[1] Francois Quesnay had developed a cruder version of this technique called Tableau économique, and Léon Walras's work Elements of Pure Economics on general equilibrium theory also was a forerunner and made a generalization of Leontief's seminal concept.
[2] Alexander Bogdanov has been credited with originating the concept in a report delivered to the All Russia Conference on the Scientific Organisation of Labour and Production Processes, in January 1921.
Thomas Remington, has argued that their work provided a link between Quesnay's tableau économique and the subsequent contributions by Vladimir Groman and Vladimir Bazarov to Gosplan's method of material balance planning.
Karl Marx's economics provided an early outline involving a set of tables where the economy consisted of two interlinked departments.
Sectors may also depend internally on a portion of their own production as delineated by the entries of the matrix diagonal.
is invertible then this is a linear system of equations with a unique solution, and so given some final demand vector the required output can be found.
A great deal of empirical work has been done to identify coefficients, and data has been published for the national economy as well as for regions.
The Leontief system can be extended to a model of general equilibrium; it offers a method of decomposing work done at a macro level.
Therefore, economists often use location quotients to create regional multipliers starting from national data.
But this is not very satisfactory because transportation requirements differ, depending on industry locations and capacity constraints on regional production.
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.
One who wishes to work with input–output systems must deal with industry classification, data estimation, and inverting very large, often ill-conditioned matrices.
Input–output models for different regions can also be linked together to investigate the effects of inter-regional trade, and additional columns can be added to the table to perform environmentally extended input–output analysis (EEIOA).
For example, information on fossil fuel inputs to each sector can be used to investigate flows of embodied carbon within and between different economies.
A main use of input–output analysis is to measure the economic impacts of events as well as public investments or programs as shown by IMPLAN and Regional Input–Output Modeling System.
By linking industrial output to satellite accounts articulating energy use, effluent production, space needs, and so on, input–output analysts have extended the approaches application to a wide variety of uses.
This model involves the direct determination of physical quantities to be produced in each industry, which are used to formulate a consistent economic plan of resource allocation.
[14] In the economy of the Soviet Union, planning was conducted using the method of material balances up until the country's dissolution.
The method of material balances was first developed in the 1930s during the Soviet Union's rapid industrialization drive.
As a result, the benefits of consistent and detailed planning through input–output analysis were never realized in the Soviet-type economies.
Moreover, the economic "snapshot" that the benchmark version of the tables provides of the economy's cross-section is typically taken only once every few years, at best.
As suggested above, the core input–output table reports only intermediate goods and services that are exchanged among industries.
But an array of row vectors, typically aligned at the bottom of this matrix, record non-industrial inputs by industry like payments for labor; indirect business taxes; dividends, interest, and rents; capital consumption allowances (depreciation); other property-type income (like profits); and purchases from foreign suppliers (imports).
Another array of column vectors is called "final demand" or "gross product consumed."
In any case, by employing the results of an economic census which asks for the sales, payrolls, and material/equipment/service input of each establishment, statistical agencies back into estimates of industry-level profits and investments using the input–output matrix as a sort of double-accounting framework.
Dynamic Leontief models are obtained by endogenizing the formation of capital stock over time.
Assuming that the productive capacity is always fully utilized, we obtain the following expression for (1) with endogenized capital formation:
[18][19] Apart from this feature, many studies have found that the outcomes obtained for this forward-looking model invariably lead to unrealistic and widely fluctuating results that lack economic interpretation.
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.
آزمون فروض تکنولوژی در محاسبه جدول داده ستانده متقارن ایران: یک رهیافت اقتصاد سنجی.