Wassily Leontief

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Wassily Leontief (August 5, 1905 – February 5, 1999) has been associated with the quantitative economics he invented: Input-Output analysis. Input-output was partly inspired by the Walrasian analysis of general equilibrium via inter-industry flows—which in turn were inspired by Quesnay's Tableau Economique, which Leontief's system most resembles. Leontief's technique involves the use of a matrix containing the various industries of an economy, and the products they buy and sell one to another. Although of fluctuating popularity, input-output analysis has been a mainstay of economics and economic policy and planning throughout the world since the middle of the twentieth century, a valuable tool in efforts to understand and maintain economic health and prosperity. Leontief won a Nobel Prize in Economics for his development of this model.


Wassily Leontief, the son of Wassily W. Leontief (professor of economics) and Eugenia, was born on August 5, 1905 in Munich, Germany. He entered the University of Leningrad in present day St. Petersburg in 1921. He earned his Learned Economist degree (equivalent to Master of Arts) in 1925 at the age of 19.

In 1925, he was allowed to leave the USSR, and he continued his studies at the University of Berlin and in 1929 he earned a Ph.D. degree in Economics with a specialty in "Input-Output Analysis and Economics."

From 1927 to 1930 Leontief worked at the Institute for World Economics of the University of Kiel. There, he researched the derivation of statistical supply and demand curves. In 1929, he traveled to China to assist the Ministry of Railroads as an adviser.

In 1931, he went to the United States and was employed by the National Bureau of Economic Research. In 1932, Leontief married the poet Estelle Marks. Their only child, Svetlana Leontief Alpers, was born in 1936. His wife died in 2005.

Harvard University employed him in its department of economics in 1932, and in 1946 he became a professor of economics. Around 1949, Leontief used the primitive computer systems available at the time at Harvard to model data provided by the U.S. Bureau of Labor Statistics to divide the U.S. economy into 500 sectors. He modeled each sector with a linear equation based on the data and used the computer, the Harvard Mark II, to solve the system, one of the first significant uses of computers for mathematical modeling (Lay 2003). Leontief set up the Harvard Economic Research Project in 1948 and remained its director until 1973. Starting in 1965 he chaired the Harvard Society of Fellows.

In 1975, Leontief joined New York University and founded and directed the Center for Economic Analysis.

Wassily Leontief died in New York City, on Friday, February 5, 1999 at the age of 93.


Leontief's most important contribution to economics will forever be the Input-output System. He realized that in order to understand and be able to manipulate the economy of a country or a region, one needs to come up with a model based on the various sectors of the given economy. His work resulted in his 1941 classic, Structure of American Industry. Leontief followed up this work with a series of classical papers on input-output economics .

Based on the assumption that each industry in the economy has two types of demands: external demand (from outside the system) and internal demand (demand placed on one industry by another in the same system), Leontief developed his model representing the economy as a system of linear equations.

Leontief's interests were not, however, limited to input-output models. His 1936 article on "composite commodities" made him, together with Hicks, the father of the famous microeconomic theorem. His early reviews of Keynes's General Theory made important contributions to the Neo-Keynesian synthesis' stress on fixed nominal wages in interpreting Keynes's theory. His 1933 article on the analysis of international trade is still studied today, and his 1946 contribution on the wage contract outlined what is now a classical application of the principal-agent model before that term was invented. His 1953 finding that Americans were exporting labor-intensive rather than capital-intensive goods—"Leontief's Paradox"—brought into question the validity of the conventional Neoclassical theory of international trade.

Input-output Model

In 1941, while a professor at Harvard, Leontief calculated an input-output (I-O) table for the American economy. Input-output analysis considers inter-industry relations in an economy, depicting how the output of one industry goes to another industry where it serves as an input, and thereby makes one industry dependent on another both as customer of output and as supplier of inputs. An input-output model is a specific formulation of input-output analysis. We present here a simple I-O model for three industries: agriculture, manufacturing, and transportation.

Each row of the input-output matrix reports the monetary value of an industry's inputs and each column represents the value of an industry's outputs. Suppose there are three industries: “agriculture,” “manufacturing,” “transportation,” plus “labor” as inputs. Row 1 reports the value of inputs to Industry 1 from Industries 1, 2, and 3. Rows 2 and 3 do the same for those industries, while the row 4 depicts the inputs of the "Labor" into the system. Column 1 reports the value of outputs from Industry 1 to Industries 1, 2, 3, and to input factor ("Labor") 4. Columns 2 and 3 do the same for the other industries.

Francois Quesnay developed a cruder version of this technique called the Tableau économique.

The matrix devised by Leontief is often used to show the effect of a change in production of a final commodity on the demand for inputs. Take, for example, a 10 percent increase in the production of “Agriculture.” With the simple input-output table of our example (and the subsequent algebraic matrix), one can estimate how much additional “Labor,” “Machinery,” and other inputs will be required to increase “Agriculture” production.

Input-output concepts are simple. Consider the production of any of the three column sectors i, such that i = 1, 2, 3, while we have 4 rows of inputs j, such that j = 1, 2, 3, 4.

We may isolate and analyze: (1) the quantity of that production that goes to final consumption or demand (Ci), (2) the quantity that goes to total output (Xi), and (3) the flows (xij) from that industry to other industries. To this end we must write a transactions tableau.

Table: Transactions in a Three Sector Economy
Economic Activities Inputs to Agriculture Inputs to Manufacturing Inputs to Transport Final Demand (Ci) Total Output (Xi)
Agriculture 5 (x ij) 15 2 68 90
Manufacturing 10 20 (x ij) 10 40 80
Transportation 10 15 5 (x ij) 0 30
Labor 25 30 5 0 60

Caution may be necessary in using I-O tables. Take for example “Transportation.” It is explicitly recognized when transportation is identified as an industry—how much is purchased from transportation in order to produce. But this is not very satisfactory because transportation requirements differ, depending on industry locations and capacity constraints on regional production. Also, the receiver of goods generally pays freight cost, and often transportation data are lost because transportation costs are treated as part of the cost of the goods.

There is yet another reason for a strong caution to be employed in using the I-O tables as axiomatic "truth." It lies in the assumption—to take the example of “agriculture”—that agricultural production requires the inputs in the proportion they were used during the time period used to estimate the table. The I-O coefficients were, most certainly computed in the past, whether in the "long" or "not so long" past is immaterial.

And therein lies the rub. Although the table is useful as a rough approximation of the inputs required, it is known that proportions are not fixed. Specifically, when the cost of one input rises, producers reduce their use of this input and substitute other inputs whose prices have not risen. The time-shift between "then" (when the I-O table coefficients were computed) and "now" (when we analyze the individual table entries) is there.

If wage rates rise, for example, producers can substitute capital for labor and, by accepting more wasted materials, can even substitute raw materials for labor. In a technical sense, input-output analysis can be seen as a special case of consistency analysis without money and without entrepreneurship, technical innovation, and transaction cost, and above all, there is the question about the stability of coefficients as production increases or decreases.

Leontief's Paradox

Early on, input-output analysis was used to estimate the economy-wide impact of converting from war production to civilian production after World War II. It has also been used to understand the flow of trade between countries.

Indeed, a 1953 article by Wassily Leontief showed, using input-output analysis, that United States exports were relatively labor-intensive compared to United States imports. This was the opposite of what economists had expected at the time, given the high level of U.S. wages and the relatively high amount of capital per worker in the United States. Leontief's finding was termed the Leontief paradox.

Since then, the paradox has been resolved. It has been argued that the US has an advantage in highly skilled labor more so than capital. This can be seen as viewing "capital" more broadly, to include human capital. Using this definition, the exports of the U.S. are very (human) capital-intensive, and not particularly intensive in (unskilled) labor.

Others have explained the paradox by reducing the importance of comparative advantage as a determinant of trade. For example, demand may play a more important role than comparative advantage as a determinant of trade—with the hypothesis that countries which share similar demands will be more likely to trade. For instance, both the United States and Germany are developed countries with a significant demand for cars and both have large automotive industries. Rather than one country dominating the industry with a comparative advantage, both countries may trade different brands of cars between them.


Leontief is primarily associated with the development of the linear activity model of General equilibrium and the use of input-output analysis that results from it. He has also made contributions in other areas of economics, such as his model of international trade where he documented the famous "Leontief paradox." He was also one of the first to establish the composite commodity theorem.

Throughout his life Leontief campaigned against "theoretical assumptions and nonobserved facts." According to Leontief too many economists were reluctant to "get their hands dirty" by working with raw empirical facts. To that end Wassily Leontief made a great advance in making quantitative data more accessible, and more indispensable, to the study of economics.

Leontief earned the Nobel Prize in Economics for his work on input-output tables. The Input-output model of economics uses a matrix representation of a nation's (or a region's) economy to predict the effect of changes in one industry on others and by consumers, government, and foreign suppliers on the economy. I-O analysis remains an active branch of economics, and one with numerous offshots. Some of its most popular applications are those that Leontief helped pioneer, including national accounts and trade, environmental studies, and technological change forecast. The methodology has been used for economic planning throughout the world, whether in Western, Socialist, or Third World countries.

Major Works

  • Leontief, Wassily. 1936. "The Fundamental Assumption of Mr. Keynes's Monetary Theory of Unemployment," QJE.
  • Leontief, Wassily. 1936. "Composite Commodities and the Problem of Index Numbers," Econometrica.
  • Leontief, Wassily. 1937. "Implicit Theorizing: a methodological criticism of the Neo-Cambridge school," QJE.
  • Leontief, Wassily. [1941] 1953. The Structure of the American Economy. Oxford University Press.
  • Leontief, Wassily. 1947. "The Pure Theory of the Structure of Functional Relationships," Econometrica.
  • Leontief, Wassily. 1947. "Postulates: Keynes's General Theory and the classicists," in: Harris. (ed.) The New Economics.
  • Leontief, Wassily. 1953. Studies in the Structure of the American Economy.
  • Leontief, Wassily. 1953. "Domestic Production and Foreign Trade: the American capital position re-examined," Proceedings of American Philosophical Society.
  • Leontief, Wassily. 1956. "Factor Proportions and the Structure of American Trade: Further theoretical and empirical analysis," REStat.
  • Leontief, Wassily. [1966] 1986. Input-Output Economics. New York, NY: Oxford University Press. ISBN 0195035275
  • Leontief, Wassily. 1985. Essays in Economics: Theories, Theorizing, Facts, and Policies. Transaction Publishers. ISBN 0878559930

ISBN links support NWE through referral fees

  • Isard, Walter. 1960. Methods of Regional Analysis: An Introduction to Regional Science. MIT Press.
  • Lay, David C. 2003. Linear Algebra and Its Applications. Addison Wesley. ISBN 0201709708
  • Miller, R.E., Karen R. Polenske, and Adam Z. Rose. (eds.). 1989. Frontiers of Input-Output Analysis. New York: Oxford University Press.
  • Polenske, Karen. 1976. Advances in Input-Output Analysis. Ballinger Pub. Co. ISBN 9780884102779
  • Rappoport, Paul, N. K. J. Rodenrys, and J. H. Savitt. 1979. Energy Consumption in the Transportation Services Section. Electric Power Research Institute.
  • US Department of Commerce, Bureau of Economic Analysis. 1997. Regional multipliers: A user handbook for regional input-output modeling system (RIMS II). Third edition. Washington, D.C.: U.S. Government Printing Office.

External links

All links retrieved May 3, 2023.


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