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Wassily Leontief (August 5, 1906 – February 5, 1999), born at St. Petersburg, Russia), was an economist notable for his research on how changes in one economic sector may have an effect on other sectors. Leontief won Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in 1973.

Biography

Wassily Leontief, the son of Wassily W. Leontief (professor of Economics) and Eugenia, 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.

He was arrested several times because of his opposition to Communism.

In 1925 he was allowed to leave the USSR, so he continued his studies at the University of Berlin ([1]) and in 1929 he earned a Ph.D. degree in Economics with a specialty in Input-Output Analysis and Economics.

From 1927 to 1930 he worked at the Institute for World Economics of the University of Kiel ([2]). There he researched the derivation of statistical demand and supply curves. In 1929 he travelled to China to assist the Ministry of Railroads as an advisor.

In 1931 he went to the USA, and was employed by the National Bureau of Economic Research ([3]).

In 1932 Leontief married the poet Estelle Marks. His wife died in 2005. Their only child, Svetlana Leontief Alpers, was born in 1936.

Harvard University ([4]) employed him in the same year (1932) in its Department of Economics ([5]), 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. Leontief 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 ([6]) and founded and directed the Center for Economic Analysis.

It is known that he enjoyed trout fishing, ballet, and fine wines.

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

Work

Leontief's Paradox

Leontief's paradox in economics was the result of an attempt to test the Heckscher-Ohlin theory by Professor Wassily W. Leontief in 1954. Leontief found that the US (the most capital abundant country in the world by any criteria) exported labor-intensive commodities and imported capital-intensive commodities, in contradiction with Heckscher-Ohlin theory (H-O theory).

For many economists, Leontief's paradox undermined the validity of the H-O theory, which predicted that trade patterns would be based on countries' comparative advantage in certain factors of production (such as capital and labor). Many economists have dismissed the H-O theory in favor of a more Ricardian model where techological differences determine comparative advantage. These economists argue 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.

Some explanations for the paradox dismiss the importance of comparative advantage as a determinant of trade. For instance, the Linder hypothesis states that demand plays 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 US and Germany are developed countries with a significant demand for cars, so both have large automotive industries. Rather than one country dominating the industry with a comparative advantage, both countries trade different brands of cars between them. Similarly, New Trade Theory argues that factors other than endowments determine trade.

Input-output Model

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 and consumers on the economy. Wassily Leontief (1906-1999) is credited with the development of this analysis. Francois Quesnay was a precursor of a cruder version called Tableu economique. Leontief won a Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for his development of these types of model for the national level. The analytical apparatus is strictly empiricist and reducing bias in the analysis. For this reason, Leontief seems to have been just about the only economist who was equally honored by communist and capitalist economists.

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.

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. 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. Column 1 reports the value of outputs from Industry 1 to Industries 1, 2, and 3. Columns 2 and 3 do the same for the other industries.

While the input-output matrix reports only the intermediate goods and services that are exchanged among industries, row vectors on the bottom record the disposition of finished goods and services to consumers, government, and foreign buyers. Similarly, column vectors on the right record non-industrial inputs like labor and purchases from foreign suppliers.

In addition to studying the structure of national economies, input-output economics has been used to study regional economies within a nation, and as a tool for national economic planning.

The mathematics of input-output economics is straightforward, but the data requirements are enormous because the expenditures and revenues of each branch of economic activity has to be represented. The tool has languished because not all countries collect the required data, data quality varies, and the data collection and preparation process has lags that make timely analysis difficult. Typically input-out tables are compiled retrospectively as a "snapshot" cross-section of the economy, once every few years.

An input-output model is widely used in economic forecasting to predict flows between sectors. They are also used in local urban economics.

Irving Hock at the Chicago Area Transportation Study did detailed forecasting by industry sectors using input-output techniques. At the time, Hock’s work was quite an undertaking, the only other work that has been done at the urban level was for Stockholm and it was not widely known. Input-output was one of the few techniques developed at the CATS not adopted in later studies. Later studies used economic base analysis techniques.

Despite the clear ability of the input-output model to depict and analyze the dependence of one industry or sector on another, Leontief and others never managed to introduce the full spectrum of dependency relations in a market economy. In 2003, Mohammad Gani, a pupil of Leontief, introduced Consistency Analysis in his book 'Foundations of Economic Science', which formally looks exactly like the input-output table, but explores the dependency relations in terms of payments and intermediation relations. Consistency analysis explores the consistency of plans of buyers and sellers by decomposing the input-output table into four separate matrices, each for a different kind of means of payment. It integrates micro and macroeconomics in one model and deals with money in a fully ideology-free manner. It deals with the circualtion of money vis-a-vis the movement of goods.

In a technical sense, input-output analysis can be seen as a special case of consistency analysis without money and without entrepreneurship and transaction cost.

The inimitable book by Leontief himself remains the best exposition of input-output analysis.

Input-output concepts are simple. Consider the production of the ith sector. We may isolate (1) the quantity of that production that goes to final consumption (Ci), (2) to total output (X_i), and (3) flows (x_ij) from that industry to other industries. We may write a transactions tableau.

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

or

x₁₁ + x₁₂ + x₁₃ + c₁ = X₁

x₂₁ + x₂₂ + x₂₃ + c₂ = X₂

x₃₁ + x₃₂ + x₃₃ + c₃ = X₃

x₄₁ + x₄₂ + x₄₃ + c₄ = X₄

We know very little about production functions because all we have are numbers representing transactions in a particular instance (single points on the production functions).

x₁ = F(x₁₁, x₁₂, x₁₃, x₁₄)

x₂ = g(x₂₁, x₂₂, x₂₃, x₂₄)

. . .

The neoclassical production function is an explicit function:

Q = f(K, L)

Where: Q = Quantity K = Capital L = Labor

and the partial derivatives ( $\partial Q/\partial K=f_{K}>0;\partial Q/\partial L=f_{L}>0$ ) are the demand schedules for input factors.

Leontief, the innovator of input-output, uses a special production function. Using Leontief coefficients (a_ijs) we may manipulate our transactions information into what is known as an input-output table.

x₁₁ = a₁₁x₁

x₁₂ = a₁₂x₂

x₁₃ = a₁₃x₃

x₁₄ = a₁₄x₄

. . . .

Or

x_ij=x_ja_ij

x₄₁=a₄₁x₁ … … …

a₁₁x₁ + a₁₂x₂ + a₁₃x₃ + a₁₄x₄ + c₁ = x₁ . . . . . a₄₁x₁ + a₄₂x₂ + a₄₃x₃ + a₄₄x₄ + c₄ = x₄

gives

x₁ - a₁₁x₁ - a₁₂x₂ - a₁₃x₃ - a₁₄x₄ = c₁

. . . . .

x₄ - a₄₁x₁ - a₄₂x₂ - a₄₃x₃ - a₄₄x₄ = c₄

rewriting

x₁ (1- a₁₁) - x₂a₁₂ - x₃a₁₃ - x₄a₁₄ = c₁

. . . . .

- x₁a₄₁ - x₂a₄₂ - x₃a₄₃ - x₄(1-a₄₄) = c₄

Writing in matrix form, we may see how a solution may be obtained. Let: File:Input-output model.png

Then:

X = AX + C

(I - A)X = C

X = (I - A)^-1C

There are many interesting aspects of the Leontief system, and there is an extensive literature. There is the Hawkins-Simon Condition on producibility. There has been interest in disaggregation to clustered inter-industry flows, and the study of constellations of industries. A great deal of empirical work has been done to identify coefficients, and data have been published for the national economy as well as for regions. This has been a healthy, exciting area for work by economists because the Leontief system can be extended to a model of general equilibrium; it offers a method of decomposing work done at a macro level.

Transportation is implicit in the notion of inter-industry flows. 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.

Walter Isard and his student, Leon Moses, were quick to see the spatial economy and transportation implications of input-output, and began work in this area in the 1950s developing a concept of interregional input-output. Take a one region versus the world case. We wish to know something about interregional commodity flows, so introduce a column into the table headed “exports” and we introduce an “input” row.

Imports

**Table: Adding Export And Import Transactions**
Economic Activities	1	2	…	…	Z	Exports	Final Demand	Total Outputs
1
2
…
…
Z

A more satisfactory way to proceed would be to tie regions together at the industry level. That is, we identify both within region inter-industry transactions and among region inter-industry transactions. A not-so-small problem here is that the table gets very large very quickly.

Input-output, as we have discussed it, is conceptually very simple. Its extension to an overall model of equilibrium in the national economy is also relatively simple and attractive. But there is a downside. One who wishes to do work with input-output systems must deal skillfully with industry classification, data estimation, and inverting very large, ill-conditioned matrices. Two additional difficulties are of interest in transportation work. There is the question of substituting one input for another, and there is the question about the stability of coefficients as production increases or decreases. These are intertwined questions. They have to do with the nature of regional production functions.

Forecasting and/or Analysis Using Input-Output

This discussion focuses on the use of input-output techniques in transportation; there is a vast literature on the technique as such.

**Table: Interregional Transactions**
Economic Activities	Ag	North Mfg	...	...	Ag	East Mfg	...	...	Ag	West Mfg	...	...	Exports	Total Outputs
North Mfg
...
...
Ag
East Mfg
...
...
Ag
West Mfg
...
...

As we see from the use of the economic base study, Urban transportation planning studies are demand-driven. The question we want to answer is, “What transportation need results from some economic development: what’s the feedback from development to transportation?” For that question, input-output is helpful. That’s the question Hock posed. There is an increase in the final demand vector, changed inter-industry relations result, and there is an impact on transportation requirements.

Rappoport et al. (1979) started with consumption projections. These drove solutions of a national I-O model for projections of GNP and transportation requirements as per the transportation vector in the I-O matrix. Submodels were then used to investigate modal split and energy consumption in the transportation sector.

Another question asked is: What is the impact of the transportation construction activity on an area? One of the first studies made of the impact of the interstate highway system used the national I/O model to forecast impacts measured in increased steel production, cement, employment, etc.

**Table: Input-Output Model for Hypothetical Economy Total requirements from regional industries per dollar of output delivered to final demand**
Purchasing Industry	Agriculture	Transport	Manufacturer	Services
Selling Industry
Agriculture	1.14	0.22	0.13	0.12
Transportation	0.19	1.10	0.16	0.07
Manufacturing	0.16	0.16	1.16	0.06
Services	0.08	0.05	0.08	1.09
Total	1.57	1.53	1.53	1.34

The Maritime Administration (MARAD) has produced the Port Impact Kit for a number of years. This software illustrates the use of I/O models. Simply written, it makes the technique widely available. It shows how to calculate direct effects from the initial round of spending that’s worked out by the vessel/cargo combinations. The direct expenditures are entered into the I/O table, and indirect effects are calculated. These are the inter-industry-relations derived activities from the purchases of supplies, purchases, labor, etc. An I/O table is supplied to aid that calculation. Then, using the I/O table, induced effects are calculated. These are effects from household purchases of goods and services made possible from the wages generated from direct and indirect effects. The Corps of Engineers has a similar capability that has been used to examine the impacts of construction or base closing. The US Department of Commerce Bureau of Economic Analysis (BEA) (1997) model discusses how to use their state level I/O models (RIMS II). The ready availability of BEA and MARAD-like tables and calculation tools says that we will see more and more feedback impact analysis. The information is meaningful for many purposes.

Feed forward calculations seem to be much more interesting for planning. The question is, “If an investment is made in transportation, what will be its development effects?” An investment in transportation might lower transport costs, increase quality of service, or a mixture of these. What would be the effect on trade flows, output, earnings, etc.?

The first problem we know of worked on from this point of view was in Japan in the 1950’s. The situation was the building of a bridge to connect two islands, and the core question was of the mixing of the two island economies.

A first consideration is the impact of changed transportation attributes, say, lower cost, on industry location, and/or agricultural or other resource based extra active activity, and/or on markets. A spatial price equilibrium model (linear programming) is the tool of choice for that. Input-output then permits tracing changed inter-industry relations, impacts on wages, etc.

Britton Harris (1974) uses that analysis strategy. He begins with industry location forecasting equations: treats equilibrium of locations, markets, and prices; and pays much attention to transport costs. An interesting thing about this and other models is that input-output considerations are no more than an accounting add-on; they hardly enter Harris’ study. The interesting problems are the location and flow problems.

Legacy

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 international trade where he documented the famous Leontief paradox. He was also one of the first to establish the composite commodity theorem.

Leontief earned the Nobel Prize in Economics for his work on input-output tables. Input-output tables analyze the process by which inputs from one industry produce outputs for consumption or for inputs for another industry. With the input-output table, one can estimate the change in demand for inputs resulting from a change in production of the final good. An unrealistic assumption of this analysis is that input proportions are fixed. It is for this reason that the use of input-output analysis is limited to rough approximizations rather than prediction. Input-output was novel and inspired large-scale empirical work. It has been used for economic planning throughout the world, whether in Western, Socialist or Third World countries.

Leontief used input-output analysis to study the characteristics of trade flow between the U.S. and other countries, and found what has been named Leontief's paradox; "this country resorts to foreign trade in order to economize its capital and dispose of its surplus labor, rather than vice versa, i.e., U.S. exports were relatively labor-intensive when compared to U.S. imports. This is the opposite of what one would expect, considering the fact that the U.S.'s comparative advantage was in capital-intensive goods. According to some economists, this paradox has since been explained as due to the fact that when a country produces "more than two goods, the abundance of capital relative to labor does not imply that the capital intensity of its exports should exceed that of imports." There also exists a trend that can be seen in the U.S. that could explain Leontief's paradox, and this is that in the last four decades, money has been becoming more expensive while labor has been becom ing cheaper. Leontief was also a very strong proponent of the use of quantitative data in the study of economics.

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 did much to make quantitative data more accessible, and more indispensable, to the study of economics.

Awards

1953: Order of the Cherubim, University of Pisa
1962: Dr honoris causa, University of Brussels
1967: Dr of the University, University of York
1968: Officer of the French Legion d'Honneur
1970: Bernhard-Harms Prize Economics, West Germany
1971: Dr honoris causa, University of Louvain
1972: Dr honoris causa, University of Paris (Sorbonne)
1973: Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, aka Nobel Prize in Economics
1976: Dr honoris causa, University of Pennsylvania
1980: Dr honoris causa, University of Toulouse, France
1980: Dr honoris causa, University of Louisville, Kentucky
1980: Doctor of Social Sciences, University of Vermont
1980: Doctor of Laws, C. W. Post Center, Long Island University
1980: Russian-American Hall of Fame
1981: Karl Marx University, Budapest, Hungary
1984: Order of the Rising Sun, Japan
1985: Commandeur, French Order of Arts and Letters
1988: Dr honoris causa, Adelphi College
1988: Foreign member, USSR Academy of Sciences
1989: Society of the Optimate, Italian Cultural Institute, New York
1990: Dr honoris causa, University of Cordoba, Spain
1991: Takemi Memorial Award, Institute of Seizon & Life Sciences, Japan
1995: Harry Edmonds Award for Life Achievement, International House, New York
1995: Dr honoris causa, Humboldt University, Berlin, Germany

In Honor

Tufts University awards the Leontief Prize for economics in his honor.

Publications

1941: Structure of the American Economy, 1919-1929
1953: Studies in the Structure of the American Economy
1966: Input-Output Economics
1966: Essays in Economics
1977: Essays in Economics, II
1977: The Future of the World Economy
1983: Military Spending: Facts and Figures, Worldwide Implications and Future Outlook co-authed with F. Duchin.
1983: The Future of Non-Fuel Minerals in the U. S. And World Economy co-authed with J. Koo, S. Nasar and I. Sohn
1986: The Future Impact of Automation on Workers co-authed with F. Dochin

Bibliography

Isard, Walter et al., Methods of Regional Analysis: An Introduction to Regional Science MIT Press 1960.
Leontief, Wassily W., Input-Output Economics. 2nd ed., New York: Oxford University Press, 1986.
Miller, R.E., Karen R. Polenske and Adam Z. Rose, eds., Frontiers of Input-Output Analysis. N.Y.: Oxford UP, 1989. [HB142 F76 1989/ Suzz]
Polenske, Karen Advances in Input-Output Analysis. 1976.
Rappoport, Paul N. K. J. Rodenrys, and J. H. Savitt, Energy Consumption in the Transportation Services Section, research for the Electric Power Research Institute, 1979.
US Department of Commerce, Bureau of Economic Analysis . Regional multipliers: A user handbook for regional input-output modeling system (RIMS II). Third edition. Washington, D.C.: U.S. Government Printing Office. 1997.

External links

References
ISBN links support NWE through referral fees

Lay, David C. (2003). Linear Algebra and Its Applications, Third Edition. Addison Wesley. ISBN 0201709708.

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