Wassily Leontief

Wassily Leontief's name 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 interindustry flows - which in turn were inspired by Quesnay's Tableau Economique, which Leontief's system most resembles. Although of fluctuating popularity, input-output analysis has been a mainstay of economics and economic policy and planning throughout the world for the past half-century.

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.

In 1925 he was allowed to leave the USSR, so 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 he worked at the Institute for World Economics of the University of Kiel . 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.

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 employed him in the same year (1932) in its Department of Economics , 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 and founded and directed the Center for Economic Analysis.

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

Work

Leontief's contributions to economics would 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.

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), the Leontief model represents the economy as a system of linear equations.

Leontief's interests were, however, not limited to input- output. His 1936 article on "composite commodities" made him, together with Hicks, the father of that famous microeconomic theorem. His early reviews of Keynes's General Theory (1936, 1937, 1947, 1948) were important stepping stones to the Neo-Keynesian synthesis's stress on fixed nominal wages in interpreting Keynes's theory. His 1933 article on the analysis of international trade is still learnt 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. One of his more stirring contributions has been his 1953 finding that Americans were exporting labor-intensive rather than capital- intensive goods - the "Leontief Paradox" - which 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 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.

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” and “Labor” input. 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.

The matrix devised by Leontief is often used to show the effect of a change in production of a final good 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 , i = 1, 2, 3, while we have 4 rows of inputs j, 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 (X_i), and ( 3 ) the flows (x_ij) 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

or

x₁₁ + x₁₂ + x₁₃ + c₁ = X₁

x₂₁ + x₂₂ + x₂₃ + c₂ = X₂

x₃₁ + x₃₂ + x₃₃ + c₃ = X₃

x₄₁ + x₄₂ + x₄₃ + c₄ = X₄

Forecasting and/or Analysis Using Input-Output

Once we have the ( x ij ) flows, we can easily derive the Leontief coefficients or “multipliers” ( a ij ) via the following definition embodied by the following algebraic notation, whereby aij = xij / Xi :

x₁₁ = a₁₁x₁

x₁₂ = a₁₂x₂

x₁₃ = a₁₃x₃

x₁₄ = a₁₄x₄

These “multipliers” or technical coefficients translate value in dollar units into a proportion and represent a quantitative expression of an initial, "exogenous" force or change that is expected to generate additional effects through interdependencies of the "endogenous" linkage system. They translate the consequences of change in one variable upon others.

Multipliers are aptly called estimators of the 'ripple' effect". In more 'technical terms', they are numerical coefficients which relate a change in (a component of aggregate) demand (or employment) to a consequent change in total income (or total employment). Thus, they are used for forecasting and analyzing of possible policy alternatives.

This specific use of Leontief’s I-O analysis is probably its best feature because we are analyzing all alternatives ( and their forecast performance ) now; the time-shift ( from the coefficient computation to “now” ), which is discussed in the next paragraph, is not an important factor any more.

To set up a predictive form of I-O analysis Leontief stated that if we can estimate changes in final demand, we can predict how an economy will react as measured in change in output. In matrix notation we combine the notation and definition of algebraic elements of the I-O Table ( in the above example ) and the two subsequent matrices it is clear that we can write:

AX + C = X,

where X…..total output from first , A……matrix of aij coefficients ( and from combination of the first and second system of four linear equation above ) follows the matrix notation.

From the above matrix notation it follows:

X - AX = C and from the standard matrix algebra we

finally obtain ( I - A ) X = C.

The major Leontief contribution is to divide both sides by ( I - A ) , getting the famous [[Leontief inverse]:

X = ( I - A ) -1 C .

Now we are able to predict change in an economic output ( X ) by specifying changes in demand ( C ) , which formally yields a I-O predictive form:

∆ X = ( I - A ) -1 ∆C.

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.

In other words, the straightforward analysis with standard I-O model ( unless the additional mathematical apparatus is added ) cannot be done when effects extended to other industries as production expenses change for a certain industry.

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 1954 article ( Leontief 1953, 1956 ) by Wassily Leontief showed, using input-output analysis, that U.S. exports were relatively labor-intensive compared to U.S. imports. This was the opposite of what economists 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. Economists have shown that in a country that 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 its imports. Hence, it could be 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.

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 themodel of 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. It has been used for economic planning throughout the world, whether in Western, Socialist or Third World countries.

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.

References
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Isard, Walter et al., Methods of Regional Analysis: An Introduction to Regional Science, MIT Press, 1960
Lay, David C., Linear Algebra and Its Applications, Third Edition|year=2003|publisher=Addison Wesley|id=ISBN 0201709708}}
Leontief, W.,"The Fundamental Assumption of Mr. Keynes's Monetary Theory of Unemployment", QJE, 1936
Leontief, W.,"Composite Commodities and the Problem of Index Numbers", Econometrica, 1936
Leontief, W.,"Implicit Theorizing: a methodological criticism of the Neo-Cambridge school", QJE, 1937
Leontief, W., The Structure of the American Economy, 1919-1939, 1941.
Leontief, W.,"The Pure Theory of the Structure of Functional Relationships", Econometrica, 1947
Leontief, W., "Postulates: Keynes's General Theory and the classicists", in: Harris ( ed.), The New Economics, 1947
Leontief, W.,Studies in the Structure of the American Economy, 1953
Leontief, W.,"Domestic Production and Foreign Trade: the American capital position re-examined", Proceedings of American Philosophical Society, 1953
Leontief, W., "Factor Proportions and the Structure of American Trade: Further theoretical and empirical analysis", REStat., 1956
Leontief, Wassily W., Input-Output Economics. 2nd ed., Oxford University Press,New York 1986
Miller, R.E., Karen R. Polenske and Adam Z. Rose, eds., Frontiers of Input-Output Analysis, Oxford UP, N.Y. 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

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