5216.0 - Australian National Accounts: Concepts, Sources and Methods, 2000  
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Contents >> Chapter 9: The input-output framework >> Using input-output tables for analysis

Using input-output tables for analysis

9.62 The basic tables and the industry-by-industry tables are essentially an accounting record of the flows in the economy in the reference year. Using simplifying assumptions the input-output estimates can serve many analytical purposes. For instance, it is possible to estimate the levels of output of the production sectors required by a given final demand. The effect on other industries of an additional final output of $100 million of the motor vehicles and parts; other transport equipment industry, or of a 25 per cent change in exports of minerals, can be calculated by assuming that average and marginal utilisation rates are the same. An impact analysis of this kind may be concerned with one, several or all sectors of the economy and can be carried out with the aid of the requirements tables described below. Because relative prices are continually changing and do change substantially from one year to the next (e.g. internationally traded basic products), it is useful to regard input-output tables as representing underlying quantities and technological relationships rather than values and value relationships. Even factor payments (compensation of employees; and gross operating surplus and gross mixed income) can be viewed as representing underlying quantities, namely quantities of employee services and of entrepreneurial and capital services. Unless the analyst makes adjustments for price changes, all proportions and values are in terms of the relative and absolute prices of the reference year.

Direct requirements coefficients

9.63 A very simple application of the input-output table is calculating inputs as a percentage of the output of an industry and using these percentages for estimating the input requirements for any given output of that industry. In all the tables included in the I-O publication (including tables with indirect allocation of imports), 100 per cent always represents total Australian production.

9.64 Direct requirements coefficients have different meanings depending on the treatment of imports in the flow table from which they are derived. If the flow table were characterised by a direct allocation of competing imports the coefficients in Quadrant 1 would only refer to the requirements for inputs from domestic production.

9.65 If the flow table were characterised by an indirect allocation of competing imports, the coefficients in Quadrant 1 would include the usage of both imported and domestically produced products. Therefore, if the usage of a product by an industry remains unchanged, substitution can take place between imports and domestic production without affecting the size of the coefficients.

9.66 The coefficients for compensation of employees, gross operating surplus and gross mixed income, taxes on products (net) and other taxes on production (net) are the same regardless of whether they are derived from the tables with indirect or direct allocation of competing imports. However, the coefficients for imports differ between these two types of tables. In the tables with an indirect allocation of competing imports, the entries in Quadrant 3 (the primary inputs quadrant) relate only to complementary imports; competing imports are included in Quadrant 1 since this shows the requirements of any given industry for the output of other industries and competing imports primary to those industries. In tables with a direct allocation of competing imports, the import entries relate to all imports used by the industry.

Total requirements coefficients

9.67 The chain of calculations of output requirements can be continued beyond the direct requirements of an industry. For example, in order to produce output from the chemicals industry, inputs are required directly from the mining industry. However, to supply this direct requirement, the mining industry itself requires inputs from the chemicals industry. To produce this indirect requirement of the mining industry, the chemicals industry needs, in turn, additional output from the mining industry, and so on in a convergent infinite series. This example has been confined to two industries directly dependent on each other, but indirect requirements can arise even in the absence of direct dependence. For example, the mining industry may not directly require any inputs from agriculture, but it requires inputs from chemicals which cannot be satisfied without input from agriculture. Therefore, there is an indirect requirement by mining for agricultural input.

9.68 The requirements can be traced, step by step, throughout the industrial structure, until the increments of output required indirectly from each industry become insignificant (which occurs after a few rounds). If this operation is carried out for all industries and the direct and indirect requirements are added together, a matrix of total requirements coefficients is obtained. However, if the number of industries is large the iterative method is too cumbersome, and so the total requirements are calculated on a computer by the method known as matrix inversion. This is why the matrix of total requirements is frequently described as the inverse matrix and its coefficients as inverse coefficients. In the Australian input-output tables, they are referred to as total requirements coefficients.

9.69 In these tables a coefficient at the intersection of row i (a typical row) and column j (a typical column) represent the units of output of industry i required directly and indirectly to produce 100 units of output absorbed by final demand (i.e. final output) of industry j. In using these coefficients one should bear in mind the assumptions about homogeneity and proportionality which are their foundation.

9.70 It should be noted that coefficients will differ according to the way imports have been allocated in the flows on which the coefficients are based. If the flow table were characterised by a direct allocation of competing imports, the total requirements coefficients in Quadrant 1 would refer only to the requirements for domestic production. Therefore, in using the coefficients, it would be necessary to assume unchanged usage of imports or, alternatively, regulate the coefficients using revised import usage characteristics.

9.71 If the flow table is characterised by an indirect allocation of competing imports, the total requirements coefficients of Quadrant 1 include the usage of both imported and domestically produced products. Therefore, provided that the usage of a product by a particular industry remains unchanged, substitution can take place between imports and domestic production without affecting the size of the coefficients. In using these total requirements coefficients, a separate assessment of the proportion of these requirements which is likely to be satisfied by imports would need to be made, unless it can be assumed that the requirements to meet a specified level of final demand can be satisfied from domestic production.

9.72 All coefficients in the requirements matrices relate to flows from industry to industry. Consequently, the answers obtained by applying these coefficients will be in terms of the output of industries and not of products primary to these industries.

9.73 All tables of total requirements coefficients characteristically have a diagonal entry in excess of 100. These small excesses over 100 shown in all diagonal entries are due to indirect requirements affecting each industry through other industries. This means that to meet 100 units of final demand for the output of a particular industry, the industry itself has to produce those 100 units (for final demand) plus any direct or indirect requirements for its output resulting from its requirement for inputs from itself or from other industries.

9.74 Impact calculations in an open input-output system require independent specification of final demand for the output of each sector in the table. If final demand is specified at purchasers' prices while the answer is sought in basic prices, the reduction of the former to the latter can be carried out with the aid of the reconciliation table which shows the relationship between basic and purchasers' prices.

Specially derived tables

9.75 Instead of being expressed as total output, the requirements can be expressed as primary input content. This amounts to looking at the other side of the fundamental national accounting identity which says that gross national expenditure plus exports of goods and services is equal to gross domestic product plus imports of goods and services. In other words, the final output of any industry is equal to the rewards paid to factors of production (compensation of employees; and gross operating surplus and gross mixed income) and other primary inputs (taxes less subsidies on production and imports) in all industries contributing directly and indirectly to this final output.

9.76 Each entry in the total requirements table represents the total output required from the industry in the row by the industry in the column for the purpose of producing $100 of output absorbed by final demand. However, each of these entries can also be thought of as the sum of its inputs and hence can be dissected into these individual components. The proportions obtained from the column of the supplying industry in the table of direct coefficients are used. These calculations are based on tables with direct allocation of all imports. According to the proportionality assumption (see paragraph 9.77 below), the amount of each kind of input used by an industry represents a fixed proportion of that industry's output.

Stability of input-output coefficients

9.77 The results of users' analyses will be correct to the extent to which input-output coefficients are stable, which in turn depends on the extent to which the main assumptions underlying the input-output estimates have been satisfied. One of these, the homogeneity assumption, postulates that:

      • each sector produces a single output (i.e. all the products of the sector are either perfect substitutes for one another or are produced in fixed proportions);
      • each sector has a single input structure (i.e. one which does not vary in response to changes in product mix); and
      • there is no substitution between the products of different sectors.

The other, called the proportionality assumption, postulates that the change in output of an industry will lead to proportional changes in the quantities of its intermediate and primary inputs (i.e. for any output, each of these inputs will be a fixed proportion of the total). Even though these assumptions may be realistic for the reference year, they become progressively less so for later years. The homogeneity assumption may be weakened by changes in product mix (and consequent changes in inputs), introduction of new products and/or materials, and substitution of imports for domestic production or vice versa. The proportionality assumption may be invalidated by economies of scale, technological change or substitution of factors (e.g. more capital, less labour).

9.78 The analyst may be in a position to allow for some of these changes. Estimates of input changes due to changed technology may be obtainable from technical experts, or other sources and adjustments can be made for import substitution. These adjustments should be made to a table of direct requirements or a transactions table, but not to a table showing total requirements. If desired, the adjusted table can then be used to derive new total requirements coefficients.

9.79 The input-output tables published by the ABS represent an open input-output system because the final demand sectors are exogenous, i.e. determined by factors outside the system. In a closed system, all sectors are defined as interdependent, which means, for example, that household consumption is treated like an industry and its inputs (i.e. the requirements of consumers) are part of the solution. The system in the Australian input-output tables is static because it is providing a view of the economy at a point in time. Dynamic systems introduce explicit periods of time into the model and allow the change from a base period to the target period to be traced.


9.80 An important tool for analysts is the input-output multipliers. These provide a way of answering some of the questions often asked by input-output practitioners. These queries tend to arise because of the types of 'what if?' analysis for which input-output tables can be used (for example, what would be the impact on employment of an x% change in output by the chemicals manufacturing industry). This type of analysis is dependent on a knowledge of input-output multipliers and their shortcomings. Using input-output tables, multipliers can be calculated to provide a simple means of working out the flow-on effects of a change in output in an industry on one or more of imports, income, employment or output in individual industries or in total. The multipliers can show just the 'first-round' effects, or the aggregated effects once all secondary effects have flowed through the system.

9.81 The ABS has published an Information Paper: Australian National Accounts, Introduction to Input-Output Multipliers (Cat. no. 5246.0), which provides a guide to the construction, interpretation and use of input-output multipliers.

Types of analysis

9.82 Input-output tables are a powerful analytical tool. Running from S-U tables through symmetric input-output tables to the inverse tables, they are put to use in various kinds of economic analysis. Some of the most important areas in which the input-output framework is used for analytical purposes are listed below and described briefly:

      • analysis of production; structure of demand, export ratios, etc.; employment; prices and costs; imports required; investment and capital; and exports;
      • analysis of energy and of environment; and
      • sensitivity analysis.

9.83 The basic role of input-output analysis is to analyse the link between final demand and industrial output levels. The inverse table, total requirements coefficient in the ASNA context, could be used to assess the effects on the productive system of a given level of final demand. Employment implications are equally important in this respect. Input-output tables can also be used for analysing changes in prices stemming from changes in costs or from changes in taxes or subsidies. The determination of the level of imports is often a vital part of an input-output exercise, particularly in economies where the balance of payments imposes a constraint on their economic policies. There are questions of direct demand for imports, and secondly, of indirect demand for imported inputs from all industries involved directly or indirectly. The input-output framework might be extended to also cover demands for fixed assets, by relating the investment table to output. One of the standard input-output applications is the analysis between exports and the necessary direct and indirect inputs, some of which may be imported.

9.84 There has been an increased use of input-output for more structural analysis. Two prominent areas might be mentioned: energy and environment. It is possible to calculate the energy content of the different products in intermediate and final demand, and thereby direct and indirect energy needs from energy matrices, either in physical or value terms. The input-output approach is an essential component in environmental analysis, as it enables the determination of direct and indirect sources of pollution by linking data on emissions in physical terms to the input-output tables. The 'pollution' content of final demand can then be calculated. Input-output tables with environment-related extensions are a major component of the basic framework for satellite accounting of the environment.

9.85 The derivation of industry estimates of changes in multifactor productivity requires coherent current price and volume estimates of output, intermediate inputs, capital services and labour input. S-U tables at current prices and in the prices of the previous year together with consistent measures of labour input can provide most of the data required. The major exception is capital services. While the estimates of capital formation from the S-U tables do not provide the required measure of capital services they are a major ingredient in its estimation.

9.86 Finally, input-output could also be used for various kinds of sensitivity analysis. Such analyses reveal the effects if some variables in the output model are changed. Increased attention has also been devoted to dynamic input-output models. The essential distinction of a dynamic model is that it traces the path of the economy from a particular year to the target year, and it may be applied to calculate the requirements of a given final output not only in the current year, but also through direct and indirect capital requirements in all preceding years. Dynamic models look at the future growth path of the economy year by year.

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