Policy Research Working Paper 10665 Trade, Outsourcing, and the Environment Erhan Artuc Konstantin Sommer Development Economics A verified reproducibility package for this paper is Development Research Group available at http://reproducibility.worldbank.org, January 2024 click here for direct access. Policy Research Working Paper 10665 Abstract This paper analyzes the effects of carbon taxation and border or abating emission-intensive intermediate production carbon adjustments in a setting where firms can choose steps. The paper finds that border adjustments that cannot to respond to taxation by abating or by outsourcing part target scope 3 emissions can lead to outsourcing, and thus of their production. For this, this paper sets up a general leakage, further down the value chain, but nevertheless equilibrium trade model, calibrated with world trade and induce higher abatement both in the countries that impose input-output data that features a discrete choice production the border adjustment and in the ones affected by it. structure, where the producers choose between outsourcing This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at eartuc@worldbank.org or ksommer@worldbank.org. A verified reproducibility package for this paper is available at http://reproducibility.worldbank.org, click here for direct access. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team ∗ Trade, Outsourcing, and the Environment Erhan Artuc† Konstantin Sommer‡ Key words: Trade, Environment, Carbon tax, Carbon tariffs, Leakage JEL codes: F13, F18, Q56 ∗ This paper has been partly supported by Whole of Economy trust fund, the Umbrella Facility for Trade trust fund and the World Bank Knowledge for Change Program (KCP). The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank of Reconstruction and Development, the World Bank, and their affiliated organizations or those of the Executive Directors of the World Bank, or the countries they represent. We would like to thank Kevin Carey, Tom Farole, Carolyn Fischer, Henri de Groot, Dirk Heine, Franc Klaassen, Daniel Lederman, Hector Pollitt, and Daria Taglioni for their comments. All errors are our responsibility. † World Bank, Development Research Group ‡ University of Amsterdam, Vrije Universiteit Amsterdam and World Bank. The author is thankful for financial support provided by the Victor Halberstadt fund. 1 Introduction A major concern of policy makers enacting some form of unilateral emission pricing is that of carbon leakage, i.e. that some of the emission reduction achieved at home is offset by increases in emissions somewhere else. This phenomenon might arise both because domes- tic firms now face higher costs of production than foreign competitors, thus leading to a relocation of production abroad, and because domestic firms could outsource parts of their emission-intense production to locations with lower environmental regulation. A way of tack- ling part of this leakage is by imposing a tax at the border that prices the emission-content of imported goods, a so called border carbon adjustment (BCA). Such border adjustments should in theory disincentivize relocation as well as outsourcing, as imports of emission- intense goods now face the same costs of emissions as domestic production. The idea of BCAs has been discussed in academic circles for a while and has recently also found its way into actual policy making. A practical concern that has emerged from this, however, is that it is hard to price the whole emission content of a good, which is why it is likely that most border adjustment schemes will (at least initially) focus on pricing the scope 1 or 2 emissions, i.e. the emissions created on-site and potentially those linked to the purchased energy, of imports, and thus exclude the emissions from inputs.1 Interestingly, as this paper will show, this can then lead to a leakage effect in exporting countries, because producers there now face similar incentives as producers in the taxing country in the case in which only the domestic tax is in place. In this paper, we quantify the impact of carbon tax on leakage in both importing coun- tries and exporting countries through outsourcing using a general equilibrium trade model in the fashion of Eaton and Kortum, 2002 and Caliendo and Parro, 2015. The model includes input-output linkages between countries and the possibility for firms to outsource parts of their production instead of domestic production as a response to carbon tax. This adjust- ment margin is conceptualized with a task structure, where varieties in different sectors are produced by performing a continuum of tasks. We assume that each task can be performed in-house or it can be outsourced similar to Grossman and Rossi-Hansberg, 2008. When the firm performs the task in-house it uses a combination of two inputs: a clean labor input and a carbon emitting input. This setup is equivalent to thinking about the firm as allocating a fraction of its input for abatement to reduce emissions. To our knowledge, we are the first to incorporate outsourcing in such a discrete choice trade model in an environmental context to 1 See for example paragraph 19 in the introduction of the EU’s regulation on Carbon Border Adjustments (European Union, 2023). 2 study the effects of input-output linkages in a quantitative trade model when implementing a carbon border tax. We assume that producers in each country operate in a perfectly competitive environment and that countries can use two policy instruments to reduce emissions associated with the carbon input. They can implement domestic taxes on emissions, and they can additionally implement a border adjustment, which prices the emissions of an import that are released during its production. Perfect competition implies that each producer sets its price equal to its marginal costs, and the production structure combined with the country-specific taxes implies that each producer optimizes its production for a certain market. That is because each producer chooses its optimal input mix for a given set of emission prices that directly influence their optimization problem through their effect on input prices. Optimizing for a market with high emission prices implies using less emissions, but higher production costs, making it impossible to compete in markets with lower taxes. Vice versa, optimizing for a market with lower taxes implies lower costs of production but a higher tax rate when selling in markets with high taxes, making the firms non-competitive in such markets. Increasing taxes in one jurisdiction then implies that firms face two options to reduce emissions: through increasing their abatement, i.e. switching from the emission input to us- ing labor; and through outsourcing parts of their production. The latter of these two choices is associated with leakage and is undesirable from the policy maker’s perspective. This leak- age can then be addressed by the policy maker by implementing a border adjustment that prices the emissions of the imported goods. Firms in other countries that have specialized in exporting to this market then face the same incentive as domestic firms did before and they can choose either to abate or to outsource parts of their production, leading to leakage further down the value chain. Our model also contains a discrete choice setup for the allocation of workers to sectors that will allow us to study adjustment processes induced by taxes and border adjustments. The model additionally incorporates emissions from the transportation of goods to highlight how changes in global production structures not only affect emissions through changes in scale, composition and efficiency, but also through changes in transportation routes. We provide a brief welfare exercise in which we compare the gains from the emission reductions to losses and gains in income in different countries. We extend the data coverage in our study compared to most other papers to cover a larger share of lower and middle income countries. These smaller economies are sometimes not included in input output tables, but the effect of a border adjustment might be most important for them, as many countries have emission-intense production and are dependent 3 on certain trade partners. Besides the emissions from production, we also include bilateral and sector-specific transportation emissions and we include both country and sector-specific emission taxes that are based on tax revenue data. Values for the substitution elasticities in our model are based on comparable estimates from the literature. To evaluate the strength of leakage effects and to assess the effects of the two policies on global emission levels and reshuffling of production, we simulate two counterfactual policy experiments. In the first, we simulate an increase in emission prices in Europe, and in the second we add a border adjustment that is equivalent to the difference in taxes between origin and destination countries and that is implemented by the European countries that increase their taxes. This border adjustment is notably different from the current plans of the EU for such a border adjustment, but shares the important feature that it does not address scope 3 emissions in the imports. For both of these experiments we aim to uncover the mechanisms that drive changes in production and emissions in Europe and the rest of the world. The first policy leads both to an increase in abatement in Europe, as well as to an increase in outsourcing. The policy also implies a loss in the competitiveness of European producers and, together with the outsourcing, this leads to an increase in production and emissions abroad, counteracting the emission reductions achieved in Europe. Implementing a border adjustment prevents outsourcing in Europe, but increases out- sourcing in the countries that are affected by the policy. This implies that it induces carbon leakage in the origin countries, where producers now also try to avoid the carbon price that they face. However, it successfully increases abatement in Europe compared to the only tax scenario and also increases abatement in countries affected by the policy, again because exporters there now face an indirect carbon price as well. This also implies that the global reduction in emissions is higher than in the only tax scenario. In our simulation, the countries most affected are primarily in close proximity, thus including both low and middle income countries. While these countries benefit from leakage effects in terms of incomes, as production moves from Europe to these countries, they lose from border adjustments as these put some of the tax burden on their own producers. We also show how a unilateral increase in taxes can increase emissions from transporta- tion, as the tax leads to an increase in outsourcing and thus increases the distances traveled by intermediate goods. The border adjustment naturally lowers emissions from transport, as it compresses trade. The changes in emissions from transportation are, however, much smaller than the adjustments in production emissions. Our results show that BCAs reduce global emissions even if they induce leakage in the 4 countries that export to the market that implements such a border tax. This is because they increase the incentive for abatement both domestically and abroad. Broadening the scope of the emissions included in such tariffs will lead to higher emission reductions, but even if these are unfeasible in the short run, the border adjustments are effective in their main target. Our results also indicate that it might be advisable to support lower and middle income countries that might be affected by border adjustments, as these countries might face decreases in aggregate income. Literature Our paper contributes to a wider literature on trade and the environment (among others: Antweiler et al., 2001; Cherniwchan, 2017; Levinson, 2009; Shapiro & Walker, 2018), but extends a much smaller literature that incorporates environmental taxation and border adjustments into quantitative general equilibrium trade models. Herein, our paper is most closely related to Farrokhi and Lashkaripour, 2021 who study optimal carbon taxes and tariffs in a global trade setting and evaluate the emission reduction potential of such policies. The authors, however, do not allow for input-output linkages and outsourcing in their firm structure, thus muting the main channels that our paper is highlighting. Larch and Wanner, 2017, similarly, study carbon taxation and border adjustments in a numerical trade model, but do not incorporate those features. The only paper that we are aware of that also includes an input-output structure in a comparable trade model is by Duan et al., 2021 who focus solely on carbon taxation and do also not explicitly model the outsourcing decision. None of these studies is trying to capture the potential effects that come from emission altering effects stemming from the transportation of traded goods. First highlighted in Cristea et al., 2013, these emissions represent about a third of global emissions associated with trade and might thus be important to consider when studying the linkage between trade and the environment. Shapiro, 2016 includes such emissions in a global trade model and studies how taxing such emissions could affect both trade and welfare. More recently, Klotz and Sharma, 2023 analyze the implications of these emissions along global value chains and the transportation of intermediate goods. There is also a related literature that incorporates environmental taxation into com- putable general equilibrium models (see: Babiker, 2005; Elliott et al., 2010). Recently, also ohringer et al., 2022. border adjustments have been included in such models, for example in B¨ We use a Eaton and Kortum, 2002 based trade model with input-output linkages sim- ilar to Caliendo and Parro, 2015. We model the production structure as a continuum of parts where firms can outsource parts of their production, conceptualized following broadly c and McLaren, 2015. Grossman and Rossi-Hansberg, 2008 and Artu¸ 5 In the following section we introduce our model, in Section 3 we discuss how we bring the model to the data and describe our data sources, in Section 4 we then describe the results of both of our simulation exercises, and in Section 5 we conclude. 2 Model 2.1 Preferences Consider N countries in which agents consume varieties categorized under J sectors. Agents derive utility from their consumption of varieties and disutility from the global level of car- bon emissions in the atmosphere. The varieties are combined by consumers in country n to σ σ −1 σ −1 produce a sectoral composite Qn j ≡ n (Q (ωj )) σ dωj , where Qn (ωj ) is the consump- tion of variety ωj and σ is the elasticity parameter. The sectoral composites enter into the utility of country n agents as n γj U n = g (E ) Qn j , (1) j where E is total global emissions, g (E ) is a function, mapping these emissions into utility, n and γj is the Cobb-Douglas utility share of sector j composite.2 The consumers in country n can either source the varieties locally, if they are produced locally, or import them from other countries. Assume that the cost of sourcing variety ωj from country m is equal to cnm (ωj ). The costs vary by the origin country due to differences in production costs, transportation costs and environmental taxes imposed by exporting coun- try m or importing country n. The following subsections will discuss the market structure and production process of varieties to unravel the components of this cost. 2.2 Market structure and production process There are infinitely many perfectly competitive producers in each country, each associated with an individual mass of zero. We assume that firms produce varieties by completing 2 Emissions can be understood as greenhouse gases in our context, such that the externality from them is truly global and there are no local effects of emissions. 6 multiple stages of production. Each stage can either be performed in-house, by using labor and carbon emitting inputs, or be outsourced directly by using components produced do- mestically or internationally. Conceptually, this setup is closely related to the trading tasks c and McLaren, 2015. model of Grossman and Rossi-Hansberg, 2008 and isomorphic to Artu¸ The producers face both local environmental taxes and carbon border adjustment taxes if they export their outputs and the importing country imposes such taxes. Both of these taxes impact their optimization problem and influence their use of the carbon inputs. Therefore the presence of border adjustments implies that the cost of the carbon input will depend on the destination. Since there are many mass zero firms operating at zero profit, it is optimal for the producers to focus on exporting to a single destination and optimize their produc- tion process accordingly. In other words, producers exporting only to a single destination would face lower production costs, relative to those that export to multiple destinations, as they can optimize the production process given the environmental taxes imposed by the destination. Therefore both origin and intended destination country indices will appear in the state-space of the producers’ optimization problem, which naturally increases the size of the state-space. Despite this complication, this structure will lead to a simple and tractable framework. 2.3 Production technology and stages Consider a technology, where each variety ωj is produced by performing a continuum of production stages indexed by ιωj ∈ (0, 1). For expositional simplicity, assume that one needs to perform each stage exactly xm (ωj ) times to produce one unit of ωj with a Leontief technology. The inverse productivity parameter xm (ωj ) will cause differences in comparative advantage patterns across countries. Each stage can be completed in-house by using a combination of a labor and a carbon- emitting input (or carbon input for short). Henceforth, we will call the combined composite of labor and carbon inputs the “in-house input”. Alternatively, stages can be completed by using outsourced material from other, local or international, producers. To complete the m m stage indexed with ι, either zΛ (ιωj ) units of composite in-house input or zM (ιωj ) units of outsourced parts can be used. For simplicity, we assume that outsourced inputs are sectors- 7 specific but not stage-specific, and that the price of one unit of outsourced input is equal to cm jM , defined in more detail below. 2.4 In-house production We denote the composite in-house input by Λ and assume that it is produced by  φ φ +1  φφ φ+1 φ+1 Lm (ιωj ) E m (ιωj ) Λm (ιωj ) =  +  , amjL amjE where Lm (ιωj ) is the number of workers, E m (ιωj ) is amount of carbon input, am m jL and ajE are the inverse productivity parameters, and φ + 1 is the elasticity of substitution between the two inputs. If countries impose a tax on an imported good based on its carbon emissions, the pro- ducers will adjust the share of carbon input accordingly. As alluded to earlier, in a perfectly competitive environment with many producers for each variety, producers will focus on sup- plying to a single destination and optimize the combination of labor and carbon input. As they operate exactly at the marginal cost, other producers cannot compete with a producer focusing on a single destination. Therefore, actual costs of in-house production will depend on the tax imposed by the destination, the carbon intensity of the production process and the endogenous share of carbon input. The minimized cost of the composite in-house input, Λ, is equal to cnm j Λ . We can express this cost as 1 −φ m −φ m nm −φ cnm jΛ = am jL wj + ajE cjE , (2) m where wj is the wage in sector j , and cnm jE is the cost of the carbon input for producers specializing in exporting to n. 2.5 Cost minimization of production stages Given the production technology, producers select between in-house and outsourced inputs for each stage to minimize production costs in a structure reminiscent of Grossman and 8 Rossi-Hansberg, 2008. Recall that all stages from 0 to 1, should be completed exactly once to receive 1/xm (ωj ) units of output. The cost of stage ι for country m producers targeted for destination n is equal to cnm (ιωj ) = min{ cnm m m m j Λ zΛ (ιωj ), cjM zM (ιωj ) }. (3) m m c and McLaren, 2015, we assume that zΛ Following Artu¸ (ιωj ) and zM (ιωj ) are drawn from Weibull distributions with scale parameters am m j Λ γς and ajM γς respectively, where γς ≡ 1 −1 Γ 1+ ς , which implies that the mean of each distribution is equal to one. The shape parameter denoted with ς is the same for all countries and sectors. Then, the optimization problem implies that the production cost of one unit of ωj in country n sourced from country m is equal to 1 −ς −ς − ς cnm (ωj ) = xm (ωj ) am nm j Λ cj Λ + am m jM cjM , (4) where xm (ωj ) is inversely proportional to productivity. 2.6 International trade Assume that the country-specific productivity variable xm (ωj ) is distributed Weibull with 1 −1 scale γθ and shape θ, where γθ ≡ Γ 1 + θ . Define a cost index 1 −ς −ς − ς cnm j ≡ am nm j Λ cj Λ + am m jM cjM , (5) where cnm j = cnm (ωj )/xm (ωj ) for any variety ωj ∈ (0, 1). Then, for country n, the share of imports from country m in sector j is equal to −θ nm cnm j τj nm πj = , (6) Φnj where the price of the composite is defined as 1 −θ nm −θ Φn j ≡ cnm j τj , (7) m 9 and τjnm is the iceberg cost which includes transportation costs and trade policy frictions. It is also important to note that Φn j is the price of sector j composite faced by consumers in country n when varieties are sourced optimally. 2.7 Outsourced inputs Recall that the intermediate inputs are sector-specific, but not stage or variety-specific. Varieties are aggregated with a CES technology first, and then combined with a Cobb- Douglas function to produce intermediate inputs m βjk σ σ −1 σ −1 Mjm = (Qm M (ωk )) σ dωk k m where βjk is the share of sector k composite in sector j material inputs. Although this structure is similar to consumer preferences, producers have different Cobb-Douglas parameters which can make intermediate inputs different from the consumed goods. This formulation implies that the price of intermediate material input for sector j is given as m βjk Φm k cm jM = m . (8) k βjk 2.8 Outline of the production structure We can summarize the production process with the following steps: • Producers choose the mix of carbon-input and labor for the in-house input Λ based on their costs. • Producers decide whether to use in-house input or outsourced input for each stage ιωj based on their costs and associated productivity draws. • After completing all stages ιωj ∈ (0, 1) with the decided mix of carbon input, labor and outsourced inputs, 1/xm (ωj ) units of variety ωj are produced. 10 • The varieties ωj are traded to be used in final consumption or as intermediate inputs similar to Eaton and Kortum, 2002 and Caliendo and Parro, 2015. Any tax, imposed by local authorities or by importing country governments, will impact the cost of production and push producers to change the mix of inputs: carbon input versus labor for the in-house production, as well as in-house production versus outsourcing. Next, we discuss the tax structure. 2.9 Carbon taxation and share of carbon input and emissions We assume that the carbon input faces both local and foreign taxes. Importers can impose a tax on exporters, based on the share of carbon in producing the exported good. We can thus calculate the total cost of carbon that an exporter faces as cnm m nm jE = pE + ε(ψj + κj ), (9) m where pE is the base cost of the carbon input, think about the energy price, ψj is the local tax and κnm j is the carbon border tax; both the local and the border tax are levied on the carbon content of the carbon emitting input. The emission intensity ε is defined as the emission per unit of carbon input. We assume that the carbon-emitting input is produced by a monopolist, who determines the extraction quantity. For simplicity, assume that the monopolist chooses the extraction quantity for carbon input QE based on a policy function QE = Z (Θ), where Θ is a vector of m all relevant state variables, such as the carbon taxes ψj and κnm j . We will consider different scenarios for the monopolist’s decision for extraction: a scenario where the extraction quan- tity is constant, another one where the monopolists adjusts the extraction quantity to target a predetermined price, and a final scenario where the monopolists maximizes profit under certain simplifying assumptions as a robustness test (see Appendix A.2 for more details). As outlined previously, there are infinitely many producers with zero profits, the produc- ers will be sorted based on their export destination and there will be a market segmentation based on the pattern of environmental border taxes. The producers that are exporting to high environmental tax countries will use less carbon input to lower their tax base, which 11 will result in higher production costs. Therefore, they won’t be able to compete in other markets. The producers exporting to low environmental tax countries will use more carbon input, and will have higher a tax base, therefore they need to charge much higher prices to high environmental tax countries compared to other producers. This market structure en- sures that each producer is focusing on destinations with the same carbon border adjustment tax rate, and optimizes their input use accordingly. This formulation implies that the share of the carbon input in the total value of sector j varieties will depend on the export destination m such that −φ −ς nm nm ajE cnm jE aj Λ cnm jΛ αjE αj Λ = −φ −φ −ς −ς , m ajG wj + ajE cnm jE aj Λ cnm jΛ + ajM cm jM nm nm where αjE is the share of carbon input in the composite in-house input, and αj Λ is the share of in-house input in total cost (which also includes outsourced inputs). The emissions by sector j producers in country m exporting to n is equal to nm nm nm Yjnm Ej = αjE αj Λ ε, (10) cnm jE and the transport emissions are Yjnm nm Tjnm = Ω , nm j (11) cnm j τj where Ωnm j is the per unit emission intensity of transportation, which is specific both to the country pair and the sector. Then, the total worldwide emissions are equal to nm E= Ej + Tjnm . (12) n m j The tax revenue is equal to Rn = in n Ej ψj + nm nm Ej κj . j i m 12 Note that, output of the carbon input producer monopolist should be equal to QE = E/ε in equilibrium when supply is equal to demand, and its revenue is equal to pE E/ε. 2.10 Labor allocation problem Assume that there is continuum of workers with measure Lm in country m. Each worker, indexed with l, draws a sector specific inverse-productivity shock ϵl j . One effective unit of labor input requires ϵl j units of worker l ’s time. As a result the worker receives productivity m l adjusted wage wj /ϵj . Workers’ productivity draws are specific to the sector and worker, but do not depend on the specific variety or the producer. We assume that the shocks are Weibull distributed with scale 1 and shape ν . Sectoral labor supply, i.e. the number of workers allocated to production of j varieties, is m ν wj Lm j = Lm , (13) Wm 1 m ν ν where W m = [ k (wk ) ] is the expected labor income. The labor demand can be calculated from the wage bill as m m αjL αj Λ n Yjnm Lm j = , (14) Wjn m where αjL is the cost share of labor in in-house production. 2.11 Equilibrium conditions Definition. The equilibrium is given by vectors of (i) composites good prices, Φn j , (ii) prices of outsourced inputs, cm nm m jM , (iii) prices of in-house inputs, cj Λ , (iv) sector-specific wages, wj , (v) a global price for the carbon-emitting input pE , and a vector of (vi) trade and production matrices Yjnm , such that I) local supply is equal to total international and local demand 13 nm Yknm = πk ( W n + R n ) + πk nm n βjk in αjM Yjin , (15) j i Consumer demand Producer demand nm −θ where πj = cnm nm n j τj /Φj is the trade matrix, W n is the labor income and Rn is the tax revenue, II) prices of sector composites are equal to their production cost (including transporta- tion): 1 −θ nm −θ Φn j = cnm j τj , m 1 −ς −ς − ς where the cost index cnm j is equal to cnm j = am nm j Λ cj Λ + am m jM cjM , III) prices of outsourced inputs are equal to their production costs from composites of traded varieties m βjk Φm k cm jM = m , k βjk IV) prices of composite in-house inputs are equal to their minimized production costs 1 −φ −φ − φ cnm jΛ = am m L wj + am nm jE cjE , where cnm nm jE is the cost of carbon input including taxes, given by equation cjE = pE + m ε(ψj + κnm j ), V) wages ensure that sectoral labor supply is equal to sectoral labor demand such that ν m m m wj m αjL αj Λ n Yjnm L = , Wm Wjn 1 m ν ν where W m = [ k (wk ) ] gives the total labor income. 14 VI) the global price of carbon input, pE clears the carbon input market QE = Z (Θ) (supply), = E/ε (demand), where Z (Θ) is the policy function characterizing the extraction amount of the carbon m input, Θ is a vector of all relevant state variables, such as the carbon tax ψj , κnm j and prices, and E is the amount of emissions as implied by production and transportation of goods, i.e Yjnm , given in equation (15). The trade and production matrix Yjnm depends on pE and taxes, which determinate the use of carbon input along with other factor prices. The emission amounts are characterized in the model with equations (11), (10), and (12). 3 Data and calibration This section describes the solution method, the data sources that we have used and the data cleaning steps that we took to calibrate our model. 3.1 Solution method and basic data requirements We solve the model by calculating the factors’, inputs’ and composites’ prices along with the trade and production matrix that satisfies the equilibrium conditions summarized in Section 2.11. For convenience, the solution is implemented by calculating changes from the initial equilibrium implied by the data, rather than levels, as it is the standard practice in the literature. While the full solution algorithm is described in Appendix A, we provide a brief sum- mary here to facilitate the discussion on data requirements. The solution method involves 15 two layers of loops: In the outer loop, we guess the carbon price associated with the extrac- tion decision of the monopolist, and in the inner loop we solve the problem of the perfectly competitive producers given the extraction decision. The inner loop characterizes a con- traction mapping and is relatively easy to solve despite the large state-space. The control variable for the outer loop is a simple scalar i.e. the carbon price, it is solved by a standard unconstrained optimization algorithm. To solve the model we need to assume fix elasticity parameters; emissions associated with production and international transportation; the share of environmental tax revenue in GDP; shares of labor, carbon input and material inputs in total cost of production; trade and production data in values; and the shares of inputs from other sectors for production (i.e., an input-output matrix). Some details are provided below and full details are in Appendices A and C. A summary of the data sources used in our calibration is given in Table 1. 3.2 Trade, production and production-related emissions data Parameter Meaning Source αL , αM , αΛ Input shares WIOD, EORA WIOD satellite accounts, αE Emission input share EORA, IEA energy prices γ, β Utility, composite shares WIOD,EORA ψ Emission tax OECD & Eurostat ϑ Tax revenue as share of GDP OECD, WIOD, EORA Yjnm Output and trade WIOD, EORA Cristea et al., 2013, Bertoli et al., 2016, CEPII, Ω Transport emissions Shapiro, 2016, Klotz and Sharma, 2023 wj Wage EORA θ Global productivity dispersion Simonovska and Waugh, 2014 ν Labor productivity dispersion Lee, 2020 Shen and Whalley, 2013, φ Elasticity between clean labor and emissions Farrokhi and Lashkaripour, 2021 ς Elasticity between outsourcing and in-house production Chan, 2017 Table 1: Sources for parameters and calibration Our main data source for input-output data and emissions is the World Input Output Database (WIOD) (Timmer et al., 2015). To extend the country coverage and include more lower income countries, which are crucial to look at when answering questions about the effects of border carbon adjustments, we use the EORA Global Supply Chain Database 16 (Lenzen et al., 2012). These data provide a 26-harmonized sector version for almost all countries of the world, which we use to split the Rest of the World category in WIOD. We do this by first aggregating all countries in EORA with a 2009 GDP below 5bn USD into an aggregate rest of the world (ROW) category. For all countries in EORA (including the new ROW group), we then exclude all countries contained in WIOD and determine the share of each country on the total supply and demand to and from all sectors (to all EORA countries, including those contained in WIOD). We then use these shares to split the WIOD ROW category into these countries from EORA. We adjust the WIOD sectoral coverage to match both that of EORA and that of the environmental satellite accounts of WIOD, which we need to determine the production emission-related parameters. A list of the final sector coverage can be found in Table C1 and an overview of the sector mappings in Table C2. Last, we enforce balanced trade between countries. We then use this input output matrix to calibrate the input shares γ and β as well as the trade matrices Y . The environmental satellite accounts are most recently available for all countries in WIOD only in 2009, which is why we base all of our analysis on data from that year. We make use of CO2 (carbon dioxide), CO4 (methane) and N2 O (nitrous oxide) data, where we convert the latter two into CO2 equivalents based on their global warming potential. The conversion factor for methane is hereby 28 and the one for nitrous oxide 265, based on their cumulative forcing over 100 years, taken from IPCC, 2014. For Luxembourg, Romania, Switzerland, Croatia, and Norway and all countries not included in WIOD we rely on the EORA environ- mental satellite accounts from the same year.3 Our data is thus based on scope 1 emissions, but we could also extend the coverage to scope 2 emissions, by reassigning the emissions of the energy sector to all other sectors. Sector-specific labor income data is for all countries taken from EORA, as the data is more detailed in this regard than WIOD. 3 We replace the data for these countries with EORA values, as they have many implausible zeros or missing values in WIOD. 17 3.2.1 Input cost shares To calibrate the input shares αM , αL and αE , we assume that the input share of the carbon emitting input is proportional to the emission intensity of a sector. We then find the costs of the emission input for each sector by using data on emission related energy inputs from WIOD and energy inputs from EORA. These data are on a per fuel basis, which allows us to combine them with data on fuel input prices provided by the International Energy Agency and the OECD (International Energy Agency, 2023)4 , to turn the emission input into an input cost. We get the value of intermediate inputs, M , from WIOD and deduct the previously calculated emissions cost from all intermediate inputs to avoid double counting. We treat the sector value added as the share of L in production. Summing M , E and L gives us the denominator for all αs. αM is derived by dividing M by this denominator, αE αΛ by dividing the emissions costs by it and αL αΛ in the same way.5 3.3 Initial tax rates We use a broad definition of emission taxes by including taxes that are levied on emissions without having to have explicit carbon pricing motives. We obtain these data from the OECD database on tax revenues from environmental taxation (OECD, 2022), available for almost all countries in our sample, and for EU countries from Eurostat. The European data is split into revenues from industry and households and further differentiates between different industrial sectors. For the EU data, we can thus derive the implicit tax rate in each country and sector by dividing these tax revenues by the emissions in this country-sector, yielding a $ per ton tax rate.6 For all other countries that we can not observe in Eurostat, we derive the sector-specific (and more importantly not household-related) taxes based on the 4 As not all countries have available data for all fuel sources, we follow the following strategy by always choosing one global fuel price: if available we take the OECD average price, otherwise we take the OECD EU average and if neither of these is available we take the price in the US. We add the underlying prices in Appendix C. 5 For the few sectors where αM becomes negative, due to an unreasonably large emission cost share, we set the αM value in this country sector combination to the αM value of the sector with the smallest intermediate input share that is still positive, and adjust αE such that the shares sum to one. 6 We hereby choose climate change related taxes to align with our emission data. 18 average derived EU taxes. More details on this can be found in Appendix C. For countries that we do not observe in the OECD database we assume that their tax rate is equal to zero. For ϑ, the carbon tax share in GDP, we take the tax income from the OECD data before dividing it by the sum of value added among all sectors in this country (i.e. GDP). We calculate ε, the emissions per unit of the carbon input for each country and sector by dividing the emissions by the emission input.7 3.4 Transport emissions We calculate transport emissions for each country pair by sector, combining multiple data sources, relying on the results of Cristea et al., 2013 and a simplification approach used in Klotz and Sharma, 2023. Transport emissions are usually calculated based on the weight of trade, the mode shares of it (i.e., how much is transported by air, road, or water), the effective distance between countries, and the emission intensity of each of the transport modes. We use the trade values derived from WIOD and EORA and convert them into weights using the weight-to-value ratios of Cristea et al., 20138 , and combine these with the mode shares from the same source. We then take bilateral distances from CEPII Conte et al., 2021 and sea distances from Bertoli et al., 2016. Within-country sea distances are not given in the data and so we use 1.96 times the within-country CEPI distance as suggested in Klotz and Sharma, 2023. Emission intensities per kilogram and km traveled by transport mode are taken from Shapiro, 2016. Our estimates do not aim to be as precise as those used in Shapiro, 2016, as transport emissions are not at the forefront of our analysis. However, including the data allows us to study how changes in production relocations can alter global emissions from all emission sources. 7 We hereby deduct the tax payments from the emission inputs costs. For negative values of ε, we choose the minimum in the respective sector. 8 We split the regions in which their data is aggregated into countries using the GTAP region classification. As mode shares and weight-to-value ratios are not available for within-country trade, we use averages with all neighboring countries to infer these values. For larger GTAP regions these data are available, and we use the values for all countries belonging to that region. We use CPI data from the Federal Reserve to convert the 2004 data from Cristea et al., 2013 into 2009 dollars. 19 3.5 Trade, input substitution and labor elasticities Our calibration is completed by four key elasticities: the productivity dispersion θ, closely linked to the trade elasticity; the substitution elasticity between M and Λ, 1 + ς ; the sub- stitution elasticity between L and E , 1 + φ; and the labor productivity dispersion, ν , linked to the labor elasticity. We currently rely on estimates of these from the literature. We choose θ to be 4.6, in line with common estimates in the literature, for example in Simonovska and Waugh, 2014. In our main specification, we chose φ to be 1.86, which is based on the average estimates from Shen and Whalley, 2013, and implies that labor and emissions are substitutes to each other. We provide an additional robustness analysis based on the estimate by Farrokhi and Lashkaripour, 2021, which implies φ = −0.374, and thus that the two inputs are complements to each other. For the elasticity between M and Λ, we rely on the average of the sectoral elasticities found in Chan, 2017 and choose ς =1.34, for ν we rely on Lee, 2020 and use 1.44. 3.6 Summary statistics We present some stylized descriptive statistics from our data, once split by countries and once by sector. In Figures 1 and 2 we plot the initial emission intensity of each country as well as the initial average emission tax rate in each country. Our sample contains 141 countries, covering almost all of Europe, most countries in the Americas and Asia and a large part of African economics. As expected, European economies are on average cleaner than economies in Asia, Africa, and most of the Americas. Similarly, carbon taxes in Europe are the highest in the world, while many countries have taxes equal to or close to zero. The presented tax rates are comparatively high, as we do not only capture direct carbon taxes, but also implicit taxation on emission use as described in Section 3.3. In Table 2, we present the same statistics - as well as the average input cost shares for outsourced materials, labor and emission inputs - but split by sector instead of by country. Due to the inclusion of methane emissions, agriculture is by far the most emission-intense sector, while simultaneously being one of the sectors with the lowest implicit tax rates. 20 Initial Emission Intensity 5295 2304 1437 991 719 508 326 67 No data IBRD 47498 | SEPTEMBER 2023 t of CO2eq./ Mil. Dollar of output Figure 1: Average emission intensity Among the manufacturing sectors, chemicals and metal manufacturing are the most emission- intensive. The emission cost share is low among all sectors, while the share of outsourced inputs is almost always above 50 percent. 21 Initial Average Tax Rate 128.84 28.10 5.36 1.89 0.31 0.00 No data IBRD 47499 | SEPTEMBER 2023 $/t, unweighted sectoral average Figure 2: Average carbon tax Sector Emission intensity Tax αM αL αE Agriculture 3264.99 2.37 0.46 0.51 0.04 Mining & Quarrying 1532.22 8.74 0.49 0.48 0.03 Food 306.15 8.74 0.74 0.25 0.01 Textiles 336.38 10.96 0.70 0.28 0.01 Wood and paper 501.05 6.81 0.69 0.29 0.02 Fuels, chemicals and minerals 1843.04 3.68 0.65 0.25 0.10 Basic and fabricated metals 1512.62 4.40 0.70 0.27 0.03 Electrical equipment, machinery 130.10 14.55 0.70 0.27 0.03 Vehicles, transport equipment 129.65 16.01 0.75 0.25 0.01 Furniture, repair, and other 351.50 24.63 0.54 0.35 0.11 Services and other 429.51 8.50 0.44 0.51 0.04 Table 2: Summary statistics by sector. Emission intensity calculated as global emissions divided by global value added (t/Mio dollars); emission tax and input cost shares are (un- weighted) country averages. 22 4 Simulation results In this section we compare the results of two policy scenarios with each other. In the first scenario, we simulate an increase in carbon taxes within the European Economic Area - Eu- ropean Free Trade Association (EEA-EFTA) countries, which are the countries participating in the EU emissions trading system. In this simulation, all countries in this group increase their environmental taxes in each sector to the highest tax among the members within this sector (“Scenario 1”).9 In the second scenario, we show how the effects of such a tax increase change when the countries simultaneously implement a border adjustment (“Scenario 2”). This border adjust- ment is equal to the importing country’s tax rate minus the tax rate charged in the exporting country, again separately for each sector. This border tax is different to the planned EU carbon border adjustment mechanism (CBAM), but shares one important feature: the bor- der tax is not levied on scope 3 emissions in the exporting country, meaning that outsourced parts (M in our model) will not be targeted by the border tax. In both experiments, we keep the supply of global emissions constant; so the carbon producing monopolist chooses prices accordingly (assumption 1 in Appendix A.2). We do this to avoid welfare considerations from changes in emissions, such that we can focus on the distribution of emissions between countries rather than on the effect of the total changes in global emissions, which we analyze subsequently separately. The assumptions on the carbon- input supply, however, do not have any qualitative effect on our results, and we are happy to share the respective results. We start by presenting the main results of both scenarios on the emission intensities of countries as well as on the embedded emissions in trade, before going into the channels that explain these results and then discussing the effects on incomes and global emission levels. 9 This scenario is notably different to the EU emissions trading system, as it is a tax and not a trading system, it also contains more sectors and a much higher price, as we include all implicit emission prices. 23 4.1 Effects on emission intensity of production and leakage We start our analysis by looking at the effect of both policy scenarios on the emission intensity of production, akin to the change in the share of E in production, in Figure 3. Clearly the countries that impose the tax reduce their emission intensity in both scenarios. The reduction in emissions per unit of output appears to be slightly larger in the only tax scenario, but the most striking difference between the two scenarios is the effect on the countries outside the EEA-EFTA. In scenario 1, almost all countries in Africa, Asia and South America increase their emission intensity, and this effect appears to be the stronger the closer the country is to Europe. This already shows the expected leakage effect from the EEA-EFTA countries to the rest of the world. In the border adjustment case, this increase in the emission intensity is lower in most places, happening in fewer countries, and moves further away from Europe. The border adjustment thus appears to be effective in reducing the emissions in countries that are tradeing with Europe. The increase in the emission intensity in North America is likely explained by changes in the energy price. As we keep emissions constant in this simulation, the demand and so the price for emissions reduces and so it becomes cheaper for countries that are less affected by the border adjustment to pollute. In Figure 4, we additionally show what the effect of both scenarios is on the emissions embedded in exports between aggregated world regions. The red arrows represent increases in emission exports, while the green arrows represent decreases. The taxing countries reduce all of their emission exports in both scenarios, which reflects their decrease in the emissions share in their production. In the only tax scenario, however, the EU increases its import of emissions from all other country groups, highlighting that some of the emissions “leaked” out of the EU into these other countries, from which emission-intense goods are then re-exported (for consumption or through value chain connections) into the EEA-EFTA. This effect completely disappears when the taxing countries also introduce a carbon border adjustment. This in fact leads to the EEA-EFTA both exporting and importing fewer emissions, thus not only greening their production but also their consumption. However, other regions start to trade more emissions with each other as a result. This comes from the 24 Change in production emission intensity (in %) Tax Only (Scenario 1) 8.32 3.84 3.24 2.90 2.67 2.29 -28.00 -58.32 No data IBRD 47507 | NOVEMBER 2023 Change in Production Emission Intensity (in %) Tax and Border Tax (Scenario 2) 7.20 3.89 3.19 1.84 -0.39 -4.34 -24.92 -56.29 No data IBRD 47514 | NOVEMBER 2023 Figure 3: Effect of both scenarios on the emission intensity of production. The emission intensity is taken on the whole economy. incentive to outsource that is now given to foreign producers that export to the EEA-EFTA and that only have to pay the carbon price for the carbon input used in their own production. 25 Change in traded emissions − Tax (scenario 1) Oth 0 er 720 0 64 0 56 0 0 48 Ro TA E EF 80 0 40 A− EE 240 320 Africa 0 160 80 0 0 80 s ica er Am 0 16 24 0 160 Change in traded emissions Asia 80 0 Increase Decrease Change in traded emissions − Tax and border tax (scenario 2) 1170 1260 1350 1080 144 0 990 15 0 3 0 O 90 0 th er TA 0 EF 81 A− 0 EE 0 72 90 0 63 180 RoE 540 270 450 360 0 360 Africa 90 270 180 180 0 90 90 0 ica 80 s 1 63 0 er Am 0 27 54 0 0 36 450 0 Change in traded emissions 360 270 90 180 Asia Increase Decrease Figure 4: Effect of both shocks (scenario 1 and 2) on emissions trade flow. Green arrows represent decreases, red arrows represent increases in traded emissions. Outer layer represent both origin and destination regions, alleviated colored bars represent the destination regions, the direction of each arrow indicates the direction of the presented change in traded emissions. The numbers on the outer circle are in mil. t and indicate the size of the change. For example, Asia exports more emissions to the EEA-EFTA, and imports less from there as a result of the first shock. Arrows are scaled to represent the same magnitude in both diagrams, and emissions include both production and transportation. This is the part that we refer to as “second-order leakage”, as it is similar to the leakage effects in a tax scenario, but one step down the value chain. The following subsections will explain the drivers of the changes in both the emission intensity of production and the changes in traded emissions. 4.2 Effects on outsourcing and abatement The main margins of adjustments for the producers that are now confronted with higher costs for the carbon input come from the choice between abatement and carbon usage and from the choice between in-house production and outsourcing. As both the tax and the border adjustment only target the emissions from in-house production, both abatement and outsourcing lower the producer’s tax burden. In Figure 5, we plot the average change in αM , i.e. the share of outsourced inputs in production from both scenarios. In scenario 1, producers in the countries that impose the tax increase their share of outsourced inputs. As the carbon input of these goods is not taxed by the policymaker (as is the case in all current carbon pricing schemes), this input becomes relatively cheaper compared to using emissions directly. The strength of this channel is determined by the elasticity of substitution between in-house production and outsourcing. At the same time, the rest of the world rather reduces its outsourcing. In the second scenario the share of intermediate inputs within the EEA-EFTA reduces, as using foreign inputs now becomes relatively more expensive, and carbon-intense production steps are now equally expensive to perform abroad. More interestingly, however, countries in the close proximity of Europe, which are most affected by the border tax, now increase their outsourcing. This is because the border tax incentivizes exporters to Europe to reduce their emissions in the same way that a domestic tax does for domestic producers. That is, these producers now have an incentive to outsource the dirty parts of their production as only the emissions of their in-house production are taxed. This shows the second-order leakage again. The carbon tax naturally induces abatement in Europe, as highlighted by an increase in m m the share of labor in production, αjL αj Λ in Figure 6. Under the given parameter choices, labor and emissions are substitutes and so an increase in the costs of emissions induces an increase in the usage of labor, which is akin to abatement in our model. Together with 27 Change in Average Share of M in Production (in %) Tax Only (Scenario 1) 0.85 0.21 0.00 -0.02 -0.03 -0.05 -0.08 -0.23 No data IBRD 47508 | NOVEMBER 2023 Averages are output weighted, keeping output fixed Change in Average Share of M in Production (in %) Tax and Border Tax (Scenario 2) 1.20 0.22 0.09 0.02 -0.01 -0.03 -0.09 -0.35 No data IBRD 47501 | NOVEMBER 2023 Averages are output weighted, keeping output fixed Figure 5: Effect of both scenarios on outsourcing through a change in the usage of interme- diate inputs. the increase in M , this explains the drastic reduction in the emission intensity in the EEA- EFTA countries. The rest of the world, however, reduces its share of L in production, which 28 Change in Average Share of L in Production (in %) Tax Only (Scenario 1) 3.65 0.89 0.05 -0.02 -0.05 -0.12 -0.22 -0.97 No data IBRD 47510 | NOVEMBER 2023 Change in Average Share of L in Production (in %) Tax and Border Tax (Scenario 2) 3.87 1.08 0.21 0.08 0.00 -0.05 -0.15 -0.78 No data IBRD 47515 | NOVEMBER 2023 Figure 6: Effect of both scenarios on abatement though increases in clean labor. 29 is explained by the fact that now these countries take over some of the dirty production that was previously done in Europe. When the EEA-EFTA also introduces a border tax on carbon, the increased costs of outsourcing lead firms within the EEA-EFTA to even increase their abatement compared to the only tax scenario. This is because these producers still have to comply with the increase in the carbon tax, but now have a higher incentive to produce in-house, thus also increasing the total labor share. This lowers global emissions, but it does not imply that emission intensities and levels in Europe decrease, because the switch from outsourcing to in-house production also implies a higher input share of the emission-input. As seen before, the reduction in the emission intensity in Europe is relatively stable between the two scenarios. Firms in the rest of the world are now also incentivized to abate, and so one can observe an increase in the labor share in the countries that previously saw an increase in their outsourcing. This effect is similar to the effect on domestic firms in the only tax scenario, as now these foreign producers have an incentive to both increase their outsourcing and their abatement in order to avoid the border adjustment. Overall, the border tax has the interesting effect of shifting the tax burden and the associated producer responses to countries outside the actually regulating area. This implies that neighboring countries of Europe now show similar patterns as the European countries in the only tax scenario, i.e. they increase outsourcing and start abating. 4.3 Effects on output We will summarize the effect on the levels of production here and provide the corresponding maps in Appendix D. In level effects, the unilateral increase in emission taxes in the EEA- EFTA also has the overall expected effects. Production decreases in Europe, as the costs of production through the emission input become higher. Production increases in almost all other places (see Figure D1), because these countries both gain in competitiveness compared to the countries that impose the tax and because these countries take over some of the emission-intense production that becomes more expensive in Europe. These changes in output of course influence the trade-embedded emissions, which we reported above, as higher exports mechanically also translate into higher embedded emissions in exports. 30 Interestingly, we show that even when also implementing a border adjustment on carbon, output decreases in the EEA-EFTA by a similar magnitude as in the only tax scenario (Figure D1). This is because such a border tax not only prevents leakage, but also lowers efficiency by increasing the costs of inputs in the EEA-EFTA and thus compresses output. Simultaneously, the border adjustment also reduces the output in other countries that now export less to Europe. 4.4 Income effects The tax, predictably, leads to a reduction in income in the EEA-EFTA countries (Figure D2). The places where production relocates to see an increase in incomes as their output also increases. The countries benefiting most are both the ones in close proximity, and others that are closely connected to European value chains, for example China and South Africa. In the border tax scenario, incomes in Europe reduce by a similar magnitude as in the only tax case, for similar reasons as for the change in output (Figure D2). Countries that had benefited a lot from the leakage in the only tax scenario now increase their incomes less, as in these countries producers now also face part of the tax burden, especially the ones that depend a lot on European value chains. This also implies that these countries would see a reduction in their incomes in a scenario in which a border tax would be implemented without an increase in taxes, as in this case the affected countries would not gain from any leakage effects. This is in so far important as many of these countries in Northern Africa, Eastern Europe, and Central Asia have lower incomes than the countries that actually implement the border adjustment. 4.5 Effects on global emission levels We have so far evaluated the effects of environmental taxation and border adjustments, while assuming that global emissions remain constant. Under this assumption, production-related emissions move in both scenarios from the EEA-EFTA countries towards the rest of the world (Figure D3). Emissions in the EEA-EFTA countries reduce less in the case where the taxing countries also impose a border tax, as in this case the countries’ in-house production 31 increases. However, to assess the policies’ effect on total production emissions we move to simulating both policy scenarios under the assumption that the emission-supplying monopolist keeps the price of emissions and not its quantity fixed (assumption 2 in Appendix A.2). In this case, global emissions decrease slightly when imposing the tax and decrease more when imposing the tax together with the border adjustment (Figure D4). The border tax also reduces the emissions in the rest of the world compared to the pre-tax scenario, which is driven by increases in abatement, induced by the tax. This also supports the environmental motivation of the border tax. We can thus see that even if second-order leakage through outsourcing in third countries is an issue under a given border tax, the tariff will nevertheless induce an emission reduction in third countries, while protecting the competitiveness of the taxing jurisdiction. Our model allows us to additionally study the effect of both policy scenarios on the trade-related emissions from transportation. When we compare those to the just discussed production emissions, changes in transportation emissions are far smaller than changes in production-related emissions, which is non-surprising given that the policies in the first in- stance target production (Figure D5). The effect on transportation emissions, however, is non-negligible and qualitatively different in both cases. While the only-tax scenario increases emissions from transportation, the border adjustment scenario reduces them. The intuition behind this is straightforward, as the tax increases outsourcing and thus global trade, emis- sions from transportation that scale with real trade, also increase. A border adjustment, however, reduces trade (and output), and thus reduces emissions through a reduction in distances traveled by freight. 32 5 Conclusion In this paper, we analyze the effectiveness of unilateral carbon taxation and carbon border taxation in a general equilibrium trade model, in which producers have the choice to either abate or outsource emission-intense parts of their production. Even though our paper shows how carbon border adjustments can lead to a leakage effect further down the value chain, we still show that they are overall emission reducing and increase the incentive to abate both domestically and abroad. Our paper contributes to a small but growing literature that tries to incorporate envi- ronmental taxation into numerical trade models. We introduce an international trade model that can account for emissions. We characterize the producers’ decisions as a choice between in-house production and outsourcing, where in-house production is done by using two inputs: clean labor and a carbon-emitting input. We assume that markets are perfectly competitive, and that governments can levy emission taxes both on domestic producers as well as on the emission-content of imported goods. Our structure implies that each producer optimizes its input choice based on its export destination, as the emission taxes directly enter the firms optimization. We simulate two policy scenarios: one in which a subset of European countries increases their carbon taxes, and one in which they also implement a border adjustment. When producers are hit by the carbon tax shock, they have the choice between abating, switching from emission usage to labor, and outsourcing parts of the production, as the emissions embedded in materials are not taxed. This induces carbon leakage, i.e. an increase in outsourcing that leads to an increase in emissions in countries that now export more towards Europe. Interestingly, a border tax has the same effects on producers in countries that are now affected by the carbon price as the domestic tax has on domestic producers. Firms start both abating and outsourcing. This outsourcing by exporters is in essence another form of carbon leakage, happening further down the value chain, which is why we call this effect “second-order leakage” . Border adjustments, however, also increase the incentive for domestic firms to abate, as outsourcing becomes more expensive, and together with the incentive for foreign pro- 33 ducers to abate, this lowers global emissions. Through a decrease in trade, emissions from transportation also decrease, further lowering global emissions. The trade-reducing effect of border taxes nevertheless decreases output and incomes, especially in the taxing countries. 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We additionally list the parameters that we retrieve from the data and list the three different assumptions that we impose on the carbon-input supplying monopolist. A.1 Algorithm I Begin the outer loop II Guess change in carbon input price pE III Move to the inner (main) loop 0→ Begin the inner loop. Guess the change in outsourced input price index cm jM , wages m wj , carbon costs cnm jE , and the change in nominal output Yj nm . Take carbon input price pE as given from the outer loop. 1a→ Calculate the change in cost index defined as 1 −φ −φ − φ cnm m m j Λ = αjL wj m + αjE cnm jE 1 −ς −ς − ς cnm j = m αj Λ cnm jΛ + m αjM cm jM −ς nm jM ) (cm 2b→ Outsourced input shares αjM = −ς (cj ) nm −φ −ς nm nm (wjm jΛ ) ) (cnm 2a→ Labor input shares αjL αj Λ = −φ −ς j ) (cjΛ ) (cnm nm −φ −ς nm nm jE ) (cnm jΛ ) (cnm 2c→ Carbon input shares αjE αj Λ = −φ −ς (cjΛ ) (cnm nm j ) 3a→ The change in prices (including iceberg costs) pnm j = τjnm cnm j 1 −θ −θ 3b→ Prince index for composites Φn j = nm m πj pnm j −θ nm (pnm ) 4→ Change trade (import) shares πj = j n −θ (Φj ) 37 1 ν ν n n 5→ Total income Wn = j Lj wj ν (wj n ) 6→ Change in labor allocation Lnm j = ν (W n ) m βjk ∗ 7→ Changes in outsourced input prices cm jM = k Φm k − ν− ν 1 m∗ nm nm nm nm 8→ Calculate the change in wages wj = n Ξj Yj αjL αj Λ Lnm j nm 9a→ Calculate new total emissions by export destination (Note that Ej 0 is the share of carbon emissions accounted for exports to n, calculated by multiplying emissions with trade (export) share Ξnm j ) nm nm nm nm 1 nm Ej = αjE αj Λ Yj Ej 0 cnm jE 9b→ Total transport emissions are Yjnm Tjnm = Tjnm 0 pnm j 10→ Calculate the change in carbon costs taking policy changes into account. Take ε = ε/pE 0 . Then ∗ m nm m nm cnm jE = pE + ε ψj + κj / 1 + ε ψj 0 + κj 0 11→ Change in the environmental tax revenue is equal to m nm n j ψj Ej + n j κmn mn j Ej Rm = m nm n j ψj 0 E0j 12→ Set Yknm∗ = DLk nm nm πk W n (1 − ϑn ) + ϑn Rn + nm nm Djk πk Ξin in j αjM Yj in j i 13a→ Calculate ξ1 = n m k |Yknm − Yknm∗ | and update Yknm = ρ1 Yknm∗ +(1 − ρ1 )Yknm 38 m∗ m∗ 13b→ Calculate ξ2 = m j |cm m m jM − cjM | and update cjM = ρ2 cjM + (1 − ρ2 )cjM m m∗ m m∗ m 13c→ Calculate ξ3 = m j |wj − wj | and update wj = ρ3 wj + (1 − ρ3 )wj nm∗ nm∗ 13d→ Calculate ξ4 = n m j |cnm nm nm jE − cjE | and update cjE = ρ4 cjE + (1 − ρ4 )cjE 14→ If ξi < 10−8 for all i = {1, 2, 3, 4} stop the inner loop, else go to step 1 and continue. nm IV Calculate total emissions E = n m j Ej + Tjnm and total carbon input QE = E/ε based on the results of the inner loop. V Check if E/ε = Z (Θ) thus carbon input market clears. If the market clears then stop the loop; if not, then go to step II and update pE . (Alternative specification for the monopolist’s decision is given below). A.2 Alternatives for the carbon input producing monopolist’s de- cision • Alternative 1: Monopolist fixes extraction amount QE = QE 0 . The total supply of carbon input, thus emissions, are constant before and after the change in taxes. • Alternative 2: Monopolist sets pE equal to the change in consumer price index in USA, i.e. sets the carbon input price equal to a constant amount in real USD. • Alternative 3: Monopolists maximizes profit assuming constant marginal cost. To implement this, calculate marginal revenue before the shock, i.e. ζ0 = ∂ (QE 0 pE )/∂QE 0 , by solving the model using initial carbon tax rates and taking numerical derivative. Then in the final step of the outer loop calculate the numerical derivative after the shock ζ1 = ∂ (QE pE )/∂QE , if the marginal cost is constant these two calculations of marginal revenues should be equal, i.e. ζ0 = ζ1 . Continue with the loop above until they are equalized. 39 A.3 Data requirements • Parameters or shares: – θ, φ, ς , and ν n – βjk n n – γj and γE • Emissions related: m nm m nm – Ej 0 (Note Ej 0 = Ej 0 Ξj ). m – ψj 0 – κnm j0 – ϑn share of environmental tax revenue in GDP – Tjnm 0 total initial transport emissions, from m to n for j • Production shares: n – αjM n – αjL n – αjE n – αj Λ • Labor shares: – Ln j • Trade data: Yjnm balanced and/or unbalanced trade matrix. Everything else related to trade and output is based on this matrix. • Initial share variables: Calculated using Yjnm and parameters above. No additional nm data is needed. They are πj , Ξnm nm nm j , Djk , and DLk . See below. 40 • Solution method update speed variables: 0 < ρi < 1, for i = {1, 2, 3, 4} (we set them arbitrarily equal to 0.1) • Changes in exogenous variables, such as iceberg costs, are set to one (unless we simulate relevant shocks) – τjnm = 1 • Imputation of trade and output variables – Consider the matrix of value of exports Yjnm . nm Yjnm – Trade (import) shares are πj = ni . i Yj Yjnm – Trade (export) shares are Ξnm j = im . i Yj – Define output Yjm ≡ n Yjnm n nm n nm – Define dnm n n jk = Yj αjM βjk πk and dnm Lk = i n n αiL αiΛ Yin γk πk nm dnm jk – The demand are Djk = dnm nm j jk +dLk nm dnm – and DLk = Lk nm nm d j jk +dLk B Additional Welfare analysis B.1 Theory To also estimate effects on welfare, we parameterize function g (E ) in (1) as:  −1 2 1 + E n  . (16) γE This functional form is taken from Shapiro, 2016 and captures all future damages from n emissions discounted into one point in time. We calibrate the damage parameter, γE by country, or world region, such that these damages are heterogeneous across countries. 41 B.2 Data n We calibrate γE based on a global social cost of carbon of 31$, which is based on Nordhaus, 2017. We derive the country-specific parameters by using a methodology also applied in Shapiro, 2016 and Larch and Wanner, 2017. For this, we derive the first derivative of the direct utility function with respect to global emissions and set it equal to the marginal damage of an additional unit of emissions: the social costs of carbon. We then use estimates from Nordhaus and Boyer, 2003 who determine how severly different regions of the globe will be affected by climate change, to split the global SCC (31$) over the countries of our sample.10 For further details, we refer the interested reader to the appendices of Shapiro, 2016 and Larch and Wanner, 2017. B.3 Results We present again simulation results based on the assumption that the global emission sup- plying monopolist fixes emission prices, and not quantities, to allow the emission level to adjust. The effects on welfare are depicted in Figure B1 and are driven by two forces: the effect of the policies on income and thus consumption, and the effects on emissions. The tax only scenario reduces incomes in the EEA-EFTA countries, thus reducing welfare here. Si- multaneously, most countries, including all within Europe, gain from the reduction in global emissions. Welfare increases most in places that benefit from the leakage effects like China, Northern- Africa or the Middle-East, as incomes here rise the most. Due to their higher vulnerability to climate change, countries around the equator gain the most from the emission reduc- tions, while countries far north like Russia and Canada actually loose from these emission reductions. In the border adjustment scenario, the EEA-EFTA countries loose less in terms of welfare, as the reductions in incomes is roughly the same between the two scenarios and global emissions reduce more with a BCA. These reductions in global emissions are also beneficial 10 If countries have a negative social cost of carbon according to Nordhaus and Boyer, 2003 we slightly adjust the first order condition as otherwise there would be no solution to the problem. Further details on this can be shared upon request. 42 for all other countries that lose from climate change, even if increases in income were smaller for many countries. Change in Welfare (in %) Tax Only (Scenario 1) 4.37 3.39 3.30 3.22 3.07 2.74 1.17 -2.33 No data IBRD 47503 | NOVEMBER 2023 Change in Welfare (in %) Tax and Border Tax (Scenario 2) 7.07 6.44 6.28 6.12 5.87 5.09 3.62 -0.62 No data IBRD 47504 | NOVEMBER 2023 Figure B1: Effect of both scenarios on aggregate welfare. 43 C Additional data information C.1 Derivation of sector-specific carbon taxes The OECD data on tax revenues has two main shortcoming that we try to address by making additional use of the tax revenue data by Eurostat. The first is that it contains tax revenues both from household and industry emission consumption, while we would like to rely strictly on industry emissions only. The urgency for this arises because a large share of tax revenues comes from fuel taxation in transportation, which we do not want to attribute to industry. The second issue is that the data is not split by sector. We use the EU data to first approximate how much of the tax revenue of countries that are only available in the OECD stems from industry taxation and then use average industry shares, based on the Eurostat data, to split the OECD data into industry shares as well. For the first, we use the average share in Eurostat country environmental tax income that comes from non-household emission consumption to transform the OECD data, and for the latter we create average sector shares in Eurostat to transform the remaining tax revenue in OECD into sectoral revenues, before calculating the implicit tax rate for each sector, by dividing the sectoral emission tax revenue by the sectoral emissions. This approach is to a large extent based on Farrokhi and Lashkaripour, 2021. To convert Euro tax income in the EU into dollar terms, we use the 2009 average exchange rate obtained from the OECD exchange rate database. 44 C.2 Overview over sector alignment between sources NACE code Sector Name A Agriculture B Mining C10-C12 Food products, beverages and tobacco C13-C15 Manufacture of textiles, wearing apparel and leather Manufacture of wood and of products of wood and cork, except furniture C16-C18 Manufacture of paper, pulp and paper products Printing and reproduction of recorded media Coke and refined petroleum products C19-23 Chemicals and chemical products Manufacture of other non-metallic mineral products Basic metals and fabricated metal products, C24-C25 except machinery and equipment Manufacture of computer, electronic and optical products, C26-C28 electrical equipment and machinery C29-C30 Manufacture of motor vehicles and other transport equipment C31-C33 Rest manufacturing Other Energy, services, others Table C1: Sectors used in analysis 45 Final sector WIOD EORA WIOD satelite A A01-A03 A secA - secB B B B secC C10-C12 C10-C12 C10-C12 sec15 - sec16 C13-C15 C13-C15 C13-C15 sec17 - sec19 C16-C18 C16, C17, C18 C16-C18 sec20 - sec22 C19-23 C19,C20,C21,C22,C23 C19-23 sec23 - sec26 C24-C25 C24,C25 C24-C25 sec27 - sec28, C26-C28 C26,C27,C28 C26-C28 sec29 - sec33 C29-C30 C29,C30 C29-C30 sec34 - sec35 C31-C33 C31-C32,C33 C31-C33 sec36 - sec37 Other All other All other All other Table C2: Sector mapping between different sources C.3 Energy prices used in analysis As described in Section 3, we are using 2009 IEA/OECD energy price data from International Energy Agency, 2023 to calculate the energy costs by sector and country in 2009. We rely on average price data, and report here which prices we used in our analysis, and on which country group this average is based on. This also gives information on the variety of fuel sources on which we base our energy costs estimates on. TOEs are then converted into TJ values, which aligns with the units in WIOD and EORA. In WIOD we aggregate hard coal and coke into coking coal, and in EORA we assign 50 percent of Coal to coking coal and 50 percent to steam coal. In both sources we group all renewables into one category and assign a price of 0 for it. For Luxemburg, Romania, Norway, Switzerland, and Croatia we use EORA instead of WIOD data, to align with the emissions data sources. 46 Fuel Source Price $ per toe Average based on: Petroleum/Light sulphur oil 498 OECD Europe Heavy fuel oil 381.7 United States Light fuel oil 631.8 OECD Diesel 1111.4 OECD Gasoline 918.4 OECD Natural Gas 383 OECD Steam (brown) coal 151.7 OECD Coking coal 223.1 United States Electricity 1235.8 OECD Table C3: Energy prices used in study 47 D Additional result figures Change in Total Output (in %) Tax Only (Scenario 1) 2.58 1.12 0.93 0.83 0.71 0.48 -0.69 -4.70 No data IBRD 47505 | NOVEMBER 2023 Change in Total Output (in %) Tax and Border Tax (Scenario 2) 2.99 1.46 1.26 1.05 0.83 0.43 -0.76 -4.97 No data IBRD 47512 | NOVEMBER 2023 Figure D1: Effect of both scenarios on aggregate output. 48 Change in Disposable Income (in %) Tax Only (Scenario 1) 0.45 0.11 0.04 0.01 -0.02 -0.06 -0.21 -1.12 No data IBRD 47506 | NOVEMBER 2023 Change in Disposable Income (in %) Tax and Border Tax (Scenario 2) 0.48 0.14 0.06 0.01 -0.03 -0.11 -0.45 -1.40 No data IBRD 47513 | NOVEMBER 2023 Figure D2: Effect of both scenarios on aggregate incomes. 49 Figure D3: Effect of both tax (Scenario 1) and tax and border tax (Scenario 2) on production emissions when keeping emissions constant 50 Figure D4: Effect of both tax (Scenario 1) and tax and border tax (Scenario 2) on production emissions when keeping emission prices constant 51 Figure D5: Effect of both tax (Scenario 1) and tax and border tax (Scenario 2) on production and transportation emissions when keeping emission prices constant 52 E Robustness: Treating labor and emissions as com- plements This section presents the differences in the simulation results from both scenarios when choosing an elasticity between labor and emissions, 1 + φ, that is based on the estimate of Farrokhi and Lashkaripour, 2021. Their estimate differs notably, as it implies that labor and emissions are in fact complements and not substitutes. This assumption makes abatement in fact impossible, as a reduction in emissions within in-house production can only be reached by reducing output, and not by switching from emissions to labor, as was previously the case. As a result from this, when we simulate a tax increase EEA-EFTA countries increase their share of M even more than in the substituion case, but decrease their input share of L, so in fact abate less (Figures E1 and E2). Like in the substitution version, however, the border adjustment again shifts the response of the producers outwards to the producers that are now targeted by the border tax. Out- sourcing increases for the countries in close proximity and as in the tax scenario the countries that are now affected by the policy reduce their labor input together with the emission input due to their complementarity. 53 Change in Average Share of L in Production (in %) Tax Only (Scenario 1)–Labor and Emissions as Complements 0.55 0.13 0.08 0.05 0.03 0.00 -0.68 -2.40 No data IBRD 47516 | NOVEMBER 2023 Change in Average Share of L in Production (in %) Tax and Border Tax (Scenario 2)–Labor and Emissions as Complements 0.51 0.22 0.03 -0.08 -0.25 -0.47 -0.93 -3.89 No data IBRD 47518 | NOVEMBER 2023 Figure E1: Effect of both scenarios on abatement, when assuming that labor and emissions are complements. 54 Change in Average Share of M in Production (in %) Tax Only (Scenario 1)–Labor and Emissions as Complements 1.34 0.16 0.01 0.00 -0.02 -0.05 -0.07 -0.29 No data IBRD 47517 | NOVEMBER 2023 Averages are output weighted, keeping output fixed Change in Average Share of M in Production (in %) Tax and Border Tax (Scenario 2)–Labor and Emissions as Complements 2.23 0.33 0.18 0.08 0.01 -0.09 -0.20 -0.92 No data IBRD 47519 | NOVEMBER 2023 Averages are output weighted, keeping output fixed Figure E2: Effect of both scenarios on outsourcing, when assuming that labor and emissions are complements. 55