The Origins of Input-Output Analysis
It is customary to trace the origins of input-output analysis to the work of Nobel laureate Wassily Leontief (1905-1999). Leontief wrote a PhD dissertation at the University of Berlin under the supervision of Ladislaus von Bortkiewicz (1868-1931).
In 1928 he published part of his work (in German) as an article with the title “The economy as a circular process”. After moving to Harvard University he further elaborated his model, and started to collect the data for the first input-output table of the United States economy. This led to the 1936 article “Quantitative input-output relations in the economic system of the United States” and then to his 1941 book The Structure of American Economy, 1919-1939. An Empirical Application of Equilibrium Analysis.Leontief himself referred to the Physiocrats and their Tableau ^conomique as his main source of inspiration. The genealogy of input-output analysis is actually quite long and diverse. Kurz and Salvadori (2010) and Kurz (2011) focused on the roots of input-output analysis in the classical political economy tradition. They pointed out that the notions of production as a circular process and of interdependency between sectors were already present in the work of William Petty (1623-1687) and of Richard Cantillon (1697-1734). In the hands of Franςois Quesnay (1694-1774), the leader of the Physiocratic movement, these notions got shaped into the Tableau ^conomique, a stylized representation of the economy of a country. The model involves two sectors of production: a productive sector, agriculture, and a sterile sector, industry, which need one another to be able to keep production going. The net product generated by agriculture ends up in the pockets of the class of property owners. In equilibrium, the system is able to reproduce itself year after year. Related constructions can be found in the writings of Achilles-Nicolas Isnard (1748-1803) and of Robert Torrens (1780-1864).
It was, however, Karl Marx (1818-1883) who seems to have benefited most from the Physiocratic ideas. His numerous and elaborate schemes of reproduction were obviously inspired by the Tableau ^conomique. Marx used these schemes also to shed light on the transformation of labour values into prices of production. Around the turn of the century, the labour value theory came under the scrutiny of Vladimir Dmitriev (1868-1913) and Ladislaus von Bortkiewicz (1868-1931), with the latter focusing on the transformation problem. Georg von Charasoff (1877-1931), a mathematician born in Georgia, also developed a highly original input-output model inspired by Marx’s schemes of reproduction.Since Leontief wrote his PhD dissertation under the supervision of von Bortkiewicz, it is tempting to conclude that input-output analysis can be seen as the culmination of an evolutionary line linking Quesnay via Marx and von Bortkiewicz to Leontief. This view has been challenged by William Baumol (2000), who argued that Leontief’s work constitutes a revolutionary departure from earlier approaches. Moreover, Leontief himself suggested that his work was related to “the neo-classical theory of general equilibrium” (Leontief 1966: 134), where he obviously had economists such as Leon Walras (1834-1910) and Gustav Cassel (1866-1945) in mind.
Prior to or roughly at the same time as Leontief, several authors formulated models which were in many respects similar to Leontief’s input-output models. The most important of these are Maurice Potron (1872-1942), Robert Remak (1888-1942), John von Neumann (1903-1957) and Piero Sraffa (1898-1983). As early as 1911, the French Jesuit engineer and mathematician Potron independently developed a complete input-output model in order to find out whether prices and quantities exist which satisfy four basic principles of a just social order. He was the first to apply the Perron-Frobenius results on non-negative matrices in an economic setting (Bidard and Erreygers 2010).
The German mathematician Remak, who wrote his dissertation under the supervision of Frobenius, published an input-output-based analysis of what he called “superposed” prices in 1929. In 1937 the Hungarian mathematician von Neumann used a fixed-point theorem to show the existence of an equilibrium in a linear economic model. Also, in 1960 the Italian economist Sraffa published his book Production of Commodities by Means of Commodities, which proved to be very influential in the capital controversy debates of the 1960s. It must be noted, however, that Sraffa had started working on his model in the 1920s. (A thorough comparison of the approaches of Leontief and Sraffa has been made by Kurz and Salvadori (2006). This was published in a special issue of Economic Systems Research “The history of input-output analysis, Leontief’s path and alternative tracks”, edited by Bjerkholt and Kurz (2006), which one should consult for a more detailed exploration of the roots of input-output analysis.)