Leontief (Reference Leontief1929) and the Statistical Determination of Supply and Demand Curves

From 1925 to 1928, Leontief was a student at the University of Berlin. In 1927, at age twenty-two, he was hired by the Institut für Weltwirtschaft (IfW) in KielFootnote ⁷ while completing his PhD dissertation. Leontief was appointed “responsible for the newly established section ‘Market analysis and elasticity studies’” (Hagemann Reference Hagemann2021, p. 80) within the department of statistical research on the world economy and trade cycle headed by Adolph Lowe.Footnote ⁸ At Kiel, Leontief developed and statistically implemented an original method for quantitatively determining both demand and supply curves and elasticities from a set of price-quantity time series. Published in 1929, it quickly became known as the “simultaneous method” or simply the “Leontief method.”

Both Leontief’s (Reference Leontief1929) “simultaneous method” and his subsequent criticism of econometric work are rooted in the econometric studies of the interwar period. Since this field of research has been thoroughly examined in previous histories of econometric ideas, notably by Mary Morgan (Reference Morgan1990),Footnote ⁹ it is unnecessary to elaborate on it here.

The field was largely shaped by the way Moore (Reference Moore1914) formulated the problem of statistically determining demand curves (Stigler Reference Stigler1962). As Morgan (Reference Morgan1990, p. 133) points out, Moore was inspired by an empirical procedure devised by Antoine-Augustin Cournot fifty years earlier. Cournot acknowledged the lack of available data and noted that one could hope to quantitatively determine the demand curve for certain products, especially foodstuffs, if a particular market conjunction allowed it. Assuming the slope of the curve remains unchanged, and the demand curve remains still while the supply curve shifts (due to weather conditions, for example), all other things being equal, the market equilibrium points would lie along the demand curve from one year to the next. Therefore, a statistical economist examining time series of market prices and quantities would statistically observe the demand curve being revealed. Moore (Reference Moore1914) essentially adopted this Cournotian empirical device, implementing it after making statistical adjustments to the data. This approach was later continued by Schultz and others.

Although Cournot had anticipated many of the difficulties and limitations of his device, Moore (Reference Moore1914) remained optimistic and applied it to various agricultural products. It was soon recognized that the assumptions underlying this approach required careful consideration. In some cases, the demand curve shifted, revealing the supply curve, rather than the supply curve shifting to reveal the demand curve. In other cases, when both curves shifted, a “path of equilibrium” (Gilboy Reference Gilboy1930, p. 609) was revealed instead. By the time Leontief began developing his own statistical technique, Elmer J. Working clarified the assumptions often left implicit in Moore’s work. Working (Reference Working1927, p. 234) summarized: “There are four questions, the answers to which it is particularly important to know. They concern (1) whether the supply or demand curve is more variable, (2) the market to which the price and quantity data refer, (3) the extent to which ’other things are held equal,’ and (4) whether the shifting of the supply and demand curves is correlated or random.”

While Moore and others developed methods that addressed the difficulties posed by Cournot’s procedure to varying degrees, these studies—including Leontief’s (Reference Leontief1929) method—shared a common approach. Starting with market price-quantity data—usually time series—they attempted to statistically derive either the demand curve, or, more rarely, the supply curve, or, even more rarely, both curves from these data only. Moore (Reference Moore1925), with his so-called cobweb framework, and Leontief (Reference Leontief1929), with his “simultaneous method,” developed techniques for determining both the demand and supply curves together from the same set of price-quantity data, relying on comparable assumptions about the shape of the curves.Footnote ¹⁰

The “simultaneous method” developed by Leontief in Kiel stemmed from Moore’s (Reference Moore1914) statistical studies. It relied on a similar framework—Marshallian-Cournotian partial equilibrium analysis—and similar assumptions. These involved in particular the constancy of the slopes along the curves and over time, and the independence of the shifts of the two curves. Leontief’s (Reference Leontief1929) technique, developed with the assistance of Kiel mathematician Robert Schmidt, was a modified least squares regression and did not require preliminary statistical adjustments to the data. Overall, Leontief’s method did not fix the troubles encountered by the usual approach, as it relied on similar assumptions and techniques (see Gilboy Reference Gilboy1930, Reference Gilboy1931a; Frisch Reference Frisch and Altschul1933b). This was immediately recognized. Yet, because it simultaneously determined supply and demand curves without requiring additional data beyond market prices and quantities, Leontief’s method made him famous at the age of twenty-five. Nevertheless, his technique was controversial. Incredulous, Tinbergen ([1930] Reference Tinbergen, Hendry and Morgan1995, p. 234) suggested with understatement that Leontief’s method had overcome an “insoluble” problem. Olaf Bjerkholt (Reference Bjerkholt2016) detailed how from 1930 to 1932 Leontief was expected to respond to his critics, but he did not. It is important to note about this field that (1) “the basic data consist of corresponding prices and quantities,” as Working (Reference Working1927, p. 215) emphasized; and (2) Leontief’s (Reference Leontief1929) “simultaneous method” did not deviate from this principle or from the general framework adopted. In other words, Leontief’s ([1931] Reference Leontief and Fisher1932) later criticism of econometric work did not rely on his own method of deriving supply and demand curves statistically. Instead, we must deduce that his method was part of the problem.

The “Official Opponent”: Leontief and the American Statistical Economists

In 1930 or 1931, Leontief did not publish as expected a reply to the criticism of his “simultaneous method.” In August 1931, Leontief left Berlin and Europe, boarding a ship for New York. On October 1, he joined the National Bureau of Economic Research (NBER) as a research associate. This was a one-year research position. The bureau expected Leontief to further develop his “simultaneous method.” At the time, the prevailing methods in the field were those developed by American economists, notably Henry L. Moore of Columbia University and his former student Henry Schultz of the University of Chicago. In October 1931, while Leontief was in New York, Moore, who had recently retired from academia due to mental health problemsFootnote ¹¹ and was in Paris at the time, wrote to him: “[You] have made yourself famous by your original research in a difficult field.”Footnote ¹² However, Leontief’s recent fame was ambivalent, as his method was considered both ingenious and controversial. Hence the eagerness of American economists to meet, and perhaps confront, the young European statistical economist. This tension was exacerbated by Leontief and the IfW having introduced and promoted the “simultaneous method” as an alternative to “the American economists” procedures, which they criticized for relying too heavily on data adjustments.Footnote ¹³ In response to this criticism from Germany, Schultz (Reference Schultz and Altschul1930, p. 97) struck back by dismissing Leontief’s results as “numerical accidents.” Thus, once in the US, Leontief found himself to be an “official opponent,”Footnote ¹⁴ as he wrote to Adolph Lowe.Footnote ¹⁵

In the fall of 1931, Leontief received invitations to participate in year-end conferences in Washington, DC, where the American Economic Association and other academic associations were convening. Importantly, the Econometric Society, founded the previous year, was to hold its first American meeting there. Leontief was invited to speak at two sessions. One session, jointly organized by the American Statistical Association (ASA) and the American Farm Economic Association (AFEA), was chaired by Howard R. Tolley. Held on December 30, it was titled “Shifts and Trends in the Demand for Agricultural Products.” As was often the case, the focus was on the demand curve rather than the supply curve. Leontief (Reference Leontief1932b) discussed a paper by Schultz (Reference Schultz1932), and E. J. Working (Reference Working1932) presented an article. The proceedings of this session were published the following year in Farm Economics. Although the session was attended by leading figures and is informative, it is of secondary importance to our examination of Leontief’s attitude toward econometrics.

Of greater interest to us is the session of the Econometric Society, chaired by its president, Irving Fisher, and organized in conjunction with the AEA. The session was scheduled for December 28. In a letter dated November 10, 1931, Fisher invited Leontief to discuss a paper at the session. Fisher also invited Leontief to attend the society’s meeting in New Orleans in January 1932, but he declined. Had he attended the New Orleans meeting, he would have heard a premiere of Frisch’s “Pitfalls” arguments.

In Washington, DC, Leontief participated in the society’s morning session, titled “Quantitative Economics.” Working also attended the session. Fisher (Reference Fisher1932, Reference Fisher1933) published short accounts. Leontief ([1931] Reference Leontief and Fisher1932) discussed an unpublished paper by Mordecai Ezekiel, an agricultural economist at the Federal Farm Board in Washington, DC, titled “The Relation Between Mathematical Economics and Statistical Price Analysis.” This discussion provides the most insight into Leontief’s thinking on econometric methodology. Fortunately, a copy of Ezekiel’s (Reference Ezekiel1931) presentation is preserved among his papers. However, this is not the case for Leontief’s discussion, which does not appear to be preserved in his papers at Harvard.Footnote ¹⁶ Nevertheless, Fisher (Reference Fisher1932; see also 1933) published an account of Leontief’s comment in a short text of less than two pages. It has scarcely been cited.

This text is one of the bases for my claim that, by 1931, Leontief had distanced himself from the usual econometric method. Therefore, it is important to clarify the authorship of his comment on Ezekiel’s paper. One reason to accept Fisher’s (Reference Fisher1932) account is by analogy with his account of Ezekiel’s presentation. The comparison shows that Fisher’s account appears to be faithful and uses Ezekiel’s own words. The same may be said for the account of Leontief’s comments. Another reason can be found in Leontief’s correspondence. In a letter dated January 7, 1932, Fisher asked Leontief for a summary of his comments and Leontief replied that he was sending “a copy of my discussion of Mr. Ezekiel’s paper.”Footnote ¹⁷ This answer is important because it suggests that Leontief himself wrote the original text, which Fisher then edited. In fact, Fisher (Reference Fisher1932, p. 23) began his account by noting, “Dr. Leontief said in part. …” The rest of the text is written in the first person, presumably with Leontief saying “I” and “me.” Therefore, I accept Fisher’s account of Leontief’s ([1931] Reference Leontief and Fisher1932) comment as a reliable source.

Now, in 1931, at the two sessions in Washington, DC, Leontief came and was received as a statistical economist, the controversial inventor of the “simultaneous method” for the statistical determination of demand and supply curves. Although the discussion did not touch on the “simultaneous method,” it naturally focused on the quantitative determination of supply and demand curves, or what was commonly called “statistical price analysis.”

“Statistical Price Analysis” in Trouble

Although not the most informative, the ASA–AFEA session Leontief attended provides some insight into the context of his participation in the Econometric Society session. The main topic of discussion was the extent to which orthodox theory, in terms of supply and demand curves, could shed light on or even help forecast prices. Conversely, participants examined the extent to which statistical data could be used to determine the “true” supply and demand curves as defined by “orthodox” theory. Schultz (Reference Schultz1932, p. 226) appeared the most enthusiastic about the role of standard theory in statistical price analysis. He defended the empirical significance of the demand curve and the elasticity of demand.Footnote ¹⁸ However, Leontief (Reference Leontief1932b) criticized Schultz’s technique in his comments for its inability to accurately determine the elasticity of demand. This was in response to Schultz’s calling Leontief’s results “numerical accidents.” Indeed, Leontief soon wrote to his former colleague at Kiel, Gerhard Colm, saying that he had recently “had the opportunity to settle the score with Schultz.”Footnote ¹⁹ Leontief’s personal account to Joseph Schumpeter was more encouraging: “I was very pleased to finally settle the score with Schultz. Now we have concluded eternal peace.”Footnote ²⁰

At the Econometric Society’s session, the problem of statistically determining the supply and demand curves was the subject of both Working’s (Reference Working1932) paper and Ezekiel’s (Reference Ezekiel1931) methodological discussion. Working’s (Reference Working1932) article is worth mentioning because it insightfully captures the difficulties of the field. He took a cautious and pragmatic approach, drawing on a few examples of statistical studies of price changes to support his discussion. Skeptical, he did not claim to have determined the “true” demand or supply curves but instead established plain statistical relationships between prices and production or consumption indexes. Using two cases, crops and livestock, Working (p. 254) highlighted the “uncertainty” of the results and offered a more general methodological comment: “There is always the problem of whether the failure to ’explain’ completely a certain change in price is due to the omission of some important cause, to the use of the wrong independent variable, to the failure to determine the precise nature of one or more of the relationships, or to inaccuracy of the data.”

Working’s methodological analysis of the possible reasons for the failure to “explain completely” a price variation is striking in its clarity. Additionally, Working deliberately set aside the tools of “statistical inference” (p. 255), such as “probable or (standard) errors, frequency distributions, and such,” i.e., those related to probability theory. He argued that “these things are usually of minor use in time series analyses.” This is a typical example in economics of explicitly rejecting statistical inference based on probability reasoning. It reflects the dominant position during the interwar period (see Biddle Reference Biddle2017; Biddle and Boumans Reference Biddle and Boumans2021). Leontief ([1931] Reference Leontief and Fisher1932) also agreed with this argument. I now turn to Ezekiel’s paper on which Leontief commented.

In his presentation, Ezekiel (Reference Ezekiel1931) discussed the very foundation of the statistical economic approach that was institutionalized the previous year with the founding of the Econometric Society. As expressed by Frisch (Reference Frisch1933a, p. 1) and defined in the society’s constitution, the project aimed to a “unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems.” Frisch insisted on the term “unification” to integrate statistical, theoretical, and mathematical economics (p. 2). Ezekiel explored the feasibility of this project by discussing “unification” in “statistical price analysis.” He was enthusiastic about the project but seemed ambivalent about its feasibility. He wrote: “Both mathematical economics and statistical analyses would be strengthened by using the results of the other. The first rests upon theory, flavored with a pinch of fact; the second, upon facts, flavored with a pinch of theory. If both were merged the result might rest equally upon all that is known of both fact and theory” (Ezekiel Reference Ezekiel1931, p. 1).

Although Ezekiel noted that “some progress is already being made toward such a unification” (1931, p. 6), he argued that a “full generalized system of valid mathematical relationships covering all of economic life is, however, still far in the distance, in spite of Moore’s brilliant synthesis of hypothetical elements” (p. 7). For Ezekiel, aiming for a statistical formulation of general equilibrium theory, as Moore proposed in his 1929 book Synthetic Economics, was unrealistic. Instead, he thought it preferable to concentrate on partial analyses to identify certain “laws and regularities” (p. 7). In fact, statistical price studies usually relied on a “partial” approach, focusing on a specific product. In this context, like Working, Ezekiel (p. 2) underlined the difficulty of interpreting negative results in order to “determine how far theory and fact agree.… Lack of full agreement—of perfect correlation—may either indicate that the hypothesis is not completely true or that the statistical manipulation is not adequate to reveal the facts.”

Although broad in scope, the discussions in both sessions focused primarily on the problem of quantitatively determining the demand curves for a given market. The main problem was interpreting the negative results obtained. Leontief examined the question raised by Schultz, Working, and Ezekiel of how to judge “how far theory and fact agree” in his comments at the society’s session.

The Approach to Statistical Price Studies as Being “Indirect”

Leontief’s ([1931] Reference Leontief and Fisher1932) intervention at the Econometric Society session provides, albeit in abstract terms, essential insights into what he called the “indirect” approach to econometrics. Though significant beyond its context, his discussion appeared in the field of statistical determination of supply and demand curves. Leontief ([1931] Reference Leontief and Fisher1932, p. 23) framed the general problem as follows: “In the statistical price analysis we deal with two sets of data—the one being represented by our price and quantity series [noted A’], the other relating to the structure of the supply and demand schedules [noted B]. Quantitative economic theory shows us a certain kind of relation between these two sets of facts.”

Thus, the theory posits two “sets of data” and assumes that prices and quantities (A’) are explained by the “structure” of supply and demand schedules (B).Footnote ²¹ That said, Leontief ([1931] Reference Leontief and Fisher1932, p. 24) added a crucial remark for understanding his distinctions: “It seems to me that the general trend in the statistical price analysis until now has been … [limited] to only one [set of facts, namely] (A’)—say, to prices and quantity series.” In other words, statistical price studies relied primarily on market price-quantity data rather than data on the “structure” of supply and demand schedules. This remark encapsulates most of Leontief’s idea of indirect versus direct methods in econometrics, which we need to decipher. What Leontief emphasized here is the general epistemic Cournotian strategy adopted by Moore (Reference Moore1914) and his followers: to start from and restrict the investigation to market price-quantity data (the set of facts A’). And Leontief’s (Reference Leontief1929) “simultaneous method” was no different in this respect.

In Leontief’s ([1931] Reference Leontief and Fisher1932) terms, the statistical economist proceeds with the “indirect calculation of unknown B [supply and demand schedules] from observed A’ [price-quantity data]” (my emphasis). In simpler terms, the data are limited to a single set of observations, since market observations are not specific to either demand or supply. Indeed, the price-quantity data are interpreted either as equilibrium points between supply and demand (Working Reference Working1927; Leontief Reference Leontief1929; Gilboy Reference Gilboy1931a), or as out-of-equilibrium states, such as Moore’s (Reference Moore1925) so-called cobweb mechanism. In the usual case, the market data points are not specific to buyers or sellers. Therefore, Leontief explained that, with the usual approach, “The other (B)—the supply and demand schedules—is usually derived statistically with the help of our theoretical assumptions.^[Footnote ^{22 ]} Any attempt to check this assumption by comparison with the results of our statistical investigation would inevitably involve us in a vicious circle.”

Indeed, since the main data are the market price-quantity set, one derives the statistical curves from these data, and then one can test them against only the same or a similar data sample. Forty years later, Leontief repeated this “vicious circle” argument in his presidential address to the AEA. He noted that, in econometric work, the “indirect statistical approach” relied on a “circular procedure” (1971, p. 4) In his address, Leontief paired the circularity argument with the assertion that econometricians perform an “about-face” with respect to theoretical reasoning. Whereas the theoretician first defines his functions (e.g., supply and demand relations) and then deduces prices and quantities, the econometrician reverses this reasoning, starting with prices and quantities to infer the shape of the supply and demand functions. Thus, Leontief (p. 4) explained: “As econometricians, engaged in what passes for empirical research, we do not try, however, to ascertain the actual shapes of these functions and to measure the magnitudes of these parameters by turning up new factual information.”

While the circularity argument was already present in Leontief ([1931] Reference Leontief and Fisher1932), the idea of reverse reasoning was not. However, Tinbergen ([1930] Reference Tinbergen, Hendry and Morgan1995, p. 233) expressed it when he noted that “the problem of determining demand and supply curves is just the reverse of [the] theory and may be generally put as follows: given p [the actual price] and u [the actual quantity] as functions of time, what are the functions n(π) and a(π)?,” with π the price variable; n(π), the demand; and a(π), the supply. For Tinbergen, it was a didactic presentation; for Leontief, it became a criticism. Working backwards from market data to the statistical determination of functional economic relations is essentially the indirect method.

Before turning to section III and the more “direct” approach, we now examine the significance of Leontief’s argument regarding the relevant data to be used. Working’s (Reference Working1927) precise wording helps to refine our understanding of what Leontief ([1931] Reference Leontief and Fisher1932) was referring to. According to Working, the statistical method used employs “for its data the quantities which have been sold in the market” (Working Reference Working1927, p. 215). Working specified repeatedly that the observations are about the “market-place,” a place where “potential buyers and potential sellers” meet (p. 216). Thus, what is studied are “the demand schedules of buyers” and the “supply schedules of sellers” (p. 221), which express “the amounts that these groups are ready to buy and sell at different prices” (pp. 216–217). However, statistical data are usually limited to market data and do not extend beyond the marketplace to include buyer-specific or seller-specific data—for instance, data on buyers from family budget surveys and data on sellers from plant surveys. From Leontief’s perspective, indirect induction relies on market price-quantity data, whereas, as I argue in section III, “direct observation” begins with specific data on buyers and data on sellers.Footnote ²³ According to Leontief, the indirect method, the market data approach, whose “lineage” (see above) can be traced directly to Moore (Reference Moore1914, Reference Moore1925) and his followers, was continued and developed by the Cowles econometricians in the 1940s, only using different statistical tools. Before and after the 1940s, econometric works largely relied on what Leontief called the “indirect” approach to statistically determining economic functional relationships. Therefore, the use of probability-based inference tools is secondary; it is more of an implication. The same is true for the use of econometric techniques, such as least squares methods or data adjustment. Most importantly, even the very theoretical framework employed—say, Marshall–Cournot partial equilibrium—is secondary to his main argument. In Leontief’s terms, when such investigations begin and are limited to the price-quantity data they are supposed to explain, they proceed by “indirect” inference. As early as 1931, Leontief contrasted this approach with a direct one.

More Insights from Leontief’s Comment at the Econometric Society Meeting

Leontief’s ([1931] Reference Leontief and Fisher1932) comment on Ezekiel’s (Reference Ezekiel1931) article is primarily of methodological significance. Leontief responded to Ezekiel by focusing on the question of how to assess the agreement between theory and fact, a verification that Ezekiel admitted was very imperfect in practice. Most importantly, in his argument, Leontief conceived of a particular statistical apparatus in which the curves would be determined separately and from specific data. Before I examine Leontief’s own words, I can restate his alternative approach as follows: rather than using price-quantity points representing the intersections of the supply and demand curves, one would use consumer-specific data to determine the demand curve and, separately, producer-specific data to determine the supply curve. Once these curves are determined separately, their validity is assessed by comparing their intersections with the observed price-quantity data. In Leontief’s ([1931] Reference Leontief and Fisher1932, pp. 23–24) words:

If our restatement of this procedure is correct, then we hold a key to understanding Leontief’s argument.

The alternative offered by Leontief is not yet precise, and my interpretation above requires more evidence. Indeed, how to find the specific and separate “sets of facts” pertaining to “the structure of the supply and demand schedules”? Leontief ([1931] Reference Leontief and Fisher1932, p. 24) called for the “expansion of the field of direct observation.” In other words, rather than developing more sophisticated statistical tools to “indirectly” derive structural relationships from market data, one should collect the specific data on those very structural schedules. Leontief would tirelessly repeat this argument. Forty years later, he criticized standard econometrics as “an attempt to compensate for the glaring weakness of the data base available to us by the widest possible use of more and more sophisticated statistical techniques” (1971, p. 2, cited above). What should be done? In 1970, Leontief answered: “To ascertain the actual shapes of these functions and to measure the magnitudes of these parameters by turning up new factual information” (1971, p. 4); that is, in his 1931 words, to proceed with the “expansion of the field of direct observation.”

What does the expansion of the field of direct observation mean? Paradoxically, Moore’s work can help clarify it. Indeed, Moore (Reference Moore1919) had tentatively experimented with a more direct approach, deriving the supply curve not from price-quantity data but from its determinants, namely the cost curve and the behavior of producers in given competitive conditions. Moore distinguished between two cases: one in which the market is free and producers do not restrict their production, making decisions based on the given market price; and another in which producers reach an agreement, taking into account both their costs and the shape of the demand curve. In the latter case, Moore (Reference Moore1919, p. 563) used data on cotton production to compute the average cost of production for different groups of farms ranked by the size of their yield rate. He found “a crude inverse relationship between the yield per acre and the cost per pound of lint.” According to Moore (p. 564), as production expands, less productive land is used, causing marginal costs to rise. From these cost figures, he derived an “empirical law of supply” associated with a positively sloping curve. However, Moore found that the availability of cost data was so limited that he had to illegitimately generalize the curve obtained from a sample of a single Texas county to the entire US market. Therefore, he did not consider this approach to be a practical solution to his statistical problem.

Schultz (Reference Schultz1924) had a similar experience studying the beef market. Since the ultimate aim of his analysis was to assess the effect of a tax on the market, Schultz noted that he needed to estimate both the supply and demand curves. However, he emphasized that the available data were primarily price-quantity data, which he believed were relevant only to determining the demand curve. Schultz assumed that the supply curve could be determined using cost data. However, he noted that the necessary data were lacking and that “without such data no complete answers to our questions are possible” (pp. 277–278). Both Moore and Schultz returned to the “indirect” method.

While Leontief’s “simultaneous method” (Reference Leontief1929) relied exclusively on market price-quantity data, his ([1931] Reference Leontief and Fisher1932) original epistemic move was not to accept this lack of data as an insurmountable condition. I argue that Moore’s (Reference Moore1919) approach to the supply curve, as derived from costs, bears a strong similarity to what Leontief described from 1931 onward. In December 1931, it is likely that Leontief had in mind Moore’s tentative experiment, as well as other similar work, especially by agricultural economists (see Akhabbar Reference Akhabbar2021). At that time, Leontief was finishing his second and final paper on his “simultaneous method,” in which he began addressing this methodological problem, albeit very tentatively. Leontief (Reference Leontief1932a) focused on determining the supply curve and attempted to use cost data, although in a very limited way, to refine the curve determined by the “simultaneous method.” In other words, at that time, Leontief was already experimenting with the idea that the functional relationships under study could be determined “directly” from the appropriate non-market data. In the debates about the statistical determination of demand and supply curves, it appears that Leontief’s specificity as a statistical economist, or econometrician, was to affirm this principle rather than accept the lack of primary data as inevitable. Once again, there is a striking resonance between this methodological principle, as outlined in 1931, and what Leontief would later say, regardless of how econometric theory changed. An examination of the context of his intervention at the Econometric Society meeting provides further insight and confirms our interpretation.

Leontief on Marschak’s (Reference Marschak1931) Elastizität der Nachfrage

Leontief’s ([1931] Reference Leontief and Fisher1932) distinction between an approach starting from market data and one starting from specific data reflects another distinction: that between variables to be explained (e.g., prices and quantities) and explanatory factors. This distinction was not new. For example, Vilfredo Pareto (Reference Pareto1909, p. 155) referred to “tastes and obstacles” as the “data of the problem of equilibrium.” In the 1930s, these “data” came to be seen as the “structural” determinants of economic functional relations, which Leontief referred to as “the structure” of supply and demand schedules (already cited). Therefore, Leontief’s argument distinguished between economic variables to be explained and non-economic factors,Footnote ²⁶ such as tastes and techniques, which were called “data” or “structure.” What Leontief suggested was nothing less than the direct study of the manifestations of tastes and technologies: beyond the marketplace lie the realms of buyers and sellers, or consumers and producers.

A virtually untapped text by Leontief sheds light on this subject. In early 1931, while still in Kiel, Leontief received from Jacob Marschak his newly published book Elastizität der Nachfrage (Elasticity of demand). Marschak, then at the University of Heidelberg, was a former member of the IfWFootnote ²⁷ and part of the “Kiel circle” (Lowe Reference Lowe1959, p. 64). Leontief replied to Marschak that he would examine the book “stereoscopically” and wanted to review it.Footnote ²⁸ Leontief’s review (1931) was promptly published, in German, in the Archiv für Sozialwissenschaft und Sozialpolitik. Leontief was largely positive, noting that the book went beyond its title, the “elasticity of demand,” to provide a “pedagogical” account of empirical analyses of market prices—including Leontief’s “simultaneous method.” Most importantly, Leontief commented on Marschak’s original methodological distinction between two approaches to the quantitative determination of supply and demand curves. This distinction perfectly matched one that Leontief would elaborate on a few months later in Washington, DC:

Leontief’s review is remarkable for several reasons. First, it contains the same distinction that he introduced in December 1931 to criticize the usual approach to market price analysis. Second, it reveals one of the sources of this distinction. Third, it sheds light on Leontief’s later choices, when he spoke of “direct observation” and determination “from below.” While the first two points are fairly straightforward, the last requires clarification.

For one thing, Leontief later often used the term “direct observation,” and sometimes “direct induction,” without explicitly explaining what he meant. Sometimes, though rarely, he meant “direct perception” by the senses or by common experience.Footnote ²⁹ But, based on the previous excerpt, we understand that direct observation means primarily, for instance, “direct” use of cost data to quantitatively determine a supply curve (as Moore experimented with in 1919) rather than “indirectly” deriving the cost curve from market price-quantity data (as Moore did in 1914). The question is not primarily about whether the data is direct or indirect but, rather, how it is used to determine a functional relationship. For instance, one might use market price-quantity data as “direct observation” when determining a single market equilibrium curve (as discussed by Elizabeth Gilboy Reference Gilboy1930 and Working Reference Working1927), but “indirect” with respect to the cost or supply curve. Hence, in Leontief’s view, the directness of “direct observation” primarily characterizes the relationship between the observations and the object studied, rather than the nature of the data. This is essentially a relational definition, from which are derived the statistical method and type of data used—such as household or plant surveys, fieldwork, etc.

In his review, Leontief (Reference Leontief1931) noted that, in the direct approach, the statistical curves are determined “from below.” Interestingly, his phrase reappeared in his work twenty years later. When presenting the first results of his research laboratory, the Harvard Economic Research Project (HERP),Footnote ³⁰ Leontief (Reference Leontief1952, p. 7) distinguished between two approaches to econometrics. He argued that the traditional method, “indirect statistical inference,” proceeds “‘from above,’ through observation of the dependent variables such as prices and total outputs,” while an alternative involves “deriving the relevant structural relationships ‘from below,’” using “engineering data,” for instance, to determine production relations, or household data for consumption (see also Leontief Reference Leontief1953, p. 8). Leontief called these the “technological, psychological, and other non-economic bases of economic relations” (1952, p. 6). Therefore, this distinction predates Leontief’s implementation of his input-output device and is not specific to input-output analysis. Leontief (Reference Leontief1952, p. 1) reiterated that the derivation of “supply and demand functions” should proceed, for the supply, “on the basis of given engineering production functions, while the [demand functions] are derived from the preference varieties of the individual households.” In this context, “indirect statistical inference” is not primarily statistical inference based on the tools of mathematical probability theory, nor is it econometrics in general. There is strong continuity between the categories Leontief discussed in his review of Marschak (Reference Marschak1931) and his later reflections on “direct observation” versus “indirect statistical inference.” But how does “direct observation” relate to input-output analysis?

Leontief (Reference Leontief and Ellis1948, p. 407; 1949; 1952; 1955) argued that his input-output method was designed to come close to such direct determination. Although it did not fully achieve the ideal of the “direct observation” method, it is a direct approach that does not proceed “from below.” Leontief (Reference Leontief1949, p. 213) also distinguished between the “statistical figures” usually employed by econometricians and the “direct information” he advocated. For instance, when determining a production coefficient—e.g., “How much coke is needed to produce a ton of pig iron”— Leontief suggested “an alternative and more direct way”: seeking engineering information, typically by “asking an ironmaster” (Reference Leontief1951, p. 20). This approach is the method of “direct observation,” as implemented “from below” and using “direct information.”Footnote ³¹ A less direct way but which does not proceed “from above,” the one traditionally used in input-output methods and made possible by input-output statistical tables, is to use the industrial statistical material on the amount of coke consumed and the amount of pig iron produced to calculate the input-output coefficient as the ratio of these two “statistical figures.”Footnote ³² Although it is not ideal because it does not proceed “from below” through “direct information,” the latter method still qualifies as “direct observation.”Footnote ³³ Although Leontief conducted some casual “fieldwork” to collect input data (Boumans Reference Boumans2016), he largely relied on economic statistics to fill the cells of his input-output tables. This was not a full-fledged “direct observation” of technical coefficients derived from “direct information.”

Consequently, typical input-output practices are not fully consistent with Leontief’s ideal of direct induction from specific data. Leontief (Reference Leontief1952, p. 5) noted that, in principle, it is possible to determine input-output coefficients directly. Given final demand, “a complete input-output table of the economy can be reconstructed from the bottom up.”Footnote ³⁴ However, input-output coefficients are not usually determined “from below.” Leontief (Reference Leontief1955, p. 11) contrasted the specific structural data, what he called the “ground floor experience,” as possessed, for instance, by “engineers, plant managers, or advertising executives,” with the data found in actual input-output tables, which he described as coming come from “a second- or even a third-floor operation.” Input-output data may even be considered to come from the “usual indirect estimating procedures” (p. 10). Therefore, we need to revise the common claim that Leontief’s input-output data “stemmed from …‘direct empirical information’” (Halsmayer Reference Halsmayer2014, p. 232).

While the input-output framework enables “direct observation,” its statistical table is an imperfect substitute for “direct information.” Furthermore, it is important to reiterate that Leontief’s concept of “direct observation” extends well beyond the scope of input-output analysis. On this point, I agree with Biddle and Hamermesh (Reference Biddle and Hamermesh2017). However, unlike the latter, I argue that Leontief’s “direct observation” does not exclude an econometric approach to estimation. To illustrate this, I trace this idea of determining structural data “from below” back at least to Leontief’s study of Marschak’s (Reference Marschak1931) determination of demand elasticity “directly” from family budget surveys.

About Marschak’s Empirical Methodology

Since Leontief drew on some of Marschak’s (Reference Marschak1931) methodological considerations, examining them more closely may provide a better understanding of Leontief’s view. Indeed, there is a strong congruence between Marschak’s and Leontief’s methodological arguments. To begin with, Marschak (Reference Marschak1931) includes the same reference to John Clapham’s “empty boxes” that Leontief would later use repeatedly. Marschak wrote: “Without the empiricist, economics has only ‘empty boxes,’ which must seem astonishingly empty even to those who expect economics to be nothing more than ‘algebra’ from the outset” (1931, pp. x–xi). Then, in his introductory reflection, Marschak addressed the notion of non-economic data, emphasizing the need to consider “‘constants,’ ‘parameters,’ ‘invariants’” that are not absolutely fixed but hold for a certain period: “relative constants” (p. xii).Footnote ³⁵ Among these, he listed elements “[that] are natural phenomena …, phenomena of the biological and physical world: Life span and cycle of humans, animals, and plants; chemical-technical ’recipes’ of every production process, which determine the proportions of the natural substances and forces to be used as well as of the human labor, soil and climate” (pp. xii–xiii).

Leontief later adopted this terminology, describing the technical constants of production as “recipes.” For Marschak, these relative constants, proportions, and recipes, together with the rational nature of individual action, produce regularities in economic phenomena: the “logical-rational maximum principle and the repeatability of natural events work together to give the body of economic knowledge a backbone of ‘relative’ constants, transforming it … from a shellfish to a vertebrate” (p. xiii). A major difference between Marschak’s and Leontief’s views was that Marschak accepted the theory of rational behavior, while Leontief considered it not descriptive but “normative” as he had already emphasized in his doctoral thesis (published in 1928, see p. 578) and reiterated later.Footnote ³⁶ Thus, Leontief and Marschak agreed on only one of the sources of the “regularity of economic events”: the “chemical-technical recipes” and “proportions.”Footnote ³⁷ For Leontief, these also encompassed consumption, though not based on a theory of rational behavior. He approached household consumption similarly to production, treating tastes and technology symmetrically.

Regarding the quantitative determination of supply and demand curves, Marschak (Reference Marschak1931, p. 2) noted that “the structure of supply and demand is subject to sociological and technical conditions” (again, the notion of “structure”).Footnote ³⁸ That is, the curves depend on the behavior of the branch (with respect to competition) and on the technical conditions of production. At this juncture, Marschak discussed the usual methods for deriving supply and demand curves from market price-quantity data. In particular, he reviewed the work of Moore, Schultz, and Leontief (Reference Leontief1929). For Marschak (Reference Marschak1931, p. 28), the market approach “urgently” required the search for alternative means of determination, “even if only for control purposes.” Leontief echoed this in December 1931, noting that “verification” based on the same price-quantity data used to determine the coefficients introduced a vicious circle (see above). Anticipating Leontief’s concerns, Marschak (p. 29) highlighted the problem of using price-quantity data as a starting point, and the limitations of relying on time series rather than cross-sectional data for homogenous products. Instead, an alternative approach is to use specific data: “Obtained from a single market and at one point in time, allowing, if possible, each of the two curves to be determined in isolation. Source for this material … is for demand: the household; and for supply: the business” (my emphasis). Therefore, the distinction between an indirect and a direct approach involved distinguishing between time series of market data and specific, non-market, cross-sectional data. The aim was to reach beyond the marketplace to households and firms. The same was true of Leontief’s views, which emphasized the pitfalls of relying on time series data.Footnote ³⁹

Importantly, as Leontief would, Marschak (Reference Marschak1931, p. 29; my emphasis) had already stated that “the direct construction of supply curves is primarily based on cost analysis, as costs are likely the most important supply factor.” He noted that the data needed for the supply curve should be obtained from plant-cost surveys. Although Marschak acknowledged that “demand studies are based on more definite material than supply studies” (p. 43), he considered that “there is no objection to the direct and precise analysis of supply curves” (p. 52; my emphasis).

Overall, Marschak was more explicit than Leontief when discussing the direct method. If we accept that Leontief’s and Marschak’s views converged on this issue, Marschak’s explanations help us clarify Leontief’s idea of “direct observation.” According to Marschak, the direct approach uses specific cross-sectional data to quantitatively determine supply and demand curves in isolation from each other. For example, the demand curve for a consumer good should be derived from family budget data, and the supply curve should be derived from surveys of plant costs. The next step, also mentioned by Leontief ([1931] Reference Leontief and Fisher1932), was to bring the two constructed curves together to check their agreement with the market data. According to Marschak (Reference Marschak1931, p. 52): “The mutual control of demand and supply curves by their confrontation in the field of direct market data [i.e., price-quantity data] is to be regarded as the ’crowning glory’ of this branch of research, from which we are, of course, still far away.”

Therefore, Marschak (Reference Marschak1931, p. 124) emphasized that the “market statistical method,” which starts from price-quantity data—usually time series—is clearly distinct from a more direct method based on specific, cross-sectional data. Marschak himself applied the direct approach to demand elasticity, deriving it from family budget data. Despite Leontief’s (Reference Leontief1931) discussion of some technical limitations in Marschak’s statistical study of family-budget surveys,Footnote ⁴⁰ the evidence shows that Leontief shared Marschak’s methodological perspective on the direct empirical method. In contrast, Schultz (Reference Schultz1933, p. 37) dismissed it, remaining faithful to the “market statistical method” popularized by Moore.

At this point, we have made progress in addressing the issues outlined in the first section. Even before 1934 and Leontief’s controversy with Frisch (Reference Frisch and Altschul1933b, Reference Frisch1934), and before he actually implemented the input-output method, it is now clear that he had already found the traditional, indirect approach based on price-quantity data—including his own “simultaneous method”—to be unfruitful. An econometrician himself, Leontief reaffirmed the distinction, already developed by Marschak (Reference Marschak1931), between an indirect and a more direct approach at the December 1931 session of the Econometric Society. In retrospect, this marked a departure from the indirect approach in statistical economics. In summary, due to its relational nature, the primary characteristic of “direct observation” is the use of specific dataFootnote ⁴¹ to derive statistical relationships separately. I contend that the other implications belong to an ideal case and are not strictly necessary. In my interpretation, Leontief’s ideal of a direct method has several practical implications: using specific data; using cross-sectional data; studying the different equations of the model separately;Footnote ⁴² and decomposing the studied phenomena to uncover their “structure” and reach the non-market substratum to derive the empirical relations “from below.” These considerations all point to the legitimization of a microeconometric approach to economic relations. We have now reached our goal. To conclude, I examine how Leontief’s ([1931] Reference Leontief and Fisher1932) project of the “expansion of the field of direct observation” relates to and surpasses input-output analysis.