Input-Output Models

Developed by Wassily Leontief in 1936, input-output models are an alternative to simple economic base and Keynesian approaches to modeling an economic system. Essentially, the models are used to describe and analyze forward and [Page 1600]backward economic linkages between industries. They compile the industrial activity of an economic system into an input-output table that is built around a matrix of monetary transactions. These transactions can be recorded by industry or sector, which are groups of industries involved in similar production processes.

The basic principle of input-output models is that the products sold (outputs) from one industry are purchased (inputs) in the production process by other industries. Therefore, it is plausible that a change in one interindustry linkage can affect the entire system of linkages. For example, the steel industry uses inputs of coal (outputs from the coal industry) to produce goods. These goods are then purchased as inputs in production by other industries, such as the construction industry. What would the impact of a rise in demand for goods produced by the steel industry be on the construction industry, other industries, and the entire economic system? An input-output model could be developed to address these interindustry interdependencies. This type of information provides geographers with a disaggregated view of an economic system in that industries are connected on the basis of buyers and sellers.

Data on the economic linkages between industries are typically collected from surveys of the economic system being modeled and compiled in a table. The table is constructed around a matrix of monetary transactions. The transactions that take place between industries represent a flow of goods and services. They are tabulated based on the value of sales (outputs) and purchases (inputs) of intermediate goods between industries. Like any table, an input-output table consists of a series of columns and rows. The rows of the table reflect the value of sales (outputs) made by each industry. Sales can be further divided to represent sales to final demand. In these categories are included sales of output made to the consumer (households), sales to government (local, state, federal), sales of investment goods (capital equipment), and sales destined to be outside the economic system being modeled (exports). The columns of the input-output table reflect the value of purchases (inputs) that are made by each industry. Purchases can be further divided to represent purchases from value added and purchases of imports. In these categories are included returns to capital (profits and dividends), labor costs (wages and salaries), and purchases of inputs made from outside the economic system being modeled.

Table 1 Basic input-output table showing general forward and backward linkages between Industries X and Y

Source: Author.

Establishing general forward and backward economic linkages between industries is fairly simple with input-output models (see Table 1). In locating the value of sales (outputs) and purchases (inputs) in the table, it is necessary to become familiar with the intersection of rows and columns and what each represents. Consider a linkage between Industries X and Y, with Industry X as the seller. To find the value of sales made from Industry X to industry Y, locate the selling Industry X along the left side of the table and then read across to find the purchasing Industry Y at the top of the table. This would show the value of outputs that are sold from Industry X to Industry Y. Following the previous example, now consider Industry X as the purchaser. To find the value of purchases made by Industry X from Industry Y, locate the buying Industry X along the top of the table and then read down to find the selling Industry Y along the left side of the table. This would show the value of inputs that are purchased by Industry X from Industry Y. Essentially, one-way or multiway economic linkages among industries are possible with input-output analysis. However, analysis of more complicated linkages requires knowledge of matrix algebra.

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