SYMMETRIC INPUT-OUTPUT TABLES

9.53 In the ESA, the product-by-product input-output table is the most important symmetric input-output table and this table is described here.

9.54 The product-by-product input-output table (see Tables 9.4 and 9.12) can be compiled by converting the supply and use tables, both at basic prices. This involves a change in format, i.e. from two asymmetric tables to one symmetric table (see paragraph 9.09.). The conversion can be divided into three steps:

1. allocation of secondary products in the supply table to the industries of which they are the principal products;
2. rearrangement of the columns of the use table from inputs into industries to inputs into homogeneous branches (see paragraph 2.114.) (without aggregation of the rows);
3. aggregation of the detailed products (rows) of the new use table to the homogeneous branches shown in the columns, if appropriate.

9.55 Step a) involves transfers of outputs in the form of secondary products in the supply table. Since secondary products appear as 'off-diagonal' entries in the supply table, this kind of transfer is a comparatively simple matter. These secondary products are treated as additions into the industries for which they are principal and removed from the industries in which they were produced.

9.56 Step b) is more complicated, as the basic data on inputs relate to industries and not to each individual product produced by each industry. The kind of conversion to be made here entails the transfer of inputs associated with secondary outputs from the industry in which that secondary output has been produced to the industry to which they principally (characteristically) belong. In making this transfer, two different approaches might be taken:

(1) by means of supplementary statistical and technical information;

(2) by means of assumptions.

9.57 Supplementary statistical and technical information should be utilised as much as possible. For example, it might be possible to obtain specific information on the inputs required to produce certain kinds of output. However, information of this kind is usually incomplete. Ultimately it will usually be necessary to resort to simple assumptions to make the transfers.

9.58 The assumptions used to transfer outputs and associated inputs hinge on two types of technology assumptions:

1. industry technology, assuming that all products produced by local KAUs in an industry are produced with the same input structure;
2. product technology, assuming that all products in a product group have the same input structure, whichever industry produces them.

The choice of the best assumption to apply in each case is not an easy one. It must, in fact, depend on the structure of national industries, e.g. the degree of specialisation, and on the homogeneity of the national technologies used to produce products within the same product group. For example, boots may be made from leather and from plastic. Assuming the same product technology for all boots (or, when a higher level of aggregation is used, e.g. footwear) can thus be problematic; assuming industry technology can then be a better alternative.

Simple application of the product technology assumption has often shown results that are unacceptable, insofar as the input-output coefficients sometimes generated are improbable or even impossible, for example, negative coefficients. Improbable coefficients may be due to errors in measurement and to heterogeneity (product-mix) in the industry of which the transferred product is the principal product. This might be overcome by making adjustments based on supplementary information or exploiting informed judgement to the fullest extent possible. Of course, another solution is to apply the alternative assumption of industry technology. In practice, employing mixed technology assumptions combined with supplementary information is the best strategy for compiling symmetric input-output tables.

9.59 The importance of the role played by the assumptions depends on the extent of secondary production, which in turn depends not only on how production is organised in the economy but also on the product breakdown. The more detailed the product breakdown, the more secondary output can be expected.

9.60 Step c) involves the aggregation of the products in the new use table to the industries that generate them according to step a) and this results in a symmetric input-output table with products cross-classified against by-products. While these amendments start from data based on local KAUs, the resulting entries are made to conform to those of ‘homogeneous units of production'.

9.61 The classifications in the symmetric input-output table coincide with those in the supply and use tables, as the former is a transformation of the latter (except of course the classification by industry/homogeneous branch).

Table 9.13 A symmetric input-output table for domestic output (product by product)

9.62 The symmetric input-output Table 9.12 should be accompanied by at least two tables:

1. a matrix showing the use of imports; the format of this table is the same as that of the import table supporting the supply and use tables (see Table 9.10), except that the product-by-product classification is used;
2. a symmetric input-output table for domestic output (Table 9.13).

The latter table should be used in calculating the cumulated coefficients, i.e. the Leontief-inverse. In terms of Table 9.13, the Leontief-inverse is the inverse of the difference between the identity matrix I and the matrix of technical coefficients obtained from the matrix (1), (1). The Leontief-inverse could also have been calculated for domestic output and competitive imports (see paragraph 9.51). It should then be assumed that the competitive imports have been produced in the same way as the competing domestic produce.