Handbook on Extended Supply and Use Tables and Extended Input‑Output Tables

7. Adding partner country information to extended input-output tables and compiling an extended multi-country input-output table

Abstract

This chapter provides guidance to compilers of extended supply and use tables and extended input-output tables for adding country detail to exports and imports and explains how to integrate an extended input-output table into a multi-country input-output table (MCIOT). It briefly describes three different approaches. Finally, it discusses how to split an MCIOT by ownership, foreign or domestic.

Introduction

This chapter provides guidance to compilers of extended supply and use tables (ESUTs) and extended input-output tables (EIOTs) for adding country detail to exports and imports and explains how to integrate an EIOT into a multi-country input-output table. There are three different approaches that compilers can take, depending on their analytical aims and the available dataset. This chapter briefly describes them, sorted by increasing difficulty and data requirements. First, countries can add partner country detail to exports and imports in their EIOT, or even integrate their EIOT into an MCIOT. This allows seeing how different types of enterprises are connected to the world economy, e.g. whether small and medium-sized enterprises (SMEs) are well-connected to emerging markets with high growth or whether they are missing out. Second, international organisations (e.g. the OECD) may want to improve the quality of globalisation indicators (such as national trade in value added or employment and emissions related to trade) by taking into account that processing exporters1 account for a large part of production in some countries. They are very different from regular exporters. This information is policy-relevant. Therefore, the OECD MCIOT distinguishes between processing trade and regular trade for industries in the People’s Republic of China (hereafter “China”) and Mexico. Preferably, national ESUTs are created first, transformed into national EIOTs then integrated into MCIOTs. A third approach is to split each industry in each country into an MCIOT by enterprise characteristics (e.g. foreign/domestic ownership). In other words, this approach compiles an extended MCIOT. Cai, Miroudot and Zürcher (2023[1]) describe the OECD Analytical AMNE Database, which is an example of this approach that allows to analyse the role of multinational enterprises (MNEs) in global value chains.

General background

Over the past years, several institutions have developed MCIOTs. Examples are the OECD and WTO’s Trade in Value Added (TiVA) (see, for example, OECD and WTO (2013[2]); Yamano et al. (2022[3])), Eurostat and the JRC’s FIGARO (Remond-Tiedrez and Rueda-Cantuche, 2019[4]), and the Asian Development Bank’s MCIOT.2 Table 7.1 provides an example.

Table 7.1. Multi-country input-output table in basic prices, a two-country, two-industry example

		Intermediate demand				Final use
		Country A		Country B		Country A	Country B	Output
		Industry 1	Industry 2	Industry 1	Industry 2
Country A	Industry 1
	Industry 2
Country B	Industry 1
	Industry 2
Value added
Output

These new data have brought new insights. For example, they provide alternative views on bilateral trade balances, quantification of the indirect involvement of non-trading industries (e.g. supporting services for exporting industries) and information about high international fragmentation of manufacturing processes. National EIOTs have several advantages. It is, therefore, not surprising that an extended MCIOT, where industries are split by another dimension, has benefits as well. For example, the literature shows that the direct trade of SMEs, compared to large enterprises, is relatively more focused on countries close by. But how does this work out for indirect trade? Can SMEs benefit from economic growth in emerging markets without exporting there themselves? Extended MCIOTs will also yield new insights related to specific types of enterprises regarding environmental pressure, social-economic responsibilities in the value chain (due diligence), dependence on specific countries, inflationary shocks, etc. Answering such questions is possible with an MCIOT, where each industry in each country is split by the desired dimension, but it is not always feasible nor necessary. It may not be feasible, since a national statistical office might have trouble finding the necessary data outside its own country. It may not be necessary, since splitting only the industries in the domestic economy might already be sufficient to answer the questions at hand.

Adding partner country detail to exports and imports in national extended input-output tables

There have been several projects where partner country detail has been added to the exports and imports in national ESUTs and EIOTs. Chong et al. (2019[5]) use their EIOT for the Netherlands and add the country dimension for trade in goods only. They find that SMEs have a much larger share in value added embodied in exports to China and the United States than their share in the gross exports to these countries. OECD and Statistics Denmark (2017[6]) created three types of MCIOTs where the domestic economies of Denmark, Finland, Iceland, Norway and Sweden were split by a given dimension. These three types were size, ownership and trader status. They found a similar pattern as in the Netherlands. Namely, that larger enterprises export relatively more to distant markets than SMEs in gross exports terms but that the differences are far smaller in trade in value-added terms. Michel and Hambÿe (2022[7])3 compile an EIOT for Belgium where manufacturing is split into foreign-oriented and domestic-oriented enterprises. They add the country dimension by integrating their EIOT into an MCIOT. Among others, they use it to estimate employment sustained in direct exports to a country and exports to a country via the value chain.

Data sources

Generally, the data sources are the same as described in Chapter 2, 3 and 4. The only additional information is the country dimension of imports and exports that can be found in trade statistics. Note that Chong et al. (2019[5]) and Michel and Hambÿe (2022[7]) consider trade in goods only. OECD and Statistics Denmark (2017[6]) consider trade in services as well, but since data are lacking, they use proxies from trade in goods. For example, they assume that in each industry the share of the SMEs’ exports of services to the United States is equal to the share of the corresponding exports of goods to the United States.

Methods

Chong et al. (2019[5]) do not embed their EIOT in an MCIOT; hence it is sufficient to add the country information in a similar way as they assign imports and exports in an industry to each type of enterprise.

OECD and Statistics Denmark (2017[6]) used software that was run at the national statistical offices of the five countries involved. The national statistical offices compiled datasets about trade, split by industry, type of enterprise, good and country, from the microdata. First, the data were used to create a national EIOT with total imports and exports, as described in Chapter 4. The basis for the national input-output table (IOT) was the OECD’s MCIOT. Then the geographical detail was added to imports and exports, embedding the extended table in the OECD MCIOT. This involved two major steps. First, the data from trade statistics might have zero imports from a country or zero exports to a country for a given type of enterprise in a given industry, whereas this is not the case in the EIOT. For example, enterprises that have no imports in the microdata might import via wholesalers. Then there is no country breakdown in the microdata, hence the country breakdown will follow that of the MCIOT. Second, total trade of an industry with a country will be different in the microdata and the MCIOT. Therefore, trade flows were distributed stepwise (increments of 1%) to countries, using the information in the microdata. As soon as assigned trade to a specific partner country was equal to the value in the MCIOT data, this country was no longer used for further distribution of trade.

Michel et al. (2023[8]) integrated their EIOT into an MCIOT created by the World Input-Output Database (WIOD) project (Timmer et al., 2015[9]). They note that the intermediate structure of their IOT is, with good reason, different from that in WIOD. This problem does not exist in OECD and Statistics Denmark (2017[6]) since they use the OECD MCIOT as a basis for the national IOT. The Belgian approach consists of five steps. They start by converting the Belgian data from euros into dollars. In the second step, they use the Belgian microdata to determine the country distribution of exports and imports of export-oriented manufacturers. Next, they assign the use of Belgian exports among the various categories in the destination countries by using proportions from WIOD. In the fourth step, all data about Belgium in the WIOD data are replaced by the Belgian data. Namely, the data about domestic transactions and about the foreign transactions from the previous step. This leads to an imbalanced MCIOT; hence, they use a RAS procedure (Junius and Oosterhaven, 2003[10]) to adapt the data for all countries except Belgium in the fifth and final step. The result is an MCIOT consistent with the Belgian EIOT.

Embedding the national extended input-output tables for one country into a multi-country input-output table

This section explains how to take the national EIOT of a given country and embed it into an MCIOT. In other words, the imports (exports) of industries split by the chosen extension criterion are disaggregated by the producing (receiving) industries and countries abroad. Table 7.2 shows an example. Here the EIOT of country A, where industries in the national IOT were extended by size class, is embedded in the MCIOT shown in Table 7.1.

Table 7.2. Multi-country input-output table in basic prices, a two-country, two-industry example, industry extended for one country

			Intermediate demand						Final use
			Country A				Country B		Country A	Country B	Output
			Ind 1	Ind 1	Ind 2	Ind 2	Ind 1	Ind 2
			SME	Large	SME	Large
Country A	SME	Ind 1
	Large	Ind 1
	SME	Ind 2
	Large	Ind 2
Country B		Ind 1
		Ind 2
Value added
Output

Note: ind: industry; SME: small and medium-sized enterprise; Large: large enterprise.

The approach is based on the description by Yamano et al. (2022[3]) of the methods used to compile the OECD MCIOT. Part of that text explains how the OECD splits several industries in China and Mexico for TiVA purposes. For China, industries are split into domestic suppliers, processing exporters and non-processing exporters. For Mexico, industries are split into domestic suppliers and global manufacturers. This addresses the substantial heterogeneity within these industries by taking into account that enterprises who produce for the domestic market are very different from those who produce for the global market. By definition, the production of enterprises who produce for the domestic market hardly goes abroad, and it is known that they import less as well. With the extension of the MCIOT, indicators about, for example, imports in exports, value added in exports and employment in exports will be less biased than with a standard MCIOT. See Table 7.2 for a fictitious example. Besides higher quality indicators, the new data also provide additional policy-relevant information. For example, in the case of China, it was relevant to know how exports of domestic produced goods fare on the world market and how they are used subsequently. Using a standard MCIOT, this is not possible, since the exports of a domestic industry are combined with the exports of the corresponding processing industry into one number.

Note that the method is similar to that of embedding a subnational IOT of a given country into an MCIOT, as in Meng, Zhang and Inomata (2013[11]) and Meng and Yamano (2017[12]).

Data sources

There are three different data sources:

• The annual MCIOTs used to estimate the extended MCIOT in Yamano et al. (2022[3]) come from the 2021 edition of the OECD MCIOT Database (http://oe.cd/icio). These industry-by-industry MCIOTs at basic prices cover 67 economies and 45 industries.

• Ideally, extended national IOTs are available. The extended input-output structures of reference years are provided by Mexico’s National Institute of Statistics and Geography (INEGI) and the Chinese Academy of Sciences, respectively.

• If national EIOTs are not available, customs trade statistics and balance of payments statistics can complement the missing industrial activity information.

In the case of China, since the customs data (General Administration of Customs, China) are available for different enterprise groups (domestic, processing exporters and non-processing exporters), the different column constraints (products imported by different enterprise groups) are available to improve the quality of the import matrices.

Methods

The process consists of several steps. In brief:

1. Adapt the national EIOT to the classifications, concepts, etc. of the MCIOT.

2. Obtain constraints for several variables in the EIOT, by industry and by type of enterprise, based on the corresponding numbers in the MCIOT by industry.

3. Adapt the numbers in the resulting EIOT such that aggregating to a national IOT corresponds with the numbers of the country in the MCIOT.

4. Balance the international trade flows by enterprise characteristics.

In the first step, the national EIOT is adapted to the MCIOT. This procedure includes the conversion to basic prices, harmonisation of industry classifications, reconciliation of the expenditure items of the final use, the estimation of an import matrix, the removal of re-exports and the transfer of re-imports to domestic transactions. If the national IOT is only available in a product-by-product format, the inter-industry intermediate transactions are converted to an industry-by-industry format using the product supply ratios from the supply table.4 After this process, aggregating the national EIOT to a national IOT yields something similar to the national part of the MCIOT, but the numbers will be different.

In the second step, the constraints for the data in the EIOT, by industry and by type of enterprise, are derived to match those in the MCIOT. To be more specific, output, value added, trade flows and domestic expenditure items have to be the same as the country’s total figures in the aggregated MCIOT, by industry and type of final use. Output and value added in each industry i are constrained by the country aggregate MCIOT as:

$\mathrm{O}\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}:X_{ip}^A+X_{in}^A={\tilde{X}}_i^A\mathrm{ }$

and

$\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{ }\mathrm{a}\mathrm{d}\mathrm{d}\mathrm{e}\mathrm{d}:\mathrm{ }{V}_{ip}^A+V_{in}^A={\tilde{V}}_i^A\mathrm{ }$

where $X_{ip}^A$ and $V_{ip}^A$ represent the output and value added of processing manufacturers and $X_{in}^A$ and $V_{in}^A$ are those for other manufacturers, respectively, while ${\tilde{X}}_i^A$ and ${\tilde{V}}_i^A$ are, respectively, the output and value added of industry i in country A from an MCIOT. The notation $\stackrel{}{~}$ indicates the country constraint variables from the cells aggregated in the reference MCIOT.

Set A as the country under concern. Set ${EX}_{ip}^{AC}$ and ${EX}_{in}^{AC}\mathrm{ }$as the cross-border exports from processing exporters and non-processing exports from industry i of country A to importing partner country C, respectively. Set ${\widetilde{EX}}_i^{AC}\mathrm{ }$as the exports of products in a reference MCIOT. Similarly, ${\widetilde{IM}}_i^{CA}$ is the variable for intermediate imports by industry j of country A from exporting partner country C in the MCIOT. Then set the following cross-border constraints:

Exports:$\mathrm{ }{EX}_{ip}^{AC}+{EX}_{in}^{AC}$=${\widetilde{EX}}_i^{AC}$

Imports: ${IM}_{ip}^{CA}+{IM}_{in}^{CA}={\widetilde{IM}}_i^{CA}$

The next part of this second step is only specific to the case under concern: processing trade. This production is for foreign markets only, but indirectly, domestic consumption might take place anyway. Therefore, the trade data have to be adapted slightly. In other cases, e.g. a national EIOT by ownership, this part is not necessary, and in trade only the constraints for exports and imports should be set into place.

By definition, products manufactured by processing exporters are not immediately consumed within the domestic territory in the single country (extended) input-output framework. This leads to the equation:

$X_{ip}^A={EX}_{ip}^A$

where ${EX}_{ip}^A$ is exports of products produced in country A’s processing trade industry. However, the exported products manufactured in the export processing zones can still be consumed by the domestic residents in the multi-country framework via direct purchases abroad. On the other hand, foreign resident households cannot consume the products from the export-processing zones in country A since these products are only sold abroad.

To tackle this issue, the inter-country exports and imports flows must be explicitly separated into direct purchases and cross-border trade flows in the MCIOT framework. Direct purchases of non-residents in country A’s territory are constrained as:

${DP}_{in}^A={\sum }_C{\widetilde{DP}}_i^{AC}$

where ${DP}_{in}^A$ is direct purchases of product i by all non-residents in country A and ${\widetilde{DP}}_i^{AC}$ is direct purchases by country C’s residents for product i of country A. By definition, ${DP}_{ip}^A$=0, since products manufactured by processing exporters cannot be obtained in country A.

Since the products from processing manufacturers are all exported, domestically produced goods used for domestic final use are all produced in the non-processing manufacturing industries. This leads to two additional constraints, namely:

${FA}_{\mathit{i}\mathit{n}}^{\mathit{A}}={\widetilde{FA}}_{\mathit{i}}^{\mathit{A}}$ and ${FA}_{ip}^A=0$

where ${FA}_{\mathit{i}\mathit{n}}^{\mathit{A}}$ is the final use expenditure in country A of products produced by the domestic non-processing trade industry i, ${\widetilde{FA}}_{\mathit{i}}^{\mathit{A}}$ is the final use expenditure in country A of products produced by the domestic industry i in the MCIOT and ${FA}_{\mathit{i}\mathit{p}}^{\mathit{A}}$ is the final use expenditure in country A of products produced by the domestic processing trade industry i.

These steps lead to constraints on output, value added, imports, exports and domestic final use expenditure, by industry and by type of enterprise.

The third step rebalances the national EIOT to the constraints given by the MCIOT. This can be achieved using a variant of bi-proportional adjustment methods such as the conventional RAS and GRAS methodologies (Junius and Oosterhaven, 2003[10]; Temurshoev, Miller and Bouwmeester, 2013[13]).

The fourth step balances the international trade flows by enterprise characteristics. In the previous step, the trade flows in the national EIOT were fully reconciled with the trade flows derived from an MCIOT. There was not yet a country extension of imports and exports in the national EIOT. This final step is for this remaining adjustment.

The intermediate exports from country A (with the EIOT) to trade partner country C are the sum of exports from the processing exporters and non-processing exporters:

${Z_{ip,j}^{AC}+Z_{in,j}^{AC}= \tilde{Z}}_{ij}^{AC}$

where $Z_{ip,j}^{AC}$ is intermediate exports by industry i from country A to country C’s industry j from processing exporters and $Z_{in,j}^{AC}$ is intermediate exports from non-processing exporters, and ${\tilde{Z}}_{ij}^{AC}$ is intermediate exports in the MCIOT.

Now assume that the trade partner shares are equal for processing exporters and non-processing exporters, hence equal to the trade partner shares calculated from an MCIOT. This leads to initial values for the bilateral trade flows for intermediate and final products.

The trade for final use is also the sum of exports from processing and non-processing exports:

$F_{ip}^{AC}+F_{in}^{AC}={\tilde{F}}_i^{AC}$

where $F_{ip}^{AC}$ denotes exports by industry i in country A for final use in country C by processing exporters, $F_{in}^{AC}$ is the same for exports by non-processing exporters and ${\tilde{F}}_i^{AC}$ is the corresponding entry in the MCIOT.

The exports from country A to all partners are constrained to the exports in the national EIOT as:

${EX}_{ip}^A={\sum }_j{\sum }_c{Z}_{ip,j}^{Ac}+{\sum }_c{F}_{ip}^{Ac}$

and

${EX}_{in}^A={\sum }_j{\sum }_c{Z}_{in,j}^{AC}+{\sum }_c{F}_{in}^{AC}$

where ${EX}_{ip}^A$ is exports from processing exporters and ${EX}_{in}^A$ is exports from non-processing exporters in the national EIOT.

The sum of intermediate imports by processing and non-processing industries are constrained to the MCIOT import flows of target country A for each trade partner C as:

$Z_{i,jn}^{CA}+Z_{i,jp}^{CA}={\tilde{Z}}_{i,j}^{CA}$

where $Z_{i,jn}^{CA}$ are intermediate imports by non-processing industry j in country A from industry j in country C, $Z_{i,jp}^{CA}$ are the same but for processing industry j, ${\tilde{Z}}_{i,j}^{CA}$ are total intermediate imports by industry i in country A from industry j in country C in the MCIOT.

The imports from all partners are constrained to the import part of the national EIOT as:

${IMZ}_{i,jp}^A={\sum }_C{Z}_{i,jp}^{CA}$

and

${IMZ}_{i,jn}^A={\sum }_C{Z}_{i,jn}^{CA}$

where ${IMZ}_{i,jp}^A$ and ${IMZ}_{i,jn}^A$ are intermediate imports by processing industries and non-processing industries, respectively, in the national EIOT. The imports of products for final use remain the same because the split is only considered in the types of enterprises; there are no differentiations in household types.

The components of exports and imports are separately balanced using a framework of linear programming optimisation. However, the optimisation constraints can be relaxed for the bilateral trade constraints from an MCIOT, since most countries’ bilateral trade flows and import matrix are derived by numerical non-survey calculations.

Splitting a multi-country input-output table by ownership: The example of the AAMNE Database

This section explains how each industry in an MCIOT can be disaggregated by the chosen extension criterion while keeping a balanced table. The result is an extended MCIOT (EMCIOT) showing, for example, intermediate sales from SMEs in industry 1 in country A to large enterprises in industry 2 in country B. Table 7.3 depicts an example of an MCIOT.

Table 7.3. Multi-country input-output table in basic prices, a two-country, two-industry example, industry extended for two country

			Intermediate demand								Final use
			Country A				Country B				Country A	Country B	Output
			Ind 1	Ind 1	Ind 2	Ind 2	Ind 1	Ind 1	Ind 2	Ind 2
			SME	Large	SME	Large	SME	Large	SME	Large
Country A	SME	Ind 1
	Large	Ind 1
	SME	Ind 2
	Large	Ind 2
Country B	SME	Ind 1
	Large	Ind1
	SME	Ind 2
	Large	Ind 2
Taxes less subsidies
Value added
Output

Note: ind: industry; SME: small and medium-sized enterprise.

The approach builds on Cadestin et al. (2018[14]) and Cai, Miroudot and Zürcher (2023[1]) who describe the methods behind splitting an MCIOT by ownership. These two OECD projects led to the Analytical AMNE (AAMNE) Database. This comprehensive database, which is publicly available, covers 76 economies and 41 industries over the period 2000-20 in its 2024 edition. The AAMNE Database includes a set of EMCIOTs derived from OECD MCIOTs that are split according to ownership. Each row in these MCIOTs (referring to output in a specific country and industry) is split between the output of domestically owned enterprises and foreign-owned enterprises. Similarly, each column in the intermediate consumption matrix distinguishes inputs used by domestically owned and foreign-owned enterprises in each country and industry. In an additional set of MCIOTs, not publicly available, rows and columns include a further split for domestic MNEs’ activities, as opposed to enterprises that do not have foreign affiliates. Another example in this direction, similar to an EMCIOT but with provinces instead of countries, is the inter-provincial input-output database distinguishing ownership in China (Chen et al., 2023[15]).

The AAMNE Database provides valuable insights into the activities of MNEs from a global value chain perspective. It supports governments, academia and industry in evidence-based policy making and research in a wide range of topics: from MNE taxation policy and informing trade agreement negotiations to tracking MNE environmental footprints and technology transfers, among many others.

Data sources

The AAMNE Database is built on two main sources: 1) data on MNE activity from official statistics for countries and industries in the MCIOT; and 2) the OECD MCIOTs, which provide the whole economic structure. The data are transformed as described in Chapter 4 to transform aggregated national statistics into a basis for compiling a national EIOT. The result is three matrices:

1. A balanced bilateral output matrix by country, industry and country of ownership. The country of ownership dimension is subsequently consolidated into domestic and foreign ownership.

2. A matrix with value added, by country, industry and ownership (domestic or foreign).

3. A matrix with exports and imports, by country, industry and ownership (domestic or foreign).

The data about output, value added, exports and imports aggregated by ownership perfectly match the corresponding MCIOT data for all years in the dataset. It is needless to say that all data are according to the 2008 System of National Accounts (SNA). Therefore, international transactions are only recorded as imports or exports when there is a change of ownership. If a foreign subsidiary of an MNE produces goods as input for the parent, the export value will be the full value of the goods minus the value of used intermediates that were owned by the parents. When the foreign subsidiary owned all used intermediates, the export value is the full value of the produced goods. When the parent owned all used intermediates, for example in some cases of processing trade, the export value is only the value of the services provided by the foreign subsidiary to process the intermediates.

Methods

Given an MCIOT and output, value added, and trade matrices as described before, the EMCIOT is compiled as follows:

1. Use the industry-ownership level output to determine the relative proportion of domestic and foreign value within each industry in each country.

2. Obtain the initial values for the intermediate trade table.

3. Obtain the initial values for the tables with final use and value added.

4. Derive constraints for intermediate trade, final use, value added, exports and imports, by country, industry and ownership. These determine additional balancing conditions.

5. Transform these starting values, which form an unbalanced EMCIOT, into a balanced table using a quadratic optimisation method,5 while respecting the constraints from the previous step.

Steps 1-3 lead to the construction of the initial unbalanced split MCIOT. Steps 4-5 yield consistent tables which reconcile AMNE data as much as possible with the original MCIOT. The resulting EMCIOT fits the MCIOT data with values as closely as possible to the AMNE matrices of output, value added, exports and imports while preserving as much of the original structure of the MCIOT as possible.

Step 1 starts by defining an MCIOT composed of $G$ countries, $n$ industries and $m$ types of final use. $Z_{ij}$ is an $n\mathrm{ }\times \mathrm{ }n$ matrix and its elements indicate the delivery of intermediate inputs from country $i$ to country j. The special case $i$ = j therefore corresponds to domestic deliveries. Let $V_i$ define a vector of dimension $1\mathrm{ }\times \mathrm{ }n$ whose elements indicate the value added in country $i$ and $Y_{ij}$ a matrix of dimension $n\mathrm{ }\times \mathrm{ }m$ that denotes final goods and services produced in industries in country $i$ and consumed by final use categories country $j$.

$X_i^{D^{\mathrm{*}}}$ and $X_i^{F^{\mathrm{*}}}$ are defined as country $i$’s output of domestically owned and foreign-owned enterprises, respectively, in the output matrix. By construction, $X_i^{D^{\mathrm{*}}}+X_i^{F^{\mathrm{*}}}=X_i$ where $X_i$ is the vector of output for country $i$. Define the vector of output ratios by domestically owned enterprises as ${\sigma }_i^D=X_i^{D^{\mathrm{*}}}/X_i$ and define the vector of output ratios by foreign-owned enterprises as ${\sigma }_i^F=X_i^{F^{\mathrm{*}}}/X_i$.

In Step 2, $Z_{ij}$ is split into four matrices using proportionality assumptions: $Z_{ij}^{DD}$, $Z_{ij}^{DF}$, $Z_{ij}^{FD}$ and $Z_{ij}^{FF}$. $Z_{ij}^{DD}$ is the matrix of intermediate inputs supplied by domestically owned enterprises to domestically owned enterprises. $Z_{ij}^{DF}$ is a matrix of intermediate inputs supplied by domestically owned enterprises to foreign-owned enterprises; and so forth for $Z_{ij}^{FD}$ and $Z_{ij}^{FF}$. This is shown in Table 7.4.

Table 7.4. The initial value for the intermediate trade block, by industry, country and ownership

			D				F
			Country i		Country j		Country i		Country j
			Ind 1	Ind 2	Ind 1	Ind 2	Ind 1	Ind 2	Ind 1	Ind 2
D	Country i	Ind 1	ZijDD				ZijDF
		Ind 2
	Country j	Ind 1
		Ind 2
F	Country i	Ind 1	ZijFD				ZijFF
		Ind 2
	Country j	Ind 1
		Ind 2

Note: D: domestically owned enterprise; F: foreign-owned enterprise; ind: industry.

The starting values Z0 of the four Z matrices are calculated using the previously defined ${\sigma }_i^D$ and ${\sigma }_i^F$ (with the hat notation used for the diagonal matrix of the vector):

${Z0}_{ij}^{DD}={\widehat{\sigma }}_i^D{Z}_{ij}{\widehat{\sigma }}_j^D$, ${Z0}_{ij}^{DF}={\widehat{\sigma }}_i^D{Z}_{ij}{\widehat{\sigma }}_j^F$, ${Z0}_{ij}^{FD}={\widehat{\sigma }}_i^F{Z}_{ij}{\widehat{\sigma }}_j^D$ and ${Z0}_{ij}^{FF}={\widehat{\sigma }}_i^F{Z}_{ij}{\widehat{\sigma }}_j^F$

This split produces the initial values in the balancing procedure. The coefficients will then change in the optimisation to reflect the constraints. At the end of the balancing process, there will be different production functions and a different mix of inputs for domestically owned and foreign-owned enterprises, both as suppliers of inputs and as purchasers of inputs.

Step 3 derives starting values for final use and value added. The final use of country j supplied by country i, the $Y_{ij}$ matrix, also needs to be split into the two matrices:$\mathrm{ }{Y}_{ij}^D$ and $Y_{ij}^F$ where $Y_{ij}^D$ is the final use of the output of domestically owned enterprises and $Y_{ij}^F$ is the final use of the output of foreign-owned enterprises. The starting values of these two matrices are calculated as follows:

${Y0}_{ij}^D={\widehat{\sigma }}_i^D{Y}_{ij}$ and ${Y0}_{ij}^F={\widehat{\sigma }}_i^F{Y}_{ij}$

The value added in country i, $V_i$, is split into two vectors: $V_i^D$ and $V_i^F$. $V_i^D$ is the value-added vector for country$i$’s domestically owned enterprises and $V_i^F$ is the value-added vector for country $i$’s foreign-owned enterprises. The starting values of these two vectors are extracted from the value-added matrix.

${{V0}_i^D=V}_i^{D^{\mathrm{*}}}$ and ${{V0}_i^F=V}_i^{F^{\mathrm{*}}}$

Step 4 derives constraints for the optimisation process. To obtain the unobservable input-output coefficients, the new intermediate input blocks in the MCIOT: $Z_{ij}^{DD}$, $Z_{ij}^{DF}$, $Z_{ij}^{FD}$ and $Z_{ij}^{FF}$, the new final use blocks, ${\mathrm{Y}}_{\mathrm{i}\mathrm{j}}^{\mathrm{D}}$ and ${\mathrm{Y}}_{\mathrm{i}\mathrm{j}}^{\mathrm{F}}$, as well as the new value-added vectors, $V_i^D$ and $V_i^F$, need to be estimated. Each block should satisfy these constraints: 1) the sum of the split new blocks should be equal to the original matrices/vectors in the MCIOT; 2) the new MCIOT should be balanced, i.e. the sum of each row and sum of each column should be equal to output.

These constraints can be written as follows:

$Z_{ij}^{DD}+Z_{ij}^{DF}+Z_{ij}^{FD}+Z_{ij}^{FF}=Z_{ij}$

${\mathrm{Y}}_{\mathrm{i}\mathrm{j}}^{\mathrm{D}}+{\mathrm{Y}}_{\mathrm{i}\mathrm{j}}^{\mathrm{F}}={\mathrm{Y}}_{\mathrm{i}\mathrm{j}}$

$V_i^D+V_i^F=V_i$

$\sum _j{Z}_{ij}^{D○}+\sum _j{Y}_{ij}^D= \sum _j{Z}_{ji}^{○\mathrm{D}}+V_i^D=X_i^{D^{\mathrm{*}}}$

$\sum _j{Z}_{ij}^{F○}+\sum _j{Y}_{ij}^F= \sum _j{Z}_{ji}^{○\mathrm{F}}+V_i^F=X_i^{F^{\mathrm{*}}}$

where the notation $○$ corresponds to the set {D, F} that identifies the domestic and foreign blocks in the split MCIOT.

Additional constraints are needed to split the exports E and imports M data in a way that is consistent with the matrices created with AMNE data. These constraints are:

$E_i^D=\sum _j{Z}_{ij}^{D○}+\sum _j{Y}_{ij}^D, j\ne i$,$E_i^F=\sum _j{Z}_{ij}^{F○}+\sum _j{Y}_{ij}^F, j\ne i$

$M_i^D=\sum _j{Z}_{ij}^{○\mathrm{D}}+\sum _j{Y}_{ij}^D, j\ne i$,$M_i^F=\sum _j{Z}_{ij}^{○\mathrm{F}}+\sum _j{Y}_{ij}^F, j\ne i$

Step 5 concerns the actual balancing process. The outcome of this process is as close as possible to the starting values created above, while respecting the constraints. Using the previous notations, the objective function in the optimisation (minimisation of distance to the starting values) is specified as:

$Min S={\sum }_{i,j}\frac{(Z_{ij}^{DD}-Z{0}_{ij}^{DD}{)}^2}{Z{0}_{ij}^{DD}}+{\sum }_{i,j}\frac{(Z_{ij}^{DF}-Z{0}_{ij}^{DF}{)}^2}{Z{0}_{ij}^{DF}}+{\sum }_{i,j}\frac{(Z_{ij}^{FD}-Z{0}_{ij}^{FD}{)}^2}{Z{0}_{ij}^{FD}}+{\sum }_{i,j}\frac{(Z_{ij}^{FF}-Z{0}_{ij}^{FF}{)}^2}{Z{0}_{ij}^{FF}}$

$+{\sum }_{i,j}\frac{(Y_{ij}^D-Y{0}_{ij}^D{)}^2}{Y{0}_{ij}^D}+{\sum }_{i,j}\frac{(Y_{ij}^F-Y{0}_{ij}^F{)}^2}{Y{0}_{ij}^F}+100*\left({\sum }_i\frac{(V_i^D-V{0}_i^D{)}^2}{V{0}_i^D}+{\sum }_i\frac{(V_i^F-V{0}_i^F{)}^2}{V{0}_i^F}\right)$$$ +100*\left({\sum }_i\frac{(E_i^D-E_i^{D•}{)}^2}{E_i^{D•}}+{\sum }_i\frac{(E_i^F-E_i^{F•}{)}^2}{E_i^{F•}}+{\sum }_i\frac{(M_i^D-M_i^{D•}{)}^2}{M_i^{D•}}+{\sum }_i\frac{(M_i^F-M_i^{F•}{)}^2}{M_i^{F•}}\right)$$

where $E_i^{D^{\mathrm{*}}}$, $E_i^{F^{\mathrm{*}}}$, $M_i^{D^{\mathrm{*}}}$ and $M_i^{D^{\mathrm{*}}}$ are the exports and imports values from the AMNE matrices created in the previous steps.

This process leads to a full split of the MCIOT by domestic and foreign ownership, producing balanced tables which are fully consistent with the initial tables that do not distinguish between foreign-owned and domestically owned enterprises.

At the national level, it is expected that extra enterprise-level data can be used to derive more accurate estimates of the intermediate consumption of domestically owned and foreign-owned enterprises as well as their respective imports and exports. Even if data are not fully available, the optimisation and balancing processes described in Chapter 5 can also be used to fill the gaps and derive a consistent EIOT split according to ownership.

Examples of the results

Just as an EIOT yields new information about the domestic economy, the extended MCIOT yields new information about the world economy: 1) in indicators describing the direct effect of MNEs, when the EMCIOT and subsequent input-output analysis is not needed; 2) in indicators describing the worldwide links of MNEs, where input-output analysis is necessary. Examples of both types of indicators follow.

Indicators about MNEs in the global economy without input-output analysis

MNEs and their foreign affiliates account for one-third of world output and gross domestic product (GDP) and half of international trade (Figure 7.1). MNEs’ contribution to world GDP was estimated at 28% in 2019, of which roughly one-third was from foreign affiliates abroad and two-thirds from MNE headquarters and domestic affiliates in the home country. Taken together, this means that MNEs produce about one-third of global output, illustrating the importance of MNEs and their networks in today’s global economy.

Figure 7.1. Direct effects of multinational enterprises in host countries, 2019

Note: GDP: gross domestic product; MNE: multinational enterprise.

Source: Calculations based on the OECD Analytical AMNE Database.

Foreign affiliates accounted for about 10% of world GDP in 2019. They relatively often sourced intermediate goods/services internationally (see below), which explains why their share in GDP is smaller than their share of output. Indeed, the value of imported intermediates is counted only once as a contribution to the original country’s GDP, while it is included in the output statistics multiple times in different countries. For instance, when a foreign affiliate sources inputs from its headquarters to be incorporated into a final product, the value of the inputs is counted twice – in the output of the home country and that of the host country of the affiliate – while it is only counted once in the GDP of the home country.

MNEs and their affiliates are found to be relatively more important in exports and imports, demonstrating the large trading activities of this group of enterprises. Foreign affiliates were responsible for 25% of global exports and 25% of global imports in 2019. These shares are similar to those of MNE headquarters (31% and 24%, respectively), but important differences exist across countries, as available data for individual countries demonstrate. For example, MNEs accounted for more than 70% of exports from both France and Hungary, but mainly because of foreign affiliates in the case of Hungary, while domestic MNEs play a much more important role in France.

Indicators using the added value of the multi-country input-output perspective

Building on an MCIOT allows for analyses beyond what is possible from foreign affiliate statistics data or ownership-split national SUTs alone, providing policy makers and researchers with a better understanding of MNE activities across borders and in global value chains.

Figure 7.2. Sourcing structure (top) and output use (bottom) of foreign affiliates globally, 2019

Note: MNE: multinational enterprise.

Source: Calculations based on the OECD Analytical AMNE Database.

The AAMNE Database shows, for example, that contrary to traditional wisdom, foreign affiliates have strong backward and forward linkages with domestic companies, including SMEs. Foreign affiliates source more than two-thirds of intermediates from their host economy (Figure 7.2, top panel) and more than 50% of domestic intermediate consumption is supplied by non-MNEs (of which the majority are SMEs). Further on, foreign affiliates operate not only as customers in host countries, but also as suppliers of intermediates and final products. More than two-thirds of the production of foreign affiliates feeds into domestic value chains: 30% of affiliates’ production in 2019 was for the final domestic market, while 44% was used locally as an input to other enterprises in the domestic economy (Figure 7.2, bottom panel). Once again, the most important domestic clients of foreign affiliates are domestic non-MNEs, buying 55% of foreign affiliate domestic intermediate production.

Leveraging the granularity of the database and its global value chain perspective to take the analysis a step further shows that MNEs use trade and investment for different purposes in the value chain and have complex strategies. Figure 7.3 shows that foreign affiliates can be involved in horizontal strategies when producing final products for the domestic market or for exports (export-platform foreign direct investment), as well as intermediate inputs used by domestic enterprises. The exports of inputs by foreign affiliates rather reflect MNEs’ vertical strategies. Figure 7.3 also suggests that these vertical strategies are not as prevalent as sometimes argued. This finding is consistent with recent evidence suggesting that the use of third-party suppliers is more prevalent within MNEs than originally thought. The literature has shown that while MNEs often prefer to source inputs from independent enterprises through non-equity partnerships like franchising, contractual relationships, strategic partnerships, etc., they mainly use their foreign affiliates to either transfer capabilities (Atalay, Hortaçsu and Syverson, 2014[16]; Ramondo, Rappoport and Ruhl, 2016[17]) or to produce technologically important inputs (Berlingieri, Pisch and Steinwender, 2019[18]).

The detail in the extended MCIOT also allows one to find differences across industries in the role played by foreign affiliates. For example, foreign affiliates in the computer and electronics industry are more involved in vertical strategies than foreign affiliates in the food industry. Moreover, foreign affiliates in the chemicals industry provide a significant share of inputs to domestic enterprises that are not part of MNEs, something not observed in the computer and electronics industry, which is another industry where the international fragmentation of production is prevalent.

Figure 7.3. Decomposition of output of foreign affiliates by type of transaction, selected industries, 2019

Note: MNE: multinational enterprise.

Source: Calculations based on the OECD Analytical AMNE Database.

References

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Notes

← 1.  Domestic enterprises import raw materials or other intermediate inputs from abroad before processing them in local manufacturing facilities. The finished goods are then exported.

← 2.  Accessible at: https://kidb.adb.org/globalization.

← 3.  See also Michel, Hambÿe and Hertveldt (2023[8]).

← 4.  See Chapter IV, “Converting supply and use tables into a symmetric I/O table: Treatment of secondary products” in United Nations (1999[19]).

← 5.  Chapter 5 explained another method to obtain a balanced table, namely a biproportional method. The reason to describe that method, and not a quadratic programming model, was explained in Chapter 5: national statistical offices often use biproportional methods to balance supply and use tables and IOTs.