Appendix 7 The Input-Output Tables

Sanjiv Mahajan and Graeme Chamberlin

A7.1 Introduction

The development of Input-Output Tables (IOTs) and their use in economics was pioneered in the 1920s by Wassily Leontief (1905–1999), an American economist of Russian descent. IOTs are closely related to (in fact derived from) the Supply and Use Tables (SUTs), so this appendix follows on from the contents of Chapter 4 which introduced the SUT framework and its many applications. The theory behind the use and applications of IOTs requires some use of matrix algebra, so the content of this appendix is more technical than Chapter 4.

The SUTs show the extent to which industries are interdependent, that is, how they rely on inputs from each other to produce output that satisfies final users and uses. They are an essential tool in forming balanced estimates of GDP and provide a rich source of detailed information to analyse changes in the structure of the economy and specific industries and sectors.

The focus of IOTs is primarily on how changes in final use might feed through the economy, given that this will also lead to an increase in use for the inputs that are needed to produce the outputs that satisfy that change in final use. A wide variety of analyses can be done using input-output (I-O) related approaches, for example:

  • What happens if the output of one or more industries changes?
  • What happens if the output of one or more products changes?
  • What happens if households or governments change their spending on one or more final use categories?
  • What happens if exports of one or more products change?
  • What happens if the cost structure of one or more industries changes?
  • What happens if a particular investment expenditure is made?
impact analysis
A systematic approach to determine and evaluate the potential consequences of disruptions and policy changes on the economy.

In fact, a very wide range of analyses are possible, for example, changes in VAT, constructing a new shopping centre or introducing the minimum wage. These types of analyses are commonly known as “impact” analyses or “what if” analyses, and have typically been the main application of IOTs through the years as an important tool for policymakers in economic modelling and planning. It was in Leontief’s native Soviet Union that extensive use of his tables was made where the Soviet planning ministry Gosplan used IOTs to set production targets for capital and consumption goods.

IOTs continue to be used by governments around the world to analyse the effects of fiscal policy on the economy, although their use had become less pervasive due to longstanding criticisms of the approach and the rise of other approaches such as computable general equilibrium (CGE) modelling. In the last decade, input-output analysis and modelling has enjoyed a renaissance. Their scope has been extended to analyse environmental impacts and the changing nature of international trade through global value chains (GVCs) which have become increasingly important areas of interest to economists and policymakers.

In this appendix we will:

  • Set out the key structure of the IOTs and how they are related to the SUT framework in Chapter 4.
  • Introduce the Leontief inverse and show how IOTs can be used in policy and other forms of impact analyses.
  • Show the exciting and relatively new applications of the IOTs on measuring the trade in value added (TiVA) and estimating environmental impacts.

A7.2 The structure of the Input-Output Tables and their relationship to the Supply-Use Tables framework

A7.2.1 The structures of the SUTs framework and IOTs

Figure 4.3 The structure of the Supply and Use Tables

The basic structure of the Supply and Use Tables framework is shown in Figure 4.3 in Chapter 4 which shows the flow of products through the economy, and importantly a map from the supply of each product to its intermediate and final uses.

The basic structure of the IOTs is shown in Figure A7.1. This looks very similar to the SUTs framework – the two sets of tables consist of the same elements, but several transformations have been made. The purpose of these transformations is essentially to reorganise the SUTs framework so that it is easier to track the impact of changes in final demands on the inputs required to satisfy those changes. This means the IOTs are more readily set up to perform the types of impact analyses set out in the introduction.

Figure A7.1 Transforming the SUTs (Figure 4.3) into IOTs (product-by-product)

Transforming the SUTs (Figure 4.3) into IOTs (product-by-product)

The key difference between Figure A7.1 and Figure 4.3 is how products and industries have been designated to the respective rows and columns of the tables. In the SUTs framework shown in Figure 4.3, you will notice that products are in the rows and industries in the columns (product-by-industry). The IOTs require the transformation of the tables to either a product-by-product or an industry-by-industry structure. The choice between the two usually depends on the type of “what if” question being asked.

The Office for National Statistics (ONS) typically focuses on products, as demand is by nature product-driven rather than industry-driven (a household demands a motor vehicle rather than the output of the motor vehicle industry). So, a product-by-product setup might be preferable if you want to track the impact of demand changes on the economy. The product-by-product IOTs describe how products (and primary inputs such as labour) are used to produce further products and to satisfy changes in final use. The structure of these IOTs is shown in Figure A7.1.

An industry-by-industry approach might be interesting if you want to see how industries are linked through supply chains, and how a specific shock to one of them may feed through to the rest of the economy. Later, we will look at inter-country Input-Output (ICIO) Tables and the Trade in Value-Added (TiVA) to see how the industries of one country are embedded in global value chains (GVCs) and analyse the impact of global demand changes on domestic output and GVA.

A7.2.2 Transforming SUTs into IOTs

To explain how the SUTs framework can be transformed into a form of IOTs, first consider the following definitions of the domestic Supply and Use Tables at basic prices as shown in Figure 4.3.

  • The domestic supply table (product-by-industry) shows the outputs of each industry.
  • The domestic use table (product-by-industry) shows the inputs to the production process of each industry and each component of final use.

The IOTs in Figure A7.1 are constructed by transforming the industry groups to product groups, so that these definitions become:

  • The transformed domestic supply table (product-by-product) at basic prices shows the outputs of the production process of each industry product group.
  • The transformed domestic use table (product-by-product) at basic prices shows the inputs of the production process of each product and each component of final use.

To derive the IOTs, first stage:

  1. Transform the SUTs from purchasers’ prices to basic prices.
  2. Remove imports of goods and services from the body of the intermediate use and final use parts of the Use Table. Imports of goods and services and taxes less subsidies on products are moved from the Supply Table in Figure 4.3 and removed from the body of the Use Table to be shown as separate rows in the primary inputs under the IOTs in Figure A7.1.
  3. Remove distributors’ trading margins from the Supply Table. They are reallocated to the relevant trade products in the Use Table in the IOTs.

Second stage:

  1. Transform the domestic output part of the remaining Supply Table by moving off-diagonal entries onto the industry of which they are the principal product. For example, the output of retail distribution services produced as a secondary output of the agriculture industry would be shifted to the retail distribution column. The total supply of each product therefore remains unaltered, but each element of off-diagonal supply has been moved to the diagonal element of the same row to which it relates.
  2. For each element of supply that was moved, its corresponding inputs (including the primary inputs) need to be moved in the intermediate use table. When we move the off-diagonal elements, we also have to move the industry structure to produce that product with them. When the farm shop is moved from agriculture to retail, the respective inputs also need to be shifted to form the IOTs.
  3. For each industry, we need to separate out the inputs for the various product groups produced by that industry. It would be impractical for producers to provide such splits, and this is therefore estimated by making a technology assumption on a case-by-case basis.

The technology assumptions are:

  • Product technology. This assumes that all products classified to a product group have the same input structure, regardless of the classification of the producer. So, this implies that the agriculture industry produces retail services output in the same way as the retail industry does, so we identify and move the inputs this way.
  • Industry technology. This assumes that all products produced by an industry have the same input structure, regardless of the classification of the product. This technology assumption implies that the agriculture industry produces retail services output using the same inputs as it does for agriculture products. This then identifies which inputs need to be moved in the Input-Output Table.

The ONS has used a hybrid technology assumption to reflect that some industries produce secondary output that is neither the input structure of the industry itself nor the principal producing industry.

A7.2.3 The basic structure of the IOTs in algebra

Reading across the top part of the IOTs in Figure A7.1 describes how the total supply or output for each product is equal to the sum of its intermediate and final demands. If there are a total of j products 1, 2, … j then, the total output of product 1 is given by:

\[q_{1} = q_{11} + q_{12} + \dots + q_{1j} + f_{1}\]

Where q1 is the total supply of product 1, q11 is the intermediate consumption of product 1 in the production of product 1, q12 is the intermediate consumption of product 1 in the production of product 2, and so on until we get to q1j which is the intermediate consumption of product 1 in the production of product j. Finally, f1 is the total final use for product 1. Therefore, for this product supply equals the sum of its intermediate and final uses.

A useful transformation which will help us to understand how the IOTs work is to divide each column in the intermediate demand and primary inputs tables by the total output of that industry. Therefore, we can define:

\[\begin{align} a_{11} = q_{11}/q_{1}, \\ a_{12} = q_{12}/q_{2}, \end{align}\]

and so on until,

\[a_{1j} = q_{1j}/q_{1j}\]

The coefficient a11 equals the intermediate consumption of product 1 in the production of product 1 (q11) divided by the total output of product 1 (q1). Another way of thinking about this coefficient is that it tells us, in money terms, the amount of product 1 required as an input to produce one unit of product 1. By the same approach, a12 tells us how much of product 2 is required to produce a unit of product 1, and so on to a1j which is the required input of the jth product to produce a unit of product 1.

We can also see that:

\[\begin{align} q_{11} &= a_{11} q_{1}, \\ q_{12} &= a_{12} q_{2}, \text{and so on until}, \\ q_{1j} &= a_{1j} q_{j} \end{align}\]

That is, the total intermediate consumption of product 1 in the production of product 1 is equal to the coefficient a11 multiplied by the total output of product 1. Using these, we can re-express the SUTs balance for product 1 as:

\[q_{1} = a_{11} q_{1} + a_{12} q_{2} + … + a_{1j} q_{j} + f_{1}\]

That is, the total supply of product 1 (q1) equals:

  • the amount of product 1 used as intermediate input into the production of product 1 (a11 q1), plus
  • the amount of product 2 used as intermediate input into the production of product 1 (a12 q2),
  • and so on for all j products; and
  • the final use for product 1 (f1).

Using this notation, we can define the total supply-use balance for all products as:

\[\text{Total output} (\pmb{q}) = \text{Intermediate demand }(\pmb{A}.\pmb{q}) + \text{Final demand }(\pmb{f})\]


\[\pmb{q} = \begin{bmatrix} q_{1} \\ \vdots \\ q_{j} \end{bmatrix}, \space \pmb{A} = \begin{bmatrix} a_{11} & \ldots & a_{1j} \\ \vdots & \ddots & \vdots \\ a_{j1} & \ldots & a_{jj} \end{bmatrix} \text{, and } \pmb{f} = \begin{bmatrix} f_{1} \\ \vdots \\ f_{j} \end{bmatrix}\]

q is a vector of the output of each of the j products

A is known as the transition matrix. This shows the amount of input of each product required to produce one unit of output of each product. These are known as the technical coefficients and can be thought of as basically the recipe for making each product.

Changes in the technical coefficients over time are useful information in themselves as they indicate changes in the structure of the economy. For example, they may change to reflect developments in technology and import substitution.

Finally, f is the vector of final demands for each of the j products.

To solve for the level of output of each product necessary to satisfy a given set of final demands, we can use a little bit of matrix algebra:

\[\pmb{q} = \pmb{[I−A]^{−1}} × \pmb{f}\]

Where I is the identity matrix

\[\pmb{I} = \begin{bmatrix} 1 & \ldots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \ldots & 1 \end{bmatrix}\]

and \(\pmb{[I−A]^{−1}}\) is the inverse of the matrix \(\pmb{[I−A]}\).

Gosplan, an abbreviation for a phrase that translates into English as “State Planning Committee”, was the central board that supervised various aspects of the planned economy of the Soviet Union in the 20th century, by translating the general economic objectives outlined by the Communist Party and the government into specific national plans. Read more about it in this article on Gosplan.

This shows how the IOTs can be used as an economic planning tool. All that is required is a set of technical coefficients telling us how to combine inputs to make each product, and then the level of output required to satisfy a given amount of final demand for each product can be calculated. This is the basic theory that underlay the Gosplan approach to economic planning in the Soviet Union for many decades.

A7.3 Multipliers and impact analysis

A7.3.1 The Leontief inverse and multipliers

Leontief inverse
The columns of the Leontief Inverse matrix show the output multipliers that measure the successive effects on the economy as a result of the initial increase in production of a particular product. This initial increase in production could be to satisfy an increase in final use for the product.

The matrix \(\pmb{[I−A]^{−1}}\) is known as the Leontief Inverse and provides a set of multipliers informing us of how changes in final use for a particular product or products (Δf) result in total changes in the output of each of the j products (Δq).

\[\Delta\pmb{q} = \pmb{[I−A]^{−1}} \times \Delta\pmb{f}\]

This demonstrates that the change in output required to satisfy the change in final use is a multiple of that change in final use. That is, normally, to produce an additional unit of final use (in money terms) for a given product will require a greater increase in the total value of output of that and other products.

The explanation for the multiplier effect of final use changes on the economy is because the impact on output changes consists of both direct and indirect effects:

  • Direct: This is the immediate effect caused directly by the change in final use. If there is an increase in final use for the output of a particular industry, there will be an increase in the output of that industry, as producers react to meet the increased use.
  • Indirect: This is the subsequent effect caused by the changes in intermediate use. As these producers increase their output, there will also be an increase in use on their suppliers, and so on down the supply chain.

The combination of these direct and indirect effects is known as a Type I multiplier. It recognises that to produce more output to satisfy final use requires an increase in inputs, but each of these inputs has their own supply chain requiring an increase in the inputs to the inputs, and so on.

It is also possible to consider further effects on the economy:

  • Induced: This is the effect attributable to the ensuing change in compensation of employees and other incomes, which may cause further spending and further changes in final use.

The ONS currently does not publish Type II multipliers for the UK, but the Scottish Government does present this analysis in the Scottish Supply, Use and Input-Output Tables

Type II multipliers also cover induced effects, as well the direct and indirect effects in the Type I multiplier.

How it’s done Understanding the multiplier

To interpret the Leontief Inverse matrix, it is useful to further consider its derivation in terms of the matrix of coefficients A.

So far, we have determined that the change in the output of products following a change in final demands is determined by the Leontief Inverse \(\pmb{[I−A]^{−1}}\), such that

\[\Delta\pmb{q} = \pmb{[I−A]^{−1}} × \Delta\pmb{f}\]

However, it is useful to think of the Leontief Inverse matrix using the following expansion:

\[\pmb{[I−A]^{−1}} = \pmb{1 + A + A^2 + A^3 + A^4 + …}\]

therefore, the change in output following a change in final use is given by:

\[\Delta\pmb{q} = \Delta\pmb{f} + \pmb{A}\Delta\pmb{f} + \pmb{A}^{2}\Delta\pmb{f} + \pmb{A}^{3}\Delta\pmb{f} + \pmb{A}^{4}\Delta\pmb{f} + …\]

This now has a fairly simple interpretation explaining the total change in output (Δq) in terms of direct and indirect effects.

  • The first term in this decomposition is simply the change in final use (Δf), the direct effect.
  • Next, the second term gives the change in intermediate use directly generated from the change in final use (AΔf), reflecting the extra inputs required to satisfy the higher final use.
  • This increase in intermediate use generates further intermediate use represented by the third term (A2Δf). These are the extra inputs into the inputs necessary to satisfy the change in final use.
  • This in turn generates an even further change in intermediate use represented by the fourth term (A3Δf), the inputs into the inputs into the inputs, and so on.

In other words, to produce a change in final use also requires changes in the consumption of intermediate products, the sum of which is the indirect effect. The change in final use generates a multiple increase in the output reflecting the sum of both these direct and indirect effects.

ONS Resource

The latest edition of the UK IOTs (referred to as input-output analytical tables) published by the ONS is for 2018. A full set of data tables for this and preceding years can be found at UK input-output analytical tables – product-by-product.

Two useful articles explaining the derivation of the IOTs and Type I multipliers are:

Howse J (2017), ‘Input-output analytical tables: methods and application to UK National Accounts’

Wild R (2014), ‘United Kingdom Analytical Tables 2010’

A7.3.2 Example: Evaluating the impact of a new programme of house building on the UK economy

We can now give a demonstration of how the IOTs can be used to estimate the impact on the UK economy of a change in final use. This makes use of the IOTs published by the Office for National Statistics, which make available the matrix of coefficients A and the Leontief Inverse \(\pmb{[I−A]^{−1}}\), both derived from the SUTs using the methods described previously in this appendix.

Suppose the government announces a £10 billion programme of house building in the UK. To evaluate the impact on the economy, we assume this increases the final use for construction products (CPA45) by this amount.

Using the latest IOTs for the UK, the output effect on each product can be found from the column of the Leontief Inverse matrix \(\pmb{[I−A]^{−1}}\) relating to the production of construction products. The total effect on UK output, in turn, is simply the sum of that column – which is summarised in Figure A7.2.

Output Effect
Construction products 1.472
Materials and machinery products 0.255
Services products 0.342
Total 2.069

Figure A7.2 The output effect (£) following a £1 change in the final demand for construction, UK, 2018

The output effect (£) following a £1 change in the final demand for construction, UK, 2018

Adding up the respective terms to produce construction products in the Leontief Inverse matrix gives a total value of 2.069. A £10 billion programme would therefore increase output by £20.69 billion. The direct effect on output of the £10 billion increase in demand for construction products would be further increased by an additional £10.69 billion in additional intermediate use of products. These are the indirect effects.

Figure A7.2 shows this increase in intermediate use consists of:

  • £4.72 billion in extra construction products in addition to the £10 billion increase in final use.
  • £2.55 billion in materials and machinery products including wood products, mining and quarrying products, cement lime and plaster products, iron and steel products, fabricated metals products and machinery and equipment.
  • £3.42 billion in services products, including wholesale, land transport, financial services, and rental and leasing services.

The transformed IOTs can also be used to allocate the multiplier change in output into its respective components – these are the column entries beneath the I-O matrix in Figure 4.3 and are shown in Figure A7.3.

Effect Multiplier
Intermediate consumption at basic prices 1.069
Use of imported products 0.125
Taxes less subsidies on products 0.037
Compensation of employees 0.416
Gross operating surplus 0.410
Taxes less subsidies on production 0.011
Gross value-added* 0.838
Output 2.069

Figure A7.3 IOTs – multiplier effects of a unit change of final use on construction products, UK, 2018

IOTs – multiplier effects of a unit change of final use on construction products, UK, 2018

*GVA can be calculated in the above table as follows: (1) GVA = Output – Intermediate consumption at purchaser’s prices or (2) GVA = Compensation of employees + Gross operating surplus + Taxes less subsidies on production.

Whereas the £10 billion increase in final use generated an increase of £20.69 billion in output, the increase in GVA was smaller at £8.38 billion. The reason for this is, because of the total increase in output, there were increases in intermediate consumption of £10.69 billion, imported products of £1.25 billion and taxes less subsidies on products of £370 million. Imports and taxes are leakages from the circular flow of income, and account for why the increase in UK GVA is smaller than the increase in final use.

The increase in GVA of £8.38 billion can also be allocated to an increase of £4.16 billion on the compensation of employees, £4.10 billion on gross operating surplus and £110 million in taxes less subsidies on production.

This simple example shows how I-O modelling can be used to estimate the effects of a change in final use for a certain product on the total output of the economy and its components. The type of exercise policymakers would undertake would be more detailed, for example, it is unlikely that a spending increase of £10 billion would hit the economy in a single year, and it is unlikely to be solely directed at one form of product. Also, the impact would be expected to last for more than one year.

Although I-O modelling approaches can yield satisfactory results for certain problems, they are now seldom used in policy analysis. This reflects several long-standing criticisms of this modelling approach, and the emergence of other more sophisticated and flexible modelling techniques that can address these shortcomings.

A7.3.3 Criticisms of input-output modelling approaches

Although the use of multipliers generated from the IOTs can provide a detailed assessment of the economic impacts of changes in demand, there are several long-standing criticisms of the approach.

  1. I-O analysis is based on a fixed “snapshot” model of the economy for a given year. The technical coefficients that govern the approach are assumed to be fixed, but these can change significantly in response to developments in technology and globalisation.
  2. The IOTs use a prescriptive type of production function. In essence there is “only one recipe by which to produce a product”, as set out by the technical coefficients. The production process is linear, so output is proportional to inputs, ruling out the possibility of economies of scale or diseconomies of scale in production.
  3. They assume spare capacity in the economy to supply any change in demand. In practice, capacity constraints can emerge for any intermediate product and other primary inputs such as labour and imports.
  4. It is assumed that prices are fixed and do not change, even in response to significant demand and supply shocks. Neither can production processes respond to price changes by allowing for substitution among inputs.
computable general equilibrium (CGE) models
CGE models combine economic theory with real data to simulate the effects of policy changes. They are more flexible than I-O modelling, especially in terms of supply-side responses, but rely on I-O based data to map the linkages in the economy between sectors and institutions and to provide a baseline to which simulated changes can be compared.

For these and other reasons, I-O modelling has been surpassed in various policy analysis circles by computable general equilibrium (CGE) models. A CGE model is a large-scale numerical model that uses data on the structure of the economy along with a set of equations based on economic theory to simulate policy and other changes. However, with the impact of COVID-19, various natural disasters, COP26, globalisation, digitalisation, etc., various techniques, models and datasets based upon SUTs and IOTs have been developed and more closely linked to policy needs.

In the UK, HM Revenue and Customs (HMRC) currently uses a CGE model with a detailed representation of the UK tax system. It is used to generate estimates of tax revenues and the economic impacts of tax changes that feed into the official fiscal forecasts published by the Office for Budget Responsibility. One notable example was the analysis on the effects of the planned reduction in corporation tax from 28% in 2010 to 20% in 2015.1

Although CGE models have been used since the early 1970s to analyse the economic effects of changes in taxation, trade, and environmental policies, they themselves have limitations and implicit assumptions. Governments and institutions such as the World Bank, Organisation for Economic Cooperation and Development (OECD), World Trade Organisation and the International Monetary Fund all use CGE models in the policy development process, but have also developed new products and approaches based on the I-O framework such as Trade in Value Added (TiVA) analyses.

CGE models can address some of the problems outlined above. However, despite being favoured by policymakers, CGE models are still strongly dependent on data from IOTs, especially in determining the inter-sectoral and inter-institutional linkages in the models. IOTs data also provide a snapshot of the economy in a single year, which is used as a baseline to compare policy simulations against.

A7.4 New applications of SUTs and IOTs

A7.4.1 Trade in value added (TiVA)

The SUTs and IOTs form useful tools to analyse:

  • The flow of products through the economy and the responses to changes in final use.
  • The interconnectedness between industries and how shocks can feed through supply chains.

The use of IOTs can be extended across economies. This allows us to consider:

  • How could domestic output and GVA respond to changes in foreign final uses and intermediate uses?
  • How do domestic industries fit into GVCs, and how could we think about industries from an international perspective?
inter-country Input-Output (ICIO) Tables
ICIO tables link together individual countries’ IOTs, thus capturing supply chains between trading partners as well as the international effects of shocks and changes to supply and demand in one or more countries.

To do this we will need inter-country Input-Output (ICIO) Tables.

Linking the SUTs and IOTs of many countries reflects the changing nature of production and international trade in recent decades. The goods and services we buy are composed of many inputs from around the world. Conventional measures of international trade tend not to reflect the flows of goods and services within these global production chains, but the exports of final goods and services to consumers abroad. According to the OECD, this type of trade only represents around 30% of all trade in goods and services in today’s global economy.

The remaining 70%, accounting for the majority of international trade, involves the flow of services, raw materials, parts, and components across borders in global value chains, from which final products are shipped to customers all over the world. Trading relationships are now far more complicated, involving a large number of interactions among a variety of domestic and foreign suppliers. For example, a computer assembled in Taiwan might include chips designed in the United States, software written in Germany, ergonomic design from the UK, and a battery using lithium mined from Australia, among many other inputs. Throughout the entire production process, each country retains some of the value added in the complete supply chain. However, international trade statistics attribute the full value to the last country in the chain.

trade in value added (TiVA)
The goods and services we buy are composed of inputs from various countries around the world. However, the flows of goods and services within these global production chains are not always reflected in conventional measures of international trade.

As a result, there is a new focus on exploring the trade in value added (TiVA), which considers each country’s value added contributions to the production of goods and services that are consumed worldwide. The OECD has led recent efforts to measure TiVA through the construction of inter-country Input-Output Tables. For example, a motor vehicle exported by country A may require significant parts, such as engines, seats, etc., produced in other countries. In turn, these countries will use intermediate inputs imported from other countries, such as steel, rubber, etc., to produce the parts exported to A. The TiVA approach traces the value added by each industry and country in the production chain and allocates the value added to these source industries and countries.

The TiVA approach reveals the underlying economic significance of exports and of imports for producing exports. Traditional measures of trade record gross flows of goods and services each time they cross a border. This “multiple counting” of trade might overstate the importance of exports to GDP. Moreover, because, in an accounting sense, imports are treated as a negative item for GDP, gross statistics for imports can paint a misleading picture of their importance to economic growth and competitiveness. They do not, for example, reveal the role played by imports as inputs for exports. Equally, they are not able to reveal the extent of a country’s own value added that is returned in its imports.

Other benefits include:

  • It provides a better reflection of who trades with whom, and the nature of inter-relationships between emerging and developed economies.
  • It provides a different measure of bilateral trade balance and the contribution made by services.

It is also important to note that a range of assumptions have had to be applied to generate these analyses.

The OECD’s considerable work on the construction of inter-country Input-Output (ICIO) Tables and the analysis of the trade in value added can be found in the OECD’s ‘Trade in value added’.

Much of the data that feeds into the OECD publications has been taken from Eurostat’s FIGARO programme (Full International and Global Accounts for Research in Input-Output analysis). This is also known as EU Inter-Country Supply, Use and Input-Output tables (EU IC-SUIOTs), and provides ICIO tables for the countries of the European Union, US, UK, and other major trading partners of the EU. This programme’s data and analysis can be found at ‘ESA supply, use and input-output tables: FIGARO

The most recently published TiVA tables (2021) cover the period 2005 to 2018, and provide linked IOTs for:

  • 66 economies including all the OECD, EU28 and G20 countries, most East and South-east Asian economies, and a selection of South American countries.
  • 45 unique industrial sectors, including aggregates for total manufactures and total services.

The basic structure of the ICIO for a given year is shown in Figure A7.4. The tables are set up to show industry-by-industry IOTs, but link each industry in each country not just to the others in that country, but to all the other industries in the rest of the world. For example, consider the first column of Figure A7.4 showing industry 1 in country 1. The total intermediate consumption consists of inputs not just from the K industries in country 1, but the same industries in all N countries.

Likewise, reading down the columns in the Final Demand table shows how the F final demand components in each country are satisfied by the industry outputs from each of the N countries.

These tables could, therefore, potentially be used to analyse the impact of final demand changes in one country on industry outputs throughout the world.

Figure A7.4 The structure of inter-country Input-Output (ICIO) Tables

The structure of inter-country Input-Output (ICIO) Tables

A7.4.2 UK industry involvement in GVCs

One of the applications of the data presented in the OECD’s TiVA database is to provide insights into a country’s participation in GVCs. This can be via:

  • The amount of foreign value added embodied in domestic exports (backward linkages).
  • The amount of domestic value added in partners’ exports and final demand (forward linkages).

Figure A7.5a shows the backward participation of the UK’s industries in GVCs. This has been measured through the proportion of the value of gross exports of each industry that is attributed to foreign value added. If this proportion had been 0%, it would imply that the industry output being exported was made using only inputs that came from the UK. If the proportion had been 100%, then it would imply that the industry was simply re-exporting output that was entirely produced overseas.

This shows that manufacturing has the strongest backward linkages to global value chains with 30.0% of the value of gross exports consisting of foreign value added in the supply chain. Government and other services have the lowest, with foreign value-added contributing 7.8% of the value of the industry’s gross exports.

Figure A7.5 Backward and forward participation in global value chains, 2018

Backward and forward participation in global value chains, 2018

Figure A7.5a Backward participation in global value chains: Foreign value added share of gross exports, by value added origin country, 2018

OECD TiVA database, 2021 edition. Available at Trade in Value Added - OECD

Figure A7.5b Forward participation in global value chains: Domestic value added in foreign exports as a share of gross exports, by foreign exporting country (p.p.), 2018

Figure A7.5b shows forward participation of UK industry in GVCs. In total, 23.7 per cent of UK gross exports in 2018 reflected value added that was subsequently embodied in the exports of foreign countries. If this proportion had been 0%, it would suggest that UK exports provided no value added to the exports of partner countries, and UK industries therefore had no forward participation in GVCs. Likewise, if this proportion had been 100%, then it would suggest that all UK exports represented value added in the exports of foreign countries, and therefore that it had complete participation in forward value chains. The chart shows the percentage point contribution of each UK industry to this 23.7% total. Manufacturing makes the largest industry contribution (13.6 percentage points) and government and other services the smallest (0.2 percentage points).

These results are common to OECD countries. GVCs are most developed for tangible manufactured goods, so increasingly the manufacturing industry in most countries is relatively highly linked to these chains, both backwards and forwards. Services industries, especially those consisting mainly of labour inputs and where a small proportion of output is exported such as government services, are correspondingly far less integrated in GVCs.

A7.4.3 UK trade in value added with other countries

The TiVA tables also show bilateral trade flows in value added between countries, which can be compared to gross trade flows. It may also give an indication as to how changes in output overseas will impact on GDP at home.

For example, Figure A7.6 shows the UK’s exports of value added embedded in foreign demand to several global regions, expressed as a proportion of that region’s GDP in basic prices. This gives a broad representation of how changes in foreign GDP impact on UK GDP via GVCs. For example, a $1 increase in EU GDP would result in an increase in UK GDP of $0.018. However, an increase in the GDP of East Asia by $1 would only result in an increase in UK GDP of $0.004. These differences are not unexpected, given the relative distance between the UK and these two parts of the world, the history of trading relationships, the relative degree of free trade, and the type of products making up trade.

Figure A7.6 UK exports of value added as a % of foreign country GDP at basic prices, 2018

UK exports of value added as a % of foreign country GDP at basic prices, 2018

A7.5 IOTs and the analysis of environmental impacts

The economy and the environment are strongly connected. Whereby the economy depends on the environment for raw materials as inputs to the economic processes, economic activities then generate outputs such as waste and emissions that affect the environment. Some of these negative impacts may then be offset through expenditures on abatement and conservation activities. The Environmental Accounts is where National Statistics Institutes look to bring these economic and environmental interactions into a single framework. These are usually reported as satellite accounts to the main national accounts and the UN System of Environmental-Economic Accounting (SEEA) sets out guidance on international best practices.

One of the main parts of SEEA is the creation of physical flow accounts that record flows of materials and energy through the economy, such as fuels, natural resources and chemicals, together with their emissions, be they air emissions, water pollution or waste, to which these flows give rise. In effect, these accounts are measuring the environmental footprint of economic activity.

ONS Resource

The ONS publishes several material flow accounts for the UK as part of the Environmental Accounts. The UK’s material footprint captures domestic and foreign extraction of materials needed to produce products used in the UK, and the latest statistical bulletin and data can be found at Material Footprint in the UK.

The methodology used to produce these estimates is based on linking UK IOTs to the rest of the world to track the flow of products, wherever they come from, that satisfies UK final uses. The paper Measuring Material Footprint in the UK: 2008 to 2016 sets out this approach.

A7.5.1 Assigning emissions responsibility to consumers

Imagine that the household sector spends £2 billion on fruit and vegetables per year. The fruit and vegetables industry generates 0.5 tonnes of greenhouse gases (GHG) to produce £1 million of output. The emissions intensity of production in terms of tonnes of GHG per £million of output (tGHG/£m) is therefore 0.5/1 = 0.5.

The emissions of GHG connected with the household consumption of fruit and vegetables is given by multiplying the emissions intensity of production by the size of final demand:

\[E = 0.5 × 2,000 = 1,000 \text{ tonnes}\]

What about the emissions created in the supply chain? Suppose that to produce fruit and vegetables, you need fertilisers, diesel to power machinery, and many other inputs. Producing these inputs would generate GHG emissions of their own. Then, each of these inputs would have their own supply chains, where further emissions are created, and so on. The GHG emissions along the complete supply chain are calculated in the same way, by using information on the emissions intensity of each unit of intermediate output such as fertiliser, and the total amount of each input required to produce a certain value of fruit and vegetables output.

Also, fruit and vegetables are simply one group of items that the household sector purchases. Similar calculations would need to be made for all the other products consumed by households.

Therefore, in general terms, allocating greenhouse gases to household demand requires the calculation of emissions connected to all the products consumed by the household, and along the entire supply chains of all these individual products. This is where the IOTs can really help us out.

Suppose the household consumes j products and the final demand for each of the products f1, …, fj is shown in the vector f.

The emissions intensity records the output of GHG required to produce each £ of output satisfying final demand, where e1, …, ej are the emissions intensity for product 1 to j respectively. These are shown as the diagonal elements in the matrix e.

Finally, the total emissions associated with the final demand for each product by the household is shown in the vector E, where E1 are the emissions associated with the consumption of product 1, and so on.

\[\pmb{f} = \begin{bmatrix} f_{1} \\ \vdots \\ f_{j} \end{bmatrix}, \space \pmb{e} = \begin{bmatrix} e_{1} & \ldots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \ldots & e_{j} \end{bmatrix}, \space \pmb{E} = \begin{bmatrix} E_{1} \\ \vdots \\ E_{j} \end{bmatrix}\]

Therefore, the total emissions associated with the final use for each product is simply given by:

\[\pmb{E} = \pmb{e} × \pmb{f}\]

Where, for example, E1 = E1 × f1 and Ej = E1 × fj.

The total emissions associated with household use can simply be found by adding up the elements of E, that is, E1 + … + Ej.

Remember though, this does not include the emissions associated with the supply chains required to satisfy the final uses.

To calculate this, we need to consider the emissions generated in producing the inputs required to make the output to satisfy final use.

These can be calculated by using the matrix of technical coefficients A described earlier, which tell us the inputs of each product required to produce each product.

\[\pmb{A} = \begin{bmatrix} a_{11} & \ldots & a_{1j} \\ \vdots & \ddots & \vdots \\ a_{j1} & \ldots & a_{jj} \end{bmatrix}\]

The emissions in the supply chain serving household final use are given by:

\[\pmb{E} = \pmb{e} × \pmb{A} × \pmb{f}\]

However, we can’t stop there. We also need to find the emissions further down the supply chain, the inputs into the inputs, which is given by:

\[\pmb{E} = \pmb{e} × \pmb{A^2} × \pmb{f}\]

Therefore, the total emissions all the way along supply chains serving household final use are given by:

\[\pmb{E} = \pmb{ef} + \pmb{eAf} + \pmb{eA^2f} + \pmb{eA^3f} + \pmb{eA^4f} + …\]

From the discussion on IOTs and the multipliers earlier in this chapter, we saw that:

\[\pmb{[I−A]^{−1} = 1 + A + A^2 + A^3 + A^4 + …}\]

Where \(\pmb{[I−A]^{−1}}\) is the Leontief Inverse matrix.

Therefore, to calculate the emissions associated with a vector of final demands for the household, we simply need to calculate:

\[\pmb{E} = \pmb{e} × \pmb{[I−A]^{−1}} × \pmb{f}\]

The Scottish Government publishes the impact of the expenditure plans set out in its budget on carbon emissions. See, for example, Scottish Budget 2021–2022: Carbon Assessment.

This has now become the standard approach to calculating the environmental impact associated with different elements of final use, whether these are greenhouse gas emissions, water usage or others, and whether they involve households, businesses or government. This further demonstrates the important role played by IOTs in calculating the impact along supply chains.

A7.5.2 Comparing production-based and consumption-based carbon emissions

Carbon dioxide is the largest by volume of greenhouse gases emissions, accounting for about 80% of the total. Policies designed to reduce these emissions often set emission reduction goals based on some previous level. For example, the Kyoto Protocol is based on 1990 levels for many countries. However, changes in emissions at the national level can occur for many reasons, including the relocation of production abroad, and/or by import substitution. This may have a negligible impact on global emissions but, if the imports use more GHG intensive production processes than the domestically produced goods that they displace, global emissions could well be higher even if that country reports a fall in their own GHG emissions.

In 2021, Greta Thunberg, the climate activist from Sweden, attracted media attention when she cited these principles to question the reported decline in the UK’s GHG emissions on the eve of the 2021 United Nations Climate Change Conference (COP26) in Glasgow.

Therefore, in establishing a particular country’s own carbon footprint, it is important to be aware of divergence between production-based and consumption-based emissions.

  • Production-based emissions are calculated directly from domestic production of goods and services.
  • Consumption-based emissions, however, calculate the emissions associated with satisfying final demands in a country, regardless of where the emissions occur.

The differences between production-based and consumption-based measures for countries are accounted for by the carbon dioxide emissions embodied in international trade. For a country where consumption-based emissions exceed production-based emissions, the country is a net importer of carbon emissions from the rest of the world. If production-based emissions exceed consumption-based emissions, then that country is a net exporter of carbon emissions to the rest of the world.

The OECD’s latest database can be found at ‘Carbon dioxide emissions embodied in international trade’.

Norihiko Yamano and Joaquim Guilhoto, two researchers from the OECD, estimate the carbon dioxide emissions embodied in final demand for the group of OECD countries.2 Their methodology follows that described above by combining the OECD inter-country input-output (ICIO) database with statistics on CO2 emissions from fuel combustion and other industry statistics. Emission intensities of production are calculated for each industry in each country. These intensities are then combined with the Leontief inverse of the ICIO system to calculate emission multipliers for final demand in each country.

A7.5.3 Carbon dioxide emissions embodied in the UK’s international trade

Between 2005 and 2015, carbon dioxide emissions across the group of OECD countries fell by 9% on production-based measures and by 11% on consumption-based measures. However, over the same period, global carbon dioxide emissions from fossil fuel consumption increased by 19%. Consumption-based carbon dioxide emissions on a per capita basis are 2.5 times higher in OECD countries than the global average.

Figure A7.7a shows how production-based and consumption-based measures of carbon emissions differ for the UK. Both measures show a downward trend, consistent with the general trend in other advanced countries, however the consumption-based measure consistently exceeds the production-based measure. This implies that the UK continues to be a net importer of CO2 emissions, meaning that the goods and services the UK imports have a higher carbon footprint than those exported. This is shown in Figure A7.7b, where the balance of trade in carbon emissions is equivalent to the difference between consumption and production-based measures.

Figure A7.7 UK carbon dioxide emissions, 1995 to 2018

UK carbon dioxide emissions, 1995 to 2018

Figure A7.7a UK carbon dioxide emissions (million tonnes), consumption-based (embodied in final use) and production-based measures for 1995 to 2018

Figure A7.7b UK carbon dioxide emissions (million tonnes) embodied in exports and imports, 1995 to 2018

A7.5.4 The UK’s net imports of carbon dioxide emissions by industry and country

Figure A7.7 shows the UK to be a consistent net importer of carbon dioxide emissions from the rest of the world. In Figure A7.8, this position is broken down, for the latest data available, in terms of (a) industry and (b) country/region.

Figure A7.8 UK’s balance of trade in carbon dioxide emissions by industry, and by country and region, 2018

UK’s balance of trade in carbon dioxide emissions by industry, and by country and region, 2018

Figure A7.8a UK’s balance of trade in carbon dioxide emissions by industry (million tonnes), 2018

Figure A7.8b UK’s balance of trade in carbon dioxide emissions by country and region, the top 10 deficits (million tonnes), 2018

Figure A7.8a shows that the UK is a significant net importer of carbon dioxide emissions associated with manufactured goods. Despite the relative size of services in both production and consumption, net carbon dioxide imports of 21.7 million tonnes in 2018 were small in comparison to net imports of 115.2 million tonnes from the combined manufacturing industries.

The Department for Environment, Food and Rural Affairs publishes estimates of the UK’s carbon footprint in a similar way to the OECD. Using a multi-region I-O model, the impact that UK consumption has on carbon dioxide emissions is estimated, considering the worldwide production of goods consumed in the UK. The analysis shows that as the structure of the UK economy continues to shift towards the service industries, more of the goods UK households consume are now produced abroad. The full report and data can be found at ‘UK and England’s carbon footprint to 2019’.

Overall, the UK runs a significant trade deficit in manufactured goods, with many of these having a relatively large carbon footprint in comparison to more labour-intensive services production. This is reflected in Figure A7.8b, where the countries/regions from which the UK is a larger net importer of carbon dioxide emissions are also those with which the trade in goods deficits are larger. China is an obvious example, and is the largest single exporter of carbon emissions to the UK, as it is to the world. The UK is also a large net importer of carbon dioxide emissions from the EU, another trade bloc where the deficit in the trade in goods is significant. These charts suggest that Greta Thunberg may have a point: the UK has outsourced some of its carbon dioxide emissions through its large trade deficit in manufactured goods.

  1. HMRC and HM Treasury (2013), ‘Analysis of the dynamic effects of corporation tax reductions’, UK Government Publishing Service 

  2. Yamano N, Guilhoto J (2020), ‘CO2 emissions embodied in international trade and domestic final demand: methodology and results using the OECD Inter-Country Input-Output Database, OECD, Science, Technology and Innovation Working Papers, No. 2020/11, OECD Publishing, Paris,