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Using I-O tables for analysis

Australian System of National Accounts: Concepts, Sources and Methods
Reference period
2020-21 financial year

22.127    The basic tables and the industry-by-industry tables are an accounting record of the flows in the economy for a given year. If simplifying assumptions are used, the I-O tables can serve many analytical purposes. For example, it is possible to:

  • estimate the levels of output of the production required to meet a given level of final demand;
  • the effect of other industries of an additional output of $100m of a product; or
  • the impact of additional exports of a product on other industries, by assuming the average and marginal utilisation rates are the same.

22.128    An impact analysis like this can be concerned with one or several industries in the economy, and can be done using the requirements table.

22.129    Relative prices are constantly changing, and do change significantly from year to year. It is useful to regard I-O tables as representing underlying quantities and technological relationships, rather than values and value relationships. Even factor payments (COE, GOS and GMI) can be viewed as representing quantities of employee services, and of entrepreneurial and capital services. Unless the analyst makes allowance for price changes, all proportions and values will be in terms of relative and absolute prices of the reference year.

22.130    The ABS I-O tables are not revised. They provide a snapshot of the Australian economy at a point-in-time and should not be used as time series.

Direct requirements coefficients

22.131    A simple application of the I-O tables is calculating inputs as a percentage of the output of an industry and using these percentages for estimating the input requirements for a given output of the industry. In all tables in the I-O releases, 100 always represents total Australian production, including tables with indirect allocation of imports.

22.132    All coefficients in the requirements matrices relate to flows from industry to industry. The application of the requirements will be in terms of the output of industries, and not of the products primary to the industries.

22.133    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 is based upon direct allocation of competing imports, the coefficients in quadrant 1 will only refer to the requirements from domestic production. If the flow tables are based upon an indirect allocation of imports, the coefficients in quadrant 1 will include the use of both imported and domestically produced products. 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. 

22.134    The coefficients for COE, GOS and GMI, net taxes on products and other taxes on production are the same regardless of the allocation of imports in the source flow table. However, the coefficients for imports depend on the two types of table. In the tables with an indirect allocation of imports, the entries in quadrant 3 (the primary inputs quadrant) relate only to complementary imports (of which none are identified in current I-O tables), and 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 imports entries relate to all imports used by the industry.

Total requirements coefficients

22.135    The chain of calculations for output requirements can be continued beyond the direct requirements for an industry. For example, in order to produce output from the chemicals industry, inputs are required directly from the mining industry and other industries. To supply this direct requirement, the mining industry itself requires inputs from other industries including the chemicals industry, and so on in a convergent infinite series. In another example, the mining industry may not directly require inputs from agriculture but requires inputs from chemicals which cannot be produced without inputs from agriculture. Therefore, mining has an indirect requirement for input from agriculture. As is the case with the direct requirements coefficients, coefficients in the requirements matrices relate to flows from industry to industry. The application of the requirements will be in terms of the output of industries and not of the products primary to the industries.

22.136    The requirements can be traced, step by step through the industrial structure until the increments of output required indirectly for each industry become insignificant. This occurs after a few rounds. If this is done for all industries, and the direct and indirect requirements are added together, the result is a matrix of total requirements. However, if the number of industries is large the iterative process is too cumbersome, and the matrix is calculated by matrix inversion. This is why the matrix of total requirements is often referred to as the inverse matrix or Leontief inverse, and its coefficients as inverse coefficients.

22.137    In the total requirements coefficients table, at the intersection of a typical row i and column j, represents the units of output of industry i required directly and indirectly to produce 100 units of output absorbed by final demand of industry j. The tables are compiled based upon the assumptions of homogeneity and proportionality and this must be accounted for when they are used.

22.138    Derived coefficients will differ according to the way imports have been treated in the flow table from which they are derived. If competing imports were directly allocated in the flow table, the resultant total requirements coefficients in quadrant 1 will only refer to the requirements for domestic production. Therefore, when using of the coefficients it would be necessary to assume unchanged usage of imports or to regulate the coefficients by using revised import usage characteristics. 

22.139    If the total requirements coefficients were derived from a flow table using indirect allocation of imports, the coefficients in quadrant 1 will be based on the usage of domestically produced and imported goods. If the usage of a product by an industry remains unchanged, substitution can therefore take place between domestic products and imports without affecting the size of the coefficients. In using the coefficients, an assessment of the proportion of the requirements that is likely to be satisfied by imports would need to be made, unless all demand can be met from Australian production.

22.140    All tables of total requirements characteristically have a diagonal entry that exceeds 100. The amounts that exceed 100 are due to the indirect requirements affecting each industry through other industries. This means that to meet 100 units of final demand for the output of an industry, the industry itself has to produce those 100 units, plus any direct or indirect requirements for its output resulting from requirements from itself, or from other industries.

Specially derived tables

22.141    Instead of being expressed as total output the requirements can be expressed as primary input content. This assumes that the final output of an industry is equal to the reward paid to the factors of production in all industries contributing directly and indirectly to this final output.

22.142    Each entry in the 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. Each of these can also be thought the sum of its inputs and can be dissected into its individual components. The proportions obtained from the column of the supplying industry in the table of direct coefficients are used. According to the proportionality assumption, the amount of each kind of input used by an industry represents a fixed proportion of the industries output.

Stability of I-O coefficients

22.143    The use of coefficients in users’ analyses will be accurate to the extent that the coefficients remain stable, which is dependent on the extent to which the assumptions of homogeneity and proportionality are valid.

22.144    The homogeneity assumption expresses that: each industry produces a single output (all products are perfect substitutes for one another, or are produced in fixed proportions); each industry has a single input structure (which does not vary in response to product mix); and there is no substitution between products of different groups. This assumption is weakened as product mixes change (with corresponding changes in input mixes), introduction of new products or materials, and as there is substitution between domestic production and imports or vice versa.

22.145    The proportionality assumption says that for any level of output the inputs will be a fixed proportion of the total. This assumption holds in the reference year but less so in each following year. The assumption may be invalidated by economies of scale, technological change, or substitution between the factors of production.

22.146    The I-O tables produced by the ABS represent an open I-O system as the final demand categories are exogenous (i.e. determined outside the system). In a closed system, all categories are defined as interdependent. For example, HFCE is treated like an industry, and its inputs (the requirements of consumers) are part of the solution. The ABS I-O tables are static as they provide a snapshot at a point-of-time. Dynamic systems introduce explicit time periods into the model and allow the change from a base period to the target to be traced.


22.147    Multipliers are a tool used by I-O practitioners to answer "what-if?" type questions. For example, 'what would be the impact on employment of a change in the output of the Chemicals manufacturing industry?' Multipliers can be used to quantify the flow-on effect of a change in the output of an industry on one or more of imports, income, employment or output on individual industries, or in total. The multipliers can be used to show "first-round" changes, or the aggregate effects once secondary effects have flowed through the system. 

22.148    The ABS has published an information paper, Australian National Accounts: Introduction to Input-Output Multipliers, 1989-90, which provides a guide to the construction, interpretation and use of I-O multipliers.

22.149    The ABS frequently receives requests from users who are seeking updated Input-Output multipliers. The ABS has not published I-O multipliers since the 1998-99 issue of Australian National Accounts: Input-Output Tables and does not plan to compile and reissue this table. As such, the ABS is unable to support user requests for assistance with multipliers.

22.150    Production of multipliers was discontinued for several reasons. There was considerable debate in the user community as to their suitability for the purposes to which they were most commonly applied; that is, to produce measures of the size and impact of a particular project to support bids for industry assistance of various forms.

Limitations of Input-Output Multipliers for Economic Impact Assessment

22.151    I-O multipliers are most commonly used to quantify the economic impacts (both direct and indirect) relating to policies and projects. While their ease of use makes I-O multipliers a popular tool for economic impact analysis, they are based on limiting assumptions that results in multipliers being a biased estimator of the benefits or costs of a project.

22.152    Inherent shortcomings and limitations of multipliers for economic impact analysis include:

  • Lack of supply-side constraints – the most significant limitation of economic impact analysis using multipliers is the implicit assumption that the economy has no supply-side constraints. That is, it is assumed that extra output can be produced in one area without taking away resources from other activities, thus overstating economic impacts. The actual impact is likely to be dependent on the extent to which the economy is operating at or near capacity.
  • Fixed prices – constraints on the availability of inputs, such as skilled labour, require prices to act as a rationing device. In assessments using multipliers, where factors of production are assumed to be limitless, this rationing response is assumed not to occur. Prices are assumed to be unaffected by policy and any crowding out effects are not captured.
  • Fixed ratios for intermediate inputs and production – economic impact analysis using multipliers implicitly assumes that there is a fixed input structure in each industry and fixed ratios for production. As such, impact analysis using multipliers can be seen to describe average effects, not marginal effects. For example, increased demand for a product is assumed to imply an equal increase in production for that product. In reality, however, it may be more efficient to increase imports or divert some exports to local consumption rather than increasing local production by the full amount.
  • No allowance for purchasers’ marginal responses to change – economic impact analysis using multipliers assumes that households consume goods and services in exact proportions to their initial budget shares. For example, the household budget share of some goods might increase as household income increases. This equally applies to industrial consumption of intermediate inputs and factors of production.
  • Absence of budget constraints – assessments of economic impacts using multipliers that consider consumption induced effects (type two multipliers) implicitly assume that household and government consumption is not subject to budget constraints.
  • Not applicable for small regions – multipliers that have been calculated from the national I-O tables are not appropriate for use in economic impact analysis of projects in small regions. This is because small region multipliers tend to be smaller than national multipliers since their inter-industry linkages are normally relatively shallow. Inter-industry linkages tend to be shallow in small regions since they usually don’t have the capacity to produce the wide range of goods used for inputs and consumption, instead importing a large proportion of these goods from other regions.

22.153    I-O multipliers represent one particular derived or modelled view of I-O data that goes beyond the publishing of the core I-O tables. Considering this, the ABS ceased production of multipliers as an extension of the I-O tables. Instead, users of the I-O tables can compile their own multipliers as they see fit, using their own methods and assumptions to suit their own needs from the data supplied in the main I-O tables.

22.154    While I-O multipliers may be useful as summary statistics to assist in understanding the degree to which an industry is integrated into the economy, their inherent shortcomings make them inappropriate for economic impact analysis. These shortcomings mean that I-O multipliers are likely to significantly overstate the impacts of projects or events. More complex methodologies, such as those inherent in Computable General Equilibrium (CGE) models, are required to overcome these shortcomings.

Types of Analysis

22.155    I-O tables are a powerful analytical tool. They can be used in many ways including;

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

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

22.157    There has been an increased use in I-O analysis recently for more structural analysis, including in the energy, and environment fields.  It is possible to calculate the energy content of the different products in intermediate and final demand, and the indirect energy needs from energy matrices in either value or volume terms. The I-O approach is an essential component in environmental analysis as it enables the direct and indirect sources of pollution by linking data on emissions in physical terms to the I-O tables. The pollution content of the components of final demand can then be calculated. I-O tables with environmental related extensions are a major component of the basic framework of the satellite accounting of the environment.

22.158    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, 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 service, they are a major element in its estimation.

22.159    The I-O tables can also be used for various kinds of sensitivity analysis. These analyses reveal the effects if some variables in the output model are changed. Increased attention has recently been shown to dynamic I-O models. The essential distinction of a dynamic model is that it traces the path of the economy from a particular year to a target year, and it may be applied to calculate the requirements of a given final output, not only in the current year but through direct and indirect capital requirements in all preceding years. Dynamic models look at the future growth path of the economy year by year. These include Computable General Equilibrium (CGE) models. CGE models are used extensively to inform government policy analysis in many areas such as development economics, fiscal policy, international trade policy and micro economic reform. The national I-O tables provide a basis from which the compilation of state and regional tables can be modelled.