A Comprehensive Input-Output Analysis Model for Quantifying Environmental Linkages and Leakages: Evidence from Greece

doi:10.21203/rs.3.rs-3729869/v1

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A Comprehensive Input-Output Analysis Model for Quantifying Environmental Linkages and Leakages: Evidence from Greece

https://doi.org/10.21203/rs.3.rs-3729869/v1

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published 17 Mar, 2025

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This paper introduces a novel approach to simultaneously estimate total (direct and indirect) greenhouse gas (GHG) emissions linkages and leakages by employing both the Leontief demand-driven and Ghosh supply-driven input-output (I-O) models. Using the Greek economy as a case study the paper contributes to the research field of environmental interindustry linkage analysis by evaluating the impact of international trade on the carbon footprint of national economies. The analysis identifies industries with significant emissions linkages and leakages, highlighting the potential for domestic input substitution as a means to reduce GHG emissions. This approach offers valuable insights for the formulation of targeted mitigation policies, contributing to the pursuit of sustainable development goals.

Input–output analysis

linkages

leakages

GHG emissions

Greece

Input-Output (I-O) analysis is a powerful tool for understanding how the various industries within an economy are linked together. There are two types of linkages between industries. Backward linkages refer to the relationship between the increased production of an industry and the subsequent rise in its demand for intermediate inputs, supplied by other industries, while forward linkages refer to the supply relationship between the increased production of an industry and the availability of its commodities as inputs to production in other industries (Miller and Lahr, 2001; Sharma et al., 2022). Obviously, in open national economies, imported commodities may also be used in the production process. Hence, when increasing production, it will also generate additional imports to support it. That kind of import is called an economic leakage (Guo and Planting, 2000; Reis and Rua, 2009) in the sense that dampen the multiplier process in the domestic economies (Mariolis, 2018; Mariolis and Ntemiroglou, 2023).

In recent years, due to public concerns regarding the environmental impacts associated with the growing release of greenhouse gases (GHG) resulting from economic growth, the I-O framework is used extensively to estimate the total (direct and indirect)¹ interindustry linkages associated with air pollutant emissions. In particular, due to the generation of pollutant emissions in the production process, the increased demand for intermediate inputs from other industries by a particular industry leads to the absorption of emission pollutants, signifying its backward emissions linkages, while the increased supply of intermediate inputs from a particular industry to other industries involves the transfer of pollutants, indicating its forward emissions linkages.

Two primary methods employed in Input-Output (I-O) analysis to assess interindustry linkages are the Traditional Linkage Method (TLM) and the Hypothetical Extraction Method (HEM). Rasmussen (1957), Chenery and Watanabe (1958) and Hirschman (1958) are considered as pioneers of the TLM, providing empirical evidence about the economic structure of productive sectors throughout an economy. Chenery and Watanabe (1958) proposed the column and row sums of the input coefficient matrix as a measure of intersectoral linkages. However, this approach measures only the direct effect of the intersectoral linkages ignoring the indirect ones. The above-mentioned problem solved by Rasmussen (1957), by suggesting the use of the column and row sums of the Leontief inverse matrix as a measure of the strength of backward and forward linkages. By this way, both direct and indirect effects of an increase in the output of a particular sector are taking into consideration. Hirschman (1958) used Rasmussen’s linkage approach for the empirical investigation of key sectors and the determination of suitable investment projects. More specific, under the Hirschman’s analysis, sectors linkages are divided by the average of all linkages. Therefore, sectors having an above both backward and forward linkage average are considered as key sectors, in a sense that their output expansion may stimulate the overall economic growth. The idea of the HEM was initially captured by Paelinck et al. (1965) and Strassert (1968) and later extended and applied by Schultz (1977), Cella (1984), and Dietzenbacher and van der Linden (1997), among others. HEM determines the significance of an industry or a group of industries by measuring the changes in total gross output that result from hypothetically removing a part of their industrial interdependencies from the economic system (Guerra 2014).²

Various environmental extensions of TLM and HEM have been widely used in academic literature to study economic structure in environmental terms. Lin and Chang (1997) employed TLM and cluster analysis to assess the environmental impact and inter-industry relationships of oil consumption industries in Taiwan, identifying fuel oil as the most impactful and recommending adjustments in the investment of key industries. Lin et al. (2012) used TLM to examine CO₂ emission linkage effects in Taiwan, identifying artificial fiber, coal products, cement, and land transportation as the top CO₂-intensive sectors related to electricity and suggesting opportunities for targeted mitigation strategies and enhanced environmental practices applicable to similar power plants in other countries. Ali (2015) used both TLM and HEM linkage indices in an environmentally extended input–output model to measure CO₂ emission linkages among productive sectors in Italy, categorizing all sectors into four groups and identifying key CO₂ emitter sectors to inform the formulation of effective mitigation policies. Beidari et al. (2017) analysed the interconnectedness and total impact of energy consumption and CO₂ emissions across 18 sectors in South Africa's economy from 1995 to 2012 by using TLM linkage analysis, identifying the top five energy-consuming and CO₂-emitting sectors and emphasizing the need for targeted strategies to reduce both direct energy consumption and CO₂ emissions in the country. Guo et al. (2018) identified key sectors influencing China's energy consumption and CO₂ emissions through TLM and demand elasticity, emphasizing the importance of sectors such as the manufacture of basic chemicals for targeted attention and policy intervention. Du et al. (2019) utilized the HEM and input-output tables to analyse CO₂ emissions in the Chinese transportation sector, revealing significant emissions transfers and identifying the road sub-sector as a major emitter. Zhang et al. (2021) used the HEM to investigate changes in industrial air pollutant emissions in China, providing a quantitative analysis of sector linkages, identifying key sectors, and offering insights for policymakers to understand the impact on pollutant emissions. Tsirimokos (2022) proposed an environmental modification of HEM to analyse energy efficiency policies in the U.S. and Chinese economies, identifying key sectors that absorb and transfer energy through the purchases and sales of intermediate inputs, offering insights for decision-makers.

In environmental interindustry linkage analysis studies, there has not been sufficient emphasis on differentiating between inputs that are produced domestically and those that are imported. If linkages are being evaluated within a single economy, it is important to only consider domestically supplied inputs as the focus is on the impact on the domestic economy.³ Failure to account for this can have significant empirical implications and may bias the results, leading to an overestimation of the multiplier effect of a particular industry (Dietzenbacher et al., 2005; Su and Ang, 2013). By accounting for the difference between imported and domestically produced inputs within the I-O framework, it becomes possible to not only accurately measure domestic emissions linkages, but also explore a new aspect of the analysis. This allows for an investigation into the impact of international trade on emission linkages and the potential for influencing the total GHG emissions of a country by estimating GHG emissions leakages.

The primary objective of this study is to contribute to the research field of the environmental TLM analysis by evaluating the impact of international trade on the carbon footprint of national economies. To achieve this objective, the study proposes a methodological framework that combines the Leontief demand-driven (1936) and Ghosh supply-driven (1958) input-output (I-O) models to simultaneously estimate GHG emissions linkages and leakages. This approach is particularly suitable for I-O tables that differentiate between domestically produced and imported inputs. To demonstrate the applicability of this framework, the study uses the Greek economy as a case study, which serves as a representative example of a small, open European economy. The study contributes to a more comprehensive understanding of the environmental implications of international trade and emphasizes the significance of considering both interindustry linkages and leakages when conducting an emissions linkage analysis.

The structure of this paper is as follows. Section 2 outlines the proposed model. Section 3 presents the empirical results of the paper along with a discussion. Section 4 provides the concluding remarks.

2.1. The general framework of the I-O Model

Symmetric national input-output tables (NIOTs) describe both the demand-side and the supply-side of an economy. The quantity demand-side of the economy is described by (values are in monetary terms):⁴

$$\mathbf{x}={\mathbf{Z}}^{\text{d}}\mathbf{e}+{\mathbf{f}}^{\text{d}} \left(1\right)$$

$$\mathbf{I}\mathbf{m}={\mathbf{Z}}^{\text{m}}\mathbf{e}+{\mathbf{f}}^{\text{m}} \left(2\right)$$

where $\mathbf{x}$ is the n x 1 vector of gross output, ${\mathbf{Z}}^{\text{d}}$ is the n x n matrix of interindustry transactions in domestic intermediate inputs, ${\mathbf{f}}^{\text{d}}$ is the n x 1 vector of final demand for domestically produced commodities, $\mathbf{I}\mathbf{m}$ is the n x 1 vector of total demand for imports, ${\mathbf{Z}}^{\text{m}}$ is the n x n matrix of interindustry transactions in imported intermediate inputs and ${\mathbf{f}}^{\text{m}}$ is the n x 1 vector of final demand for imported commodities.

The matrices of direct input coefficients are given by:

$${\mathbf{A}}^{\text{d}}\equiv {\mathbf{Z}}^{\text{d}}{\widehat{\mathbf{x}}}^{-1} \left(3\right)$$

and

$${\mathbf{A}}^{\text{m}}\equiv {\mathbf{Z}}^{\text{m}}{\widehat{\mathbf{x}}}^{-1} \left(4\right)$$

where ${\mathbf{A}}^{\text{d}}$ and ${\mathbf{A}}^{\text{m}}$ are respectively the matrices of direct input coefficients for domestically produced and imported commodities.

Multiplying equations (3) and (4) from the right with $\mathbf{x}$ yields to:

$${\mathbf{A}}^{\text{d}}\mathbf{x}={\mathbf{Z}}^{\text{d}}\mathbf{e} \left(5\right)$$

and

$${\mathbf{A}}^{\text{m}}\mathbf{x}={\mathbf{Z}}^{\text{m}}\mathbf{e} \left(6\right)$$

By introducing Eq. (5) into Eq. (1) and solving for $\mathbf{x}$, yields to:

$$\mathbf{x}=\mathbf{L}{\mathbf{f}}^{\text{d}} \left(7\right)$$

where ${\mathbf{L}\equiv [\mathbf{I}-{\mathbf{A}}^{\text{d}}]}^{-1}$ is the n x n Leontief inverse matrix for domestically produced commodities.

Similarly, by substituting Eq. (6) into Eq. (2) and then using Eq. (7), we get:

$$\mathbf{I}\mathbf{m}={\mathbf{A}}^{\text{m}}\mathbf{L}{\mathbf{f}}^{\text{d}}+{\mathbf{f}}^{\text{m}} \left(8\right)$$

The quantity supply-side of the economy is described by:

$${\mathbf{x}}^{\text{T}}={\mathbf{e}}^{\text{T}}{\mathbf{Z}}^{\text{d}}+{\mathbf{e}}^{\text{T}}{\mathbf{Z}}^{\text{m}}{\mathbf{e}}^{\text{T}}+{\mathbf{v}}^{\text{T}} \left(9\right)$$

The matrices of direct output coefficients are given by:

$${\mathbf{B}}^{\text{d}}\equiv {\widehat{\mathbf{x}}}^{-1}{\mathbf{Z}}^{\text{d}} \left(10\right)$$

and

$${\mathbf{B}}^{\text{m}}\equiv {\widehat{\mathbf{x}}}^{-1}{\mathbf{Z}}^{\text{m}} \left(11\right)$$

where ${\mathbf{B}}^{\text{d}}$ and ${\mathbf{B}}^{\text{m}}$ are respectively the matrices of direct output coefficients for domestically produced and imported commodities.

Multiplying equations (10) and (11) from the left with ${\mathbf{x}}^{\text{T}}$ yields to:

$${{\mathbf{x}}^{\text{T}}\mathbf{B}}^{\text{d}}={\mathbf{e}}^{\text{T}}{\mathbf{Z}}^{\text{d}} \left(12\right)$$

and

$${\mathbf{x}}^{\text{T}}{\mathbf{B}}^{\text{m}}={\mathbf{e}}^{\text{T}}{\mathbf{Z}}^{\text{m}} \left(13\right)$$

Equation (9) can be formulated, through equations (12) and (13), as follows:

$${\mathbf{x}}^{\text{T}}={{\mathbf{x}}^{\text{T}}\mathbf{B}}^{\text{d}}+{\mathbf{x}}^{\text{T}}{\mathbf{B}}^{\text{m}}+{\mathbf{v}}^{\text{T}} \left(14\right)$$

$${\mathbf{x}}^{\text{T}}=({\mathbf{x}}^{\text{T}}{\mathbf{B}}^{\text{m}}+{\mathbf{v}}^{\text{T}})\mathbf{G} \left(15\right)$$

where ${\mathbf{G}\equiv [\mathbf{I}-{\mathbf{B}}^{\text{d}}]}^{-1}$ is the n x n Ghosh inverse matrix for domestically produced commodities.

2.2. Total GHG emissions interindustry linkages

The direct GHG emissions of the industries by a demand-driven perspective can be obtained as follows:

$$\mathbf{c}=\varvec{\Phi } \mathbf{y} \left(16\right)$$

where $\varvec{\Phi }\equiv \widehat{\mathbf{q}} \mathbf{L}$ is the n x n matrix of the total backward GHG emissions linkages and $\widehat{\mathbf{q}}$ is the diagonal matrix of direct GHG emissions intensities.⁵ Each element $ij$ of the matrix $\varvec{\Phi }$ denotes the degree of change in the GHG emissions of commodity $i$, induced by the increase of one-unit in the final demand for domestically produced commodity $j$, both directly as the GHG emitted by an industry $j$ ’s production process and indirectly as the GHG emissions embodied in industry $j$’s intermediate inputs.

The total backward GHG emissions linkages index of industry $j$ is estimated by the sum of the elements in the $j$th column of the matrix $\varvec{\Phi }$:

$${BLINK}_{j}\equiv {\mathbf{e}}^{\text{T}}\varvec{\Phi } {\mathbf{e}}_{j} \left(17\right)$$

where ${BLINK}_{j}$ denotes the changes on the direct and indirect amount of GHG emitted by all the industries of the economy.

On the other hand, the direct GHG emissions of the industries by a supply-driven perspective is given by:

$${{\mathbf{c}}^{\text{T}}}^{*}=({\mathbf{x}}^{\text{T}}{\mathbf{B}}^{\text{m}}+{\mathbf{v}}^{\text{T}})\varvec{\Psi } \left(18\right)$$

where $\varvec{\Psi }\equiv \mathbf{G} \widehat{\mathbf{q}}$ is the n x n matrix of the total forward GHG emissions linkages. Each element $ij$ of the matrix $\varvec{\Psi }$ denotes the degree of total change in the GHG emissions of commodity $j$, induced by the increase of one-unit in the value added in domestically produced commodity $i$.

The index of the total forward GHG emissions linkages of industry $i$ is estimated by the sum of the elements in the $i$th row of the matrix $\varvec{\Psi }$:

$${FLINK}_{i}\equiv {\mathbf{e}}_{i}\varvec{\Psi } \mathbf{e} \left(19\right)$$

where ${FLINK}_{i}$ denotes the changes on the direct and indirect amount of GHG emitted by all the industries of the economy.

2.3. Total GHG emissions interindustry leakages

To assess the influence of imports on the overall GHG emissions of an economy, the concept of GHG emission leakages is employed. This framework builds upon the environmental modification of the economic leakage concept proposed by Reis and Rua (2009), operating under the assumption that imported intermediate inputs are substituted with domestically produced ones.

The total backward GHG emissions interindustry leakages of the economy are estimated based on the following equation:

$$\varvec{\Gamma }\equiv \widehat{\mathbf{q}} {\mathbf{A}}^{\text{m}}\mathbf{L} \left(20\right)$$

where $\varvec{\Gamma }$ is the n x n matrix of the total backward GHG emissions leakages. Each element $ij$ of the matrix $\varvec{\Gamma }$ denotes the total change in GHG emissions that occur during the production of imported intermediate inputs of commodity $i$, due to a one-unit increase in the final demand for domestically produced commodity $j$.

The index of the total backward GHG emissions leakages of industry $j$ is estimated by the sum of the elements in the $j$th column of the matrix $\varvec{\Gamma }$:

$${BL{\rm E}{\rm A}{\rm K}}_{j}\equiv {\mathbf{e}}^{\text{T}} \varvec{\Gamma } {\mathbf{e}}_{j} \left(21\right)$$

where ${BL{\rm E}{\rm A}{\rm K}}_{j}$ denotes the additional changes on the direct and indirect quantities of GHG emissions produced by all industries within the economy.

On the other hand, the total forward GHG emissions interindustry leakages of the economy are estimated using the matrix:

$$\varvec{\Delta }\equiv \mathbf{G} {\mathbf{B}}^{\text{m}}\widehat{\mathbf{q}} \left(22\right)$$

where $\varvec{\Delta }$ is the n x n matrix of the total forward GHG emissions leakages. Each element $ij$ of the matrix $\varvec{\Delta }$ denotes the total change in GHG emissions that occur during the production of imported intermediate inputs of commodity $j$, as a result of a one-unit increase in the value added of domestically produced commodity $i$.

Thus, the index of the total forward GHG emissions leakages of industry $i$ is estimated by the sum of the elements in the $i$th row of the matrix $\varvec{\Delta }$:

$${FL{\rm E}{\rm A}{\rm K}}_{i}\equiv {\mathbf{e}}_{i} \varvec{\Delta } \mathbf{e} \left(23\right)$$

where ${FL{\rm E}{\rm A}{\rm K}}_{i}$ denotes the additional changes on the direct and indirect amount of GHG emitted by all the industries of the economy.

2.4. Extensions of the Model

To enhance the analysis of interindustry GHG emissions, the model can be extended and estimate the total internal and external GHG emissions linkages and leakages. Specifically, when an industry experiences an increase in its final demand (value added) for its domestically produced commodity, it stimulates a higher demand (supply) for intermediate inputs sourced from its own production as well as other industries. Consequently, this surge in final demand (value added) leads to a corresponding rise in the total GHG emissions of the economy. The GHG emissions absorbed (transferred) by the industry from (to) its own production processes are known as internal backward (forward) emissions linkages, highlighting the emissions impact that the industry's own activities have on its overall GHG emissions. Conversely, the emissions absorbed (transferred) by the industry from (to) other industries are referred to as external backward (forward) emissions linkages. These linkages show the impact of emissions that the industry has on other industries within the economy, emphasizing the interconnectedness of emissions between industries. However, since internal emissions linkages specifically refer to the GHG emissions embodied within a particular industry, it can be inferred that internal backward and forward GHG emissions linkages exhibit identical absolute values.

On the other hand, the internal backward (forward) emissions leakages of an industry represent the GHG emissions that the industry absorbs (transfers) from (to) itself through its demand (supply) for (of) imported intermediate inputs, signifying the emissions linked to the industry's dependence on its own imported inputs. On the other hand, the external leakages express the emissions resulting from the industry's utilization of imported intermediate inputs sourced from other industries within the economy.

In particular, internal backward and forward GHG emissions linkages and leakages are given by the values of the main diagonal elements of the matrix $\varvec{\Phi }$ and $\varvec{\Psi }$, and $\varvec{\Gamma }$ and $\varvec{\Delta }$, respectively:

$${BLINK}_{j}^{I}\equiv {FLINK}_{i}^{I}={\phi }_{ij}={\psi }_{ij}, i=j \left(24\right)$$

$${BLEAK}_{j}^{I}\equiv {\gamma }_{ij}, i=j \left(25\right)$$

$${FLEAK}_{i}^{I}\equiv {\delta }_{ij}, i=j \left(26\right)$$

On the other hand, external backward and forward GHG emissions linkages and leakages are given by:

$${BLINK}_{j}^{E}={BLIN{\rm K}}_{j}- {BLINK}_{j}^{I} \left(27\right)$$

$${FLINK}_{i}^{E}={FLIN{\rm K}}_{i}- {FLINK}_{i}^{I} \left(28\right)$$

$${BLEAK}_{j}^{E}={BL{\rm E}{\rm A}{\rm K}}_{j}- {BLEAK}_{j}^{I} \left(29\right)$$

$${FLEAK}_{i}^{E}={FL{\rm E}{\rm A}{\rm K}}_{i}- {FLEAK}_{i}^{I} \left(30\right)$$

Moreover, the model can be extended to quantify the changes in total GHG emissions of the economy resulting from a one-unit change in industries' direct GHG emissions intensity. This can be achieved by calculating relative GHG emissions linkages and leakages (i.e., total GHG emissions linkages and leakages per unit of industries' direct GHG emissions intensity). By incorporating this relative approach, the analysis focuses on the indirect GHG emissions interdependencies among industries while accounting for variations in their direct emissions intensity. Thus, based on equations (17), (19), (21) and (23), the relative GHG emissions interindustry linkages and leakages are given by:

$${BLINK}_{j}^{R}={BLINK}_{j}/{q}_{j} \left(31\right)$$

$${FLINK}_{i}^{R}={FLINK}_{i}/{q}_{i} \left(32\right)$$

$${BLEAK}_{j}^{R}={BLEAK}_{j}/{q}_{j} \left(33\right)$$

$${FLEAK}_{i}^{R}={FLEAK}_{i}/{q}_{i} \left(34\right)$$

respectively.

3.1. Empirical Results

The analysis presented above is applied to the case of the Greek economy, using a symmetric national I-O table and GHG emissions data for the year 2018. The described industries along with the data processing are reported in Table A.1 in Appendix A.

Table 1 reports the values of different types of total backward GHG emissions linkages and leakages. [see equations (17), (21), (24), (25), (27) and (29)]. To illustrate the practical implications of the estimated values, the first industry is used as an example. In this case, if the final demand for industry 1's domestically produced commodity increases by 1 million USD, it triggers a corresponding rise in the demand for its domestic intermediate inputs from both other industries and itself. As a result, the overall GHG emissions of the Greek economy increase by a total of 789 tCO2e. Notably, industry 1 absorbs the highest amount of GHG emissions from its own production, with 646 tCO2e (or 81.84%) attributed to the demand for domestic intermediate inputs from within the industry itself. Additionally, industry 1 absorbs 143 tCO2e (or 18.16%) of emissions resulting from its demand for domestic intermediate inputs sourced from other industries. By examining the plot of the matrix $\varvec{\Phi }$ [see Figure B.1(a) in Appendix B], it becomes apparent that industry 15 plays a crucial role in contributing to these external emissions, accounting for 69.99 tCO2e (or 48.82%). Additionally, significant contributions are observed from industries 19 and 16, accounting for 26.46 tCO2e (or 18.46%) and 14.51 tCO2e (or 10.12%), respectively. The remaining industries contribute 32.39 tCO2e (or 22.59%) to the total external backward GHG emissions linkages.

In relation to the backward leakage of GHG emissions, an increase of 1 million USD in the final demand for industry 1's domestically produced commodity stimulates a higher demand for its imported inputs from all industries, including itself. As a result, there is an additional increase of 65.2 tCO2e in the overall GHG emissions of the economy. Industry 1 absorbs 12.83 tCO2e (or 19.69%) through its demand for its own imported inputs and 52.34 tCO2e (or 80.31%) through its demand for imports obtained from other industries. Based on the plot of the matrix $\varvec{\Gamma }$ [see Figure B.2(a) in Appendix B], it becomes evident that industry 2 holds a prominent position in the external emissions leakages, accounting for 13.33 tCO2e (or 25.46%). Additionally, notable contributions are observed from industry 7, representing 10.00 tCO2e (or 19.10%), and industry 19, contributing 7.96 tCO2e (or 15.20%). The remaining industries contribute 21.06 tCO2e (or 40.23%) to the total external backward GHG emissions leakages.

Table 1

The total backward GHG emissions linkages and leakages.
Industry $j$ or$i$	${BLINK}_{j}$	${BLINK}_{j}^{I}$	${BLINK}_{j}^{E}$	${BLEAK}_{j}$	${BLEAK}_{j}^{I}$	${BLEAK}_{j}^{E}$
1	789 (6)	646 (6)	143 (17)	65.2 (13)	12.83 (6)	52.34 (17)
2	775 (7)	688 (5)	86.01 (23)	30.9 (23)	10.13 (8)	20.81 (25)
3	538 (9)	194 (10)	343 (3)	81.4 (9)	3.32 (10)	78.10 (6)
4	242 (14)	5.05 (24)	236 (7)	74.2 (12)	0.57 (13)	73.65 (9)
5	236 (15)	50.92 (12)	184 (11)	60.7 (15)	7.06 (9)	53.63 (15)
6	377 (10)	292 (9)	84.80 (25)	419 (1)	11.74 (7)	407 (6)
7	684 (8)	535 (7)	148 (15)	123 (5)	61.32 (2)	62.25 (11)
8	205 (16)	19.91 (16)	184 (12)	57.0 (17)	0.31 (15)	56.67 (13)
9	2,163 (2)	1,902 (2)	260 (5)	153 (2)	52.16 (4)	101 (5)
10	1,007 (4)	317 (8)	688 (2)	135 (3)	59.64 (3)	75.71 (8)
11	306 (12)	50.89 (13)	254 (6)	108 (7)	1.18 (12)	107 (3)
12	258 (13)	46.90 (14)	211 (8)	108 (8)	2.51 (11)	105 (4)
13	170 (21)	6.16 (23)	163 (14)	77.1 (10)	0.13 (16)	76.93 (7)
14	173 (20)	4.40 (25)	168 (13)	64.0 (14)	0.02 (23)	63.94 (10)
15	3,529 (1)	3,467 (1)	61.82 (26)	74.9 (11)	19.90 (5)	54.96 (14)
16	1,981 (3)	1,288 (3)	692 (1)	53.0 (18)	0.05 (17)	52.98 (16)
17	368 (11)	46.64 (15)	321 (4)	118 (6)	0.05 (18)	118 (2)
18	182 (19)	58.63 (11)	123 (20)	59.3 (16)	0.48 (14)	58.82 (12)
19	846 (5)	738 (4)	107 (21)	128 (4)	78.90 (1)	49.27 (19)
20	200 (17)	7.07 (19)	192 (9)	50.6 (19)	7x${10}^{-4}$ (25)	50.65 (18)
21	143 (24)	2.58 (28)	140 (18)	35.4 (22)	0.04 (19)	35.32 (22)
22	34.4 (29)	0.96 (29)	33.48 (29)	6.1 (30)	0.04 (20)	6.10 (30)
23	32.1 (30)	0.04 (30)	31.92 (30)	10.5 (28)	${10}^{-6}$ (30)	10.49 (28)
24	91.7 (26)	6.78 (21)	84.94 (24)	27.3 (24)	0.02 (22)	27.25 (23)
25	143 (23)	6.77 (22)	136 (19)	38.8 (21)	0.03 (21)	38.73 (21)
26	66.6 (27)	11.24 (17)	55.41 (27)	12.0 (27)	5x${10}^{-4}$ (27)	11.96 (27)
27	55.5 (28)	2.83 (27)	52.70 (28)	8.1 (29)	3x${10}^{-5}$ (29)	8.05 (29)
28	96.3 (25)	4.06 (26)	92.28 (22)	27.2 (25)	6x${10}^{-4}$ (26)	27.17 (24)
29	158 (22)	9.32 (18)	148 (16)	19.0 (26)	0.02 (24)	19.02 (26)
30	192 (18)	6.87 (20)	185 (10)	41.8 (20)	2x${10}^{-4}$(28)	41.77 (20)
Note: The numbers in parenthesis represent the ranking of the industry.

Table 2 reports the values of different types of total forward GHG emissions linkages and leakages. [see equations (19), (23), (24), (26), (20) and (30)]. Specifically, when the value added of the domestically produced commodity in industry 1 increases by 1 million USD, it results in a higher supply of its domestic intermediate inputs to all other industries, including itself. This leads to a total increase of 705 tCO2e in the GHG emissions of the entire economy. Similar to the backward linkages, industry 1 plays a significant role as the primary transmitter of GHG emissions from its own production. Precisely, it transfers 646 tCO2e (or 91.62%) through the supply of its domestic intermediate inputs to itself. Additionally, it transfers 59.09 tCO2e (or 8.38%) through the supply of domestic intermediate inputs to the other industries. Based on the plot of the matrix $\varvec{\Psi }$ [see Figure B.1(b) in Appendix B], noteworthy contributions in these external forward GHG emissions linkages come from industry 3, accounting for 48.51 tCO2e (or 82.09%), and industry 15, contributing 3.50 tCO2e (or 5.92%). The remaining industries contribute 7.08 tCO2e (or 11.98%) to the external forward GHG emissions linkages.

In terms of the forward leakage of GHG emissions, an increase of 1 million USD in the value added of industry 1's domestically produced commodity stimulates a higher supply of its imported inputs to all industries, including itself. Consequently, there is an additional increase of 25.2 tCO2e in the overall GHG emissions of the economy. Industry 1 transfers 13.60 tCO2e (or 54.05%) through its supply of its own imported inputs, while 11.56 tCO2e (or 45.95%) is transferred through its supply of imports to other industries. Based on the plot of the matrix $\varvec{\Delta }$ [see Figure B.2(b) in Appendix B], industry 3 has a notable impact on the external emissions leakages, accounting for 8.30 tCO2e (or 71.77%). Finally, the remaining industries contribute 3.27 tCO2e (or 28.23%) to the overall external forward GHG emissions leakages.

Table 2

The total forward GHG emissions linkages and leakages.
Industry $j$ or$i$	${FLINK}_{i}$	${FLINK}_{i}^{I}$	${FLINK}_{i}^{E}$	${FLEAK}_{i}$	${FLEAK}_{i}^{I}$	${FLEAK}_{i}^{E}$
1	705 (6)	646 (6)	59.09 (19)	25.2 (19)	13.60 (7)	11.56 (22)
2	957 (4)	688 (5)	268 (1)	2,672 (1)	4.96 (9)	2,667 (1)
3	224 (11)	194 (10)	28.85 (23)	12.9 (23)	3.09 (10)	9.84 (24)
4	31.2 (26)	5.05 (24)	26.17 (25)	36.2 (17)	0.57 (14)	35.68 (15)
5	190 (16)	50.92 (12)	138 (10)	74.1 (13)	7.05 (8)	67.03 (10)
6	510 (8)	292 (9)	217 (4)	149 (4)	13.78 (6)	135 (4)
7	632 (7)	535 (7)	95.98 (14)	467 (2)	60.48 (2)	407 (2)
8	43.2 (24)	19.91 (16)	23.32 (26)	34.6 (18)	0.31 (16)	34.26 (16)
9	2,024 (2)	1,902 (2)	120 (12)	116 (6)	50.79 (4)	65.94 (11)
10	367 (9)	317 (8)	49.60 (22)	104 (8)	59.26 (3)	45.58 (13)
11	217 (13)	50.89 (13)	166 (7)	77.5 (10)	1.26 (12)	76.22 (7)
12	113 (19)	46.90 (14)	66.59 (18)	193 (3)	2.39 (11)	191 (3)
13	107 (20)	6.16 (23)	101 (13)	129 (5)	0.13 (17)	129 (5)
14	206 (15)	4.40 (25)	201 (6)	86.0 (9)	0.02 (23)	85.98 (6)
15	3,724 (1)	3,467 (1)	256 (2)	57.8 (14)	23.91 (5)	33.93 (17)
16	1,371 (3)	1,288 (3)	81.98 (16)	14.5 (22)	0.47 (15)	14.00 (21)
17	98.8 (21)	46.64 (15)	52.13 (21)	10.1 (24)	0.07 (18)	10.05 (23)
18	224 (12)	58.63 (11)	164 (8)	51.0 (15)	0.65 (13)	50.39 (12)
19	829 (5)	738 (4)	90.38 (15)	111 (7)	78.54 (1)	33.15 (18)
20	17.4 (28)	7.07 (19)	10.29 (28)	1.7 (29)	3x${10}^{-3}$ (26)	1.67 (29)
21	80.1 (22)	2.58 (28)	77.42 (17)	21.8 (20)	0.04 (19)	21.74 (19)
22	210 (14)	0.96 (29)	208 (5)	75.9 (11)	0.04 (20)	75.83 (8)
23	128 (18)	0.04 (30)	127 (11)	16.1 (21)	2x${10}^{-5}$ (30)	16.14 (20)
24	253 (10)	6.78 (21)	246 (3)	74.7 (12)	0.03 (21)	74.69 (9)
25	159 (17)	6.77 (22)	152 (9)	39.8 (16)	0.03 (22)	39.79 (14)
26	38.9 (25)	11.24(17)	27.71 (24)	4.0 (27)	4x${10}^{-3}$ (25)	3.99 (27)
27	10.1 (29)	2.83 (27)	7.29 (29)	2.1 (28)	1x${10}^{-4}$ (29)	2.12 (28)
28	8.8 (30)	4.06 (26)	4.74 (30)	0.8 (30)	1x${10}^{-3}$ (28)	0.85 (30)
29	26.7 (27)	9.32 (18)	17.40 (27)	5.6 (26)	0.02 (24)	5.61 (26)
30	63.5 (23)	6.87 (20)	56.63 (20)	6.0 (25)	1x${10}^{-3}$ (27)	6.04 (25)
Note: The numbers in parenthesis represent the ranking of the industry.

Table 3 reports the values of the relative GHG emissions linkages and leakages [see equations (31) to (34)]. In relation to the relative emissions linkages, if the direct GHG emissions intensity increases by 1 tCO2e, due to an increase in its final demand, the total increase in the GHG emissions within the Greek economy is expected to be 1.4 tCO2e. This rise of 1.4 units comprises a one-unit increase from direct emissions and an additional increase of: $1.4-1=0.4$ units sourced from indirect emissions changes throughout the economy, triggered by interconnected industry activities. Furthermore, when focusing on the impact of changes in value added, a unit increase in the direct GHG emissions intensity of industry 1 results in a total increase of 1.2 tCO2e in GHG emissions. This signifies that a unit increase in industry 1's direct emissions intensity induces an additional increase of: $1.2-1=0.2$ units of indirect GHG emissions.

Table 3

The relative backward and forward GHG emissions linkages and leakages.
Industry $j$ or$i$	${BLINK}_{j}^{R}$	${FLINK}_{i}^{R}$	${BLEAK}_{j}^{R}$	${FLEAK}_{i}^{R}$
1	1.4 (24)	1.2 (26)	0.11 (26)	0.04 (28)
2	1.3 (28)	1.6 (22)	0.05 (28)	4.41 (13)
3	2.9 (22)	1.2 (27)	0.44 (23)	0.07 (26)
4	48.6 (3)	6.3 (9)	14.94 (2)	7.29 (7)
5	5.5 (19)	4.4 (11)	1.41 (19)	1.72 (11)
6	1.4 (26)	1.8 (21)	1.49 (18)	0.53 (19)
7	1.3 (27)	1.2 (28)	0.23 (24)	0.89 (15)
8	10.3 (14)	2.2 (18)	2.88 (12)	1.75 (10)
9	1.2 (30)	1.1 (29)	0.09 (27)	0.07 (27)
10	3.5 (20)	1.3 (25)	0.47 (22)	0.37 (20)
11	6.3 (16)	4.5 (10)	2.25 (17)	1.61 (12)
12	5.5 (18)	2.4 (17)	2.33 (15)	4.17 (9)
13	27.7 (8)	17.5 (7)	12.58 (5)	21.20 (3)
14	39.9 (4)	47.4 (3)	14.72 (3)	19.79 (4)
15	1.3 (29)	1.3 (24)	0.03 (30)	0.02 (29)
16	1.6 (23)	1.1 (30)	0.04 (29)	0.01 (30)
17	8.1 (15)	2.2 (20)	2.61 (14)	0.22 (23)
18	3.3 (21)	4.0 (12)	1.06 (21)	0.92 (14)
19	1.4 (25)	1.3 (23)	0.21 (25)	0.18 (25)
20	28.3 (6)	2.5 (16)	7.18 (6)	0.24 (22)
21	59.1 (2)	33.2 (5)	14.65 (4)	9.02 (6)
22	38.8 (5)	236 (2)	6.92 (7)	85.48 (2)
23	900 (1)	3,599 (1)	295 (1)	454 (1)
24	14.3 (13)	39.5 (4)	4.25 (11)	11.65 (5)
25	23.1 (10)	25.7 (6)	6.26 (9)	6.43 (8)
26	5.9 (17)	3.5 (14)	1.07 (20)	0.36 (21)
27	19.9 (11)	3.6 (13)	2.88 (13)	0.76 (17)
28	23.9 (9)	2.2 (19)	6.75 (8)	0.21 (24)
29	18.9 (12)	3.2 (15)	2.28 (16)	0.68 (18)
30	28.2 (7)	9.3 (8)	6.12 (10)	0.89 (16)
Note: The numbers in parenthesis represent the ranking of the industry.

In terms of relative emissions leakages, the substitution of imported intermediate inputs with domestically produced ones in industry 1 as well as a one-unit increase in its direct emissions intensity due to an increase in its final demand, would lead to a total increase of 0.11 tCO2e in the GHG emissions in the economy. This suggests that while the direct emissions increase is one unit, the process of replacing imported intermediate inputs with domestic ones generates a decrease of: $0.11-1=-0.89$ units in GHG emissions elsewhere in the economy. This decrease is considered an indirect effect, potentially due to more efficient domestic production or superior supply chain practices. On the other hand, a one-unit increase in its direct GHG emissions intensity due to an increase in its value added, results in a total increase of only 0.04 tCO2e in the GHG emissions within the economy. This reflects indirect emissions decrease of: $0.04-1=-0.96$ units.

3.2. Discussion

It is crucial to accurately understand and interpret the different types of indices related to emissions linkages and leakages. The total GHG emissions linkages indices capture the overall change in GHG emissions resulting from a one-unit change in the final demand (i.e., ${BLINK}_{j}$) or value added (i.e., ${FLINK}_{i}$) of domestically produced commodities, providing a comprehensive view of the direct and indirect effects of changes in economic activities on GHG emissions. In contrast, the indices for relative GHG emissions linkages focus on the change in total GHG emissions caused by a unit change in the direct emissions of industries, driven by an increase in the final demand (i.e., ${BLINK}_{j}^{R}$) or value added (i.e., ${FLINK}_{i}^{R}$) of their domestically produced commodities. These indices specifically investigate the indirect effects among interconnected industries, emphasizing the relationships and transmission of emissions between them.

The indices for emissions leakages evaluate how the substitution of imported intermediate inputs with domestic ones influences the economy's total GHG emissions. They assess the extent to which changes in GHG emissions are affected by this substitution and the associated interplay between intermediate imports and final demand or value added of domestically produced commodities. By considering the potential emissions reduction resulting from the use of domestic inputs, these indices shed light on the environmental implications of import substitution strategies. Specifically, total emissions leakages measure the absolute amount of GHG emissions that would occur if the imported intermediate inputs were replaced with domestically produced ones. This is due to a unit increase in the final demand (i.e., ${BLEAK}_{j}$) or value added (i.e., ${FLEAK}_{i}$) of a specific industry. On the other hand, relative emissions leakages are normalized measures that show how many times the industry's direct GHG emissions intensity would the total GHG emissions increase, due to a unit change in the direct emissions intensity of the industry induced by an increase in its final demand (i.e., ${BLEAK}_{j}^{R}$) or value added (i.e., ${FLEAK}_{i}^{R}$). These indicators provide an understanding of the emissions intensity associated with the industry, accounting for the indirect effects that come from changing the direct emissions intensity. It should be noted that when the values of the relative leakages are less than one, it signifies that the economy-wide increase in emissions is less than the direct increase in emissions intensity, due to indirect emissions reductions elsewhere in the economy. This highlights potential emissions reduction opportunities through the adoption of more efficient domestic production or superior supply chain practices.

Finally, understanding the internal emission linkages and leakages of an industry is essential for assessing its own production processes' contributions to GHG emissions. These internal indices (i.e., ${BLINK}_{j}^{I}, {BLEAK}_{j}^{I}, {FLINK}_{i}^{I}$and ${FLEAK}_{i}^{I}$) reveal the extent to which an industry's own activities generate emissions and provide insights into potential emission reduction opportunities through internal adjustments and improvements. External emission linkages and leakages (i.e., ${BLINK}_{j}^{E}, {BLEAK}_{j}^{E}, {FLINK}_{i}^{E}$and ${FLEAK}_{i}^{E}$) illuminate the emissions spillover effects between industries. These indices highlight the interdependencies among different sectors, emphasizing the importance of collaborative efforts in achieving sustainable emissions reduction.

This paper aimed to contribute to the research field of environmental interindustry linkage analysis by proposing a methodological framework for estimating simultaneously interindustry GHG emissions linkages and leakages. The framework employed both the Leontief demand-driven and Ghosh supply-driven I-O models to evaluate the impact of international trade on the carbon footprint of national economies, using an I-O table that differentiate between domestic intermediate inputs and imported ones. To demonstrate the application of the framework, the study used the case of the Greek economy for the year 2018. Specifically, it is found that:

(i). Industries 15 ('Electricity, gas, steam and air conditioning supply'), 9 ('Manufacture of rubber and plastic products and other non-metallic mineral products'), and 16 ('Water supply; sewerage, waste management and remediation activities') are identified as the top three industries with the highest total backward and forward GHG emissions linkages. High linkages in both directions signify these industries' significant roles in influencing and being influenced by other industries in terms of GHG emissions within the economy. These industries not only have a substantial direct impact on emissions, but they also play a crucial role in either absorbing emissions through their demand for domestic intermediate inputs or transferring emissions through their supply of domestic intermediate inputs, emphasizing their importance in the overall carbon footprint of the economy. Consequently, any shifts in their production, demand, or supply patterns can have a domino effect, affecting the total GHG emissions of the economy. For instance, the high emissions linkages in industry 15 are primarily driven by its foundational role in supplying essential services to various industries. Thus, by focusing on increasing energy efficiency within the industry to reduce direct emissions and encourage the adoption of renewable energy sources to mitigate the carbon intensity of electricity generation, policymakers can contribute to a more sustainable and resilient economic ecosystem.

(ii). The primary industries in terms of the most substantial total backward GHG emissions leakages are industries 6 ('Manufacture of coke and refined petroleum products'), 9 ('Manufacture of rubber and plastic products and other non-metallic mineral products') and 10 ('Manufacture of basic metals'). On the other hand, industries 2 ('Mining and quarrying'), 7 ('Manufacture of chemicals and chemical products') and 12 ('Manufacture of computer, electronic and optical products, electrical equipment, machinery and equipment n.e.c') are recognized as the top three industries with the highest total forward GHG emissions leakages. The reliance of these industries on imported intermediate inputs significantly contributes to the total GHG emissions. A strategic focus on enhancing the efficiency of domestic processes and reducing dependency on imported inputs can effectively curb the level of GHG emissions and meet national environmental targets. For instance, industry 6 demonstrates notable leakages due to its dependency on imported inputs for various stages of its production process. Thus, policymakers could explore measures such as promoting domestic sourcing of raw materials or fostering collaborations to develop more sustainable supply chain.

(iii). Industries 23 ('Real estate activities'), 21 ('Information and communication') and 4 ('Manufacture of textiles, wearing apparel and leather products') are identified as the top three industries with the highest relative backward GHG emissions linkages, while industries 23 ('Real estate activities'), 22 ('Financial and insurance activities) and 14 ('Manufacture of furniture; jewellery, musical instruments, toys; repair and installation of machinery and equipment') exhibit the highest relative forward emissions linkages. On the other hand, industries 23 ('Real estate activities'), 4 ('Manufacture of textiles, wearing apparel and leather products') and 14 ('Manufacture of furniture; other manufacturing; repair and installation of machinery and equipment') are identified as the top three industries with the highest relative backward GHG emissions leakages. Finally, Industries 23 ('Real estate activities'), 22 ('Financial and insurance activities') and 13 ('Manufacture of motor vehicles, trailers, semi-trailers and of other transport equipment') demonstrated the highest relative forward GHG emissions leakages. These industries, signifies their profound influence on interconnected industries through the indirect effects of changes in their direct GHG emissions intensity. Thus, policymakers should prioritize targeted initiatives such as implementing green technologies, encouraging circular economy practices, and promoting sustainable production methods to address the indirect emissions implications.

The findings of this paper align with and complement the results presented by Tsirimokos (2023), where the HEM was employed to investigate GHG emissions interindustry linkages in the Greek economy for the same year. Both TLM and HEM, despite their methodological differences, provide consistent insights into the environmental implications of economic activities. The combination of these two approaches provides a more thorough understanding of the complex dynamics of environmentally interindustry linkages, strengthening the reliability of policy recommendations. Therefore, future research endeavours should explore the integration of both the TLM and the HEM in estimating environmentally interindustry linkages and leakages, offering a more comprehensive perspective on the environmental consequences of economic activities and trade patterns.

The proposed methodological framework offers a powerful tool for evaluating the environmental impacts of economic activities and international trade. The simultaneous estimation of the emissions linkages and leakages enables a more holistic understanding of the economy-wide GHG emissions dynamics, facilitating the formulation of effective strategies for sustainable development and emissions reduction. By identifying the industries with high GHG emissions linkages and leakages, policymakers can design targeted mitigation policies and promote the use of eco-friendly technologies and production processes to reduce emissions. In addition, the framework highlights the potential for domestic input substitution to decrease GHG emissions leakages. Thus, policymakers can encourage domestic production of intermediate inputs and reduce reliance on imported inputs in the identified industries to minimize emissions. This will not only reduce the carbon footprint of the economy but also contribute to the development of a circular and sustainable economy. Overall, this study adds to the growing body of research on environmental interindustry linkage analysis, presenting a methodological framework that can be adapted for use in estimating interindustry relationships not only in terms of pollutant emissions but also of other environmental critical factors such as energy, water consumption, and land use.

Notes

Direct GHG emissions refer to the emissions generated within the domestic economy and are calculated from a production-based perspective. Indirect GHG emissions, on the other hand, are emissions that result from the intermediate inputs used by industries. Thus, the total GHG emissions account for the balance between the production and consumption sectors by estimating the embodied emissions in the intermediate inputs from other industries, which is calculated from a consumption-based perspective (Sun et al., 2017).

For a detailed description of the HEM analysis covering all possible extraction cases, see Miller and Lahr (2001). For a deeper understanding of the intrinsic controversies between the TLM and HEM, see Cai and Leung (2004). For an analytical and empirical comparison of various linkage measures based both on TLM and HEM, see Temurshoev and Oosterhaven (2014).

On the other hand, if linkages are being evaluated to compare the economic structure of different countries, it may be more appropriate to examine total intermediate transactions. This is because the primary focus is typically on the production methods employed in each country rather than the origins of the inputs used in those processes (Miller and Blair, 2022).

Matrices are indicated by boldfaced capital letters (e.g. $\mathbf{A}$), column vectors are indicated by boldfaced lowercase letters (e.g. $\mathbf{x}$), letter ‘T’ indicates transposition (e.g. x^T), a symbol of hat ‘^’ indicates a diagonal matrix (e.g. $\widehat{\mathbf{x}}$) with the elements of a vector on its main diagonal and all other entries equal to zero, scalars (including elements of matrices or vectors) are indicated by italicized lowercase letters (e.g. $e$), $\mathbf{e}$ denotes the summation vector (e.g. ${\mathbf{e}}^{\text{T}}\equiv {[\text{1,1},\dots ,1]}^{\text{T}}$) and ${\varvec{e}}_{i}$ is the i th unit vector.

The element ${q}_{j}$ of the diagonal matrix $\widehat{\mathbf{q}}$ is obtained by dividing GHG emissions in industry $j$ by the gross output of industry $j$ (i.e., ${q}_{j}={c}_{j}/{x}_{j}$), denoting the amount of GHG emitted directly by industry $j$ per unit of industry $j$’s worth of output and representing the direct linkages of industry $j$.

Author Contribution

There is only one author.

Data availability statement

The 2018 symmetric national input-output table (NIOT) for the Greek economy obtained from the Organisation for Economic Co-operation and Development Structural Analysis Statistics (OECD STAN) (https://doi.org/10.1787/f9a66c3a-en) (OECD, 2022a), while the 2018 GHG emissions data where sourced from the OECD Air Emissions (https://doi.org/10.1787/data-00735-en) (OECD, 2022b).

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No competing interests reported.

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A Comprehensive Input-Output Analysis Model for Quantifying Environmental Linkages and Leakages: Evidence from Greece

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Abstract

1. Introduction

2. The Model

2.1. The general framework of the I-O Model

2.2. Total GHG emissions interindustry linkages

2.3. Total GHG emissions interindustry leakages

2.4. Extensions of the Model

3. Empirical Results and Discussion

3.1. Empirical Results

3.2. Discussion

4. Concluding Remarks

Declarations

Author Contribution

Data availability statement

References

Additional Declarations

Supplementary Files

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