of production,” or the determinants of the amount of “wealth” that a society would produce, and the “laws of distribution,” or the determinants of how that wealth was divided among society’s members.Footnote ³ In seeking laws of production, the classical economists began with a conceptualization of production in which wealth was created by combining “labor,” or human effort; “land,” or the free gifts of nature; and “capital,” which meant previously existing wealth that was used up in the process of creating new wealth. The conceptualization could be applied at the level of a single farm or factory, an industry, or society as a whole. It was understood that land, labor, and capital were aggregated categories of heterogeneous elements, but for analytical purposes they were often treated as three distinct and homogenous requisites to the production of wealth, and termed the “agents” or “factors” of production.

This conceptualization created questions of interest for the classical economists regarding the relationship between the quantities of the three factors employed in a production process and the amount of wealth produced. One question concerned the impact on the quantity of wealth produced of increasing all the factors of production by the same proportion. If, for example, the amounts of land, labor, and capital used in production were all doubled, would the amount of wealth produced also double, fall short of doubling, or more than double? By the early twentieth century, these three possibilities were commonly labeled “constant returns to scale,” “decreasing returns to scale,” and “increasing returns to scale” in production.

A second question concerned the impact of increasing the quantity of one factor of production while leaving the quantities of the other factors unchanged. The classical economists assumed that the “law of diminishing returns” provided the answer to this question: successive, equal-sized increases of any factor of production, holding constant the amounts of the other two factors employed, would lead to successively smaller increases in wealth. This “law,” when applied to the production of wealth by society as a whole, became a fundamental assumption underlying some of the most important propositions of classical economic theory.

The classical economists’ discussion of the distribution of wealth ran in terms of three social classes, landlords, laborers, and capitalists, each consisting of the owners of one of the factors of production. The share of society’s wealth claimed by each of these classes depended on the price of the factor of production they owned – the rent of land, the wage rate for labor, and the rate of profit on the money that producers spent on capital. There were competing theories about how these factor prices were determined, and how they were likely to change over time with the growth of population and of the quantity of society’s wealth set aside as capital for future production, but assumptions about returns to scale and diminishing returns – that is, the assumed laws of production – played key roles in those theories.

During the 1870s, several economists made similar and strikingly innovative contributions to economic theory. The work of these economists and their immediate followers has been called “the marginal revolution” in economics, and it led to the creation of a new approach to and body of economic theory that came to be known as “neoclassical economics.”Footnote ⁴ Neoclassical economics would eventually become the dominant paradigm in economics in the United States and Western Europe, but this process had hardly begun at the time Cobb and Douglas introduced the Cobb–Douglas regression. The decades of the 1920s, 1930s, and 1940s have been well described as the period of “interwar pluralism” in economics, during which the literature of the subject included arguments for and examples of a variety of distinct approaches to economic analysis, each characterized by different ideas about the scope and method of economics, including the role of statistical data in economic research, and about the assumptions that should form the starting point for economic theory (Morgan and Rutherford Reference Morgan and Rutherford1998). Further, a single economist might employ theories and concepts drawn from more than one of these approaches, Paul Douglas himself being one example.

Certain aspects of the emerging neoclassical school are particularly relevant to the story of the Cobb–Douglas regression. A first was the belief of many neoclassical economists that the first language of economic theory should be mathematics; that is, to as great an extent as possible, the assumptions of an economic theory should be expressed in mathematical form, and the propositions of the theory derived from those assumptions through mathematical analysis. This idea, to which almost no classical economist would have subscribed, was pushed by only some of the marginalist pioneers, and during the interwar period, both the degree of enthusiasm for it and the extent to which it was put into practice, while increasing, still varied considerably across enthusiasts for the neoclassical approach.Footnote ⁵

Second, central to the contributions of the marginalist pioneers and the subsequent neoclassical school of economics was a new theory of distribution, one that was tightly linked to a theory of production, and that proposed a single principle, “marginal productivity,” to explain the price received by sellers of any specific factor of production, for example, a tool, a building, an acre of grazing land, an hour of labor of an accountant, or an of hour unskilled labor. The theory sought to describe the determination of the prices of factors of production in settings in which producers sought to maximize profits, and all factors of production and outputs of production were traded in perfectly competitive markets.Footnote ⁶ It did so by characterizing an equilibrium in such markets, a balance of economic forces that rested ultimately on the preferences of the people participating in the markets and the technologies available for creating goods and services from factors of production, an equilibrium that would change in predictable ways should preferences or technological knowledge change.

The basics of this “marginal productivity theory of distribution” can be presented efficiently using mathematical notation, an approach that was becoming common by the interwar period. Consider first a twice differentiable mathematical function describing the relationship between some quantity of good or service produced (y), and the quantities of the m factors of production (x₁, x₂…x_m) used to create the good or service:

By the mid-twentieth century, it was becoming standard for neoclassical economists to refer to a function such as Eq. (1.1) as a “production function.” Also, the x’s were increasingly being referred to a “inputs,” and y the “output” of the production function, although the language of “factors of production” was still commonly used.

Choices could be made about the characteristics of this function to embody the common types of assumptions that had been employed by the classical economists in theorizing about production. The derivative of the function with respect to some x_j, that is, $\partial y/\partial x_j$, was termed the “marginal productivity” of input x_j, and was trivially assumed to be positive for all inputs. If the second derivative of the function with respect to an input was negative, then that input was said to be characterized by diminishing marginal productivity, or to use the older phrasing, subject to the law of diminishing returns. A common assumption in the basic form of the theory was that all inputs were subject to the law of diminishing returns. Assumptions about the form of the function also determined the nature of the “returns to scale” in production (decreasing, constant, or increasing), which might be different for different levels of output.Footnote ⁷

Letting r_j represent the price, or rental rate, of a unit of input x_j, the marginal productivity theory held that in equilibrium, for every factor of production,

$r_j=p\frac{\partial y}{\partial x_j}$(1.2)

where p was the price per unit of y. The quantity on the right was termed the “value marginal product” of x_j, that is, the increase in the producer’s revenue obtained by increasing the amount of input x_j by one unit, although sometimes in describing this central implication of the theory, the word “value” was left implicit. Also, if the input x_j was used in the production of many goods and services (as was, for example, unskilled labor), the value marginal product of x_j in the production of any of those goods and services would be equal to r_j. Put another way, there would be only one price for the input x_j no matter how it was used. The condition (1.2) characterizing the prices of factors of production also explained incomes – the income of an individual would be the sum received from selling the factors of production he owned. So, for example, the total income of an unskilled laborer who had no input to sell except labor would be the hourly wage rate (the value of his marginal product in any type of production activity) times the number of hours worked.

Again, Eq. (1.2) describes the equilibrium state of an economic environment in which markets are perfectly competitive and the preferences of individuals, technological knowledge, and the supplies of non-manufactured inputs (in particular, labor inputs) are held constant. Neoclassical economists understood this to be an abstraction, not a description of reality in any part of the economy. They believed, however, that circumstances and processes in the real economy were often close enough to those captured by the abstract theory for the theory to provide compelling explanations for observed differences or changes in the prices of factors of production, and thus the incomes of the owners of those factors.

Douglas saw the Cobb–Douglas regression as a means of determining the characteristics of actual production functions using statistical data. Given the close relationship between the characteristics of the production function and the distribution of income posited by the marginal productivity theory, it is obvious how valuable such a procedure could be to the neoclassical research program.Footnote ⁸ For example, knowledge of the rate at which the productivity of unskilled labor diminished (the second derivative of a function like Eq. (1.2) with respect to unskilled labor) would provide quantitative answers to questions about how wages would be affected by changes in the quantity of unskilled labor due to migration, population growth, or education. And Douglas would, beginning in the 1930s, argue that his procedure could provide a statistical test of the marginal productivity theory itself, via a comparison of actual wage levels to the statistically determined value of marginal product of labor in production.

During the interwar and early postwar decades, there was a certain flexibility in the way that the neoclassical production function concept was used, in the sense that a production function might be assumed to describe the relationship between inputs employed and output created in the production of one particular good, or by a single firm, or by an industry (several firms producing the same output), or in the economy as a whole. In the latter case, the analysis ran in terms of concepts similar to those employed by the classical economists – land, labor, and capital as factors of production, and an aggregated, homogenized total output concept. This last type of production function came to be known as an aggregate production function, as did the production function used by Douglas, which portrayed the relationship between inputs employed by and output produced by the US manufacturing sector taken as a whole.

This flexibility reflects another important aspect of neoclassical economics at this time: Several distinct variants of the marginal productivity theory existed, two of which are particularly important to understanding Douglas’s own arguments about what his empirical technique could accomplish, and the reaction of other economists to Douglas’s research with the technique. The first variant had its roots in the version of the theory proposed by American economist John Bates Clark. His was a theory of how the wealth produced by society as a whole ended up being divided between the owners of two factors of production, labor and capital, with land being considered by Clark to be a form of capital. The marginal productivity of a homogenous “social” labor input in the production of wealth determined the single wage rate in the economy, while the marginal productivity of a social fund of capital determined the rate of interest. Clark’s version of the theory, then, was compatible with an aggregate production function defined at the level of the economy as a whole.

A second variant of the marginal productivity theory can be called the “Walrasian” variant, as it was built on the theoretical contributions of the early French marginalist Leon Walras. Like the other marginalist pioneers, Walras was particularly interested in understanding how the prices of goods and productive factors were determined in a competitive market economy. He insisted, however, that an adequate theoretical account of the process of price determination must embody the interrelatedness of all markets in such an economy, in the sense that the price of any one of the myriad of unique goods or productive factors in an economy would depend on the conditions affecting the supply of and demand for every other good and productive factor – that potentially, the price of ice cream could be affected by a change in the demand for, or the technology for producing, hammers. This, coupled with a belief that economic theory should be expressed in mathematical form, led him to represent the equilibrium of input and output prices in a competitive market economy as the solution to a system of simultaneous equations.Footnote ⁹

Economists who built on Walras’s contributions still arrived at the conclusion expressed in Eq. (1.2), that the price of any input to production would be equal to its value marginal productivity, but in their models they assumed (as did Walras) that each good in the economy had a distinct production function. Aggregation – grouping goods together into categories for the purposes of analysis –was something the Walrasian neoclassicists worked hard to avoid, as it obscured some of the intermarket relationships that they considered a crucial feature of price determination. In describing factors of production, a term like “capital” might be used but only as a category label for a heterogeneous collection of “capital goods,” or goods used in the process of production, like the various types of buildings, tools, and machines. Using a homogenous “capital” concept for analytical purposes could be misleading. Similarly, although there might be a mathematical relationship between the quantity of a somehow aggregated collection of goods and services, and the quantities of somehow aggregated collections of capital goods and labor types used in their production, these relationships would necessarily be complicated and difficult to disentangle amalgams of the production relationships that really mattered for the determination of prices and the distribution of income – those characterizing the production functions of distinct individual goods. As shall become more clear, many economists who embraced the Walrasian variant of the marginal productivity theory were critical of Douglas’s use of the phrase “production function” to describe the relationships he estimated using the Cobb–Douglas regression.

Empirical Economics in the 1920s

At the time that Cobb and Douglas’s “A Theory of Production” appeared, there was something of a revolution underway in empirical economic research. Prior to World War I, as today, economists used statistical data to discern and represent what was really going on in the economy, to buttress claims about the causes and effects of economic phenomena and policies, to defend or test the assumptions and conclusions of theory, and so on. But with the exception of the work of a few pioneers such as Wesley Mitchell, Warren Persons, and Irving Fisher, most economists who used statistical data simply presented raw numbers or percentage shares in tables or in the text of their books and articles, making no use of derived statistical measures such as means, standard deviations, or index numbers. This began to change, and change rather quickly, during the 1920s, and by the end of that decade, the well-trained empirical economist understood basic statistical theory and applied it in constructing index numbers, tabulating frequency distributions, and calculating summary statistics.Footnote ¹⁰

Douglas’s own development as an economic statistician paralleled these changes in what represented good statistical practice for economists. For example, in his early work on immigrant skill levels and labor turnover, he reported numbers and percentages in tables and text (Douglas Reference Douglas1918, Reference Douglas1919). In his research during the 1920s on trends in real wages and working conditions, however, Douglas showed his ability to construct and critique index numbers, and to calculate means and measures of average deviation to illustrate relevant points (Douglas Reference Douglas and Lamberson1921, Reference Douglas1930). It seems likely that Douglas taught himself the statistical skills necessary to keep up with the advancing field during the 1920s, as his account of his graduate education makes only the briefest reference to a class in statistics, while offering several hints that he needed to work on his own to make up for general deficiencies in his graduate training.Footnote ¹¹

Douglas’s work on real wages also exemplifies an important strand of the 1920s literature in empirical economics. Often the chief task of an author was simply to provide, through statistics, as accurate a portrayal as possible of some aspect of economic activity, such as recent movements of the retail price level or the pattern of international trade flows. Because government programs for collecting economic statistics were still in their infancy, one of the more valued skills of a good empirical economist was the ability to construct a credible and comprehensive quantitative account of some economic phenomenon of interest from the fragmentary statistical evidence available on that phenomenon. Among other things, this required the researcher to locate the relevant data sources, to extrapolate from time periods or sectors for which data were relatively complete to time periods or sectors in which they were more scarce, and to defend or assess the likely accuracy of the results using logic, implicit theorizing, and various consistency checks across data from different sources. For example, the US Census of Manufactures might provide comprehensive statistics on manufacturing output at five-year intervals, while a trade organization might provide annual data on output for a particular industry. An author might then use information from two censuses on the ratio of the latter industry’s output to total manufacturing output to produce annual estimates of total manufacturing output for intercensal years. Data from a few state-level censuses from these years might then be used as a check on the results. This type of work required detailed reporting and explanation of the various steps used to build up estimates, and also a fair amount of persuasion, as the author tried to convince readers not only that the steps taken to produce the estimates were the most reasonable ones under the circumstances but also that the resulting statistical picture, with all its shortcomings, was still accurate enough to be useful.

As noted, this type of statistical work and argumentation was an essential feature of Douglas’s work on real wages, but it was also an important part of his work with the Cobb–Douglas regression, especially in the early years. And while critics of this aspect of Douglas’s work sometimes faulted the strong claims he made for the accuracy of his results, they seldom criticized the thoroughness of his search for data sources or his decisions about how to build estimates from the limited data resources available to him.

Douglas’s initial research employing the Cobb–Douglas regression also had two features in common with work at the frontier of empirical economics in the late 1920s and early 1930s. One was the use of least squares regression and correlation analysis. The second was the explicit attempt to estimate, using statistical data, functional or causal relationships implied by economic theory. During the 1920s and early 1930s, there was a growing literature in which regression techniques were used in an attempt to estimate the real-world counterparts of the supply and demand curves of theory. As Morgan (Reference Morgan1990) has shown, this work played an important role in shaping the approach to combining statistical methods and economic theory that become the standard econometric practice in the later decades of the twentieth century. Still, it should be remembered that at the time it first appeared, this research program, which I shall call the neoclassical-econometric program, was rather speculative and esoteric. Douglas, however, saw it as the wave of the future, and in The Theory of Wages explicitly linked his own work to it:

So, when the Cobb–Douglas regression made its debut, it represented a bold attempt by an established empirical economist to join up-to-date statistical methods with a still-controversial theoretical framework. During the 1930s, new and more technically sophisticated statistical methods were being introduced into the empirical economics literature, and acceptance of the neoclassical framework by economists was increasing. The debate over Douglas’s production function research would reflect both these trends.

The Debut of the Cobb–Douglas Regression: “A Theory of Production”

As noted above, the results of estimating a Cobb–Douglas regression first appeared in 1928 in the article “A Theory of Production” (Cobb and Douglas Reference Cobb and Douglas1928). And while Douglas’s Reference Douglas1934 book The Theory of Wages would make very clear the connection he saw between the estimation of the Cobb–Douglas regression and the project of testing and giving quantitative content to the marginal productivity theory of distribution, this connection was at most implicit in the 1928 article. The article opened with a statement of goals. Given that “refined” measures of the volume of manufacturing output for recent years now existed, Douglas argued, it seemed worthwhile to attempt to measure the relative amounts of labor and capital used to produce that output. If these amounts could be even approximately ascertained, a number of interesting tasks could be undertaken. They included determining the extent to which increases in output were due to increases in the quantities of labor and capital vs. improvements in technique; measuring the marginal physical product of labor and capital; discovering whether the “theories of decreasing imputed productivity” were historically valid, and if so, attaching quantitative approximations to these “assumed tendencies”; and finally, with estimates of imputed physical product in hand and measures of real wages available, determining “whether or not the processes of distribution are modeled at all closely upon those of the production of value.” This vague assertion of a possible relationship between production and distribution was clarified a bit at the end of the paper, when Douglas argued that he had revealed a decided tendency for distribution to follow the laws of imputed productivity while noting that this alone allowed no ethical or policy conclusions to be drawn (Cobb and Douglas Reference Cobb and Douglas1928, 139–40, 163–64).

Douglas next described and defended his measures of capital and labor. Capital presented the greatest challenge. On the way to presenting an index of the amount of capital employed in US manufacturing from 1899–1922, Douglas catalogued a daunting array of problems with the existing data on capital along with his solutions to these problems, solutions that he frankly critiqued but also defended as adequate to the task at hand. For example, Douglas believed that the “capital” he should be measuring was fixed capital (buildings, tools, equipment, and machinery), but not “working capital,” which included raw materials, goods in process, and inventories. While every Census of Manufactures reported the total value of capital employed, only some of them segregated out the value of buildings, machinery, and equipment.Footnote ¹² Douglas described how he used the share of total capital represented by fixed capital in the census years for which it was reported to estimate a trend in this proportion, and then used this estimated trend to assign a value to fixed capital for census years in which it was not separately reported. Douglas defended his procedure by pointing out that the value it produced for 1922 (fixed capital representing 46.5 percent of total capital) was close the value reported for Missouri in that state’s 1923 census.

A tougher problem was created by the fact that, according to an expert Douglas queried at the Census Bureau, dollar values of capital reported to the census probably represented original cost rather than current value, requiring Douglas to (i) estimate what proportion of a given year’s fixed capital stock had been added in each of a number of preceding years and (ii) reduce each year’s estimated increment to the value of the fixed capital stock to a constant dollar value, using a capital-price index of some sort. Without getting into the details of how Douglas handled this problem, suffice it to say that it required him to construct price and quantity indexes for two categories of capital goods using partial data on the production and prices of various basic commodities (e.g., pig iron and coke) along with an index of money wages, liberally applying proportionality assumptions throughout the process.Footnote ¹³

These brief descriptions of Douglas’s methods of producing his capital series actually underrepresent their complexity and the number of heroic assumptions upon which they rested, and indicate the large number of potential points of contention presented to any critic of Douglas’s work. It should not be forgotten, however, that these were the sort of things that empirically oriented economists of the time did, and felt they had to do, in order to build up the statistical pictures of economic activity that they believed were required for economic science to move forward.

Estimating the aggregate quantity of labor used in manufacturing was more straightforward, at least in census years, in which manufacturing establishments reported the average number of “wage earners” employed throughout the year. Employment numbers for intercensal years were filled in with the help of annual employment counts from New Jersey, Massachusetts, and Pennsylvania along with reasonable rules for dealing with the differences in employment growth between census years in these states vs. the nation as a whole. Douglas commented that the measure would have been better if it had included clerical workers, and better still if it had been based on man-hours rather than number of men. As a measure of the output of the manufacturing sector, Douglas borrowed “E. E. Day’s well known index of the physical volume of production for the years 1899–1922” (Cobb and Douglas Reference Cobb and Douglas1928, 149–50; Day and Persons 1920), noting later in the paper that this involved the assumption that the level of manufacturing output moved proportionately with the level of total output. Douglas presented his three series for capital, labor and product (C, L and P) as index numbers taking the value of 100 in 1899.Footnote ¹⁴

The first of two sections written by Cobb (the paper’s initial footnote identified which sections were written by each author) presented the paper’s promised “theory of production”: aggregate manufacturing output was a linear homogenous function of aggregate labor and aggregate capital; the general form of the function was P = bL^kC^1-k; and the specific form of the function was P = 1.01L^.75C^.25. Beyond mentioning that the values chosen for b and k were the “best … in the sense of the Theory of Least Squares,” no details of the estimation procedure were reported (152).Footnote ¹⁵

Using P’ to represent the value of the production index predicted by the regression and P the actual value, Cobb portrayed the goodness of fit of the regression in a number of ways: tabulating and plotting the percentage deviation of P from P’ in each year, calculating the mean absolute (percentage) deviation (4.2 percent), noting that P was closer to P’ than to its own three-year moving average, reporting the correlation coefficients between P and P’ (.97), and between the deviations of P and P’ from their respective moving averages (.93).

Cobb’s second section discussed and derived mathematical properties of the fitted function, including its implied functions for the productivities of total capital and total labor, the marginal productivities of capital and labor, and the elasticities of product with respect to capital and labor. Then, using the actual values of P, L, and C along with formulas for marginal productivity, he plotted the values of marginal productivity of capital and labor implied by the data along the theoretical curves of marginal productivity implied by the estimated regression.

It remained for Douglas to make the case that “the equation P = 1.01L^3/4C^1/4 describes in a fairly accurate manner the actual processes of production in manufacturing during this period.” He reviewed the evidence of goodness of fit, both the “close consilience between P and P’” and the clustering of data-based measures of marginal productivity along the theoretically derived marginal productivity functions. He raised the possibility that the good fits were due to spurious correlation between trending series, noting that “it has some times been charged that … equally good results would be secured by comparing the relative movements of hogs in Wisconsin, cattle in Wisconsin, with the physical product in manufacturing,” but dismissed this charge by arguing that there was an a priori theoretical connection between capital, labor and output that did not exist for pigs, cattle, and output, and by reminding readers of the high correlation between the deviations of P and P’ from their three-year moving averages. Employing a tactic that he would use throughout his 20-year defense of his production research, Douglas then explained that even observations for which P’ was a poor approximation for P strengthened the case for the estimated equation. If one looked at years with large differences between predicted and actual output, those in which P was below P’ were recession years, and those in which P was above P’ were years of prosperity. Since the capital index measured existing capital rather than capital utilized, and the labor index was men rather than man-hours, one would expect this pattern: in a recession, when plants were idled and overtime eliminated, the capital and labor indexes overstated the amount of the inputs actually employed, and so the equation produced a predicted output that was too high. Likewise, prosperities were periods of full capital utilization and long, intense hours for workers, leading the indexes to understate true input use (Cobb and Douglas Reference Cobb and Douglas1928, 160–61).

Douglas’s final argument in defense of the validity of his “theory of production” was to show that “the process of distribution approximate(s) the apparent laws of production.” Doing so required additional constructive data work. Combining Cobb’s formulas for marginal product with his own basic data series for L, C, and P allowed Douglas to create an index of physical productivity of labor. He converted this to a value-product series by using the wholesale price indexes published by the Bureau of Labor Statistics (BLS) to construct an annual series of the price of manufactured goods relative to all goods. The resulting index of value product per worker was then compared to an index of real wages in manufacturing that Douglas had recently created (Douglas Reference Douglas1926). Douglas reported that the wage and value-product series had a correlation of .69. Douglas also cited a number that ended up having a large impact on readers of the Cobb–Douglas paper: the National Bureau of Economic Research (NBER) had estimated that over the 1909–19 period, wages and salaries represented 74 percent of the total value added in manufacturing, a number stunningly close to the .75 estimate for k produced by the production regression.

The law of production had not been “solved,” Douglas concluded, but an approximation had been made and a line of attack on the problem indicated. Much more work remained to be done. The series for labor, capital, and output could all be refined. Other formulas, including one that allowed k to vary over time, could be tested. Other sets of data could be analyzed, eventually allowing comparisons between manufacturing and other sectors and international comparisons as well. Natural resources could be included as a productive factor in future work. Interestingly, Cobb had also included an assessment of where the research stood and where it should go in one of his sections, and it was somewhat more tentative than Douglas’s: “It is the purpose of this paper, then, not to state results, but to illustrate a method of attack. In choosing a definite Norm for Production as a first approximation, it is not at all certain that we have arrived at the best possible. The advantage of choosing a norm at all seems to be that it involves us in logical consequences that can be compared to the facts as we get the facts.” (Cobb and Douglas Reference Cobb and Douglas1928, 156).

Reactions to “A Theory of Production”

Douglas made bold claims in “A Theory of Production”: Using generally available data and accessible statistical techniques, he had shown that the actual relationship between the amount of capital and labor used in manufacturing and the quantity of manufacturing output could be closely approximated by a simple function, one that embodied and allowed quantification of the hypothesis of diminishing marginal productivity of labor and capital. He had demonstrated a relationship between the characteristics of this “law of production” and the distribution of income between labor and capital, a relationship posited by a well-known but still-contested theory of distribution. It is thus not surprising that the paper attracted the attention of a number of economists.

Sumner Slichter was assigned to discuss the paper at the AEA meetings, and his comments were decidedly negative. He harshly criticized Douglas’s capital index, citing the known unreliability of census capital figures and of the price data that Douglas had used to deflate capital values. He showed how small biases caused by inaccurate price indexes in early years of the series could cumulate, and noted that the capital series was altered considerably if different years were chosen as base years for deflating. These problems “rob[bed] Prof. Cobb’s computations of the significance they would otherwise possess” (Slichter Reference Slichter1928, 168).

Slichter’s complaints went beyond issues of data quality, however, as he believed the entire project to be wrong-headed. Despite the fact that the marginal productivity theory was not explicitly mentioned in the paper, Slichter thought he could see a hidden agenda, and he did not approve: “Professors Cobb and Douglas conclude that it has been statistically demonstrated that the relationship between the agents of production on one hand and the volume of output on the other meets the requirements of the marginal productivity hypothesis.” Slichter disputed this specific claim, and argued more generally that marginal productivity theory had little to offer as a framework for thinking about distribution. “The description of the relationship between productive agents and physical output sheds little light upon what happens in the market place where distribution of income actually takes place.” (Slichter Reference Slichter1928, 168) Marginal productivity theory required instantaneous and complete adjustment of factor prices to changes in output prices and vice versa, something that clearly was not the case, since “every one knows” that factors like land and capital are obtained on long-term contracts and that wages are sticky. Entrepreneurs could not know the marginal contribution of each agent, and, for that matter, entrepreneurship had not even been included as a factor in the Cobb–Douglas analysis. Nor was there any element of the equation that accounted for possible technological change. Slichter closed with a final indictment of the research:

Douglas recalled in later years that his initial work with the Cobb–Douglas production function was, in general, poorly received by the profession (Douglas 1979, 905; Reference Douglas1971, 614; Samuelson Reference Samuelson1979, 924). This is not quite true: while almost all economists who commented on or reviewed “A Theory of Production” or The Theory of Wages did find fault with various details of Douglas’s method, most of them expressed considerable enthusiasm for the “method of attack” represented by the research, and some offered constructive suggestions for pushing the research program forward.

A good example of a “friendly critic” of this sort is J. M. Clark, whose article “Inductive Evidence on Marginal Utility” appeared within a few months of “A Theory of Production” and was devoted solely to discussing issues raised by the Cobb–Douglas paper (Clark Reference Clark1928). His criticisms were numerous, but most were constructive, aimed at improving the Cobb–Douglas analysis of marginal productivity rather than discrediting it. Like Slichter, he questioned the accuracy of Douglas’s capital and labor series, but took it for granted that “they will be improved and refined as the authors continue their researches,” offering several suggestions for how this might be done (Clark Reference Clark1928, 451). He suggested an approach for estimating the return to fixed capital using only the (more reliable) data on total capital, and even estimated his own augmented version of the Cobb–Douglas regression. Clark believed that the Cobb–Douglas equation offered a good account of the “normal” or long-run relationship between labor, capital, and output, but did a poor job of representing the impact of cyclical fluctuations in labor and capital utilization, which were governed by a “different law.” He proposed altering the function so that the normal relationship between capital and labor could be adjusted by a factor representing cyclical swings, and suggested P = L^kC^1-k(L/L_n)^m, where L_n represented the “normal” level of employment, meaning that which the capital stock was designed to accommodate.Footnote ¹⁶ Clark defined L_n as a seven-year centered moving average of Douglas’s L. He fixed k at 2/3, as Cobb had found this to fit the prewar years better than k=.75, and Clark believed the war years too abnormal to include in the analysis. A sort of grid search procedure was used to set .63 as the value for m. For the years Clark included, 1902–16, his formula produced a lower sum of squared errors than the Cobb–Douglas formula, because it did a better job of matching the amplitude of the cyclical fluctuations in P.

Clark was troubled by the fact that the Cobb–Douglas regression left no room for improvements in technology to affect productivity. Accurate measurement of marginal products required that the impact of technological progress be isolated or eliminated, but experience suggested that such progress was the main cause of the growth of output observed in the data. Clark argued that either some means of adjusting the capital and labor series to remove the impact of technological development should be developed, or else the growth in output attributed by the regression to growth in capital should be partly attributed to “progress.” His tentative suggestion as to how such data adjustments or attributions might be made only served to indicate how difficult this problem was. But it could be solved, Clark believed, if not with data based on historical aggregates, then with comparative studies of “simultaneous” data from different industries. Clark concluded that the Cobb–Douglas study was “a bold and significant piece of pioneer work in a hitherto neglected field,” which he clearly hoped would be followed up by others (Clark Reference Clark1928, 467).

Another prominent early critic who believed that the Cobb–Douglas approach should be “modified, not abandoned” was Douglas’s colleague from University of Chicago Henry Schultz (Schultz Reference Schultz1929). Schultz’s main criticism was that Cobb and Douglas’s statistical procedure, which employed time series data but made no adjustment for secular changes, could not result in a verification of a static theory like the marginal productivity theory.Footnote ¹⁷ Referring to his own approach to estimating neoclassical supply and demand curves, Schultz described the strategy of adjusting the data to remove long-term trends, then correlating deviations from those trends in order to isolate relationships that were closer in principle to the concepts of static theory. Long-term relationships between variables, such as those estimated by Cobb and Douglas, were likely to be interesting for their own sake, but by adopting alternative methods, perhaps including some of those employed in empirical studies of demand, one could also potentially identify short-run marginal productivity curves and the factors that shifted them.

The second published estimates of Cobb–Douglas regressions appeared in 1930 in a short article by Cobb, in which he used time series data from the annual Massachusetts Census of Manufacturing to estimate the regression. Cobb reported that he had encountered difficulties in attempting to estimate the Cobb–Douglas regression, and had sought the advice of Ragner Frisch. As a result, Cobb made two changes in the estimation method: he estimated the coefficients of capital and labor separately, thus relaxing the assumption that the production function was linear homogenous, and he estimated the function using “diagonal mean regression.” Diagonal mean regression had been proposed by Frisch in part as a solution to what Morgan (Reference Morgan1990, 138) called the “regression choice problem”: in using regression to estimate the relationship between several economic variables, which variable should be chosen as the dependent variable?Footnote ¹⁸ Frisch began with an assumption that there was a deterministic relationship between the variables, and that the only reason the actual data did not reveal this exact relationship was because variables were measured with error. For example, if two variables were related by the linear equation X₁ = a + bX₂, and both variables were measured with error, the true value of b would be bounded by the regression estimate of b obtained using X₁ as the dependent variable and the estimate obtained using X₂ as the dependent variable. Where within these bounds the true b fell depended on the relative variances of the measurement errors in X₁ and X₂. Frisch’s diagonal mean regression amounted to estimating the true b as the geometric mean of the two bounds. It was a concession to the fact that the variances of the errors were typically unknown, and also an unsuccessful attempt to produce regression estimates that were invariant to changes in the scale of measurement of the variables.

It is easy to imagine why Cobb felt that the diagonal mean regression estimator was “particularly well adapted” to his project (Cobb Reference Cobb1930, 705), as it was clear that all three of his variables were measured with error, while there was no solid information concerning which were more error-ridden. Cobb gave no economic reason for wanting to relax the restriction that the coefficients summed to one. In any case, following Frisch’s suggestions created difficulties for Cobb rather than solving them. Estimating the regression for six different industries and for manufacturing as a whole in three different time periods, Cobb got coefficient estimates that were all over the map, including negative values and values greater than one. The sum of the coefficients in these regressions ranged from .94 to 5.17. When he applied the same method to the US data from the Cobb–Douglas paper, the coefficient for labor was 1.63 and for capital .48. Beyond a few unconvincing attempts to make economic sense of some of the more bizarre results, Cobb had little to say about what had happened, and this paper marked the end of his work with the Cobb–Douglas regression.

Cobb’s article should be classed as a criticism of Douglas’s research program because it raised very serious questions about the credibility of marginal productivity estimates produced by estimating the Cobb–Douglas function. Douglas’s reaction to it was rather curious – he ignored it completely, even in subsequent works in which he discussed his own estimates derived from the same Massachusetts data,Footnote ¹⁹ and even though Douglas would wrangle with other critics for several years over how the regression choice problem should be treated in the case of production function estimation.Footnote ²⁰

The reasons for the differing reactions of Cobb and Douglas to Cobb’s discouraging results – with Cobb moving on to other areas of research and Douglas deciding that further work with the regression was a potential path to establishing his scientific respectability (Douglas Reference Douglas and Brown1967) are largely a matter of speculation, but I would argue that one reason is the difference in the two men’s academic training and orientation. Douglas’s undergraduate and graduate training was in economics, during which he read the classical works in the field and used several of the standard economics textbooks of the time. Cobb was trained as a mathematician, serving on the faculty of mathematics at Amherst and having received a Ph.D. in mathematics from the University in Michigan in 1912 (Collier Reference Collier2016).Footnote ²¹ In his reminiscences about the writing of “A Theory of Production,” Douglas would refer to Cobb as a friend and a mathematician. I suspect that the Cobb–Douglas collaboration was not the result of a shared interest in the economic questions underlying Douglas’s research at the time, but one of convenience – Douglas had an essentially economic question, in that he wanted to characterize the relationship between capital, labor, and output that he saw in his time series data with a simple mathematical function, and sought help from a mathematician that he had befriended during his short time in Amherst. And Cobb had a quick answer for Douglas (Douglas Reference Douglas1934).

But the two men thought about the regression they had fit to the economic data in two different ways. Cobb saw it as a mathematical-statistical object, with results to be interpreted with the aid of statistical theory. When thinking about the changes in the coefficient estimates associated with changing the choice of what variable was “dependent” in the regression, Cobb was drawn to Frisch’s approach to the problem, which involved considering the relative error variances of the three statistical variables involved, and/or altering the objective function to be minimized. Douglas, however, thought about the regression as an economic object, so that economic theory had a role to play in specifying the regression and interpreting the results. He has already indicated this in “A Theory of Production,” when he responded to the criticism that “equally good results would be secured by comparing the relative movements of hogs in Wisconsin, cattle in Wisconsin, with the physical product in manufacturing” by commenting that “there is a logical and economic connection between labor, capital, and product which is not present in the attempted reductio ad absurdum” (Cobb and Douglas Reference Cobb and Douglas1928, 160). In Douglas’s view, the choice of dependent variable in the Cobb–Douglas regression was obvious because economic theory and common sense clearly indicated the causation ran from the quantity of the inputs to the quantity of the output, and he would later make this point forcefully when the sensitivity of the regression results to the choice of dependent variable became an important issue on the debate over the value of Douglas’s technique.

Bringing the Marginal Productivity Theory to the Forefront: The Theory of Wages

Though clearly stung by some of the criticisms of “A Theory of Production,” Douglas pushed ahead with his new method, making the Cobb–Douglas regression the centerpiece of his The Theory of Wages.Footnote ²² The first section of the book was devoted to a history of production and distribution theory and an explication of the marginal productivity theory, focusing mainly on J. B. Clark’s version of that theory. Several pages were devoted to explaining the meaning of the assumption of constant returns to scale and its relationship to linear homogenous functions, Euler’s theorem and the question of whether paying all factors their marginal contributions would exhaust the product. He defended this assumption, which was of course embodied in the original Cobb–Douglas regression, by variously labeling it a “common sense” assumption, the “most probable” relationship between inputs and outputs, and a good first approximation to the true relationship. He also cited the arguments of A. A. Cournot and Knut Wicksell that increasing returns would lead to widespread monopoly and decreasing returns to an economy of one-man firms, neither of which obtained in the real world.

Perhaps with an eye to critics like Slichter, Douglas included a chapter on the assumptions of the marginal productivity theory, both explicit and implicit, with long discussions of the extent to which each was valid for the United States. After arranging the key assumptions on a scale ranging from “largely valid but not wholly so” to “partially true but on the whole not true” he commented that

Such critics, Douglas argued, seemed ignorant of the fact that the method of deduction and abstraction used to build the marginal productivity theory was also the method that had achieved great success in the natural sciences.

Another type of unfriendly critic was exemplified by Douglas’s colleague Frank Knight, who argued that the key concepts of (neoclassical) economic theory were essentially static and abstract, while historical data was dynamic, reflecting the action of forces that were assumed away in static theory. Thus, statistical methods could never quantify theoretical concepts.Footnote ²³ Douglas dismissed such arguments rather undiplomatically in The Theory of Wages:

The inductive portion of Douglas’s book began with a slightly revised version of “A Theory of Production.” In his discussion of the data, he now addressed those who had questioned his capital series on the basis of the Census Bureau’s own misgivings about its capital statistics. These “doubting Thomases,” Douglas noted, had overlooked the fact that he had taken specific steps to address the concerns of the bureau’s statisticians. He also cited a new study estimating the capital of American corporations in the 1920s and showed that its results could be made fairly consistent with his own, although this required considerable work. He created an alternative version of his labor series that accounted for changes in salaried and clerical employment as well as that of wage earners, and that also reflected changes in man-hours rather than employment, but these adjustments made little difference to the results.

In rewriting Cobb’s section of the Reference Cobb and Douglas1928 paper, Douglas referred to the estimation method as “modified least squares,” without offering elaboration, though later he listed the normal equations that were solved in constructing the estimates. He also expanded his response to the argument that his results might be due to spurious correlation, and added a reference to a study by two of his students in which the regression was estimated using the trend ratios of his three series, producing .84 as an estimate of k.Footnote ²⁴

The Theory of Wages also reported results from estimating the Cobb–Douglas regression using other data sets. In one chapter, Douglas thanked Cobb for allowing him to publish the results of Cobb’s analysis of the data from Massachusetts. But the results published were not those Cobb had published in 1930. Only the aggregate data for all industries were used. There was no mention of Cobb’s experiment with diagonal mean regression, nor his relaxation of the linear homogeneity assumption. Instead, “values for b and k were chosen so that the squares of the deviations of the computed P’ from P would approach a minimum” (161). This led to an estimated k of .743 when data covering 1890–1926 were used, almost identical, Douglas noted, to the estimate obtained from US data. However, Douglas admitted, this estimate changed considerably if the years after 1920 were excluded from the sample. The deviations of P from P’ in both absolute and percentage terms were tabulated and averaged, and by this measure the fit for Massachusetts was not as good as the fit for the United States. Also, the pattern in which the predicted P’ exceeded actual P in recessions but fell short of it in prosperities, a pattern that Douglas believed enhanced his claim to have estimated the true normal relationship between inputs and output in manufacturing, was not present in the Massachusetts case, and Douglas had no ready explanation for this.

University of Chicago graduate student Aaron Director had estimated the Cobb–Douglas regression using annual manufacturing data from New South Wales from the years 1900 to 1921, and Douglas devoted a chapter to describing Director’s data and reviewing his results. For New South Wales, k was .65, and the average annual deviation of P’ from P smaller than for the United States.

With these results in hand, Douglas returned to the question of the relationship between the estimated laws of production and the processes of distribution. He reminded readers of the striking correspondence between his estimated coefficient of labor for the United States and the NBER’s estimate of labor’s average share of manufacturing output, and then moved to comparisons of the movements over time of value product per worker and real wages. Now, however, he conducted this analysis for each of nine manufacturing sectors and for coal mining. To do so, he drew on government data sources, the estimated indexes of various sorts he had compiled for Real Wages in the United States, and some series specifically created for this analysis. When the real wage indexes were plotted on a graph along with the average productivity indexes on an industry-by-industry basis, Douglas was confronted with a welter of conflicting evidence: productivity indexes soaring above wage indexes in some industries, productivity and wages fluctuating in opposite directions in others, and in a few industries, such as coal, close co-movements of the two series. Working to make sense of these graphs that agreed with neither each other nor the strict marginal productivity theory, Douglas cited various industry-specific factors such as data problems, wartime dislocations of production, and monopoly power. He took the position that the marginal productivity theory implied only long-run or “normal” relationships between movements in productivity and wages, and was less likely to hold for cyclical fluctuations, and noted that the consilience between productivity and wage movements would have been closer had he graphed moving averages. All things considered, he was willing to assert that he had found a “striking agreement” between movements of real wages and “social marginal productivity” up until 1922, and that “the failure of this correspondence to continue … may have been responsible in part for the cumulative breakdown which began in 1929” (Douglas Reference Douglas1934, 183–192, 488).

Simple correlation coefficients between the industry-level wage and productivity measures provided friendlier evidence for Douglas. They ranged from .3 to .8, with most above .6. In keeping with the idea that the marginal productivity theory described long-term rather than short-term relationships, correlations increased when five-year moving averages were used, and decreased (but remained positive) when deviations from the trend were used. Douglas was willing to invoke theory to provide some meaning to these positive correlations, concluding that “since the movements of average value productivity are beyond doubt the causative factors, this relationship furnishes further statistical corroboration that the principles of imputed marginal productivity do appreciably determine what the movements of real wages will be” (Douglas Reference Douglas1934, 198).Footnote ²⁵

The New South Wales’ data provided another challenge for Douglas. Director had estimated a coefficient of .65 for labor in New South Wales’ manufacturing, but when Douglas calculated, on an annual basis, the share of value added in manufacturing formed by wages and salaries, the average value was 56 percent. However, Douglas was willing to submit that these two numbers were “not greatly at variance” (Douglas Reference Douglas1934, 198). The year-to-year movements in real wages and value product were only weakly correlated, but Douglas reminded readers that the expected relationship between wages and productivity was a long-run relationship, and might not show up when annual movements were correlated, especially in a place like New South Wales, where the basic wage rate was set by state agencies. To reveal the “normal” relationship between wages and productivity, Douglas graphed and correlated the five-year moving averages of the two series. He reported a correlation of .97 with a probable error of .011, which could “only cause one to believe that there is a remarkably close relationship between changes in the ‘normal’ amount of value which is imputed to each worker and changes in the ‘normal’ movement of real wages” (Douglas Reference Douglas1934, 202). Examination of the graph showing the five-year moving averages, however, could only cause one to wonder how a correlation of .97 could be found between the two series, and indeed this figure is erroneous. The actual correlation between these two series is .41.Footnote ²⁶

Douglas had much to say about the implications of the results he had presented and how they might be built upon. He cautioned readers strongly that the “close correspondence” between the estimated marginal productivity of labor and the wages of workers did not “furnish an ethical justification for the present economic order,” and that the equation of production “need not be the same for all periods and economies.” Differences in the exponent of labor might arise because of different capital/labor ratios, or differences in the mix of industries making up the manufacturing sector, given that different industries might have different values for k (Douglas Reference Douglas1934, 202–3). He reviewed many of Clark’s (Reference Clark1928) comments on the original Cobb and Douglas paper, including the proposed modifications to the Cobb–Douglas regression, and noted that while Clark’s formula led to a better fit in the prewar years, it did worse than the original in the postwar years. Still, Douglas allowed, an augmented version of the original Cobb–Douglas formula that allowed the coefficients to vary over time might be in order, and he reviewed a suggestion along these lines that he had received in private correspondence from Sidney Wilcox (Douglas Reference Douglas1934, 216, 224–25).

The suggestion that the value of k might vary over time was linked by Douglas to the observation that the original Cobb–Douglas function implied that labor’s share in distribution would be at least approximately constant over time. He pointed out that studies by Arthur Bowley and Josiah Stamp of income data in the United Kingdom seemed to indicate such a constancy of labor’s share in distribution for that country, but that German data showed large fluctuations in labor’s share. Douglas believed that the data from the United States were still insufficient to allow a firm conclusion to be drawn concerning the behavior of labor’s share over time. However, looking at distribution data from five countries and various time periods, he found it striking that labor’s average share of national income seemed limited to a narrow range between 60 and 71 percent, which, he believed, pointed to some broadly similar influences at work in all the countries. And, taking the logic of the Cobb–Douglas function one step further, he made the pregnant suggestion that if one were willing to assume that processes of distribution followed those of production, data on the shares of national income going to labor and capital would allow one to estimate the elasticities of the marginal productivity curves of those factors (Douglas Reference Douglas1934, 221–24, 490–91).

In both 1928 and 1934, Douglas had listed as an important end to be sought in his production research the determination of the extent to which increases in output over time had been due to technological progress. However, he admitted, it was a “disconcerting feature” of his analysis based on the Cobb–Douglas regression that it “seems to eliminate ‘progress’ or dynamic improvements in the quality of capital, labor, and the industrial arts from the industrial history of the periods studied” (Douglas Reference Douglas1934, 209). As noted, this misgiving had been raised in print by Clark (Reference Clark1928), but also according to Samuelson (Reference Samuelson1979), by Joseph Schumpeter.Footnote ²⁷

Douglas’s first response to this potential problem with his procedure was to point out how it actually represented a move forward in attempts to understand economic progress. In the past, he noted, some had viewed the increase of total production as a measure of progress, but this was clearly wrong, as it ignored the fact that rising output accompanied by rising population could mean that labor productivity and average consumption were both declining. Output per worker, the measure of progress most commonly used by modern economists, was also flawed in that it could increase solely because of increases in the quantity of capital per worker with no change in “technical efficiency.” The Cobb–Douglas procedure corrected this flaw by explicitly taking into account the quantity of capital as well as the quantity of labor.

However, in each set of data to which the procedure was actually applied, the whole of the increase in total production over the sample period was accounted for, with a seemingly high level of accuracy, by mere quantitative increases in labor and capital. In the face of the obvious revolution in manufacturing technique in these periods, such a conclusion was “incredible”; it was a paradox demanding a reconciliation between “the reality of qualitative progress and the validity of the formula” (Douglas Reference Douglas1934, 210–11).

Douglas admitted that he had no such reconciliation to offer, only some suggestions on this “tangled question.” He proposed that when the equation was estimated for a particular time period, one might suspect the existence of technical progress in shorter periods within or adjacent to that period during which the growth of output exceeded what one would predict using the estimated equation, or which led to different estimated coefficients for the equation than those produced by the entire period. Douglas pointed to the period 1921–26 as one that showed progress by this metric. Douglas also suggested that the some of the progress in US manufacturing from 1899 to 1922 was “concealed in and made possible” the reduction in the average work week and the falling ratio of production to non-production workers. Further, Douglas argued, there was reason to believe that the quality of the average worker had been increasing along with the quality of capital, and he quoted at length J. M. Clark’s (Reference Clark1928) argument that part of the estimated productivity of capital was due to the improved quality of capital. Douglas did not, however, develop the statistical implications of possible improvements in the quality of labor and capital for his method of estimating the marginal productivity of these two factors, beyond saying that if the qualitative improvement of workers balanced the qualitative improvement of capital, progress could have affected the size of the total product without being reflected in his marginal productivity estimates.

Douglas reported having had useful conversations on the topic of technical progress with William Ogburn and S. C. Gilfillan, two colleagues with demonstrated expertise on the subject.Footnote ²⁸ Douglas was particularly interested in Gilfillan’s classification of the 120 inventions of the last generation “with the most important social effects” into the categories of labor saving, land saving, capital saving, and developments of consumer goods (Douglas Reference Douglas1934, 214; Gilfillan Reference Gilfillan1932). Douglas noted the ratio of capital- and land-saving inventions to labor-saving inventions (1 to 1.5), and related Gilfillan’s opinion, conveyed in an unpublished communication to Douglas, that while labor-saving inventions tend to raise the capital/labor ratio, and capital-saving inventions to lower it, the second effect is offset somewhat by the necessary investment in new types of capital and the reduced need for labor to operate the reduced quantity of capital. In reading these passages, one senses that Douglas believed that these observations were very relevant to the question of how technical change affected the meaning of the estimates produced by his regression, but also understood that he was not yet seeing all the necessary connections.

Another communication received by Douglas bearing on the relationship between his regression and technical change came from Morris Copeland, in which Copeland reported the results of fitting a straight-line trend to the logarithm of Douglas’s output per worker series. The resulting regression predicted actual output just as well as the Cobb–Douglas regression, leading Copeland to conclude that the hypothesis that all the growth in labor productivity was due to technical change was as firmly supported by Douglas’s data as the hypothesis that it was all due to a growing quantity of capital. This finding clearly troubled Douglas,Footnote ²⁹ as it would others who later encountered it in The Theory of Wages, and Douglas closed his discussion of “Progress and the Equation of Production” by admitting that “the whole question needs to be gone into more thoroughly” (Douglas Reference Douglas1934, 215).

Responses to The Theory of Wages

The Theory of Wages was widely discussed in the social science literature, both in standard reviews and in longer articles. The reviews were generally favorable in tone: Douglas had performed “an invaluable service” (Bigge Reference Bigge1934); the book was “brilliantly incisive and appallingly exhaustive,” and would “endure as an outstanding pioneer accomplishment in the synthesis of abstract and realistic materials” (Dickenson Reference Dickinson1934). Rowe (Reference Rowe1934) also called Douglas a “true pioneer,” with his equation of production representing the book’s most original and interesting contribution to knowledge. Such reviews were not without criticisms. Berman (Reference Berman1934), who called the book “one of the most important works of a theoretical nature ever published in this country,” still expressed concern about the quality of the data. Bigge thought Douglas’s causality claims were too strong, and several reviewers expressed misgivings about the problems raised for Douglas’s equation by technological progress. Some were impressed by the goodness of fit of the estimated equation of production, others by the correspondence between coefficient estimates and distributive shares. An outlier was Don Lescohier (Reference Lescohier1935), a student of J. R. Commons from Wisconsin. He was not impressed by the good fit produced by Douglas’s production equation, arguing that the analytical method was designed specifically to produce a good fit, and he remained “unconvinced of the quantitative conclusions” drawn concerning marginal productivities, as the procedure was based on so many untrue assumptions.

Lescohier’s doubts about the significance of Douglas’s results, like those of Slichter (Reference Slichter1928), were in part a result of Lescohier’s rejection of the marginal productivity theory of distribution. Another important set of reactions to The Theory of Wages, however, came from mathematical economists who embraced marginal productivity theory, and who were trying to make sense of the relationship between Douglas’s regression equation and the equations of their theoretical systems. In the November 1934 issue of the Quarterly Journal of Economics, Wassily Leontief took up the question of whether or under what conditions the regressions estimated by Douglas could be squared with “the marginal productivity theory of interest as it appears to emerge from the writings of Jevons, Bohm-Bawerk, Wicksell, and their successors.”Footnote ³⁰ Leontief’s main criticism was that the Cobb–Douglas production function did not allow for the time-consuming nature of production, nor for the fact that that the length of the period of production (or the rate of turnover of capital) was likely a choice variable for the entrepreneur. Starting with a production function that did have these characteristics, Leontief developed a mathematical model of the profit-maximizing firm and used it to evaluate Douglas’s methods and results. Leontief was a friendly critic, however. He was not rejecting Douglas’s idea, only Douglas’s function, and offering his own modified production function as a better basis for the statistical investigation of the laws of distribution (156). Leontief concluded that whatever flaws subsequent investigators might find in Douglas’s work, “it is not to be spoken of without admiration. It will remain a most outstanding contribution to economic literature” (Leontief Reference Leontief1934, 156, 161).

Jacob Marschak (1935) also expressed support for Douglas’ project. Pure theory was valuable, he noted, but could only go so far. It could indicate the likely signs of relationships between economic variables, but not the magnitudes. Douglas was boldly attempting to find, using statistical data, the shape of the production function of economic theory. Marschak saw problems in Douglas’s execution, however. Like Leontief, Marschak embraced the Bohm-Bawerk/Wicksell view of capital and interest, and thus he asserted that Douglas’s use of a single measure of aggregate capital was theoretically suspect under the assumption that units of capital consumed at different points in the production process had different marginal productivities. Marschak’s larger concern was statistical. Like Schultz’s (Reference Schultz1929) comments on the Cobb–Douglas paper, Marschak’s statistical critique grew out of contemporary debates over the estimation of supply and demand functions. Citing Elmer J. Working’s (Reference Working1927) article on statistical identification of supply and demand relationships, Marschak explained that Douglas’s curve-fitting procedure implicitly assumed that observed variations in output were not due to changes in the production function to be estimated, but occurred because the amounts of capital and labor employed were changing for other reasons. Marschak noted that this was not a condemnation of Douglas’s method, but a warning that those who used it should take care in thinking about the issue of which relationships in their data were shifting and which were stable.

David Durand provided the most detailed scrutiny of the relationship between the estimated production relationships in Douglas’s The Theory of Wages and the concepts of marginal productivity theory, which, in Durand’s case, meant the version of that theory associated with French economist Leon Walras. Durand’s (Reference Durand1937) article, “Some Thoughts on Marginal Productivity Theory, with Special Reference to Professor Douglas’ Analysis,” began with a mathematical description of equilibrium on the production side of a Walrasian economy with fixed output prices. Durand assumed that each firm had a distinct production function in which output could be a very general (but differentiable) function of inputs, described how profit maximization led to a situation in which factors received payments equal to their marginal productivity, explained how entry and exit drove firms to the point of their production function characterized by constant returns to scale and minimum cost, and counted equations and unknowns to establish the existence of equilibrium values for all factor prices. Having laid out this “clear and precise statement of the marginal productivity theory,” Durand proceeded to explain why there was absolutely no relationship between the concepts and elements of this theory and the quantities estimated by Douglas. According to Durand, marginal productivity theory “can be applied only to individual firms. It is a great mistake to attempt to extend the theory to industrial society in general, to the so-called social organism” (Durand Reference Durand1937, 745). There was no way to aggregate the different outputs of individual firms to a single total output. Aggregation problems arose in dealing with productive factors as well, as the theory required that they be very specifically defined, rather than being grouped as land, labor, and capital. The theory was static, assuming that factor supplies were constant, and that marginal increments of factors supplied to one firm were bid away from another, while the marginal increments of a factor to society were newly created.

Turning specifically to Douglas’s statistical analysis, Durand objected to the assumed linear homogeneity of the Cobb–Douglas function. Theoretical production functions could not be linear homogeneous throughout their range, as was the Cobb–Douglas function, or there would be no single minimum cost point and no determinate equilibrium. Nor did anything in the theory justify the idea of an industry-level production function with constant returns to scale – such a conclusion would have to be established empirically. Also, Douglas placed undue emphasis on the good fit of his regression. A good fit showed only that the function was statistically accurate, not that it was theoretically accurate, nor that it revealed causal relationships. Other functional forms fit the data just as well. These good fits were all a consequence of the fact that the three series Douglas worked with were highly collinear. Durand’s review of Douglas’s attempts to deal with trends in the data and cyclical fluctuations served to illustrate further the uncertainty about what the estimates of the Cobb–Douglas regression actually represented.

Then, however, Durand took an unexpected turn, and placed himself firmly in the camp of Douglas’s friendly critics. “All that has been said thus far,” he wrote, “might be construed as a decrial of quantitative studies of production. This is not the case. Statistical studies of all sorts are desirable, and Professor Douglas’s is no exception.” Douglas simply should have chosen a function that was “a little more general.” Durand proposed two adjustments to the Cobb–Douglas equation: first, the assumption of constant returns to scale should be relaxed, and the coefficients of labor and capital estimated separately. Second, the formula should be adjusted to allow those coefficients of labor and capital to change over time. Durand implemented the first suggestion himself with Douglas’s data, and found very little change in the results. He also made some calculations to show that Douglas’s data suggested a value of k that changed over time, thus supporting the need for his second adjustment. Pushing Douglas’s program forward, Durand concluded, would be difficult but desirable (Durand Reference Durand1937, 755).

Douglas, in all his subsequent production function studies, would estimate the coefficients of capital and labor separately, attributing this idea to Durand,Footnote ³¹ and would offer Durand’s concern with a changing k value as one reason for his switch from using time series to cross-section data in those studies. It is worth mentioning, however, one thing Durand did not do in his article. Having argued at length that there was no relationship between the quantities estimated by Douglas and the concepts and relationships of marginal productivity theory, Durand offered few hints regarding what he thought one did or should hope to obtain from “quantitative studies of production” in the Douglas mode. Although his arguments in support of his proposed adjustments to the Cobb–Douglas formula seemed to indicate a belief that the relationship between inputs and output in an economy with growth and technological change could be characterized by a stable function (Durand Reference Durand1937, 754–55), the matter of the theoretical significance of the estimated parameters of such a function was left undiscussed.

In The Theory of Wages, Douglas usually referred to the regression equation he was estimating as a law of production or a theory of production, and only rarely as a production function. It was in the articles by Leontief, Durand, and Marschak, as well as the very critical article by Mendershausen discussed in Chapter 2, that the label “production function” was first consistently applied to the relationship that Douglas was seeking to estimate, although Douglas quickly adopted the phrase himself. This labeling of the Douglas regression, while arguably contributing to its eventual widespread acceptance, also altered the nature of the discussion surrounding its validity and significance.

In the mid-1930s, the phrase “production function” was rare in the economics literature, used almost exclusively by those engaged in the program of mathematical formalization of some version of the neoclassical model and/or the statistical estimation of the components of those models. As mentioned earlier, in 1934 Douglas presented his production studies as part of the neoclassical-econometric research program, a complement to efforts to estimate the supply and demand curves of neoclassical theory. In referring to Douglas’s regression as a production function, leading young econometricians such as Leontief, Marschak, and Oskar Lange (Reference Lange1939) were affirming this conception of Douglas’s. In doing so, they linked the Cobb–Douglas equation more closely to a research program that was on the ascendency, identifying the equation as a starting point or possible building block for the mathematical and econometric systems that constituted the research output of the program.

However, while the neoclassically oriented econometricians of the late 1930s and early 1940s were embracing Douglas’s program as complementary to their own, they were also redefining the objectives of the program, and developing criteria for evaluating Douglas’s methods and results that Douglas himself would not have accepted. This is partly because these pioneering econometricians were operating with versions of neoclassical value and distribution theory different from the one that had motivated Douglas as he developed his empirical research strategy in the late twenties and early 1930s. They thought about marginal productivity theory within the context of Walrasian general equilibrium theory, in which the production function was a characteristic of a firm, or Marshallian theory, in which it was the characteristic of an industry. As a result, when they contemplated the output of estimating a production function using time series data aggregated over several industries, or cross-section data at the industry level, certain questions naturally seemed crucial: Did the estimated coefficients say anything useful about the true parameters of the underlying industry or firm production functions? Were they averages of those parameters in some sense? If so, in what sense? I would argue, however, that because of the way Douglas was trained, these questions were never crucial for him, nor were they even at the forefront of his mind as he began his research. As he notes in his autobiography, he was taught theory at Columbia University by John Bates Clark, and received “a thorough drilling in (the marginal productivity) principle, which served me well a decade later when I started my own inductive work in the theory” (Douglas Reference Douglas1971, 29). But Clark’s formal analysis of factor-price determination, unlike that of Walras or Alfred Marshall, ran in terms of aggregates: the basic wage rate and the interest rate depended on the marginal products of “social” capital and “social” labor (Stigler Reference Stigler1941, 307). A student of Clark would have had no trouble thinking of an aggregate production function as a primal entity to be estimated, and its parameters as significant theoretical quantities.

During the years that Douglas was defending his production function studies, when critics questioned whether there was any relationship between his estimates and theoretical parameters of production functions of firms or industries, Douglas was not dismissive, but neither was he particularly bothered. The production functions of single firms should be estimated if and when firm-level data became available, but currently they were “nonoperational” concepts for the purposes of inductive studies. Production functions estimated with cross-industry data or aggregate time series data were “different type(s)” of production functions from each other and from those of Walrasian theory, but interesting in their own right (Bronfenbrenner and Douglas, Reference Bronfenbrenner and Douglas1939, 779, 780–82; Douglas Reference Douglas1948, 9, 22–23).

This attitude also grew out of a methodological difference between Douglas and many critics, both friendly and unfriendly, who raised the issue of the relationship between Douglas’s estimates and the production functions of individual firms. In The Theory of Wages, Douglas had commented:

When Durand provided the first extended treatment of the question of whether Douglas’s regression yielded estimates of the production functions of (Walrasian) neoclassical theory and answered in the negative, he went on to implicitly endorse Douglas’s methodological position concerning the existence and significance of an aggregate production function. Discussion of the issue of whether the parameters of a Cobb–Douglas (or any) production function estimated with cross-industry or aggregate time series data could be rigorously related to the parameters of the firm-level production functions of theory, and, if not, what theoretical or practical significance they held, would continue. It would be taken over, however, by members of the neoclassical econometric research program who were more fully committed to methodological individualism, in a form something like that articulated by Haavelmo (Reference Haavelmo1944) and defended by Tjalling Koopmans in his well-known “Measurement without Theory” debate with Vining (Koopmans Reference Koopmans1947; Vining and Koopmans Reference Vining and Koopmans1949). From this standpoint, parameters that described the preferences and constraints of individual actors, including parameters of firm-level production functions, were the holy grail of econometrics, and statistical methods and results were to be judged largely on the basis of what they revealed about these parameters.Footnote ³²

Douglas’s Final Time Series Study: Handsaker and Douglas (1937–1938)

Following the publication of The Theory of Wages, Douglas continued to work on production studies from 1935 until fall of 1942, when he enlisted in the Marine Corps. These were also years during which a small group of econometricians was introducing new ways of thinking about empirical work in economics that involved novel and explicit applications of the mathematical theory of probability in the design, discussion, and evaluation of statistical methods and results. Although their work had little impact on the practice of empirical research in the profession as a whole prior to 1950 (Biddle Reference Biddle1999), these econometricians were disproportionately represented among those who cited Douglas’s production studies, and in the neoclassical econometric research program in which Douglas was now a participant. Thus, the econometricians were an important group for Douglas to persuade, and after 1935 his presentations, discussions, and defenses of his own statistical methods and results were increasingly conducted within their conceptual frameworks using their analytical tools.

A small move in this direction can be seen in Douglas’s first study following the publication of The Theory of Wages, which appeared as a two-part article in the Quarterly Journal of Economics coauthored with University of Chicago graduate student Majorie Handsaker. This study, the last one in which Douglas estimated the regression with time series data, was the first in which a standard error for the k estimate was reported. Douglas had in previous work reported either the standard errors or probable errors of the correlation coefficients he presented, but had said next to nothing about the meaning or significance of these measures.Footnote ³³

This use of a standard error along with an estimated regression coefficient to place a bound on the true value of some parameter is based on the assumption, usually implicit, that one’s data represent a random sample from a larger population. This way of thinking about data has now become a fundamental feature of applied econometrics but was not at all common in the 1930s (Biddle Reference Biddle2017). Indeed, Frederick Mills, in his widely read statistics textbook, warned readers that the standard formulas derived from probability theory for calculating the likely errors of estimates should be used with great care, because the assumption that one’s data were a random sample from some population of interest would seldom be met (Mills Reference Mills1924, chapter 16). Be that as it may, Handsaker and Douglas did not articulate any formal, sample/population framework for thinking about their time series sample or their estimates, but simply asserted the probability theory–based bounds on the estimate of k without further explanation.Footnote ³⁴ The introduction and use of the standard error of k may have been Handsaker’s idea. For reasons discussed more fully below, I believe that after 1935 Douglas sought coauthors who could, among other things, bring cutting edge statistical knowledge to the project, helping Douglas to understand the implications of his results, to explain them to the econometricians in his audience and, more importantly, to rebut the criticisms of those econometricians.

In most other respects, the Douglas/Handsaker article, which estimated the Cobb–Douglas regression using data from the Australian state of Victoria, looked much like the previous Cobb–Douglas regression studies. The article began with a review of those studies, with emphasis on the goodness of fit of the Cobb–Douglas equation and the close correspondence between labor’s share in distribution and the coefficient of labor in the production function. Analysis of data from another economy, the authors argued, would help to establish whether the Cobb–Douglas function was adequate to represent “real facts of economic life,” or whether this seemingly positive evidence had been merely “accidental” (Handsaker and Douglas Reference Handsaker and Douglas1937, 4).

A brief review of differences between the manufacturing sector in Victoria and in the United States was followed by a discussion of how data from Victoria’s Census of Manufactures had been used to construct the time series for product, labor, and capital. The task was made easier by the fact that the Victorian census data were annual, so that no interpolation was required, but it did require an index of total manufacturing output to be built up from data on a subset of manufacturing industries,Footnote ³⁵ and it still involved creating price indexes for capital in order to convert annual additions to the value of buildings, plant, and machinery into estimates of annual increases in the stock of physical capital. The tone of the discussion was that the data were adequate for the task, but no reader could complain that potential weaknesses in the data had been hidden.

Using the three constructed series, the least squares value of k in the function P’ = bL^kC^1-k was .79. For the first time, Douglas provided a derivation of the formula used to estimate k, making it clear that it resulted from a linear regression involving logs of the series values. The estimated regression was then put through the familiar paces. P’ was compared to P on a year-by-year basis both graphically and in tables, and in both absolute and percentage terms. This, readers were told, represented a “stringent test” of the equation of production. The average absolute deviation was slightly smaller than that found for the US data, and the correlation coefficient between P and P’ was .97. It was argued that most of the large deviations could be explained by business-cycle factors, as was the case in the US data, or by the disruption of labor supply and the reallocation of capital caused by the war, although it was admitted that a few large deviations escaped easy rationalization. The authors concluded that all in all, actual production in Victoria was “fairly closely approximated” by the estimated function.

Next came the test of marginal productivity theory via the comparison of the k estimate to labor’s share of the value of output.Footnote ³⁶ The results were somewhat unsatisfactory, as the average annual share of the net value of product paid in wages was about 61 percent, which was deemed to be an “appreciable” deviation from the 71 percent one would have expected from the regression results, and far larger than the deviation found for the United States. It was not mentioned that the deviation between labor’s share and the labor coefficient in Director’s study of the neighboring state of New South Wales was almost equally large, though Douglas had pronounced the two New South Wales quantities to be “not greatly at variance.”

Handsaker and Douglas offered an array of possible explanations for the deviation they had found. The first argument was based on the standard error of the k estimate, which, as discussed earlier, had been reported along with the coefficient estimate. In an argument that would certainly have been quite novel to most readers of the Quarterly Journal, Handsaker and Douglas explained that since the standard error of the coefficient estimate was .065, the true value of the coefficient for Victoria could be as low as .71 minus .065, which would bring it much closer to the average value of labor’s share. They did not report the formula used to calculate the standard error, nor did they cite a source, and they did not explain why one standard error was used to construct their lower bound rather than some other multiple.Footnote ³⁷

Handsaker and Douglas next argued that there were good reasons for believing that their estimate of the growth of the capital stock overestimated the true growth, which would cause the regression procedure to overestimate the labor coefficient. Two additional possible reasons for the deviation between the k estimate and labor’s share of value added were based on economic theory. The equality of wage and marginal product was a theoretical prediction for economies with competitive labor markets, the authors noted, but wages in Victoria were set by government fiat. Australian data showed that government-set wages had lagged far behind price increases during periods of inflation. During those same periods, labor’s share was below its average for the entire period. Further, if one looked only at a period of stable prices, labor’s share averaged 65 percent, close to the lower bound for k calculated by subtracting one standard error from the estimate.

The newly developed theory of imperfect competition provided a final possible explanation for the relatively low value of labor’s share. Citing Edward Chamberlain (1933) and Joan Robinson (Reference Robinson1933), Handsaker and Douglas explained that when a firm was large enough relative to its industry that its output level influenced product price, marginal revenue would deviate from average revenue (i.e., price), and the firm would produce the level of output at which marginal cost equaled marginal revenue. They continued:

Robinson’s (Reference Robinson1933) book had actually analyzed several models in which imperfect competition of one form or another would lead to monopolistic or monopsonistic exploitation of labor. In the passage quoted above, Handsaker and Douglas referred to a chapter in Robinson’s book dealing with “the monopolistic exploitation of labor,” in which Robinson analyzed models of a single industry, assuming that changes in employment in that industry would have no significant effect on other industries or the general level of prices. However, Handsaker and Douglas’s reference to the impact on real wages of the higher prices brought about by imperfect competition, along with the equation they presented to describe labor’s marginal physical product under imperfect competition, suggest that they were actually thinking in terms of another model of monopolistic exploitation that Robinson presented in her chapter on “A World of Monopolies” (Robinson Reference Robinson1933, 307–12). That model involved an economy in which different competitive industries produced different commodities that were imperfect substitutes for one another, with factors of production supplied perfectly elastically to the industries, though fixed in total supply. Robinson analyzed the consequences for that economy of placing output decisions for each industry into the hands of a different monopolist, with the owners of the existing firms being converted into salaried managers and nothing else changing. Assuming no collusion between the monopolists, she described the “monopolistic exploitation” that would characterize the resulting equilibrium, giving a verbal specification for the equilibrium wage that matched Handsaker and Douglas’s formula (Robinson Reference Robinson1933, 311).

I think it likely that Handsaker and Douglas were raising the possibility that the manufacturing sector of Victoria approximated Robinson’s “world of monopolies,” with “a considerable degree of collusive and non-competitive fixing of prices behind the tariff wall” (Handsaker and Douglas Reference Handsaker and Douglas1938, 231). The manufacturing sector was a large enough segment of the total economy that the impact of monopoly prices on real wages was non-negligible. And if the Victorian manufacturing sector approximated Robinson’s “world of monopolies,” labor’s share of value added in manufacturing, averaged over all the industries, would be below an accurate measure of the true k. In any case, Handsaker and Douglas did not ultimately place too much stock in imperfect competition as an explanation of the deviation of labor’s share from k in Victorian manufacturing. After citing statistics bearing on the level of industry concentration in Australian manufacturing, they pointed out that although US manufacturing seemed to be no less concentrated than Victorian manufacturing, labor’s share in the United States equaled the estimated value of k for the United States. Also, they had nothing more to say about the possibility of monopsonistic exploitation beyond the sentence in the passage quoted earlier. However, the nature of monopolistic and monopsonistic exploitation, and the possibilities for detecting it statistically with a Cobb–Douglas regression, would soon become a controversial issue for Douglas’s research program.

As in Douglas’s earlier studies, the legitimacy of the Cobb–Douglas function was also tested by looking at correlations between the year to year movements of real wages and the estimated marginal physical productivity of labor (which, given the Cobb–Douglas function, would be proportional to movements in average product per laborer). After explaining the complicated process used to construct indexes of real earnings, Handsaker and Douglas reported correlation coefficients above .8 between various measures of the two variables, including four-year moving averages.

The Handsaker and Douglas paper is the only one of Douglas’s production studies that presents empirical evidence on the relationship between the return to capital and the productivity of capital. The authors noted that the marginal productivity of capital implied by the Cobb–Douglas function, as proxied by P/C, had declined by 30 percent over the sample period, while the return to capital, as proxied by the return on Australian government bonds, had risen by 43 percent. Although the authors admitted that this evidence would seem to “completely disprove” the productivity theory underlying their study, they provided two possible grounds for rejecting the Australian interest rate as a measure of the return to capital. First, appealing to Irving Fisher, they argued that Australian interest rates would include a premium for expected inflation, and that the middle of the sample period had been a period of rapid inflation. Second, appealing to J. M. Keynes, they speculated that interest rates might have been pushed upward by a secular increase in liquidity preference, although they admitted that they could identify no obvious cause for such a secular shift (Handsaker and Douglas Reference Handsaker and Douglas1938, 249–51).

Douglas and Handsaker also responded to some of Douglas’s friendly critics. Durand’s (Reference Durand1937) arguments against imposing the constant returns to scale assumption when estimating an aggregate production function were pronounced “just”; relaxing the assumption led to an estimate of .84 for k, and .23 for the coefficient of capital, which Douglas now labeled j. While this version of the regression, which will henceforth be referred to as the unrestricted Cobb–Douglas regression, fit the data “slightly better” than the original or restricted Cobb–Douglas equation, Douglas seemed to want to cast doubt on its validity, as he pointed out the fact that the least squares value of b dropped from 1 to .715 “raise[d] a very decided question as to the practical meaning of the results.”Footnote ³⁸

A footnote mentioned Schultz’s (Reference Schultz1929) proposal that a linear trend be added to the regression, but this suggestion was not taken up. Leontief’s suggestion that working capital be included as a separate term in the production function could not be implemented, as Handsaker and Douglas had no measure of working capital, but J. M. Clark’s (Reference Clark1928) analysis of how the inclusion of working capital would influence the coefficient estimates was reviewed (24, 245–46). Douglas and Handsaker also tested Clark’s method of adjusting the Cobb–Douglas equation to capture cyclical fluctuations in capital utilization; the fit of the augmented equation was “slightly” better than that of the original. The authors concluded the article by reminding readers that they did not claim to have found “the precise production exponents” or “the exact slopes of the marginal productivity curves of the two major factors,” only an approximation to conditions in Victorian manufacturing. Readers were reminded, however, that there was a “striking” degree of agreement between the Victorian results and those for the United States, Massachusetts, and New South Wales (Handsaker and Douglas Reference Handsaker and Douglas1938, 250).

Although the Handsaker and Douglas study was the last in which Douglas would estimate the Cobb–Douglas regression using original time series data, it presages two characteristics of Douglas’s work with the cross-section version of the Cobb–Douglas regression over the next five years. The first has already been mentioned, that is, the effort to stay up to date in terms of the statistical tools and methods used to present and interpreting the statistical results. The second is Douglas’s consistent emphasis on the economic nature of the economic/statistical tool that he had developed. Handsaker and Douglas attempted to make sense of their results using not only the statistical theoretical concept of the standard error, but also novel economic theoretical models and concepts taken from Joan Robinson and J. M. Keynes. In subsequent studies Douglas would continue to rely on arguments from both statistical and economic theory, both when rebutting the attacks of his critics and when making the positive case that his statistical results were revealing valid information about fundamental economic relationships.