Appendix 1. GVC model under the Three-Country IIO Model
Let us assume a three-country GIO table presented in Figure
5, where each country produces in a single tradable sector. Each country produces a good that can be consumed as a final good or used as an intermediate input.Footnote 21 Here, for three countries i and j, \({\mathbf{Z}} = \left( {{\text{Z}}^{ij} } \right)\) and \({\mathbf{F}} = \left( {{\text{F}}^{ij} } \right)\) are matrices of intermediate goods and final goods transactions, respectively; \({\mathbf{Y}} = \left( {{\text{Y}}^{i} } \right) = \left( {{\text{Y}}^{j} } \right)^{\prime }\) is a vector of gross output and \({\mathbf{V}} = \left( {{\text{V}}^{j} } \right)^{\prime }\) is vector of value-added inputs. Then we can easily derive the input–output equation, for the GIO table given in Figure 5, in matrix form as:
$${\mathbf{Y}} = \left( {{\mathbf{I}} - {\mathbf{A}}} \right)^{ - 1} {\mathbf{Fu}} = {\mathbf{LFu}},$$
(1)
where A is 3 × 3 global intermediate input coefficient matrix, L is the global Leontief inverse matrix of size 3 × 3, F is a matrix of size 3 × 3 and u is a 3 × 1 vector of ones.
Now, let us rearrange transactions of intermediate and final goods as vectors of domestic use and export, such that\({\mathbf{Z}}^{D} = \left[ {\begin{array}{*{20}c} {{\text{Z}}_{1}^{D} } \\ {{\text{Z}}_{2}^{D} } \\ {{\text{Z}}_{3}^{D} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {{\text{Z}}^{11} } \\ {{\text{Z}}^{22} } \\ {{\text{Z}}^{33} } \\ \end{array} } \right]\) \({\mathbf{F}}^{D} = \left[ {\begin{array}{*{20}c} {{\text{F}}_{1}^{D} } \\ {{\text{F}}_{2}^{D} } \\ {{\text{F}}_{3}^{D} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {{\text{F}}^{11} } \\ {{\text{F}}^{22} } \\ {{\text{F}}^{33} } \\ \end{array} } \right]\) \({\mathbf{E}}^{Z} = \left[ {\begin{array}{*{20}c} {{\text{E}}_{1}^{Z} } \\ {{\text{E}}_{2}^{Z} } \\ {{\text{E}}_{3}^{Z} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {{\text{Z}}^{12} + {\text{Z}}^{13} } \\ {{\text{Z}}^{21} + {\text{Z}}^{23} } \\ {{\text{Z}}^{31} + {\text{Z}}^{32} } \\ \end{array} } \right]\) \({\mathbf{E}}^{F} = \left[ {\begin{array}{*{20}c} {{\text{E}}_{1}^{F} } \\ {{\text{E}}_{2}^{F} } \\ {{\text{E}}_{3}^{F} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {{\text{F}}^{12} + {\text{F}}^{13} } \\ {{\text{F}}^{21} + {\text{F}}^{23} } \\ {{\text{F}}^{31} + {\text{F}}^{32} } \\ \end{array} } \right],\) where ZD and EZ are intermediate goods supplied to domestic market and foreign countries, respectively; FD is domestically consumed final goods; and EF is the exported finished goods. It follows that,
$${\mathbf{Zu}} = {\mathbf{Z}}^{D} + {\mathbf{E}}^{Z}$$
(2)
and
$${\mathbf{Fu}} = {\mathbf{F}}^{D} + {\mathbf{E}}^{F} .$$
(3)
Substituting Eq. (3) in Eq. (1), we get,
$${\mathbf{Y}} = {\mathbf{L}}\left( {{\mathbf{F}}^{D} + {\mathbf{E}}^{F} } \right) = {\mathbf{LF}}^{D} + {\mathbf{LE}}^{F}$$
(4)
Equation (4) implies that the gross output vector (Y) is sum of productions induced by domestic consumption (FD) and export (EF) vectors of finished goods. Thus the value-added associated with induced production can be written as
$${\mathbf{V}} = {\hat{\mathbf{v}}}\left( {{\mathbf{LF}}^{D} + {\mathbf{LE}}^{F} } \right),$$
(5)
where \({\hat{\mathbf{v}}}\) is diagonal matrix of value-added coefficients.
The global value chain (GVC) in existing literatures estimates the induced value-added generated by gross export (say,\({\mathbf{E}}^{G} = {\mathbf{E}}^{Z} + {\mathbf{E}}^{F}\)) using the GIO data as follows:
$${\mathbf{GVC}} = {\hat{\mathbf{v}}\mathbf{LE}}^{G} = {\hat{\mathbf{v}}}\left( {{\mathbf{LE}}^{Z} + {\mathbf{LE}}^{F} } \right).$$
(6)
Here, Eq. (6) represents the value-added associated with the production induced by export of intermediate goods (\({\mathbf{LE}}^{Z}\)) and that induced by export of final goods (\({\mathbf{LE}}^{F}\)). Now, the gross production under GVC assumption (say, YGVC) can be written as sum of productions induced by domestic final demand vector FD, export vector of final goods EF and export vector of intermediate goods EZ, and using Eq. (4) we get:
$${\mathbf{Y}}_{GVC} = {\mathbf{LF}}^{D} + {\mathbf{LE}}^{F} + {\mathbf{LE}}^{Z} = {\mathbf{Y}} + {\mathbf{LE}}^{Z} .$$
(7)
Note that, for the given global Leontief inverse matrix L and non-zero EZ, YGVC exceeds the gross output Y provided in the GIO table, which is an impossible phenomenon. In GIO framework, global transaction of intermediate goods are treated as endogenous variable and are induced by production of final goods only. It means that, inclusion of production induced by intermediate goods estimated by using the global Leontief inverse matrix will evidently overestimate the actual gross production and hence overestimates the actual value-added amounts. However, if a national Leontief inverse (computed from single-country IO table) is substituted for the global Leontief inverse, then Eq. (7) holds true. Because, in single-country IO model, both EF and EZ are exogenous variable.
Appendix 2. Endogenous and exogenous countries of the YNU-GIO table
(a) Endogenous country list:
Asia (11)
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North America (3)
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Europe(12)
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Others (3)
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Japan (JP)
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USA (US)
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France (FR)
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Australia (AU)
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China (CH)
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Canada (CA)
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Germany (GR)
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Brazil (BR)
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Korea (KR)
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Mexico (MX)
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Austria (AT)
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South Africa (SA)
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Taiwan (TW)
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Belgium (BG)
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Singapore (SG)
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Finland (FN)
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Malaysia (MY)
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Ireland (IR)
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Thailand (TH)
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Italy (IT)
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Indonesia (ID)
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Luxembourg (LX)
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Philippines (PH)
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Netherlands (NL)
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Vietnam (VT)
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Portugal (PT)
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India (IN)
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Spain (SP)
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UK (UK)
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(b) Exogenous country list:
Country/group
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List of countries
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HK (1)
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Hong Kong
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ROA (30)
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Afghanistan, Bangladesh, Bhutan, Maldives, Nepal, Pakistan, Sri Lanka, Armenia, Azerbaijan, Bahrain, Brunei Darussalam, Cambodia, Macau, North Korea, Georgia, Israel, Jordan, Kazakhstan, Kyrgyzstan, Lao PDR, Lebanon, Mongolia, Myanmar, Oman, Syria, Tajikistan, Turkey, Turkmenistan, Uzbekistan and Yemen
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ROE (16)
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Russia, Bulgaria, Cyprus, Czech Rep., Denmark, Estonia, Greece, Hungary, Latvia, Lithuania, Malta, Poland, Romania, Slovakia, Slovenia and Sweden
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OPEC (12)
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Algeria, Angola, Ecuador, Iran, Iraq, Kuwait, Libya, Nigeria, Qatar, Saudi Arabia, UAE and Venezuela
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ROW
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Rest of the World
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Numbers in parenthesis represent number of countries treated endogenously in the YNU-GIO Database. ROA, ROE and OPEC represent Rest of Asia, Rest of Europe and oil producing countries, respectively.
Appendix 3: List of production industries of the YNU-GIO table
Industry Code
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Name of Industry
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Y01
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Agriculture, hunting, forestry and fishing
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Y02
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Mining and quarrying
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Y03
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Food products, beverages and tobacco
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Y04
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Textiles, textile products, leather and footwear
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Y05
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Wood and products of wood and cork
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Y06
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Pulp, paper, paper products, printing and publishing
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Y07
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Coke, refined petroleum products and nuclear fuel
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Y08
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Chemicals and pharmaceuticals
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Y09
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Rubber and plastics products
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Y10
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Other non-metallic mineral products
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Y11
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Basic metals
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Y12
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Fabricated metal products, except machinery and equipment
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Y13
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Machinery and equipment
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Y14
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Office, accounting and computing machinery
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Y15
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Electrical machinery and apparatus
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Y16
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Radio, television and communication equipment
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Y17
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Medical, precision and optical instruments
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Y18
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Motor vehicles, trailers and semi-trailers
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Y19
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Other transport equipment
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Y20
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Other manufacturing; recycling (include furniture)
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Y21
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Electricity, gas and water supply
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Y22
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Construction
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Y23
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Wholesale and retail trade; repairs
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Y24
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Hotels and restaurants
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Y25
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Transport
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Y26
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Post and telecommunications
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Y27
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Finance and insurance
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Y28
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Real estate activities
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Y29
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Renting of machinery and equipment
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Y30
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Computer and related activities
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Y31
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Research and development
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Y32
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Other business activities
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Y33
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Public administration and defense; compulsory social security
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Y34
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Education
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Y35
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Health, social work and other services
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Appendix 4: Descriptions of Data used for Estimation of the YNU-GIO Tables
We basically use single-country input–output tables (or equivalently, national input–output tables, NIOT) published by OECD for years 2000, 2005 and/or nearest one. As many Asian economies are not covered in OECD input–output database, we further collect national IOTs of Malaysia (2000 and 2005 from Department of Statistics, Malaysia), the Philippines (2006 from National Statistical Coordination Board, the Philippines), Singapore (2005 and 2007 from Singapore Department of Statistics, Singapore), Thailand (2000 from Office of the National Economic and Social Development Board, Thailand) and Vietnam (2007 from General Statistics Office of Vietnam) and reorganize all the tables in common 35 industrial classification compatible with the OECD tables in millions of respective national currency at current price.
We use annual national accounts data at current prices in national currency (GDP, 7 industry breakdown value-added, export and import of goods and services) and annual exchange rate data vis-à-vis US dollars obtained from the United Nations Statistics Division’s National Accounts Main Aggregates Database. Sources for Taiwanese national account data and exchange rates data are National Statistics, Republic of China (Taiwan) and CEIC database, respectively.
Detailed manufacturing industry (two-digit ISIC3 classification) data on output and value-added in million current national currency are taken from the UNIDO Industry Statistics Database (UNIDO INDSTAT). Industrial classification of UNIDO data are rearranged as per 35 classifications in YNU-GIO’s manufacturing industries.
Annual trade data are download (4- or 5- digit SITC3 classification, in current US Dollar) from the UN Comtrade database website. We convert SITC3 data into YNU-GIO classification according to its use for production (used as intermediate goods) or for final consumption (i.e., final goods) based on the Broad Economic Categories (BEC). We do not use the trade data directly while compiling the YNU-GIOs, but calculate source and destination breakdown trade shares of intermediate goods and final goods in all the endogenous countries, which is finally used to reorganize the globally linked input–output table.
Appendix 5: Estimation of the YNU-GIO Tables
Our estimation process of annual YNU-GIO tables follows flowchart presented in Fig.
6. First of all, we collect NIOTs,Footnote 22 for 29 endogenous countries, valued in corresponding national currencies and rearrange them according to the YNU-GIO industry classification system for benchmark years 2000, 2005 and/or nearest years. In the meantime, we also prepare YNU-GIO classified industry-specific outputs, intermediate goods demand and intermediate goods supply, value-added, exports and imports in annual basis from 1997 to 2012 using UNSD National Accounts DatabaseFootnote 23 and UNIDO INDSTAT Database. Then we apply RAS methodFootnote 24 on the benchmark tables along with the industry-specific output and intermediate goods supply and demand data for each of the endogenous countries, which yields 16 annual (1997 to 2012) NIOTs for each 29 endogenous countries valued in respective national currency. Thus estimated NIOTs in national currencies are then converted into the US dollar based NIOTs with respect to annual exchange rates provided by UNSD’s National Account Main Aggregates Database. Major advantage of using national currency based NIOTs for the RAS estimation is that the newly estimated NIOTs are less likely to be affected by fluctuation of the bilateral exchange rates.
Secondly, we split intermediate goods and final goods transactions of each NIOTs into domestically procured goods and imported goods. We further separate import blocks of intermediate goods and final goods according to its source country using source country breakdown import shares of intermediate and final goods, respectively. The source country breakdown import shares are calculated from 3121 categories of 4- or 5-digit SITC3 commodity trade data, which are separated into intermediate goods and final goods (combination of 713 categories of consumption goods and 475 categories of capital goods) on the basis of Broad Economic Category (BEC classification), converted into YNU-GIO industry classification system.
Third, we organize domestic transactions and source country breakdown imports of all 29 endogenous countries as a single inter-country transaction matrix, in such a way that the domestic transaction lies on the diagonal block and corresponding source and destination countries lies on the off-diagonal block for both intermediate goods and final goods transactions. By re-organizing inter-country transaction blocks for intermediate goods and final goods transactions, value-added blocks, and output blocks, we get the unbalanced version of globally linked input–output table. In other words, at country level, sum of intermediate inputs (both domestic and imported) and value-added in the unbalanced table corresponds to gross input. However, sum of domestic and exported intermediate and final goods does not add up to gross output on the unbalanced table. Such difference occurs due to the use of source country breakdown import share to figure out the source country of imported goods. As we know that disparity in trade data as a reporter and partner is inevitable (i.e., in trade data country A’s import of goods from country B is not same as country B’s export to country A or vice versa.), we must adjust the unbalanced table to get the balanced one because difference in gross input and gross output contradicts the fundamental law of input–output table, which states that the gross input and gross output must be equal.