EN/SUT/2014/Doc/14

Chapter 13: Supply and use tables and input-output tables

13.1. Introduction

  1. This chapter provides the sequence of steps that are required to convert SUTs to Input-Output (I-O) tables and use of I-O tables for economic analysis. The chapter also presents simplified procedures for preparing I-O tables, I-O models and for carrying out economic analysis with an example of a three-sector economy.
  1. The input-output framework comprises, (i) supply table at basic prices with transformation to purchasers’ prices, (ii) use table at purchasers’ prices, which is subsequently transformed to basic prices, and (iii) symmetric I-O tables, which are built up from the SUTs at basic prices. While the supply and use tables (SUTs) are product by industry tables, the I-O tables are either product by product or industry by industry tables. Both the SUTs and I-O tables provide the inter-industry dependencies and relationship between producers and consumers. They, thus offer a most detailed picture of the economy, which essentially involves (a) production - industries producing products in the form of goods and services, (b) consumption – both intermediate (purchases of goods and services by industries) and final (purchases of goods and services by domestic final users comprising households, non-profit institutions serving households (NPISHs) and general government (all levels of Government in the economy)), (c) accumulation that involves gross fixed capital formation (GFCF) and change in inventories, and (d) transactions with the rest of the world (exports and imports).
  1. SUTs are the basis for the construction of symmetric I-O tables. I-O tables cannot be compiled without passing through the supply and use stage. Symmetric I-O tables are the basis for input-output analysis. While SUTs are close to statistical sources and actual observations, I-O tables serve in a better way analytical purposes for economic analysis.
  1. The I-O table is derived from the use table at purchasers’ prices, which, as mentioned earlier, is a product by industry table. The use table constructed is often rectangular with more products than industries in general. However, for the I-O table, rows and columns should both have either products or industries with individual row totals and columns totals to be equal, which necessitates that the I-O tables are square and symmetric. A simple three sector square SUTs at purchasers’ prices are presented in the following two tables. These tables have been used in this chapter to demonstrate the preparation of I-O tables and economic analysis.

13.2. Conversion of SUTs at purchasers’ prices to I-O tables

  1. The various steps involved in transforming the SUTs at purchasers’ prices to I-O tables at basic prices are:

(i)Making SUTs square[1]: Transformation of rectangular SUTs at purchasers prices to square SUTs at purchasers’ prices, with products in rows representing the characteristic products of industries shown in columns;

(ii)Converting the square SUTs at purchasers’ prices to square SUTs at basic prices;

(iii)Application of standard models for transformation of square SUTs at basic prices to product by product or industry by industry symmetric I-O tables[2].

Table 16: Supply table with transformation from basic to purchasers prices

Product\Industry / Agriculture / Industry / Services / Domestic output / Imports / Supply at basic prices / Trade and transport margins / Taxes less subsidies on products / Supply at purchasers’ prices
1. Agriculture / 2900 / 100 / 50 / 3050 / 123 / 3173 / 30 / 105 / 3308
2. Industry / 100 / 4503 / 250 / 4853 / 750 / 5603 / 100 / 295 / 5998
3. Services / 245 / 560 / 6294 / 7099 / 94 / 7193 / -130 / 380 / 7443
Output at basic prices / 3245 / 5163 / 6594 / 15002 / 967 / 15969 / 0 / 780 / 16749

Table 17: Use table at purchasers’ prices

Product\Industry / Agr / Ind / Serv / II-Use / X / HFCE / GFCE / GCF / Uses- PP
1. Agriculture / 400 / 450 / 130 / 980 / 57 / 2229 / 15 / 27 / 3308
2. Industry / 160 / 2050 / 1000 / 3210 / 513 / 1271 / 130 / 874 / 5998
3. Services / 242 / 1217 / 1362 / 2821 / 275 / 2466 / 817 / 1064 / 7443
6. Total IC at PP / 802 / 3717 / 2492 / 7011 / 845 / 5966 / 962 / 1965 / 16749
7. GVA at BP (8-6) / 2443 / 1446 / 4102 / 7991 / IC: intermediate consumption; PP: purchasers’ prices; BP: basic prices; GVA: gross value added; COE: compensation of employees;
TLS: taxes less subsidies; CFC: consumption of fixed capital; OS/MI: operating surplus/mixed income; II-Use: inter-industry use; X: exports, HFCE: household final consumption expenditure; GFCE: government final consumption expenditure; GCF: gross capital formation
7.1 COE / 1000 / 700 / 2000 / 3700
7.2 Other TLS on production / 0
7.3 CFC / 240 / 140 / 410 / 790
7.4 OS/MI / 1203 / 606 / 1692 / 3501
8. Output-BP / 3245 / 5163 / 6594 / 15002

(i) Making SUTs square with products corresponding to industries

  1. For transforming rectangular SUTs to square SUTs, the procedures involved are to (a) disaggregate or aggregate the products included in the SUTs so that they represent the characteristic products of industries shown in the columns; or (b) disaggregate or aggregate the industries included in the columns of SUTs so that they correspond to the products shown in the rows. In either option, the resultant square SUT will show in rows, the characteristic products corresponding to the industries included in the columns. The choice of one of the two options mentioned here depends on the size of the I-O table to be compiled from the SUTs. As products included are often more than the industries in the rectangular SUTs, the option of disaggregating the industries will result in a larger size I-O table. On the other hand, if products are aggregated to correspond to the industries, the size of I-O will be smaller. In normal situations, it is generally preferable to follow the aggregation approach, as disaggregation requires lot more efforts in collecting detailed data and the compilations involved will almost be equivalent to compiling the SUTs afresh.
  1. For classifying industries in the SUTs, SNA recommends the use of International Standard Industrial Classification (ISIC) for industries and Central Product Classification (CPC) for products. Since the SUTs use the ISIC and CPC classifications or country-specific classifications based on ISIC and CPC, it is possible to align the products with industries in the SUTs, based on standard concordance tables available in the UNSD website. Using these concordance tables, the square SUTs at purchasers’ prices can be prepared from the rectangular SUTs at purchasers’ prices, in which the industry classification and the product classification are fully aligned with each other, industries and products correspond to each other and the number of industries and the number of products are the same.

(ii) Conversion of SUTs at purchasers’ prices to SUTs at basic prices

  1. The next step involved in the long process of converting rectangular SUTs at purchasers’ prices to symmetric I-O tables, is the transformation of square SUTs at purchasers’ prices to square SUTs at basic prices[3]. For this purpose, it is necessary to bring both the supply and the use tables to basic price valuations. It may be recalled that the rectangular supply table at basic prices, initially compiled is already at basic prices, as domestic output and imports, c.i.f. are at basic prices. Therefore, supply table at basic prices is an integral part of the supply table at purchasers’ prices, since this table includes a transformation of products from basic prices to purchasers’ prices by adding the vectors of trade and transport margins (TTM), and taxes less subsidies (TLS) on products. Thus, the square supply table at basic prices is readily available from the square supply table at purchasers’ prices.
  1. Thus, the task remains is only to compile a square use table at basic prices[4] from the square SUTs at purchasers’ prices. The cell values corresponding to the products (quadrant I and quadrant II) in the use table at purchasers’ prices include values at basic prices, trade margins, transport costs and taxes less subsidies on products in an integrated manner. For the use table at basic prices, each of these components need to be segregated from these cell values and placed in the respective rows of trade, transport and taxes less subsidies on products. While the trade and transport rows already existing in the use table will now include the total values segregated from the corresponding cells in the same columns, a separate row needs to be introduced for taxes less subsidies on products at the end of the product rows, as intermediate consumption of industries would still need to be valued at purchasers’ prices.
  1. The calculations involved in segregating the cell values mentioned above, include compilation of a set of valuation matrices for trade and transport margins and taxes less subsidies on products. The dimension of each of these valuation matrices corresponds to the dimension of the use table at purchasers’ prices for products. In practice, a table of trade and transport margins and a table of taxes less subsidies on products are separately compiled using the same structure as the use table in purchasers' prices. The values in these tables are then deducted from the corresponding values in the use table at purchasers' prices. Then, the row of column sums of the table of trade and transport margins is added back to the row of trade and transport services. Similarly, an extra row of taxes less subsidies is created in the use table which takes the values of the row of the column sums of the table of taxes less subsidies.
  1. It should be noted that the columns totals for the trade and transport margin matrices always sum up to zero, as there is no trade activity at purchasers’ prices. If a trade margin has to be added to a basic price for the goods to calculate a purchasers’ price, the same value has to be deducted from the corresponding trade service. This reallocation of margins will not affect the size of GDP, as trade and transport margins are either included in trade and transport services at basic prices or included in the output of goods at purchasers’ prices.

Table 18: Matrix of trade and transport margins

Product\Industry / Agr / Ind / Serv / II-Use / X / HFCE / GFCE / GCF / Uses
1. Agriculture / 3.6 / 4.1 / 1.2 / 8.9 / 0.5 / 20.2 / 0.1 / 0.2 / 30.0
2. Industry / 2.7 / 34.2 / 16.7 / 53.5 / 8.6 / 21.2 / 2.2 / 14.6 / 100.0
3. Services / -6.3 / -38.3 / -17.9 / -62.4 / -9.1 / -41.4 / -2.3 / -14.8 / -130.0
Total / 0.0 / 0.0 / 0.0 / 0.0 / 0.0 / 0.0 / 0.0 / 0.0 / 0.0

Table 19:Matrix of taxes less subsidies on products

Product\Industry / Agr / Ind / Serv / II-Use / X / HFCE / GFCE / GCF / Uses
1. Agriculture / 12.7 / 14.3 / 4.1 / 31.1 / 1.8 / 70.8 / 0.5 / 0.9 / 105.0
2. Industry / 7.9 / 100.8 / 49.2 / 157.9 / 25.2 / 62.5 / 6.4 / 43.0 / 295.0
3. Services / 12.4 / 62.1 / 69.5 / 144.0 / 14.0 / 125.9 / 41.7 / 54.3 / 380.0
Total / 32.9 / 177.2 / 122.8 / 333.0 / 41.1 / 259.2 / 48.6 / 98.2 / 780.0
  1. The matrices for TTMs and taxes less subsidies on products for the SUTs shown in the previous tables are presented above. In practice, it is preferable to prepare these matrices at as detailed level of individual vectors of trade, different modes of transport, different product taxes and subsidies, as the source data permits.
  1. The resultant use table at basic prices as use table at purchasers’ prices minus use table of TTMs minus use table of taxes less subsidies on products, is presented below.

Table 20: Use table at basic prices

(Table 17-Table 18-Table 19)

Product\Industry / Agr / Ind / Serv / II-Use / X / HFCE / GFCE / GCF / Uses
1. Agriculture / 384 / 432 / 125 / 940 / 55 / 2138 / 14 / 26 / 3173
2. Industry / 149 / 1915 / 934 / 2999 / 479 / 1187 / 121 / 816 / 5603
3. Services / 236 / 1193 / 1310 / 2739 / 270 / 2382 / 778 / 1024 / 7193
4. IC at BP / 769 / 3540 / 2369 / 6678 / 804 / 5707 / 913 / 1867 / 15969
5. TLS-products / 33 / 177 / 123 / 333 / 41 / 259 / 49 / 98 / 780
6. Total IC at PP / 802 / 3717 / 2492 / 7011 / 845 / 5966 / 962 / 1965 / 16749
7. GVA at BP / 2443 / 1446 / 4102 / 7991
7.1 COE / 1000 / 700 / 2000 / 3700
7.2 Other TLS / 0
7.3 CFC / 240 / 140 / 410 / 790
7.4 OS/MI / 1203 / 606 / 1692 / 3501
8. Output BP / 3245 / 5163 / 6594 / 15002
Segregating domestic output and imports in the SUTs at basic prices
  1. The balanced SUTs at basic prices are required for the transformation into symmetric I-O table at basic prices. However for economic analysis, the use table could be separated into a use table of domestic output and a use table of imports. The main reason for this separation is to assess the economic impacts on the domestic industries in the economic analysis. The next task, therefore, is to separate the use table at basic prices into

(i)Use table for domestic output at basic prices; and

(ii)Use table of imports at basic prices.

Table 21: Use table of imports

Product\Industry / Agr / Ind / Serv / II-Use / X / HFCE / GFCE / GCF / Uses
1. Agriculture / 14.9 / 16.7 / 4.8 / 36 / 2.1 / 82.9 / 0.6 / 1.0 / 123
2. Industry / 20.0 / 256.3 / 125.0 / 401 / 64.1 / 158.9 / 16.3 / 109.3 / 750
3. Services / 3.1 / 15.6 / 17.1 / 36 / 3.5 / 31.1 / 10.2 / 13.4 / 94
Imports / 38 / 289 / 147 / 474 / 70 / 273 / 27 / 124 / 967

Table 22: Use table of domestic output at basic prices

(Table 20 minus Table 21)

Product\Industry / Agr / Ind / Serv / II-Use / X / HFCE / GFCE / GCF / Uses
1. Agriculture / 369 / 415 / 120 / 904 / 53 / 2055 / 14 / 25 / 3050
2. Industry / 129 / 1659 / 809 / 2597 / 415 / 1028 / 105 / 707 / 4853
3. Services / 233 / 1178 / 1293 / 2704 / 267 / 2350 / 767 / 1011 / 7099
4. IC at BP / 731 / 3251 / 2222 / 6204 / 734 / 5434 / 886 / 1743 / 15002
5.1 TLS-prod / 33 / 177 / 123 / 333 / 41 / 259 / 49 / 98 / 780
5.2 Imports / 38 / 289 / 147 / 474 / 70 / 273 / 27 / 124 / 967
6. Total IC at PP / 802 / 3717 / 2492 / 7011 / 845 / 5966 / 962 / 1965 / 16749
7. GVA at BP / 2443 / 1446 / 4102 / 7991
7.1 COE / 1000 / 700 / 2000 / 3700
7.2 Other TLS / 0 / 0 / 0 / 0
7.3 CFC / 240 / 140 / 410 / 790
7.4 OS/MI / 1203 / 606 / 1692 / 3501
8. output BP / 3245 / 5163 / 6594 / 15002
  1. In the SUTs, imports are shown by products in the supply table, while not distinguishing between uses in the use table. The import values are included in the basic price cell values together with values from domestic sources. A vector for imports of goods and services is available in the supply table at basic prices. For the compilation of a use table of imports at basic prices, this import vector from supply table is used while assuming at the same time that the output structure for products in the use table at basic prices is also valid for the import matrix. In other words, it is assumed that industries and final users in the economy have no specific preference towards domestic and imported products. An alternative version of this table can be presented by showing imports as a vector instead of a separate row. In this case, the cell values of uses of products will include imports as well.

Table 23: Use table of domestic output at basic prices

Product\Industry / Agr / Ind / Serv / II-Use / X / HFCE / GFCE / GCF / -M / FD / Output -BP
1. Agriculture / 384 / 432 / 125 / 940 / 55 / 2138 / 14 / 26 / 123 / 2110 / 3050
2. Industry / 149 / 1915 / 934 / 2999 / 479 / 1187 / 121 / 816 / 750 / 1854 / 4853
3. Services / 236 / 1193 / 1310 / 2739 / 270 / 2382 / 778 / 1024 / 94 / 4360 / 7099
4. IC at BP / 769 / 3540 / 2369 / 6678 / 804 / 5707 / 913 / 1867 / 967 / 8324 / 15002
5. TLS-prod / 33 / 177 / 123 / 333 / 41 / 259 / 49 / 98 / 447 / 780
6. Total IC at PP / 802 / 3717 / 2492 / 7011 / 845 / 5966 / 962 / 1965 / 967 / 8771 / 15782
7. GVA at BP / 2443 / 1446 / 4102 / 7991
7.1 COE / 1000 / 700 / 2000 / 3700
7.2 Other TLS / 0 / 0 / 0 / 0
7.3 CFC / 240 / 140 / 410 / 790
7.4 OS/MI / 1203 / 606 / 1692 / 3501
8. Output BP / 3245 / 5163 / 6594 / 15002

(iii) Transformation of SUTs at basic prices to symmetric I-O tables

  1. The transformation process involves converting square SUTs at basic prices to symmetric I-O tables. The symmetric I-O table is a square table that has either products or industries in both its rows and columns. It is compiled by merging the fully balanced supply and use (flow) tables by application of technology assumptions and transformation models.
  1. Four basic models are commonly used for the transformation of SUTs to symmetric I-O tables. They include two models which are based on technology assumptions which will generate product-by-product I-O tables. In this case, the I-O tables are comprised of homogeneous products in the rows and homogeneous units of production (branches) in the columns. The other two basic models are based on assumptions of fixed sales structures and generate industry-by-industry I-O tables. The results are I-O tables with products provided by industries in the rows and industries in the columns.
  1. The reason that manipulation of SUTs is needed to produce an I-O table is the existence of secondary products. There are three types of secondary production:

(a)Subsidiary products: those that are technologically unrelated to the primary product;

(b)By-products: products that are produced simultaneously with another product but which can be regarded as secondary to that product;

(c)Joint products: products that are produced simultaneously with another product that cannot be said to be secondary (for example beef and hides).

  1. If there were the same number of industries as products, and if each industry only produced one product[5], the supply table for the domestic economy would be unnecessary; the column totals for industries would be numerically equal to the row totals for products and the inter-industry matrix would be square as originally compiled.

Product by product tables

  1. In a product × product table both rows and columns represent the product group sectors. If the secondary products of an industry group along-with the inputs are transferred to the industry group where they are the principal products, the resulting table is a product by product I-O table. There are two ways in which a product by product matrix can be derived. These are:

(a)The industry technology assumption where each industry has its own specific means of production irrespective of its product mix.

(b)The product technology assumption where each product is produced in its own specific way irrespective of the industry where it is produced.

  1. Under the industry technology assumption, the coefficients showing how manufactured products are produced are assumed to depend on the industry they happen to be produced in. It is assumed that the input structure of all products (both principal and secondary) put out by a particular activity is the same, so the input structure associated with a particular product may differ depending on which activity produces it. The industry-technology assumption is always applied in conjunction with the "market share hypothesis". It states that industries have fixed shares in the supply of products. This combination of assumptions implies that the use of product i in the production of product j is a weighted average of the use of product i by the various industries, the weights being the shares of the industries in total supply of product j.
  1. Under the product technology assumption, the coefficients showing how manufactured products are produced are those of the manufacturing industry regardless of where they are actually produced. It is assumed that there are specific input structures for particular products, i.e. the input structure of a particular product is assumed to be the same regardless of where (in which activity) it is produced.Usually product technology assumption is followed for subsidiary products and industry technology assumption is appropriate for joint products and by-products.

Industry by industry tables

  1. In an industry × industry table, on the other hand, both rows and columns represent industry group sectors comprising of a mix of different product groups. The row of a sector in this table gives the supply of all products and secondary product (as a mix) produced by the corresponding industry group for different intermediate and final uses. Just as in the case of above matrix, there are two ways in which an industry by industry matrix can be derived. These are:

(a)The fixed product sales structure where it is assumed the allocation of demand to users depends on the product and not the industry from where it is sold.

(b)The fixed industry sales structure where it is assumed that users always demand the same mix of products from an industry.

  1. Thus, the four basic transformation models are based on the following assumptions:

1)Product technology assumption (Model A)

  • Each product is produced in its own specific way, irrespective of the industry where it is produced.

2)Industry technology assumption (Model B)

  • Each industry has its own specific way of production, irrespective of its product mix.

3)Fixed industry sales structure assumption (Model C)