Holbrook Working and the Early Financial Economics Free

Abstract

Where does financial economics come from? This article studies the origins of foundational ideas of financial economics such as price spreads, arbitrage, and the interpretation of price as a reflection of information. Based on his publications and archival and interview materials, this article traces Holbrook Working's intellectual journey between the 1920s and 1960s. Working was a leading North American agricultural economist who conducted pioneering analyses of futures markets and speculation and strongly influenced early financial economists like Paul Samuelson, Paul Cootner, Hendrick Houthakker, and Lester G. Telser. Working sheds light on a North American view of speculation that contrasted with the prevailing British view.

In December 1960, the American Economic Association held its seventy-third annual conference, in St. Louis. The conference program, devised by Paul Samuelson, included a session titled “Frontiers in Uncertainty Theory: The Evidence of Futures Markets,” organized in conjunction with the Econometric Society. One of the speakers was Holbrook Working, a Stanford agricultural and institutional economist. Working was then nearing retirement, and his contribution recapped several decades of his research on speculation in futures markets. Speculation and uncertainty were fashionable new topics at the time, and his talk attracted a younger generation of economists.

The methodological tension in the room between generations was palpable. American economics was undergoing a major transformation: the old American institutionalism was on the wane and mathematization in the offing. Working outlined his approach to economic method. Drawing on the views of James Conant,¹ one of the leading US scientists of the day, Working advocated a bottom-up approach, with advances being made by formulating “new concepts” arising “from the results of thoughtful, well-directed observation” (Working 1961: 161). Discussing Working's paper, the young agricultural economist Michael Brennan regarded this empiricist view “as a myopic, distorted notion of scientific method.” Defending a position similar to Milton Friedman's (1953), he argued that it was not the “concept” that needed to be empirically tested but the prediction of the underlying model and that “historically speaking the best assumptions [were] often the more abstract” (Mack, Brennan, and Nerlove 1961: 190). Despite these disagreements, the new generation of economists still unanimously viewed Working as one of the leading US scholars on speculation. In 1960, in a recommendation letter, Paul Samuelson regarded Working's research as “the best work that has been done in this whole area,” even if “it did not probably get the attention it deserves” (Samuelson Papers, correspondence with Holbrook Working, 1953–77, box 78).

Now, just what did an agricultural and institutional economist have to say about speculation? How did he become a leading authority for the first generation of financial economists? Based on his published writings, interviews, and archival material, I trace Holbrook Working's intellectual journey from the 1920s to the 1960s and appraise its influence on early financial economics. I document the development of Working's thinking on the functioning of speculative markets and the social role of speculation.

Working trained as an agricultural economist and an early econometrician in the 1920s. Concurrently with British research on futures markets prompted by Keynes, he built his own theory of futures markets: “the price of storage.” For Working, the primary function of futures markets was not to cover against price risk but to correctly process available information and correctly allocate the available supply of products over time. By seeking arbitrage opportunities and using available information as best as they could, futures traders operated in such a way that futures prices reflected unbiased market expectations about future market conditions.

This article examines how Working developed this vision of finance and speculation. Although not unknown to economic historians, Working's contributions to economic thought have come in for little study. Berdell and Choi (2018) provide the most comprehensive account and focus on Working's debate with regulators in the 1930s. Delcey and Noblet (2024) investigated how the interwar information policy conducted by the Department of Agriculture influenced Working's thought. Justin Fox's (2011) popular book is, to my knowledge, the first attempt to reassess Working's contribution to financial theory.

This article contributes to the literature in two ways. First, it documents Working's thinking on arbitrage and information. I review his intellectual journey, from his early research in the 1920s to his theoretical achievements in the 1950s. This sheds light on the contribution from agricultural economics and institutional economics to early financial economics. Moreover, it highlights the breaks and continuities between institutionalism and postwar economics in their analyses of finance and speculation. Working's research offers a window for historians to understand the origins of ideas such as arbitrage and the interpretation of prices as reflecting information. Arbitrage and the informational role of asset prices arguably are core concepts of financial economics, but we still know but we do not know much at all about their historicity.² By tracing Working's intellectual journey, I study the gradual development of a financial style of reasoning in the United States in the first half of the twentieth century.

Second, I use his original correspondence and interviews with his colleagues—and thereby bring in new materials to the literature on Working—to assess his influence on the emerging field of financial economics in the late 1950s and early 1960s. By way of conclusion, I offer some insights into why Working, despite exerting a very real influence, received little credit from subsequent research in finance.³

1. Background

Working completed his PhD in agricultural economics at the University of Wisconsin in 1921. His doctorate was one of the first in the field, which was barely institutionalized in the United States at the dawn of the twentieth century; the American Farm Economic Association and the Journal of Farm Economics—now respectively the Agricultural & Applied Economics Association and the American Journal of Agricultural Economics—were founded in the 1910s.

Agriculture quickly became a major research area in American economics. In the interwar period, as many as half of all Americans still lived in rural areas, and agriculture remained a vital part of their livelihood. Many agricultural economists worked in the agricultural experiment stations set up in the land-grant colleges in the late nineteenth century,⁴ while the largest contingent in the interwar period worked for the Department of Agriculture's Bureau of Agricultural Economics, founded in 1922. The bureau was the main research institution in the field. It produced most of the data and dictated the country's agricultural economic policy.

The emerging agricultural economics was greatly influenced by American institutionalism, an intellectual movement characterized by its empirical and pragmatic approach. The University of Wisconsin, where Working did his PhD, was a stronghold of institutionalism, led by John R. Commons, who was one of Working's advisers.⁵ Unsurprisingly for someone trained within institutionalism, Working was an empiricist, valuing data and observations above all else. His general methodological approach consisted in identifying unexplained statistical facts and then building a theory based on the available data. Agricultural economists pioneered the use of econometrics, and like many of them, Working was at the cutting edge of statistical analysis in the first half of the century.⁶

His focus on data does not mean he took no interest in theory. At the University of Wisconsin, he studied neoclassical economics, which was the main theoretical framework for agricultural economists. In the 1920s and 1930s, Working was apparently not conversant with the research of John Maynard Keynes. His main theoretical reference was Alfred Marshall. Working sought to reconcile neoclassical price theory with what he actually observed in American agricultural markets. As an illustration, at a 1930 conference, looking back on his early research on the behavior of wheat prices, Working (1930: 730) stated that “as a student . . . at the University of Wisconsin and subsequently through two years of endeavoring to expound Alfred Marshall to students, I improved my command of theory as it stood then and, in the main, still stands. Now, after several years’ work on wheat prices . . . I shall not present and am not ready to present a theory of wheat prices.”

In his early research, Working encountered the same issue faced by many early econometricians researching price analysis. They struggled with the gap between the ceteris paribus world of Marshallian theory and the world of collected data where nothing is constant or given (Morgan 1991: 142–43). Clearly for Working, the gap had to be filled by theory that needed to adapt to and be reconciled with statistical facts.

After completing his PhD in 1921, Working joined the University of Minnesota and its agricultural experiment station. His research there focused on collecting and analyzing data from major agricultural exchanges in the Midwest, the heartland of US farming (Working 1922, 1925. The exchanges, such as the Chicago Board of Trade and the Chicago Mercantile Exchange (initially the Chicago Butter and Egg Exchange), had been major players since the late nineteenth century. Their growth had gone along with the emergence of a new class of urban dealers and speculators.⁷

Agricultural exchanges operated much as banks did at the time. Farmers, shippers, and dealers deposited their products in a warehouse against a receipt equivalent to a banknote. They could trade these receipts among themselves more easily than the actual products. Because city warehouses mixed the products from different farmers, the exchanges had to use a grading system to differentiate among products of different quality. This standardization encouraged transactions between cities. New communication technologies, first the telegraph, and later the radio, further integrated these local markets. Before the telegraph, sending a message from New York to Chicago took days; now it took only a few hours.⁸

One of the research programs of agricultural economists was to compile and analyze those numerous statistical data on the prices on these exchanges. Working's first study (1922), for instance, was of the potato market and the nationwide pattern of prices. Figure 1 reproduces a map Working created for his study.

The map illustrated the emergence of national public statistics, a development studied by Emmanuel Didier, enabling statisticians like Working to capture “America as a whole” (Didier 2012: 28). Working's map was based on statistics from the Department of Agriculture's Bureau of Crop Estimates. The data opened up economic analysis to the study of regional prices and their determinants. Understanding price relationships naturally led economists to investigate economic agents’ capacity to exploit arbitrage opportunities. Although Working's 1922 paper did not explicitly formulate the nonarbitrage hypothesis, he used similar reasoning to account for the relative prices observed. Producer areas were characterized by low prices due to abundant supply, whereas the farther a region was from where the products were produced, the higher the prices; thus, the price difference mainly reflected transportation costs (Working 1922: 7).

This style of arbitrage reasoning was not particularly innovative among economists—it was a commonsense proposition for Working—but it became central in a context of increasing market integration and the emergence of statistical data enabling the study of the relationship between prices across space, and as we will see, over time. Working was an early advocate of what he called “price-difference analysis” (the analysis of the relationships between prices), when many of the early econometricians were carrying out correlation analyses on price levels rather than price differences (see Working 1935).

In 1925, Working joined the Food Research Institute established at Stanford University on the initiative of Herbert Hoover. Founded in 1921, it brought together scholars in biology, agronomy, and economics, with one expert from each discipline initially codirecting the center. In the interwar years the Food Research Institute was a rare example of a private institution doing research in agricultural economics.

The institute's head economist was Joseph J. Davis, codirector for more than thirty years, from 1921 to 1952. He was a leading economist in the first half of the century in the United States, president of the American Economic Association in 1944, and a government expert on agricultural issues for the Republican administrations of Herbert Hoover (1929–33) and Dwight D. Eisenhower (1953–61). Under Davis's guidance, the Food Research Institute regularly contributed to public debate, often expressing skepticism of direct market intervention. Davis, for instance, was critical of the Agricultural Adjustment Act—the New Deal's attempt to restore America's agricultural economy—that introduced price controls (Davis 1937). Working was a regular commentator on economic policies as well, and especially of what he deemed overly stringent regulation of speculation in futures markets (Berdell and Choi 2018). Working remained a loyal member of the institute and ended his career there in 1960 as a vice-director.

2. Observing Speculative Markets

Between 1925 and 1945, the Stanford Food Research Institute's main contribution to agricultural research was the Wheat Studies, a journal focusing on the world wheat situation. Working authored several of the studies, and notably the “Survey,” three monographs on wheat prices issued annually. This empirical work represented the bulk of Working's research over this period. This is not to say he shunned theoretical considerations. Indeed, it is likely that Working's most fundamental intuitions emerged in this decade while collecting price data and observing market participants in commodity exchanges. Retrospectively, in a letter to Paul Samuelson in 1961, to which I will return later, he wrote,

However, in the 1930s, Working had not yet formed the idea of informational efficiency. His focus during this period was rather, absent any appropriate theory of prices, to identify important stylized facts in the price movements of speculative markets.

2.1. Random-Difference Series

A first important stylized fact crucial to Working's intellectual journey came to light in his 1934 paper “A Random-Difference Series for Use in the Analysis of Time Series.” Working suggested that wheat prices, like many other commodity and stock prices, exhibit random changes, which he termed “random-difference series” (Working 1934b: 11). Retrospectively, financial economists saw in this article an early formulation of the random-walk model (e.g., Fama 1970: 390).

Working (1934b) did not directly model prices by stochastic processes. Modern probability theory was barely developed and would become popular among American economists only after the Second World War. Instead, he compared graphs of real price series with those of artificial price series subject to random change.⁹ The role of randomness in the behavior of economic series was just beginning to be recognized—one of the best-known examples cited by Working was Eugen Slutzky's 1927 paper demonstrating how random shocks could create predictable cycles (Slutzky [1927] 1937).

Working's paper was innovative in its discussion of the practical implications of these phenomena for trading investment. Trying to make predictions by looking for trends in price series is pointless, Working argued, if the series behave like random-difference series. In particular, he observed that “students of stock and commodities prices attribute great forecasting significance to certain ‘formations’ that appear more or less conspicuously in the charted price data.” But such formations “are without forecasting significance, for it is known that changes in a random-difference series are quite unpredictable” (Working 1934b: 21).

Working, however, did not primarily address his paper to investors but to his contemporary econometricians. In the early econometrics, traditional approaches to analyzing time series sought to reveal predictable price patterns, either by identifying cyclic components or by fitting a trend (Morgan 1991). Most of Working's own early research sought to identify major fitted trends or cycles in the series of agricultural prices (e.g., Working and Hotelling 1929; Working 1931). But, in the case of a random-difference series, he argued that any apparent trend would be an illusion: “In a series composed of purely random changes (a strict random-difference series) conspicuous trends will be found. Such ‘trends,’ however, must be regarded merely as generalized descriptions of the course of the series over a certain period, not as norms, nor as bases for predicting the future course of the series over even the briefest subsequent period” (Working 1934b: 12).

Working's discussion in the 1934 paper was an illustration of his methodological approach. He sought primarily to highlight stylized facts in price movements, and then to use those “facts” to demonstrate the (in)adequacy of a concept or a theory. Cycles and fitted trends, Working argued, were “inappropriate and misleading” concepts when applied to time series whose main property was to exhibit random changes (Working 1934b: 11).

Although, with hindsight, “A Random-Difference Series” was one of his major achievements, Working barely addressed the random character of price changes in his subsequent research. The fact that price changes looked random was a statistical curiosity with interesting implications for traders. But Working was, for the moment, unable to attribute any economic significance to such behavior of prices. He came to a solution only after a long detour on another issue: explaining the behavior of prices in futures markets.

2.2. The Futures Price Spread

Futures markets appeared in the Chicago grain markets in the second half of the nineteenth century. At that time, forward transactions, that is, transactions allowing a future delivery of agricultural goods at a price set beforehand, became common in agricultural exchanges. These “forward” contracts were over-the-counter transactions; they came to be known as “futures” in the United States when standardized by the Chicago Board of Trade, which offered contracts with both standardized grain quality and maturities (Cronon 1991: 124–26). Futures contracts were used by businesspeople whose activities involved storing grains (such as elevator operators, farmers, shippers, or millers) and who wanted to hedge their stocks. They also offered new profit opportunities for these agents, who could gamble on whether the price of a particular commodity would rise or fall. The futures market was quick to thrive in the United States, with the volume of futures transactions overtaking spot market transactions soon after its establishment (124–26).

Futures markets soon became controversial in the public debate (see Jacks 2007: 344, 358). Since they exceeded the spot markets in volume, many took the view that trading in futures markets was fictitious and driven primarily by speculators rather than by merchants owning and using the commodities. In the 1920s, opposition to futures markets intensified owing to suspicions that cartels were manipulating prices.¹⁰ In 1922, Congress passed the Grain Futures Act establishing the Grain Futures Administration (GFA), the forerunner of today's Commodity Futures Trading Commission. The GFA became an invaluable source of data for pioneers in the study of futures markets like Working (Berdell and Choi 2018).

The concept that became fundamental in Working's research was the price spread, the difference at any given time between two futures prices with two different delivery dates (or between spot prices and futures prices). Working published several Wheat Studies on the topic, in particular on the Chicago and the Liverpool markets (e.g., Working 1933, 1934a; Hoos and Working 1938). The first was published in 1933 and analyzed the spread between the July and September futures prices in Chicago. The choice of July and September was not arbitrary. This was harvesttime in the Midwest and resulted in a major change in the available wheat stocks. Harvesting could begin in June, but transport to the exchanges took time and was not completed until September. Working wanted to examine how, in June, the forthcoming harvest affected the spread between July and September.

His study contained the essential components of what agricultural economists today call the theory of storage. The theory of storage states that a high stock implies a positive spread and low price volatility, while a low stock implies a negative spread and high price volatility. Working observed the relationship between stocks with both the price volatility and the level of spread. In particular, Working introduced what is known today as the “Working curve” (see fig. 2).

The Working curve showed the following pattern: the price spread was highly correlated with the level of available stocks. When stocks were relatively abundant, preharvest contract prices tended to be relatively lower than postharvest prices. When stocks were relatively lean, preharvest contract prices tended to be relatively higher than postharvest prices. In his 1933 paper, Working did not offer a consistent explanation for this stylized fact and focused on reporting his statistics. Working devoted important space to pointing out exceptions to this empirical trend. On this point, Working showed his attachment to American institutionalism and his in-depth knowledge of the Chicago wheat market. He carefully explained how each deviation from the curve could be attributed to contingent events.¹¹

It was primarily during the 1940s, as we will see in the next section, that Working began to develop a consistent explanation of the price spread behavior. This explanation, which is essentially based on a no-arbitrage argument, will be the first step in the development of a more global theory of speculation.

3. Theories of Speculative Markets

Working made a substantial effort to publish his own understanding of futures markets in a series of papers around 1950. This “theoretical turn” may be explained by several elements. The publication of the Wheat Studies was discontinued in 1945, freeing up time for theoretical research. Working also discovered research by British economists on the futures market, and this clearly spurred him to publish his own theoretical account. Moreover, in the early 1950s, Working's research caught the eye of Merrill Lynch and its Foundation for the Advancement of Financial Knowledge. The Food Research Institute received a grant to pursue its research on futures trading. Working took on a PhD student, Claude Brinegar, who had just completed a master's degree in statistics at Stanford. He was Working's second and final student in his entire career (the first being Robert Calkins, who embraced an administrative career at California and Columbia). Brinegar submitted his dissertation, titled “A Statistical Analysis of Speculative Price Behavior,” in 1954. It drew explicitly on Working's theories. As Brinegar put it, “Working did the intellectual side and I did the brute force” (Fox, interview with Brinegar).

3.1. Explaining the Price Spread

The first paper in which Working seriously discussed theory was probably his 1942 paper, “Quotations on Commodity Futures as Price Forecasts.” Its structure reflected the way Working typically built a theoretical argument: he began by setting out the theoretical claims of other economists, and then criticized them in the light of the facts before putting forward his own theoretical argument. By “facts,” Working essentially meant his own empirical research, in particular, the Wheat Studies, which he cited extensively. This approach reflected the way he systematically prioritized the empirical over the theoretical. Unfortunately, his determination to adhere as closely as possible to the facts did not make his arguments any more readable. Whenever Working set out a theoretical argument, it was generally submerged in a detailed discussion of the facts, pointing out exceptions and qualifying the generality of its own claim.

In his 1942 paper, Working criticized a claim that he described as “a general opinion among economists,” which held that futures prices reflected the market's anticipation of future prices while the spot price did not (Working 1942: 39).¹² Working refuted this argument on the basis of his Wheat Studies. Working had observed that any news about the forthcoming harvest affected futures prices expiring either before or after the harvest:

Why did the prices of current crops integrate information on events that affect only new crops? The insights that emerged in Working's mind to explain this fact was that market participants were exploiting any differences between two prices and, thus, news affecting remote maturities would be integrated into contracts with closer maturities. If, for example, bad news spread about the forthcoming harvest, individuals anticipated a relative increase in the wheat price after the harvest. The expected rise in the postharvest price offered them an opportunity to make a profit by storing wheat at present and selling futures. They could repeat the process until the difference between the futures price and the spot price equaled the cost of carrying the commodity. The spread, thus, reflected the cost of carrying the commodity. This explanation was consistent with his observation of 1933. The levels of price spread he had observed in figure 2 were determined by the cost of carrying the commodity, and this cost of carrying was not constant and was itself a function of the level of stocks.

The exploitation of such arbitrage opportunities implied that spot market prices were always logically determined by futures market prices. In a subsequent paper, Working illustrated this claim by describing, in an institutionalist vein, his own observations of the practice of market participants in the American exchanges: “At the cash-grain tables,” he argued, “buyers and sellers ordinarily do not discuss prices; they bargain in terms of cents ‘over’ and cents ‘under.’ When agreement is reached in these terms the premium or discount settled on is applied to the latest quotation for the ‘basic’ future to arrive at a formal price.” He then concluded that “the cash market is therefore clearly subsidiary from the standpoint of price formation” (Working 1948: 7).

One difficulty of his theory was that the spread (and thus the “cost of carrying”) was often negative, as illustrated in figure 2. The idea that a positive spread reflected the cost of carrying commodities was intuitive and well understood by agricultural economists, but it was not very clear how it could also reflect a negative spread (e.g., Vance 1946). What was the meaning of a “negative cost”? And why would traders hold on to a positive stock of wheat when they could sell it for a higher price today? Working explained this by the existence of traders on the market, “merchants, millers, and growers [who were] willing to carry considerable stocks of wheat although they have reason to expect to take a loss on the amount carried into the new crop” (Working 1942: 43). For some traders, maintaining a positive stock was compulsory in order to maintain productivity and potentially take advantage of unanticipated opportunities. Maintaining a stock was costly, then, but it did yield a positive return.

This characteristic was an integral part of the arbitrage relationship suggested by Working. If the futures price fell (as a result of good news about the forthcoming harvest), the classes of traders who were able to reduce their stocks would take advantage of the opportunities by selling on the spot market. If stocks were low and held mainly by a class of traders who were unwilling to sell, the spot price could remain above the futures price, and the market would show a negative spread reflecting the yield of carrying commodities for these merchants and millers.

Working was not the only one to develop the idea of a “negative cost” of carrying the commodity. This fundamental idea had also been introduced by Nicholas Kaldor in his 1939 paper “Speculation and Economic Stability.”¹³ In Working's words, it was once his 1942 paper “had been set in type” (Working 1942: 43). For some traders, maintaining a positive stock was compulsory in order to maintain productivity and potentially take advantage of unanticipated opportunities. Maintaining a stock was costly, then, but it did yield a positive return.

This characteristic was an integral part of the arbitrage relationship suggested by Working. If the futures price fell (as a result of good news about the forthcoming harvest), the classes of traders who were able to reduce their stocks would take advantage of the opportunities by selling on the spot market. If stocks were low and held mainly by a class of traders who were unwilling to sell, the spot price could remain above the futures price, and the market would show a negative spread reflecting the yield of carrying commodities for these merchants and millers.

Working was not the only one to develop the idea of a “negative cost” of carrying the commodity. This fundamental idea had also been introduced by Nicholas Kaldor in his 1939 paper “Speculation and Economic Stability.”¹³ In Working's words, it was once his 1942 paper “had been set in type” (Working 1942: 51) that he discovered Kaldor's paper and the research on futures markets by other British economists. Working probably knew Keynes, Kaldor, and Hicks before, but he seriously read them then. The discovery of this body of research would have a profound impact on Working's intellectual journey. Working, an empiricist by training and an empiricist for the first twenty years of his career, read British economists and devoted the latter part of his career to developing an alternative theory of futures markets and speculation.

3.2. Discovering British Theories

In Britain, the futures markets and the behavior of speculative prices came in for much discussion in the late 1930s. Keynes addressed the issue in a few pages of his Treatise on Money in 1930, and a decade later, his theory was developed by other British economists and notably John Hicks, Ralph Hawtrey, and Nicholas Kaldor. As with Working, one explanation for the price spread put forward by Keynes and others was the cost of carrying the commodity. But the theory developed by British economists was more general and included factors such as risk and expectations.

There is not enough space here to go into detail on the ideas of British economists and how Working addressed them.¹⁴ In 1942, when Working discovered their work, the central contribution was Kaldor's 1939 paper. Kaldor reformulated the ideas that Keynes had developed in his Treatise on Money as simple algebraic equations. One central idea under discussion among British economists was the relationship between FP, the futures price; EP, the expected spot price; and $r,$ the risk premium:

The expected spot price was an unobservable abstraction to be distinguished from the futures price. This distinction enabled Keynes and other British economists to emphasize the risk management function of futures markets. Holding a futures contract eliminated the price risk (the risk for a holder of an asset that its price decreases) and was thus less risky than buying a cash contract. Hence, all things being equal, Keynes argued that the expected spot price had to be higher than the futures price by the amount of the risk premium.

Working added an appendix to his 1942 paper commenting on the British theory. He warned that “readers familiar with this recent British discussion will have already met the concept of ‘cost of carrying,’” but they “will be struck by the absence there of attention to the factor of risk or uncertainty as an element in the difference between spot and futures prices” (Working 1942: 51). Working did not reject the role played by risk and uncertainty in determining the price spread, but he believed those factors explained only a small amount of the statistical facts and so were not a good starting point for a sound theory: “In a discussion of the main phenomena observable in relations between spot and futures prices in the Chicago and Liverpool wheat markets, it appears that risk may be left out of account” (51). Working was also generally uncomfortable with the theoretical concepts of British economists. He criticized the concept of “expected price” and “risk premium” as being too abstract and unobservable: “There is no one rate of discount for risk and uncertainty,” he argued, “nor is any useful average rate to be found at a given time” (52).

Working made a substantial effort to publish his own understanding of futures markets in a series of papers in the late 1940s and quoted British economists abundantly (e.g., Working 1948, 1949a, 1949b). One of the main disagreements was the issue of arbitrage. British economists did emphasize the role of arbitrage in determining the price spread, but Working thought that they failed to take this reasoning to its limit. One of Working's harshest criticisms concerned an argument by Kaldor (1940: 198) that “there [was] no limit, apart from expectations, to the extent to which the futures price may fall short of the current price.” Working rejected this idea that expectations could affect the spread, as he did in his 1942 paper. Apart from considering this claim to be empirically refuted, Working also thought that it wrongly implied that the market was dysfunctional in exploiting an arbitrage between futures and spot prices. “This theory,” he argued, “was clearly inapplicable to wheat prices in the United States and may be quite generally untenable. It rests in part on the mistaken assumption that hedging is not arbitrage” (Working 1948: 5).

Overall, the dialogue between Working and British economists was one-sided, but it remained a fruitful one for the elaboration of Working's theoretical thinking. In the United States, Working's main interlocutors were public authorities such as the Grain Futures Administration and the Federal Trade Commission that were looking to better understand the futures market in order to regulate it. British economists had developed by far the most comprehensive account of futures markets, and Working was able to use their research to develop his own insights. The British discussions of arbitrage and its limits enabled Working to move beyond a purely empirical account and develop his own understanding of futures markets more systematically. In a subsequent 1948 paper, for instance, he renamed the concept of “cost of carrying” as “price of storage,” which he presented through an algebraic equation following the British methodology:

where $Ps$ is the “price of storage” and $P1$ and $P2$ are two contracts at different maturities. The equation did not bring any new insights, as the “price of storage” was a new name to capture the same idea: the spread reflected the yield and the cost of carrying the commodities that he already discussed in 1942. The equation shows, however, how Working was thinking in an increasingly abstract way.

The theoretical differences between Working's and the British frameworks reflected different views, or at least a different emphasis, on the social function of futures markets and speculation. The British primarily understood the futures market and hedging as a means of transferring price risk and focused accordingly on concepts capable of capturing this function such as the risk premium; Working valued futures markets for their role in price formation and their capacity to integrate expectations into current spot prices through the mechanism of arbitrage.

Working believed that the main motivation for traders deciding to hedge was to exploit a difference between spot and futures prices. “Hedging,” he argued, “is not properly comparable with insurance. It is a sort of arbitrage” (Working 1953a: 325). For Working, typical agents who hedged in commodities markets were informed merchants, such as millers in wheat markets, whose business involved storing stocks of the products. In the presence of a futures market, such merchants decided to hedge not because they feared a loss but because a difference in the current price spread led them logically to hedge:

Working obviously recognized that futures markets allowed traders to reduce price risk. But he viewed the idea that hedging was transferring the risk to speculators as misleading. Reducing the risk was not the only or the main motivation of futures traders. For Working, the idea that hedging avoided or reduced risk concealed a range of practices and motivations on the part of hedgers. Producers, processors, merchants, and professional traders all hedged, and although their motivations were different, they did not share in common a desire to reduce their risks but to exploit an advantageous spread between two prices.¹⁵

Symmetrically, Working took a different view from British economists of the social function of speculators who faced the hedger in the transaction. The social function of speculators for British economists, as Working understood it, was to handle risk, and speculators were remunerated accordingly through the risk premium. For Working, the main desirable effect of speculators was their ability to keep informed and thus to improve price formation by integrating their opinions about current and future conditions. It was again in discussing the work of the British economists, in particular, Keynes's General Theory and his chapter 12 on speculation, that Working fully developed this ideas. He notably developed a model of unbiased expectations able to explain the random character of price changes he had observed in 1934.

3.3. The Unbiased Expectations Model

The idea that asset prices somehow reflect expectations about future business conditions has always been widespread among economists. This was particularly obvious for prices subject to speculative activities. From the end of the nineteenth century, many pamphlets argued that the social value of financial markets lay in their capacity to freely deliver, through the pricing system, the opinion of traders about current and expected economic conditions (Preda 2004). From the 1930s, expectations became a subject of growing importance in economics (Young, Leeson, and Darity 2004: 1). At that time, most of the profession viewed expectations as somewhat biased. For instance, the risk premium in British theories of the futures market implied that the futures price was systematically a downwardly biased expectation of the future spot price. Keynes famously argued, in chapter 12 of his General Theory, that expectations were potentially determined by self-referential and mimetic behaviors. Even in agricultural economics, Ezekiel (1938) introduced an example of extrapolative expectations in popularizing the so-called cobweb theorem.

Working's main contribution to the issue of expectations was his 1949 paper “The Investigation of Economic Expectations.” Working addressed a broad audience and intended to discuss expectations in economic theory in general, but he was clearly inspired by his work on futures markets and his reading of British economists. He began his argument by introducing the following equation:

where $FP$ is the futures price and $E$ and $r$ are respectively “some sort of combination” of individual expectations and individual risk premiums (Working 1949a: 152). The equation was similar in spirit to equation (1) introduced by Kaldor (1939), and Working believed that it encapsulated the British view of futures markets. Working defined

as the main factor determining the futures price (again he downplayed the importance of $r$⁠). At first approximation, thus, the futures price of a product could be interpreted as the “market expectations” of prices of this product.

What were, Working asked, the possible errors in expectations observable in the behavior of futures prices? He distinguished two possible types of error, those that are “randomly inaccurate and those that are biased” (Working 1949a: 152). Working acknowledged the existence of biases and discussed them extensively. In particular, he discussed chapter 12 of Keynes's General Theory and interpreted the well-known beauty contest as an “exaggerative bias—a supposed tendency for market expectations to respond excessively to day-to-day news and rumors” (158). While Working acknowledged the existence of such biases, he minimized their importance: “Concentration of attention on bias in market expectations involves emphasis on the imperfections of expectation without due consideration of their relative magnitude. Excessive attention to bias, if I may say so, risks creating a biased impression” (158).

Working did not, however, postulate the absence of errors in expectations. Since any prediction depends on an uncertain future, he acknowledged the existence of “necessary” errors, namely, an “irreducible minimum of inaccuracy which must result from response of prices to unpredictable changes in supply and in consumption demand schedules” (Working 1949a: 158). All errors that did not fall into this category had to be considered “objectionable.” Working ended the main argument of his paper by defining an ideal market as one in which market expectations (the futures price) have only necessary errors. In such a market, the price should be “completely unpredictable” because “ideal market expectations would have taken full account of the information which permitted successful prediction of the price change” (160).

From this line of reasoning, Working suggested that his 1934 studies on the random-difference series should be reinterpreted, as should the studies of Alfred Cowles (e.g., Cowles 1933), who famously attacked the financial analysts William Peter Hamilton and the poor performance of his predictions. Working argued that Cowles's findings were actually consistent with a well-functioning market. Regardless of whether or not forecasting was a failure at the individual level, at the aggregate level it reflected the “perfection of the market” where knowledgeable traders competed with each other (Working 1949a: 161).

The fundamental innovation of “The Investigation of Economic Expectations” was to distinguish between objectionable and necessary errors. In the paper, Working introduced the issue of the accuracy of expectations through an analogy with the accuracy of a rifleman's shooting:

This analogy highlights the influence of the war on Working's economic thinking, where he developed a course on statistical quality control for the arms industry.¹⁶ It was a symptom of a more general change in economics as a profession, which, to paraphrase Cherrier (2017: 553), entered the war as a science of production and emerged from it as a science of decision-making.

Working's 1949 paper clearly marked a shift in his methodological approach and reflected his newfound willingness to increasingly employ abstract hypotheses. A few years before, Working (1942: 51) had criticized in line with institutionalism the concept of the expected spot price introduced by Kaldor because it made “insufficient allowance for difference in expectations of different individuals.” In 1949, he used it as the starting point of his theory of unbiased expectations (Working 1949a: 152).

Working dedicated his next writings to grounding his “ideal market” in the individual behaviors of market participants. Working's 1958 paper, “A Theory of Anticipatory Prices,” represented his clearest effort to model the decision-making processes of economic agents. What Working called a “model” was a series of literal assumptions that he considered as departing from reality: (1) the absence of price takers, (2) the absence of false information, and (3) a market composed of persons with “exceptional trading ability and judgment, emotionally stable, with a large fund of pertinent knowledge, skilled in using their knowledge and [giving] all their working time and energy to the business of trading and keeping appropriately informed” (Working 1958: 193–94). The last assumption was clearly central for Working, and it reflected his view of professional traders, whose main activity was searching for relevant information:

For Working, too much information was available and was forcing traders to specialize in acquiring and processing information:

This “model” explained what Working viewed as the two main features of speculative price fluctuation: the very frequent and the random character of price changes. Because “there is an almost continuous flow of such information, through private channels of information as well as through public channels,” Working argued, “it is reasonable that price changes should be frequent,” and since the information on which traders made their predictions is unpredictable, “the price changes generated by the model are unpredictable price changes” (195).

The 1949 and 1958 papers were rare attempts by Working to generalize his views beyond futures markets to all speculative markets. His PhD student Brinegar recollected that Working viewed his theory of expectations as “a very fundamental bit of writing” (Fox, interview with Brinegar). Working devoted the final few years of his career to disseminating his ideas to the new generation of economists.

4. Disseminating His Ideas

Toward the end of his career, Working witnessed big changes in research on finance. The thriving business schools promoted research in finance through massive funding from private foundations (Fourcade and Khurana 2013). This fostered research on expectations and intertemporal price behavior under uncertainty. From the late 1950s to the 1960s, business schools at Chicago and the Massachusetts Institute of Technology became the two major research groups in finance (Jovanovic 2008).

Working became an important reference for economists contributing to the field of finance like Paul Samuelson (1957), Paul Cootner (1960, 1961), Hendrick Houthakker (1957, 1961), and Lester Telser (1956, 1958). They all had a close interest in the intertemporal behavior of prices, and they considered Working to be one of the pioneers in the area. Futures markets were an important source of data for economists working on finance theory at a time when data collection on capital markets was less developed (this was to change with the establishment of the Center for Research in Security Prices at the University of Chicago in 1960). The research, Houthakker recalled, “started in commodity markets where the data [were] much better” (Fox, interview with Houthakker).

Working's influence first reached MIT. He met Houthakker at Stanford University in the early 1950s, and he introduced Working's research to Samuelson in the early 1950s.¹⁷ Samuelson became Working's most enthusiastic supporter. In 1957, Samuelson published his first paper on the behavior of speculative prices, a contribution that he considered to be a “prologue to a theory of speculation.” In the paper, Samuelson reformulated the problem of price spread in a formal model. He cited Working as a leading authority on the subject and discussed his “price of storage” concept (Samuelson 1957: 182).

Samuelson sent a copy of his article to Working in July 1958. Working's reply was somewhat negative. Working acknowledged that he was “delighted that an economic theorist of stature and abilities had turned his thought to intertemporal price relations,” but he added that he was “discouraged and disappointed by what you did in the paper” (Samuelson Papers, box 78). His disappointment arose from a claim by Samuelson (1957: 190, 194) suggesting that new expectations about crops had an effect on the price spread, an argument, as we saw, Working dismissed several times.

Working's lukewarm reaction reflected his disappointment at Samuelson's failure to fully appreciate his “price of storage” concept. He made the same criticism of Houthakker, who formulated a similar claim a year later (Houthakker 1959). But Working's disappointment mainly reflected a methodological difference with the modeling methodology of the two postwar economists. For Samuelson and Houthakker, the challenge was to build a formal model of futures markets that did not then exist. They attacked the problem by modeling very simple cases with unrealistic hypotheses. They assumed no carryover of current stock to the next harvest, and it logically implied, in the world of their models, that expectations of the next harvest would not influence the current price.

Working was not really averse to formal models per se, but his own experience in building a model or a theory diverged from postwar US economics. For Working, the hypotheses used to build a model of futures markets had to be empirically grounded in careful observations of those markets. Working, for whom the sole interest of a model was to explain empirical facts, did not appreciate Samuelson's modeling strategy. In a subsequent letter of May 1961, Working confessed to Samuelson that his “experience in having the results of deductive reasoning disproved by statistical evidence . . . made me skeptical about the reliability of deductive reasoning” (Samuelson Papers, box 78).

Despite these methodological differences, Working definitely influenced Samuelson and his work on market efficiency. Although they did not share the same methods, they did share the same ideas. In the letter of May 1961, Working explained to Samuelson how he came to his expectation theory:

Samuelson replied to Working by presenting an early version of a theorem that would become his celebrated martingale model (Samuelson 1965).¹⁸ The theorem, which demonstrated conditions under which futures prices could follow a martingale, was inspired by Working's theory of “ideal markets.” Samuelson remained a close reader and admirer of Working, and he portrayed him in the following decades as a great pioneer who challenged Keynes's speculation theory: “In a well-known passage, Keynes has regarded speculative markets as mere casinos for transferring wealth between the lucky and unlucky, the quick and the slow. On the other hand, Holbrook Working has produced evidence over a lifetime that futures prices do vibrate randomly around paths that a technocrat might prescribe as optimal” (Samuelson 1973: 3).

Working's influence also spread to Chicago. Working was already well known to the Chicago group of agricultural economists headed by Theodore Schultz. When he was at Chicago, Houthakker hired Lester Telser as a research assistant and urged him to pursue his own research on commodity markets (Telser 2017: 42). Telser completed his dissertation, “The Supply of Stocks: Cotton and Wheat,” in 1956, with Milton Friedman and Theodore Schultz as his advisers. Telser (1956, 1958) followed in Working's footsteps by proposing a theory of futures prices as unbiased expectations of spot prices. Before joining the Chicago Department of Economics in 1964, Telser was professor at the business school, and it would not be surprising that such an idea had permeated the minds of his students like Fama.

However, Telser remained critical of Working's contributions. “The big guru on futures trading, especially on wheat futures, [was] Holbrook Working,” he recalled. “How should I put it? Our swords crossed on several occasions, and we did not agree on many aspects of futures trading” (Telser 2017: 60). In an appendix to his dissertation, Telser gave a harsh review of Working's contributions and, in particular, of the 1933 Working curve. He confessed that he felt “uneasy with the statistical methods used” (Working's curve, among other things, was handmade and not regressed). Moreover, the explanation provided by the price of storage focused on the supply of a commodity; it ignored the demand side and “failed to develop a logically complete explanation of the determination of equilibrium in the futures market” (Telser 1956: 121). Telser viewed Working as a pioneer but an outdated scholar in terms of econometrics and also of theory. “I thought most of his theories were mistaken,” he recollected in 2021. “Working ignored both Keynes's and Hicks's contributions to the understanding of futures trading” (personal interview, November 2021).

Without being as critical as Telser, most of the young generation of economists were unwilling to abandon Keynes's theory and, in particular, the concept of risk premium. The issue at stake was not only to have the theory that best explained the data. Cootner, for instance, supported the Keynesian liquidity preference, which, he believed, was the very basis for a theory dealing with uncertainty. His goal was to reconcile Working's and Keynes's theories (Cootner 1967: 67).

Working retired and had ceased most of his research by the early 1960s. He died more than two decades after his retirement in 1985, and although he witnessed the emergence and maturation of financial economics, he left no writings or commentaries on the research published in the 1970s and 1980s.

5. Working's Legacy

Even though he contributed to the early stages of financial economics, Working is seldom mentioned in the canonical history of the field. At first sight, it may seem puzzling that, after receiving some attention at the end of his career, Working's contributions did not receive more credit from financial economists who were, in the context of the emergence of the subdiscipline, looking for precursors and legitimacy (Jovanovic 2008; MacKenzie 2008). Although figures like Samuelson praised him, the most influential writings, notably those of Fama, cited only his 1934 paper on random differences and claimed that his argument “lacked the force” of other pioneers (Fama 1970: 390). Why did he receive so little credit? Historically, questioning Working's legacy does not aim at evaluating his merits but instead at shedding light, through his lack of success, on what was successful in the emerging financial economics (e.g., Düppe and Weintraub 2014).

The first reason for Working's lack of credit was sociological and related to his inability to build a “school.” The Food Research Institute did not have a teaching program before the 1950s. Working supervised only two doctoral students throughout his career, and like many institutionalists, they did not stay in academia. Robert Calkins left in 1952 to lead the Brookings Institution. In the mid-1950s, Brinegar joined the oil industry and eventually embraced a political career. The Food Research Institute was arguably not the right place to launch a research program on finance and speculation. The institute was important in the network of agricultural economics but unknown to a new generation of business school–educated financial economists.

Paul Cootner joined Working in 1970 at Stanford and chaired the finance workshop at the business school. However, Cootner died prematurely in 1978, and although he was a prominent financial economist in the 1960s, he did not leave the legacy of a figure like Fama. Overall, Working corresponded with and was read by outsiders to the emerging financial economics, like Samuelson, Houthakker, and Telser. They were not financial economists per se but general economists, and while they enthusiastically participated in the emergence of financial economics, they left the field open to the younger generation in the 1970s. Working's research was also less relevant to financial economists in business schools, whose focus was essentially on capital markets.¹⁹ Working did not interact much with scholars from the Chicago business school, like James Lorie, Lawrence Fisher, Merton Miller, and Eugene Fama. Yet, over the following decades, Chicago's scholars became the major research group on finance. They wrote their own history of the emergence of financial economics, and most of the pioneers like Working, Cootner, and even Telser were left out (Jovanovic 2008).

Stanford tried to carry on his legacy in the subsequent decades. The Food Research Institute issued Working's unpublished writings in the 1970s (Working 1974). They also published Brinegar's dissertation in 1970, more than a decade after its completion. As Brinegar recollected, the agricultural economist Bill Jones, then director of the Food Research Institute, believed that “Chicago was taking some of our ideas” and pushed for the publication of his dissertation (Fox, interview with Brinegar). In the Department of Economics at Stanford, a Holbrook Working Professor of Commodity Price Studies Chair was created, probably in the late 1970s. The second holder of the chair, Anne Peck, edited the selected writings of Working in 1977 (Peck 1977).

However, these efforts were insufficient, and it was mainly the group of economists at Chicago who succeeded in forming a community and a research program. Chicago's economists took the lead in collecting data on capital markets and financial econometrics. They developed the canonical tests of market efficiency, what would become known as the “three forms of the efficient market hypothesis” (Fama 1970). The reuse of this theoretical framework, but also criticism of it, would indirectly ensure the fame of their research.

Working's theoretical framework and his concepts did not share the same destiny. Another reason for Working's lack of success was methodological and related to the fact that his research was difficult to comprehend for postwar economists. Working belonged to a declining breed of economists, the applied statisticians who had emerged from the American institutionalism of the interwar period (Biddle 2017). The discussion of his 1961 paper at St. Louis, referred to in the introduction, and the tension between Working and Telser were illustrative of the profound changes in postwar US economic methodology and the difficulty for young economists in reading and understanding Working. Between the abstract character of theories and particularities of data, Working always chose data and thus was no longer in sync with the profession. “Working knew too much to accept any general theory,” recalled Houthakker; “as soon as anybody came up with a theory, he would know counterexamples. That's why he didn't embrace the efficient market hypothesis” (Fox, interview with Houthakker).

Indeed, although he himself had developed a hypothesis similar to the efficient market hypothesis, Working never fully embraced this hypothesis. It was obvious to him that his 1949 ideal market of futures markets was only an approximation and a contradictio in terminis. In his ideal market, “no speculators would be able to consistently make money, and the speculation necessary to maintain even an approximation to ideal price behavior would tend to vanish.” “Since many professional traders do make money,” Working concluded, “the price behavior is not ideal” (Working 1953a: 329). Younger generations of economists, such as Fama and Samuelson, would be more critical of traders claiming to possess superior (and profitable) knowledge. Working took the problem the other way around: although he was doubtful those traders did turn a profit, such traders scrutinizing the news were the raison d’être of rational price formation (Working 1967).

Working did not fit into the postwar economic framework, nor was he remembered as a typical and prominent institutionalist. He was also slightly misaligned with the institutionalist approach in which he had been trained. Working's intellectual journey led him to engage with highly theoretical works, such as those of Kaldor and postwar economists, and it is clear that he was influenced by their abstract approaches to economic problems. Working's theory of speculation, for instance, drew its inspiration from Kaldor's concept of expected spot price to establish his theory of “unbiased market expectation.” That is not to say that Working was no longer an institutionalist by end of his career but rather that his intellectual journey led him to backtrack on certain points from this way of thinking and to adopt a hybrid approach between the old institutionalism and the new postwar economics.

Working's research was arguably out of step with the emerging financial economics. But he definitely left his mark on the field. His research illustrates, in this respect, how financial economics originated in the first half of the twentieth century. In particular, it sheds light on an early American view of speculation that was inspired by, but that also contrasted with, the prevailing British view. The price spread, traders as arbitragers, and price as an entity conveying information were ideas already firmly rooted in American economics. Although Working was arguably not the only one to produce and popularize such ideas, his intellectual journey shows us remarkably well the slow and gradual emergence of this style of financial reasoning that was to gain momentum in the second half of the twentieth century.

I am indebted to Justin Fox, who shared with me his notes from his interviews with Hendrick Houthakker and Claude Brinegar, colleagues of Holbrook Working. I am also grateful to Lester G. Telser, who kindly answered my questions. I would like to thank the Center for the History of Political Economy and the Rubenstein Library at Duke University for assistance in consulting the Samuelson papers. Finally, this research has benefited from the suggestions from the two anonymous referees and the participants of conferences at which I presented early versions of the paper. I am especially grateful to Andrej Svorenčík, Paul Dudenhefer, Vincent Carret, and Maria Cristina Marcuzzo.

Notes

References