Carbon border adjustment mechanism in the transition to net-zero emissions: collective implementation and distributional impacts

As an instrument to minimize carbon leakage, the effects and feasibility of Carbon Border Adjustments Mechanism (CBAM) will depend on multiple design options. While the EU has committed to introducing CBAM as part of its green climate deal, pursuing climate efforts to successfully limit global warming requires a collective implementation involving major emitters China and the US. This paper quantifies the distributional impacts of a joint CBAM implementation of in a climate alliance or a club of the EU, the US, and China. Differing from a myriad of studies that focus on unilateral CBAM, this analysis emphasizes collective implications on leakage, sectoral competitiveness, and welfare by projecting climate neutrality relative to current policies and climate targets. Our findings confirm that coalition reduces leakage, improves production on energy-intensive industries, and increases club’s welfare relative to a non-CBAM and a unilateral implementation. These are in contrast with some unilateral analytical studies, especially for the US. It is further proof of the potential of CBAM as collective instruments to facilitate mitigation and trade competitiveness.


Introduction
As a pioneer in global climate mitigation, the European Union (EU) has been taking more serious action in regards to the policy initiative of the European Green Deal (European Commission 2019), aiming to reach carbon neutrality by 2050 (European Parliament 2019). In achieving this, the EU Commission has initiated the Carbon Border Adjustment Mechanism (CBAM) to support transition to stop free allowances and in long term to reduce the risk of carbon leakage and ensure competitive price (European Commission 2019). CBAM can be imposed either as import tariffs for certain goods that imported to the EU or export rebates for the EU export. In early 2021, the EU Parliament expressed its support, and the first legislative proposal was released on July 14, 2021, as part of the Fit for 55 legislative packages (European Commission 2021b, c).
On the other hand, the EU's strong commitment and its unilateral move are still subject to caveats. EU contributions as an economic union are still limited to making meaningful differences in global emissions targets without equal effort from the major emitters such as China and the US. A coordinated multilateral action shall be considered since domestic reductions in emissions are likely counter-balance by emissions outside the EU (Condon and Ignaciuk 2013;Clora and Yu 2022). In addition to this, the carbon cost discrepancy has been expanding dramatically in the EU ETS sectors, indicating a higher growing burden on the European industries compared to other regions (Mathieu 2021).
A climate alliance or club has been a long-discussed approach to global warming, as a study proposed by Nordhaus (2015). Aligning acclimate club with CBAM is feasible as participating countries could manage emissions at a stringent level and coordinate tariffs on imports to solve the leakage and burden sharing issue (Branger and Quirion 2014;Böhringer et al. 2021). The EU legislative proposal opens this opportunity to coordinate with the affected regions that motivates to form a climate club, which includes the opportunity for agreements with China and the US 1 since both have also committed to a more stringent climate approach to reach climate neutrality.
With the US, the EU, and China accounting for 61% of the global gross domestic product and 43% of goods imports, forming a climate club has geopolitical advantages. A tripartite deal also supports China's green revolution with no extra cost on the export (Li and Zhang 2012) and fits with the US's strategy on China's technology and intellectual property (Tagliapietra and Wolff 2021). A collective CBAM implementation involving the EU, China, and the US is critical to achieve universal abatement commitments from others. China and the US are net gainers from unilateral mitigations, but these net gains are bolstered by universal climate abatement (Perdana and Tyers 2020). An import tariff in CBAM increases production costs and acts as a punitive instrument that alter countries' decisions to join and change other countries' dominant strategy from free riding. As the cost of reducing emissions 1 3 Environmental Economics and Policy Studies (2023) 25:299-329 falls, the cost of joining the club will decline, so China and the US' decisions to form a coalition and implement CBAM alongside the EU is a decisive factor for others countries to follow (Helm et al. 2012;Böhringer et al. 2016).
This paper aims to assess the distributional impacts of the climate club of the EU, China, and the US imposing the CBAM. Despite studies measuring the implication of CBAM, none specifically focused on analyzing the impacts when a border tariff protection is implemented amongst a climate club consisting the EU, the US, and China. 2 Though the impacts of unilateral policy are measurable, the magnitude of the resulting leakage will depend on the current climate policies, implementing countries, and sectoral coverage. Unlike previous studies, we start the analysis from the current policy and climate targets for these regions, then move to their latest climate neutrality targets. CBAM is then introduced under this neutrality framework and being assessed for its potentials of CBAM to reduce emissions leakage, sectoral competitiveness, and their distributional allocations in each region or as a club. Scenario development also involves sectoral analysis, the basis and the adjustment tariff target in order to improve the global-cost effectiveness.
Our analysis confirms that collective implementation reduces leakage and improves productivity especially in energy-intensive industries (EII). The collective implementation also improves welfare relative to a non-CBAM and or unilateral implementation, where welfare contribution from trade is stronger for the US than for the EU or China. The following section discusses the current literature of CBAM, the critical aspect and the implications. A modelling approach is addressed in Sect. 3, and Sect. 4 elaborates the scenario development, numerical results and analysis. Results are concluded in Sect. 5.

Literature review
In general, studies investigating CBAM report impacts due to changes in production output (Babiker and Rutherford 2005;Mattoo et al. 2009;Böhringer et al. 2010;Winchester et al. 2011). Three aspects emerge from these prior analyses. The first is CBAM's impact on reducing leakage and improving overall cost effective if it is unilaterally implemented. The second aspect is whether CBAM limits the negative effect on the production of EII. And if it creates negative terms of trade effects that impact the welfare (Gros 2009).
The coalition scenario created to address the leakage channels will determine how effectively CBAM reduces leakage (Branger and Quirion 2014). Most studies that focus on the EU as a unilateral region or as a central player in the coalition, confirm that CBAM reduces leakage (Elliott et al. 2010;Böhringer et al. 2012c; 1 3 Bednar-Friedl et al. 2012;Perdana and Vielle 2022) despite the significance and the magnitude of the reported results not always being in agreement. In contrast, the analysis centralizing on the US finds no significant evidence for leakage. McKibbin et al. (2016) finds non-positive leakage in the unilateral implementation of the carbon tax in the US. Implementing carbon tax lowers growth in the US and slows down the global economies. It further results in declining in global emissions. Policy scenarios with a CBAM tax on imports with the baseline reflecting current policies also find no evidence of leakage (McKibbin et al. 2012).
The leakage effect may also differ between macro and sectoral levels. Kuik and Hofkes (2010) and Antimiani et al. (2013) confirm a modest reduction effect in the EU macro-levels. Nonetheless, the sectoral rate of EII's leakage such as in the iron and steel industry may be reduced significantly. Böhringer et al. (2012a) discovers that production losses fall from 2.8 to 1% compared to the reference case, implying carbon border adjustment's competence in protecting the competitiveness of energy intensives industries in abating regions.
In contrast, McKibbin et al. (2018) study discovers potential declines in export when quantifying the economic and environmental impact of carbon taxation in the US in the presence of a CBAM. Imposing CBAM tends to produce lower net exports than the carbon taxes alone. It raises the value of the dollar relative to other currencies, thus lowering exports more than imports. This finding is consistent with standard results in the international trade literature on the effects of import tariffs and export subsidies on real exchange rates, yet often overlooked in the discussion of domestic carbon policy.
On the other hand, China has been chiefly seen as a vital target country of CBAM. Among the few qualitative analyses, Li and Zhang's initial study (2012) ensures CBAM will result in relocations of outputs across regions and countries. Although, when compared to a unilateral tax, CBAM would be a costly and inefficient policy instrument to reduce emissions, it could function as a coercion strategy. This coercion strategy might significantly influence China's motivation to impose carbon tariffs. China is a large economy and energy consumer that is very open to international trade. Looking ahead, the Chinese government considers potential interactions between China and other economies when designing tax reforms (Lin and Li 2012). Seeing the interaction between the US and the EU that tends to be confrontational, China may impose a carbon tax to give an equal game to play, or it may not. A simulation study of China's imposing carbon tax against American carbon tariffs results in fluctuation in China's GDP and greatly impacts high-carbon industries (Zhu et al. 2020).
From these current literature, three things can be concluded. First, a unilateral CBAM implementation between the EU and the US will likely lead to opposite results; effective for the EU but contradictory to the US. Second, the non-existing literature on China implementation in CBAM should be a priority in further research. And third, an assessment of the collective implementation of CBAM between these major emitters is important to project the effect on global leakage, sectoral competitiveness, and welfare in each region. Implementing CBAM would change the payoffs in climate negotiation and be an incentive for abating their emissions.

3
Environmental Economics and Policy Studies (2023) 25:299-329 The projected impacts of unilateral implementation policy are well known (Felder and Rutherford 1993), but the relative magnitude of resulting leakages, competitiveness level, and welfare impacts if countries move collectively remains an empirical question, which all depends on the policies in place, the implementing countries, and the affected sectors. This paper aims to address this empirical question. It focuses on scrutinizing the impact of CBAM on the EU, the US, and China collectively as a club, based on the current climate policies and targets. A carbon neutral commitment is the conditional factor to join the climate club for collective CBAM, which have been all indicated by the EU, China and the US.
The analysis will prove a hypothesis of ineffective CBAM of a small coalition by Antimiani et al. (2013). The notion of a coalition was introduced by Buchanan (1965) and then up-scaled by Nordhaus (2015) by positing climate as a public goods. Increasing tariffs unilaterally increases leakage (Jakob et al. 2013), but leakage is still likely to occur in a limited coverage coalition and consequently offset emissions reduced by the coalition (Veenendaal and Manders 2008). A small coalition still causes a reallocation of emission reductions; thus, this is also not effective in reducing leakage. Furthermore, the implementation should be directed towards a global solution rather than a domestically oriented point of view. In addition to this, widening the scope of the coalition could avoid abuse of pure protectionists, which could lead to retaliatory tit for tat trade wars.
For competitiveness analysis, Weitzel et al. (2012) argues that the EU has the strongest incentives followed by the US, to increase carbon-based border tax prices across regions once a coalition is formed. Strategic use for the terms of trade is more substantial than environmental use for reducing carbon emissions. Böhringer et al. (2017) claim that protective measures in CBAM increase the comparative advantage and competitiveness, but may reduce output value due to negative Income Effect (IE) should the coalition be formed. Reduction in output value should also be the center of analysis of collective CBAM implementation. Sub-global abatement inevitably induces changes in trade, comparative advantage, and competitiveness and arguably affects the coalition welfare.

The GEMINI-Emodel
The vast majority of research around CBAM is built on the Computable General Equilibrium (CGE) models, where carbon leakage and distributive allocation between sectors could adequately be assessed. The CGE is widely adaptable to address the economic impact of climate-change mitigation policies and the level of ambition required to reach the commitments. The multi-sectoral calibration and dynamic global scope encompass international trade and emissions and adequately address the impacts in terms of allocation of production, international trade and emissions of Greenhouses Gases (GHGs). For simulations and analytical purposes, this study uses the latest modification of GEMINI-E3 based on the study by Bernard and Vielle (2008). The model incorporates multi-country, multi-sector, recursive computable general equilibrium model that assumes of total flexibility in both macroeconomic markets such as capital and international trade markets (with endogenously driven associated prices being the real rate of interest and the real exchange rate) and microeconomic or sector markets (goods, factors of production, etc.).
The current version is built on the GTAP 10 data base (Aguiar et al. 2019) with the year 2014 as the reference year. For analytical purposes, the regional aggregation of this version covers the EU, the US, China and the rests of the world which is represented by eight countries and regions. The number of sectors is limited to 11 for a tractable and acceptable computation time. GEMINI-E3 is recursive dynamic, with backward looking (adaptive) expectations.
For each sector, the model computes the demand of its production based on of household consumption, government consumption, exports, investment and intermediate uses. Total demand is then divided between domestic production and imports using the Armington assumption (Armington 1969), which assumes that domestic and imported goods are not perfectly homogenous.
Production technologies are described by a nested Constant Elasticity of Substitution (CES) functions. Simulations use the endogenously carbon price for the CBAM tariff, not a stylized unilateral carbon pricing, to tackle the possibility of endogenously decreasing supply elasticities and sharply increasing marginal leakage rates for large coalitions as indicated by Boeters and Bollen (2012). This technique avoids an overestimation of industrial output loss and underestimation the increase in the CO 2 embodied in imports that affect the accuracy of efficiency of border carbon adjustments at reducing leakage (Caron 2012).
GEMINI-E3 calibrates GHG emissions (CO 2 and non-CO 2 ) from policy databases of countries to sectoral level of aggregation. This feature enables the imposition of CBAM, either as an import tariff or export subsidy, and estimates its impacts, especially for leakage and decomposition. The way the carbon contents are computed in GEMINI-E3 is detailed in Appendix B. 2 In all the scenario preformed in this paper, we assume that the government's deficit or surplus is fixed. When a CBAM is implemented, the revenue collected will be redistributed to households as lump sum transfer.
The total emissions leakage for a country is equal to the emission change by sectors and household consumption. Other critical features of GEMINI-E3 including its GHG emissions, leakage decomposition and methods of welfare assessments, are detailed in the Appendices A and C. 3

Current policies implemented in the club
The scenario design of current policies follows the CD-Links policies database, International Energy Agency (2020) to ensure a more updated complementary climate-development policy until the year 2030. The assumptions on demography, GDP, energy prices and technology costs follow our previous work on the H2020 Paris-Reinforce project, detailed in Giarola et al. (2021) and Sognnaes et al. (2021). This scenario includes a subset of the high-impact policies collected and analyzed for the period 2015 to 2030. For robustness, the scenario will be projected until 2040 to fit the undefined climate policies post-2030 and the feasibility of policy implementation due to technological and sectoral granularity in the model. All relevant policies are listed in the Table A.13 of Appendix.
Particularly for the EU, the reference scenario uses still targets in 2030 climate and Energy Framework of the −43% emissions decrease with respect to 2005 for ETS and the −30% for non-ETS emissions. These two carbons' prices are then assumed to grow in line with GDP per capita rates until 2040. 4 Table 1 shows keys performance indicators for the selected regions in the year 2020. The current policies scenario results in GHG emissions as described in Fig. 1.
Around 16% of the world production of energy-intensive goods are traded among countries), 5 and the exchange of these goods amounts to 7′515 billion of US$ 6 by 2040 ( Table 2). The club represents 46% of the exports and 44% of the imports. As expected, China is not only a net exporter to the US and the EU, but also is a net importer from the other regions.

Climate policies implemented in the club
The climate policies scenario integrates the new targets recently decided by the alliance as elaborated in the previous subsection. In line with the EU's new target to cut GHG emissions by at least 55% from 1990's levels, we follow the proposal of the  In the US, even if the commitments defined by the Biden administration have not been specified in detail, we assume that the existing regional cap-and-trade programs already implemented into the electricity generation sector 7 will be extended to other states and merged (Hibbard et al. 2018). We also assume that the US EII will participate into the US ETS market. For China, our climate policy scenario sets no specific targets for their ETS sectors, since the trading market has not been escalated to the national level. National abatement targets are adjusted linearly to achieve net-zero emissions by the targeted year. The abatement target for China is 100% in 2060, with national abatement targets linearly adjusted (25% of 2020 in 2030, 50% in 2040, and 75% in 2050) to reach this net zero emissions target. Table 3 lists these new targets.
In this scenario, we implement the GHG and CO 2 targets in the club with unilateral CO 2 prices. In the EU, an ETS price and a GHG tax (applied on the ESR sectors) are implemented simultaneously, followed by the assumption of a fully auctioned quota in the ETS sector. A similar protocol is used for the US. With no precise definition of the climate policy, especially for ETS markets (Li et al. 2019;Yan et al. 2020), we assume that a uniform carbon price is implemented in China. Table 4 shows the results of CO 2 prices. Integrating the "Fit for 55" package results in a higher EU ETS price, which is now equal to 131 US$ in 2040. 8 The CO 2 price applied in the EU ESR sectors reach 3353 US$ showing the stringency of the emissions reduction in these sectors, especially in the transportation and in non-CO 2 GHG emissions. In the US, both the ETS and the CO 2 price will emerge in the year 2030.The ETS reaches 275 US$ in 2040 with increasing pressure now placed on other sectors, raising the CO 2 prices to 1080 US$ in 2040. 9 For comparison, China's CO 2 price is relatively the same compared to the EU and the US. Despite being lower than predicted in a recent study by Yuan et al. (2021) with an estimated 99 US$ in 2030, our projected CO 2 price is consistent with similar simulations for China using CGE models (Cao et al. 2021). Table 5 shows the impact of these unilateral carbon prices on CO 2 emissions. Global CO 2 emissions decrease by 10.1 GT CO 2 or 23%, whereas global GHG emissions are reduced by 12.4 Gt CO 2 -eq or 20% by 2040. As can be expected, GHG emissions increase in all regions beyond the club. The leakage rate is equal to 4.8%.
The EII production fall range between 4.8 and 12.2%, whereas amongst non-alliance member, production increase occurs mainly in Russia (+ 22.9%), followed by the Middle East (+ 12.5%) due to the specialization of these regions in energy-intensive industries. The world GDP slightly decreases by 1.1%, due to the depressive impact of the climate policy within the club. Outside the coalition, GDP increases; however, the welfare measure gives a different picture where all regions are negatively affected. The US, EU and China suffer from negative welfare changes due to the GHG taxation. And others, mainly energy-exporting countries, have revenue loss from energy exports. Positive change in GHG emissions in all regions beyond the club indicates the occurrence of leakage. To distinguish the contribution from EII, we use a different approach for leakage decomposition. It starts from the leakage related to production changes without considering the emission changes induced by relative price changes (mainly the decrease of international fossil energy prices). For EII, we decompose this component as related to change in global reallocation (i.e. trade) and the one linked to domestic demand. It is then followed by decomposition related to the component of aggregated production change for non-EII sectors and consumptions. The residual is called "other general equilibrium effects", which is mainly driven by reduced international fossil energy prices. Figure 2 shows the leakage decomposition in these four components. 10 At the worldwide level, the price component ("OGE" in Fig. 2), the non-EII component, and the EII component related to trade account for around one-third of leakage. At the regional level, we find many more disparities according to national conditions. Leakage related to EII (blue bars in Figure) dominates in the Middle East, India and Brazil. The decrease of international fossil energy prices induces a CO 2 emission decrease in India. A lower international natural gas prices generates the substitution of domestic coal by imported natural gas in Indian electricity generation, which decreases CO 2 emissions in this sector. The international trade of EII goods falls by 16% at the worldwide level. Exports from the club decrease by 30%, but imports from the Club remain un-changed except for China (Table 6).

CBAM integration
CBAM could be implemented by a border charge on imports, a border rebate for exports, or full border adjustment. The tendency, however, goes to implementation of CBAM as a border charge on import for less complexities (Mehling and Ritz 2020) and its consistency with the World Trade Organisation (WTO) rules (Evans et al. 2021). Implementing CBAM as an export subsidy may violate international trade law for its conditional upon exportation classified as a prohibited subsidy under the Agreement on Subsidies and Countervailing Measures (Holzer 2014). Following Cosbey et al. (2019), there are three following categories or scopes of calculating emissions contents in CBAM. Carbon contents could be based on either direct emission from fuel combustion within the sector boundary (Scope 1), direct emissions plus the CO 2 content of electricity consumed by the sector or indirect emissions associated with energy use (Scope 2), or direct emissions and any indirect production-related emissions including all the CO 2 content of intermediate consumption by the sector (Scope 3). Computing the CO 2 content with Scope 1 is the simplest, while complexity grows with Scope 2, and 3. Methodologies for calculating these emission contents are detailed in the Appendix.
As legal issue might be prohibitive to a collective implementation of CBAM (Böhringer et al. 2012b), the system is thus more likely to comply with international law characterized by low rates and limited coverage. This brings to the likelihood that the potentials of CBAM go with scope 1 or 2 rather than scope 3, since the carbon content for compensation at the border includes indirect emissions associated with intermediate non-fossil inputs that are less likely to comply with WTO. The global cost-effectiveness of unilateral climate policy is also degraded rather than improved by a more complicated and detailed system in scope 3 (Böhringer et al. 2017). From environmental policy perspectives, the tariff is too high and fails to acknowledge a key behavioral response to redirect output in other markets. For comparative analysis, scenario development in this paper will evaluate CBAM, in all scopes and measure the impact on leakage, competitiveness and welfare indicators.
The analysis includes only CO 2 contents for CBAM to avoid complexity and to keep the robustness of estimated results. We consider it as the limitation of our study, as CBAM should correspond to GHG emissions covered by Annex I to the EU ETS (European Commission 2021c) in Directive 2003/87/EC, including nitrous oxide (N 2 O) and perfluorocarbons (PFCs). Initial work to model non-CO 2 emissions is done by Clora et al. (2021) using GTAP 10 non-CO 2 database, with a shorter projection frame of 2030. This is clearly a matter for our future work.
The final aspect in implementing CBAM is the technique, whether the carbon contents will be based on the best available technology in abating countries or unregulated countries outside the club (Antimiani et al. 2013). The chosen technique is critical, especially if CBAM is applied as an import tariff. We follow the assessment by Ismer and Neuhoff (2007) to use domestic emissions of the exporting countries and to impose CBAM equal to projected carbon price of the importing countries (members of the club). Tons of carbon from domestic or international sources are subject to similar treatment consistent with WTO rules.

Determining industries candidate for CBAM
Following most literature focused on EII (i.e. industries where energy consumption represents a significant share of production costs), a holistic sectoral assessment to evaluate the gain in implementing CBAM is critical. As the first step in developing a climate policy scenario with CBAM, we analyze the impacts of implementation of CBAM as import tax for electricity generation, agriculture, EII, and other goods & services. The scenario runs using the direct emissions from fuel combustion within the sector boundary, or "scope 1" for CBAM implemented in all regulated countries in the club. Results are significant only for EII, where CBAM reduces the leakage effect and protects domestic productions (Fig. 3). The production change on other goods & services is non-negligible, but to include this sector in the CBAM is impractical for the heterogeneity of goods aggregated in this sector. Further analyses on the following sections particularise to the EII.

Determining CO2 content that must be used (scopes)
In determining the basis of the CO 2 content in collective CBAM, the second step compares the implication of CBAM as an import tax using scopes 1, 2 and 3. The results of the three scenarios are reported in Fig. 4 for collective CBAM. Switching from scopes 1 to 2 significantly reduces leakage from 180 to 284 Mt CO 2 and increases EII's production from 253 to 450 million US$. The gain of scope 3 to scope 2 is much more limited, where leakages are reduced to 315 Mt CO 2 and EII production only reach 527 million US$. Scope 3 also has the particularity of raising practical problems of implementation due to its complexities. Following this rationality, further analysis focuses on scope 2 on CBAM implementation.

Implementation of CBAM on EII with scope 2
The implementation of a CBAM decreases the leakage rate and limits production loss amongst countries of the club. CBAM also improves the welfare for club members but not for non-members, following the loss of production in energy-intensive products. Moving from unilateral (Table 7) to collective implementation of CBAM further reduces leakage, increases the competitiveness of EII and provides higher welfare improvement, proving the effectiveness of coalition to attain CBAM objective. Production change of EII in China has slightly declined by joining the club, indicating a slight competitiveness loss by the US and EU products in the global market. However, this is insignificant, as welfare change in China is still higher by collective implementation in the club.
Welfare decomposition shown in Table 8 reveals that implementing CBAM improves regions gains from trade (GTT), which justifies increasing competitiveness and net negative deadweight loss (DWL). The US's trade effect on welfare is more substantial, yet lower DWL gives more dominant effects for both the EU and China. These findings prove that implementing CBAM, either unilateral or collectively, will positively impact US EII trade competitiveness. Further, these indicate that strategic use of the terms of trade is more substantial for the US, for the more robust incentives to increase the carbon tax by joining the coalition. These findings are still relevant to Weitzel et al. (2012), although the most robust incentives happen in the US instead of the EU. These also highlight the importance of constructing Fig. 4 Leakage, production, and welfare change relative to scenario without CBAM in the function of CO 2 content used. Source: Estimation as described in the text the simulation based on current (and updated), instead of assuming of no climate policies taken, affect simulations results' robustness. In the absence of CBAM, the deadweight loss is higher in the EU than in the US and China due to more stringent abatement targets. When CBAM is implemented, the DWL is significantly reduced by revenue gained from import tax (Felbermayr et al. 2015).
In terms of export, CBAM reduces more of EII exports products. Table 9 shows more distortion in exports for the EU, US and China than the absence of CBAM (Table 6). Protective measures in CBAM may increase comparative advantages and competitiveness, but reduce the output value due to the negative Income Effect. Reduction of the output value is quite significant for EII because of considerable declines in the import of energy-intensive intermediate goods that reduce production. We assess that this factor is more justifiable than the effects of import tariffs on exchange rates as suggested by McKibbins. As the coalition grows, the effects of import tariffs on exchange rates will become less significant, as the value of local currencies of club members will appreciate.

Full implementation of CBAM-import tariff and export subsidies
The analysis expands once collective CBAM is complemented with an export subsidy, in addition to an import tariff (full implementation). Figure 5 compares leakage, competitiveness, and welfare change effects between the import tariff and the full implementation. The latter gives slightly higher leakage reduction, more EII production, and insignificant differences in welfare change. Export decomposition in Table 10 also reveals minor differences than with import tariffs. Subsidies cause no significant improvements in export reductions, validating the stronger impact of negative Income Effects of a higher cost of intermediate goods that reduces the output.
Second, the implementation of CBAM has to be applied only in EII in order to be effective in reducing leakage effects and protecting domestic productions. Its impact on other sectors remains insignificant. In determining the basis of the CO 2 content in CBAM, switching from a direct carbon content basis (scope 1) to include the electricity consumption (scope 2) significantly reduces leakage and increases EII production. These findings contradict the recent EC proposal on CBAM, which calculates based only on direct CO 2 emissions (Scope 1) for both EII and electricity generation (European Commission 2021c). Extending the scenario to include indirect emissions contents (scope 3) results in an insignificant reduction in leakage and production improvement. Following these results, compatibility with WTO rules, and complexities of implementation, means that adoption of scope 2 is likely to result in far more effective impacts of CBAM.
Third, a coalition reduces more leakages, improves production on energyintensive industries, and increases club's welfare relative to a non-CBAM and or unilateral implementation. Switching from unilateral to collective implementation of CBAM results in more leakage reduction, confirming the effectiveness of CBAM in a bigger coalition. Production of EII goods escalates in the EU and the US, but slightly reduces in China due to trade competition. Gains on trade improves welfare for the US, while the negative deadweight loss of revenue gained from import tax is more dominant for the EU and China.
Fourth, CBAM reduces further EII product exports. CBAM may increase the comparative advantage and competitiveness, but reduces the output value due to the negative Income Effect of post-import tariff on imported intermediate goods. This caused is more significant than the implication of exchange rates suggested by several studies. Switching into full implementation of CBAM by adding the export subsidies results in no further significant effects on leakage reduction but slightly improves production with no change in welfare.
Finally, the significant impacts of CBAM on aggregated EII emphasizes the importance of scrutinizing the impacts on each type of these energy industries. However, representing full disaggregated EII requires detailed inclusion of non-CO 2 gas, as well as necessitates extending three methodologies of imposing CBAM based on emissions contents. In addition to this, mapping the source of non-CO 2 to different classifications of energy industries (should this sector be disaggregated) is complex and requires secondary feedbacks for data robustness. This remains a limitation of this current work and should be regarded in further research. scenarios, abatement for non-CO 2 gases are calculated based on the marginal abatement cost.

Assessing welfare cost
Welfare cost of countries are measured through compensating variation of income (CVI) to capture the change in structure of prices, which is the main effects of climate change policies. The cost consists of the domestic component or deadweight loss of taxation (DWL) and the imported component or gains from terms of trade (GTT). The GTT represents spill-over effects due to changes in international prices, mainly from the drop-in fossil energy prices resulting from the decrease in world energy demand. Decomposition of the welfare cost aims to approximate decomposition between domestic and imported cost to obtain a general idea of their relative importance (Harrison et al. 2000;Böhringer and Rutherford 2002). This approach is justified by the fact that the change in prices, in particular the prices of foreign trade, is fairly small. In practice, compensative variation income is first calculated from the results of the model, and the specification and coefficients of the demand function. GTT is then calculated based on the results of the involved scenario using the following equation: where ∆Pexp i and ∆Pimp i represent changes in the exports and imports prices (for product i), with respect to the reference scenario; and Export i and Import i represent the levels of exports and imports, respectively, in the reference scenario. Finally, the DWL is the difference between the compensative variation income and the GTT. The total emissions leakage for a country is equal to the sum of leakage by sector plus the emissions change related to household consumption (denoted CO H 2 ).
First, we can approximate the emissions that are related only to production change at the sectoral level without considering the emissions change that is induced by relative price changes, like the decrease of fossil energy prices. We compute this term by multiplying the variation of production in percentage (relative to the current policies scenario) to the emissions level of the sector in the current policies scenario.
Variables Production i and CO i 2 represent the production level of sector i and its CO 2 emissions in the current policies scenario.
For household, the same computation can be done using change in aggregate household consumption: In a second step, leakage related to production change can be decomposed into two components; one that is related to international trade, i.e. production change coming from change in imports and exports of the goods produced by the sector, and the other related only to domestic demand.
Finally, the residual leakage represents all other general equilibrium effects, which are mainly driven by the decrease of international energy prices and is represented by Authors contributions Both authors contribute to the conception and design of the study, acquisition of data, and the analysis. Both are also drafting and revising the manuscript. All persons who meet authorship criteria are listed as authors, and all authors certify for full participation in the work to take responsibility for the content in the concept design, analysis, writing or the revision of the manuscript. Each author certifies that this material has not been published before. Data availability An excel sheet that includes the numerical results will be provided once the paper is accepted, uploaded on a Zenodo space.

Conflict of interest
The authors declare that we do not have a competing financial interest that could have been appeared to influence the work reported in this paper.

Ethical approval
The research involved no human participants or animals; thus, compliance with the ethical standard is unnecessary.
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