An input-output table records transactions between industries, and input-output (I-O) analysis uses these data to examine the interdependence between sectors and the impact which changes in one sector have on others. This can be seen as a quantitative development of neoclassical general equilibrium analysis used by economists such as L.Walras. Its origins can be traced back to Quesnay’s ‘Tableau Économique’ in 1758. The key figure has been Wassily Leontief, who completed the first I-O table in the USA in 1936 and has done much pioneering development work.
An I-O table (such as that shown in Figure 1) records in its columns the purchases by each industry, A, B, and C (that is, the inputs into the production process), and in the rows the sales by each industry. Also included are sales to final purchasers and payments for factors of production (labour and capital), thus showing the necessary integration into the rest of the national accounts.
Figure 1
The production of a commodity requires inputs from other industries, known as direct inputs, and from the I-O table a matrix of technical coefficients can be derived which shows direct inputs per unit of output, for example, in matrix A below 0.1=20/200. In turn the production of each of these commodities used as inputs requires inputs from the other industries, and this second round of production then imposes demands on other industries, and so on. All these subsequent inputs are known as indirect inputs. Tracing all these ramifications is a laborious process in a large I-O system, but it can be shown mathematically that the solution lies in the matrix (I−A) 1where I is the unit matrix and A is the matrix of direct input coefficients. Such a matrix, known as the Leontief Inverse, shows in its columns the total direct plus indirect inputs required per unit of output of the column industry (see Figure 2). This matrix is the key to I-O analysis as it encapsulates the interdependence of industries in the economy. For instance, a demand from, say, consumers for 1000 units of A requires the production of 1077 units of A, 351 of B and 141 of C (using col. A of matrix (I−A) 1). The extra 77 units of A are needed by B and C to produce the inputs which A takes from them and which they take from each other.
Figure 2
Using such a model it is possible to calculate the effect of a change in demand in an economy on the output in all industries. The analysis can be extended to cover the inputs of factors of production which are closely related to the output levels, and in this way the precise effect which a change in demand for one product has on employment in that industry and in all others can be calculated with perhaps additional information on types of skill. The I-O table can be extended to include purchases of imports, thus enabling the import requirements of any given level of demand to be calculated; of particular interest to the balance of payments is the import content of exports.
Just as the production of a commodity has ramifications back through the chain of production, so a change in the price of an input has effects forward on to many other products, both directly and indirectly. The price of any product is determined by the prices of its inputs, and these can all in turn be traced back to the ‘price’ of labour, capital and imports, using the formal Leontief Inverse. It is thus possible to calculate the effects on final prices of, for example, an increase in wages in one industry or of a change in import prices due perhaps to changes in the exchange rate or changes in foreign prices.
All the above aspects of input-output analysis can be combined into a planning model which will give a comprehensive and internally consistent picture of the economy 5–10 years ahead. This enables policy makers to see the implications which, say, a certain growth in the economy has for particular industries, employment, prices, the balance of payments and so on, and to locate key sectors. Most countries compile I-O tables, usually identifying fifty or more industries, although models have lost some of their popularity in western Europe. They are, however, extensively used in the CIS and eastern Europe and in developing economies. Here they are well suited to measuring the impact of marked changes in demand and supply patterns which are expected. Further refinements of I-O analysis include disaggregation by region and making a dynamic model so that investment needs are incorporated.
A.G.Armstrong
University of Bristol
Further reading
Leontief, W. (1966) Input-Output Economics, New York.
United Nations (1973) Input-Output Tables and Analysis, Studies in Methods, New York.
