Distributional Effects of Carbon Tax in Ethiopia A Computable General Equilibrium Analysis

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Policy Research Working Paper 10476
Developing countries are increasingly giving attention to carbon pricing to reduce their emissions, particularly in meeting their nationally determined contribution under the Paris Climate Agreement. However, they would like to understand the potential economic, distributional, and environmental impacts of carbon pricing policies before they consider implementation. Using a computable general equilibrium model of Ethiopia, this study examines the effects of a hypothetical carbon tax (US$20/total carbon dioxide) under several alternative schemes to recycle carbon tax revenue to the economy. The study finds that a carbon tax would be regressive in all schemes considered except those when the tax revenue is recycled, as a cash transfer, to household income groups either equally or inversely proportional to their incomes. The schemes that make the carbon tax progressive also cause a higher reduction of carbon dioxide emissions, thereby ensuring the alignment of equity and environmental outcomes of the carbon tax. However, these schemes are not necessarily economically efficient because they cause higher reductions of gross domestic product compared to other options considered.
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 gtimilsina@worldbank.org.

Introduction
Ethiopia is a landlocked country located in Sub-Saharan Africa. While the country is classified as a low-income economy by the World Bank, with a per capita income of less than US$1,085 in 2021, 3 it was one of the fastest-growing economies in the last decade (2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020). It achieved the highest economic growth in the world, on average, 9.3% per year during the 2010-2020 period (World Bank, 2022). The economic growth was also accompanied by the rapid increase in CO2 emissions from fuel consumption, 12% per year, on average (World Bank, 2022).
Considering the rapid growth of CO2 emissions along with its economy, Ethiopia has committed its Nationally Determined Contribution under the Paris Climate Agreement to limit its greenhouse gas (GHG) emissions by 68.8% below the business-as-usual situation in 2030 (FDRE, 2021).
Carbon pricing instruments, such as carbon tax, could be economically efficient for reducing GHG emissions (see e.g., Aldy et al. 2010;Timilsina, 2022;Timilsina et al. 2022). More than 120 countries, including developing countries, have considered carbon pricing as one of the policy options to achieve their NDC targets (World Bank, 2023). However, most countries do not know how these policies will impact their economy and the population. As low-income households' expenditure share on energy commodities is likely to be higher than that of highincome households, the burden of energy price increases resulting from a carbon tax might fall on them disproportionally (see, e.g., Ohlendorf et al. 2021;Williams et al. 2015;Rausch et al. 2011).
In the case of the United States, Rausch et al. (2011) find that a carbon pricing policy is regressive.
Through a meta-analysis, Ohlendorf et al. (2021) report that the distributional impacts of carbon pricing are heterogeneous across countries depending on their economic structures and the energy supply mixes.
The regressive economic impacts of a carbon tax are politically sensitive. Developing countries might be interested in a carbon tax if it can be designed in such a way that it is progressive and welfare-improving. Some existing studies investigate situations when a carbon tax could be made progressive. For example, Garaffa et al. (2021) find that a carbon tax with tax revenue transferred to low-income households would increase their income by 4.5% in Brazil. Wu et al. (2021) find that a standard ETS (emission trading scheme) would be regressive if the carbon revenues were used for government expenditures or to cut existing income taxes. The ETS would be slightly progressive if revenues are used to lower consumption taxes and most progressive with revenues recycled to households through equal lump-sum transfers. They also find that the impacts are different between rural and urban households. While analyzing the distributional effects of a carbon tax in the US, Goulder et al. (2019) find that the use-side impacts 4 of the carbon tax would be negative and also regressive under all four schemes they considered for carbon tax revenue recycling (lump-sum transfer to households, payroll tax cut, personal income tax cut, and corporate income tax cut). On the other hand, the type of revenue recycling scheme determines whether a carbon tax is progressive or regressive. It would be progressive if tax revenue is recycled to households as a lump-sum transfer. Under other schemes for revenue recycling, it is not necessarily progressive unless the value of leisure is also accounted for. Dissou and Siddiqui (2014) investigate the distributional impacts of a carbon tax by decomposing the impacts channeled through commodity and factor markets. They find that the impacts of carbon taxes passed on to the households through these two markets have opposite effects on income inequality. While a carbon tax reduces inequality through the factor price channel, it increases income inequality through the commodity price channel. Thus, the relationship between carbon taxes and inequality is U-shaped (non-monotonic). Carbon taxes are unpopular and yet, they could be the most effective tool to mitigate climate change. Steckel et al. (2021) find heterogeneous distributional impacts across countries when analyzing the effects of four carbon pricing schemes in eight Asian developing countries (Bangladesh, India, Indonesia, Pakistan, Philippines, Thailand, Türkiye, and Vietnam). 5 They find that all four carbon pricing schemes are progressive in Pakistan and the Philippines. In Bangladesh and Indonesia, all schemes, except the carbon pricing on liquid fuels, would be progressive. Most carbon pricing schemes would be regressive for Thailand. They also find the vertical distributional 4 The use-side impact refers to the impacts on households due to changes in the prices of the goods and services, whereas source-side impact is the impacts due to changes in a household income (i.e., labor, capital, and transfer incomes). effects (i.e., within income groups) more pronounced than the horizontal distributional effects (i.e., across income groups). Alonso and Kilpatrick (2022)  Ethiopia also subsidizes fossil fuels. While subsidies are gradually reduced, there was a significant subsidy to petroleum products in 2016, the base year used for this analysis. It would be relevant to understand the economic and distributional impacts of removing fossil fuel subsidies before analyzing the impacts of a carbon tax. It would be also interesting to compare the economic impacts removal of fossil fuel subsidies and the introduction of a carbon tax. It would be further important to analyze the economic impacts when both policies are implemented simultaneously.
However, the lack of necessary data in the social accounting matrix (SAM), the main database for the analysis, we could not include the impacts of fossil fuel subsidy removals in this study.
The paper is organized as follows. Section 2 highlights the key features of the CGE model, and the database used for the study, followed by descriptions of scenarios considered in Section 3.
The main results and their interpretations are presented in Section 4. This section also presents sensitivity analysis on selected model parameters. Finally, key conclusions and policy implications are derived in Section 5.

The CGE model
The study uses a static (single period) CGE model. The economy has four economic agents: households, government, enterprises and the rest of the world (ROW). The modeling of each economic agent is briefly described below.

Modeling the production sectors
Production sectors are classified into 19 sectors ( Table 1). The behavior of the representative firm in each sector is modeled through a nested functional form which uses either constant elasticity of substitution (CES) or Leontief functional forms in different nests (Figure 1) The top tier of the nested structure presents a CES combination of the aggregated production factors (value added) and the aggregate intermediate input. It can be expressed as: where is the total production of sector i, and are the input of value-added and the aggregate intermediate input in sector , respectively. and are the share parameters and efficiency parameters. is related to the elasticity of substitution (σ) as follows: = −1 . , is the substitution elasticity between the value-added and the aggregate intermediate input.
Maximizing the Equation (1) subject to the budget constraint given in Equation (2) will yield the relationship in Equation (3).
where PAi is the producer price of sector i, and are the prices of value-added and the aggregate intermediate input in sector i.  where is the substitution elasticity between labor and capital.
Like in Equations (2) and (3) above, the demand and price are defined as follows: where and are, respectively, labor and capital prices in sector . In the right-hand side of the middle tier in Figure 1, the aggregated energy good and the aggregated non-energy good are combined through a CES functional form as follows: where and are the input of non-energy aggregate and energy composite in sector i, respectively, and are the share parameters and efficiency parameters; is the substitution elasticity parameter between the input of non-energy intermediates and energy, and , is the substitution elasticity between the non-energy intermediate inputs and energy. The demands and prices are derived as follows: where and are the price of the non-energy aggregate and energy composite, respectively.
The relationship of the price of the input of non-energy aggregate and energy component is given as: In the right-hand side of the bottom tier, the aggregate energy is obtained by combining electricity and petroleum products through a CES function as follows: where and are the input of petroleum products and electricity in sector i, respectively, and are the share parameters and efficiency parameters; is the substitution elasticity parameter between the input of fossil fuels and electric power, and = 1 (1− ) , is the substitution elasticity between the input of fossil fuel aggregate and electric power. The optimal prices and quantities are derived as follows: where and are, respectively, prices of petroleum products and electricity used in sector i. 'indt' is indirect tax rate. Subscripts 'pp' and 'el' refer to petroleum and electricity. In the lefthand side of the bottom tier in Figure 1, the quantities of individual non-energy intermediate inputs are derived using a Leontief functional form as follows: The price of an individual intermediate input is given by where , and PNEAi are the quantity and prices of non-energy input j in sector i, , is the fixed proportion of non-energy commodity j in the total non-energy intermediate aggregate input of sector i.

Modeling international trade
As shown in Figure 1, the output from a sector is allocated for the domestic market and foreign market (exports) using a Constant Elasticity of Transformation (CET) functional form as follows: where and are the supply of commodities produced in sector i to the domestic market and exports, respectively, and are the share parameters and efficiency parameters; is the transformation elasticity parameter between domestic market supply and export, and = 1 ( −1) , is the transformation elasticity between the domestic and the export markets. Maximizing Equation (15) subject to Equation (16), we will get the following relationships for demand and prices: where and are the domestic price and export price of the commodity produced by sector i. PEXi is related to global price (PWEi) through the exchange rate (EXR): Total domestic demand for a good is a CES composite of domestically produced and imported components and given by: where , and are the demand for composite commodity i, domestic commodity i and import commodity i, respectively, and and are the share parameters and efficiency parameters; is the substitution elasticity parameter between domestic and import commodities, , is the substitution elasticity between domestic and import commodity. The demand and prices are derived through an optimization process and given as: where is the price of composite commodity , is the price of domestic commodity i, is the price of import commodity i. Price of imported commodity (PMi) is linked to its world price through exchange rate as follows: where is the import tariff rate of commodity i.

Modeling household behavior
Households are disaggregated into five categories (quintiles) based on their income. For each quantile, the households' income (YHh) is composed of wage income, capital rents, and transfer payments from domestic institutions and foreign countries. It is given as: where TGHh and TWHh are the transfers of payments to household income group h from the government and foreign countries (or rest of the world), respectively, and ℎℎ refers to the share of household h in ownership of capital. The consumption function of households is assumed to be derived from Stone-Geary utility function (Boer 2009;Geary 1951;Stone 1954). This functional form allows households to consume a minimum level of each good and service irrespective of its price or the consumer's income. Households' choice for the consumption of a good or service above the minimum threshold level is based on the income and price of the good or service.
Selection of this functional form to represent households' behavior can be rationalized from the facts a level of basic goods such as food, and drinking water is essential for survival, and it is not a question of choice. In the case of basic goods, the choice is relevant above the minimum threshold level whereas it is relevant for the entire level of consumption for other goods and services. The demand function derived from the Stone-Geary utility function is a linear expenditure system (LES) with a fixed level of expenditure allotted for the minimum consumption of subsistence goods and services. Thus, the final consumption of households is given as follows: where ,ℎ is the consumption of commodity of household income group h, ℎ is the marginal propensity to consume of household group h, γi,h is the minimum consumption of commodity i in household group h, and , ℎ is the share of commodity in the household group h' consumption expenditure. Adding direct tax expenditures and transfers of payments of households to the rest of the world (THW), enterprises (THE) and the government (THG) on consumption expenditure will give the total household expenditure (EH) as follows: Household saving is disposable income (DI) minus total household expenditures:

Modeling the government
The total government revenues (YG) are generated through personal and corporate income taxes, excise taxes, import duties, and transfers from other economic agents (i.e., households, rest of the world).
where , , and are rates of import duty, excise tax, capital tax and labor tax respectively. sek is share of capital owned by enterprises and tei is corporate income tax rate. THG, TWG, and TEG are transfers from households, rest of world and enterprises to the government.
CTREV is carbon tax revenue. The total government revenue is allocated for public expenditures, transfers to other agents, and public savings. The total government expenditure is fixed at the baseline level and allocated to various services (e.g., public administration) at the same proportion as in the base case. This means public expenditures, which mostly refer to expenditure on public administration, is kept at the level in the baseline.
where is government expenditure, QGi is consumption of good i by the government. TGH, TGW and TGE are the government's transfer payments to households, foreign countries and enterprises. The government saving (GSAV) is given by:

Modeling enterprises
Enterprises get their income from capital rents and transfers as follows, Where is enterprise income, is share of capital owned by enterprises, , and are transfers from government, households and foreign countries to enterprises. Enterprise's expenditure which includes taxes and transfer payments, is computed as follows Where EExp is enterprise expenditure, te is the direct tax rate paid by enterprises and TEG, TEH and TEW are transfer payments from enterprises to the government, households and foreign countries. Finally, enterprise saving is the difference between enterprise income and expenditure, given as

Market clearing and macroeconomic closure
A CGE model assumes an economy remains in equilibrium in terms of goods and services markets, factor markets and macroeconomic fronts. The closing rules for the commodity market is as given as follows: where is the demand for commodities i used as investment good. The factor market assumes that total demand for labor and capital is equal to their supplies.
where QKS and QLS are total labor and capital supplies in the economy. The factor market assumes that total labor and capital demand equals their supplies. Labor and capital are mobile across sectors, but their total supply or endowment for a given year is fixed. Prices of labor (wage rate) and capital (user costs of capital) are different across the sectors. The macroeconomic balance suggests that the total value flow out of the country (due to imports) and into the country (due to exports and foreign borrowings) should be balanced. This condition determines the current account balance or surplus through the following relationship: where remittance earning which is linked to total labor income through a fixed ratio.
FSAV is foreign savings, which is equal to the current account surplus if it is positive and the current account balance if it is negative. The total investment is financed by the sum of all savings: where is the total investment, is the dummy variable, and ℎ is the share of commodity used as an investment in the total investment. The real GDP is calculated using the expenditure approach as follows:

CO2 emissions and carbon tax
CO2 emissions are calculated by multiplying fuel inputs in each production sector and final demand sectors by emission coefficients. CO2 emissions from sector i is calculated as: Where coefpp is CO2 emissions coefficient of petroleum products expressed in terms of ton of CO2 per unit monetary value of its consumption, carbon tax (CTAX) which is exogenous to the model, is converted to equivalent indirect tax 'ctr' as follows: This equivalent indirect tax rate is added to the existing indirect tax rate (indt).

Data
The main data source used for this study is the social accounting matrix (SAM) of Ethiopia.
The SAM was built by the Policy Studies Institute of Ethiopia (PSI) using 2016 input-output tables and national accounts. It is available on request. 6 Other data needed are values for various parameters, such as elasticity of substitution used in CES functional forms used to model the 6 It can be argued that the analysis based on six-year-old data might not represent the economic reality of today in Ethiopia.
However, SAMs are developed occasionally (such as at 5-year intervals) even in developed economies. Building a SAM more frequently in developing countries is challenging. Use of a SAM that is 5-10 years old is common practice in CGE modeling for two reasons. First, a SAM represents the structure of an economy, which is unlikely to change in a short period. Second, a CGE approach basically models the behavior of economic agents (consumers, producers). Behavioral change also requires a long period. The key findings of the model are unlikely to change even if a new SAM is built and used. Building a SAM is itself a data and time-intensive exercise.
production sector, and parameters used in the LES functional form to model the households. The values for elasticity of substitution are not available for Ethiopia. The only sources of these parameters are existing studies for developing countries which provide values for the elasticities of substitution. We use the values from Chen et al. (2013) and Mosa (2018). The parameters used in the LES function are taken from Mosa (2018) and Diao et al (2012). Since the values of elasticity of substitution and other parameters are taken from the literature, sensitivity analyses on these values should be conducted to validate the finding of the study. Other parameters such as household saving rates, rates for transfers between the agents, and distribution of total government consumption to individual categories are calibrated from the SAM.

Design of Scenarios
The study considers a hypothetical carbon tax with a rate US$20/tCO2. We have developed one baseline scenario and four main scenarios depending on how the carbon tax revenue is recycled into the economy. These scenarios are defined in Table 2. A scenario comes up with multiple subscenarios or cases depending upon the criteria used to recycle the revenue under a given scenario.
The selection of a single tax rate is guided by the objective of the study. The objective is to compare the distributional impacts of a carbon tax policy under the alternative schemes for revenue recycling. The rate may not be relevant for this purpose because the comparison is expected to hold unless the tax rates are altered by its multiples (e.g., two times, three times). In practice, tax rates are increased gradually overtime so that the economy can adjust to it. Moreover, if we use multiple rates, we will have too many cases because of the large number of alternative revenue recycling schemes considered in the study. It will introduce complications in the interpretation of the results and articulation of the main message.

a) Like in base case
Carbon tax with tax revenues allocated in the same way the government allocates its total revenues in the baseline (a) Investment Carbon tax with tax revenues allocated for investment 2. Cash transfer to households (a) Income Carbon tax with revenue rebated to different household income groups in proportion to their income. A household income group with the highest income gets the highest rebate (b) Equal Carbon tax with revenue rebated to all household income groups equally

(c) Reverse income
Carbon tax with revenue rebated to different household income groups in inversely proportion to their income. A household income group with the lowest income gets the highest rebate

Personal income tax cut
Carbon tax with tax revenues recycled to cut personal income taxes of employers in sectors excluding fossil fuels and thermal electricity generation sectors 4. Corporate income tax cut

(a) (a) CO2 Intensity
Carbon tax with tax revenues recycled to cut corporate income taxes in sectors except for fossil fuels and thermal electricity generation sectors; tax revenues are reallocated to a sector inversely proportional to its CO2 intensity (a sector with a higher emission-intensity gets lower carbon tax revenues as the rebate) Carbon tax with tax revenues recycled to cut corporate income as in the previous case but tax revenues are reallocated to a sector in proportion to its share of capital account to the total capital account (a sector with a higher capital account gets a higher rebate) (c) Export intensity Similar to above two corporate income tax cut cases, but tax revenues are reallocated to a sector based on its export intensity (a sector that exports a higher volume of outputs gets a higher carbon tax rebate) Scenario 1 considers that the government uses the carbon tax revenue. It has two cases. In the first case, the government uses the revenue as it does with the rest of the revenues ("Like in the base case"). It means the government reallocates the carbon tax revenues for government expenditures, savings and transfers to other agents in the same proportions it does in the base case.
In the second case, the carbon tax revenue is specifically used for public investment ("Investment"). Simulating scenario 1a does not need any change in the model described above.
For the remaining scenarios, first, the increased revenue due to the carbon tax (YGAP) is calculated as follows: where YG0 is the government revenue in the base case. The intuition here is that government revenue is kept neutral to the carbon tax, this is because the government is not supposed to lose its revenue because of the carbon tax. The government might want to keep the incremental revenue and allocate it like in the baseline (Scenario 1), but there would be more economic loss doing so.
Therefore, alternative schemes are considered for revenue recycling. But only revenue in excess of the baseline is recycled. Under the Scenario 1b ('Investment'), the incremental revenue is added to the capital supply and Equation (35) is revised as follows: One could also implement this scenario by adding the YGAP in total investment in Equation (37).
Doing so, however, can be interpreted as paying the foreign debt (or lowering foreign savings) instead of injecting the incremental revenue into the production process because foreign saving is endogenous in the model. If foreign savings is exogenous to the model, the investment scenario can be incorporated by adding incremental revenue to Equation (37).
In the second scenario ("Cash Transfers to Households"), the government gives the carbon tax revenues to households as a cash transfer. This is the most important scenario for analyzing the distributional effects of a carbon tax. There could be several ways how the cash transfers are actually implemented. We have considered three cases here. In the first case (Scenario 2a), the carbon tax revenue is rebated to different household income groups in proportion to their income ("Income" case). It means a household income group with the highest income gets the highest rebate. This case is more favorable to rich households and the results would be regressive, yet we consider it to examine the economy-wide impacts even though it may not be a desirable scenario from a distributional perspective. It is implemented by revising Equation (23) as follows: Under Scenario 2b, carbon tax revenue is transferred to all households equally ("Equal" case). This case is likely to be progressive (which we will confirm in the model simulation to be presented in the result section later) as the poorer households get relatively higher rebates than the richer households. This is because the recycled revenue accounts for a higher share of the total household income for lower-income households as compared to that in higher-income households.
To incorporate this scenario, Equation (23) is revised as follows: Under Scenario 2c, the carbon tax revenues will be recycled to different income groups of households inversely proportional to their income ("Reverse Income" case). This means poor households receive more revenue (in absolute term) than rich households. This scenario is incorporated by revising Equation ( In Scenario 3 ("Personal Income Tax Cut" scenario), carbon tax revenues are used to cut personal income taxes paid by the labor force employed in productive sectors except fossil fuel and thermal electricity sectors. To incorporate this scenario, we first calculate a rate that will be used to adjust the wage rate and user cost of capital. The rate is calculated as follows: Where is a weight computed from the SAM and used to adjust the rebate for all non-energy sectors according to their carbon intensity such that sectors with higher carbon intensity have a lower rebate then is used to adjust corporate tax expenditure in Equation 31 as follows: In Scenario 4b ("Capital account share" case), carbon tax revenue is recycled to non-fossil fuel sectors in proportion to their capital accounts. A sector with a higher capital account gets a higher rebate in this scenario, the tax rebate for corporates is computed as: In the last case ("Export Intensity" case), the carbon tax revenue is recycled to non-fossil fuel sectors in proportion to exports of their outputs. In this case, more export-oriented sectors get higher rebates from carbon tax revenues. Altogether, we have 9 cases. In all cases, we follow government budget neutrality, meaning that only the incremental government revenue due to the carbon tax is recycled.
Then, is used to modify equation 31 in the same way as 4a and 4b.

The distributional impacts
The normal indicator to measure the distributional impacts of a policy by the householdincome group is the change in their income due to the policy. Table 3 presents the percentage change in household income by quantile due to the carbon tax. There are several important observations discussed below. The households gain from the carbon tax under some scenarios, whereas they lose under other scenarios. All groups of households gain when (a) carbon tax revenue is used for investment, (b) when it is transferred to households as a lump-sum rebate (i.e., cash transfer) based on their income or reverse income, (c) when the carbon tax revenue is used to cut personal income taxes and (d) when more carbon tax revenue is recycled to less emission-intensive industries (or inversely proportionally to their CO2-intensity) to cut their corporate income taxes. On the other hand, all groups of households will experience income loss due to the carbon tax (a) when the government uses carbon tax revenue for public consumption and saving as in the base case, (b) when carbon tax revenue is recycled to industries to cut their corporate income taxes based on their export-intensity and (c) when the carbon tax revenue is recycled to industries to reduce their corporate income tax and the recycling is based on the amount of corporate income tax they pay.
In the rest of the cases, some groups of households gain, whereas others lose.
While the impacts of carbon taxes on different groups of households under some scenarios goods and services account for 99% of the total household consumption in the case of the lowest income group or household income group 1 (Figure 3a). Of the total household expenditure of the low-income group (HH1), almost 70% goes to food (56% for primary agriculture products, 8% for processed food or food products, beverages and tobacco and 5% for livestock and fisheries). On the other hand, food accounts for only 40% of the total household expenditures of the high-income group (HH5). This group spends 17% on financial services and real estate (FSRE), whereas the lowest-income group spends only 3% on FSRE. Of 20 commodities, 13 accounts for 99% of the total household consumption.
The carbon tax causes income to rise in all groups of households under Scenario 4a because low-emission intensive goods and services (Figure 2a) account for more than 95% of the total household consumption in all household groups (Figures 3a-3e). Since the production of these goods and services become relatively cheaper due to the carbon tax revenue recycling, households' real income increases. On the other hand, only half of the total carbon tax rebate goes to goods and services that account for more than 90% of the total household expenditure of each household group under Scenario 4b and 4c. The other half of the total carbon tax rebate goes to goods and services that account for less than 10% of the total household expenditure by each group of households under these scenarios. Therefore, the household income impacts of the carbon tax are negative in these scenarios for all household groups.
The carbon tax is regressive under most scenarios. However, it is found progressive when the carbon tax revenue is transferred to households either equally or inversely proportional to their income. A carbon tax is considered regressive when it favors high-income households relative to low-income ones. It occurs under three conditions. First, if the carbon tax causes an increase in income for all household groups, the percentage of income increase of richer households is higher than that of poorer households. Second, if the carbon tax causes all income groups of households to experience income loss, the percentage of income loss of the poorer households is greater than that of, the richer groups. Third, when the carbon tax increases the income of high-income households and reduces the income of low-income households. Results presented in Table 3 illustrate these conditions of the regressivity of the carbon tax. A carbon tax is considered progressive if each of these conditions are reversed. There are some exceptions or irregularities in some of the cases. These might be caused due to data problems. This finding implies that carbon tax could remain regressive unless the carbon tax revenue is recycled targeting low-income households.     Table A5 in Appendix A). This is because the higher the household income of a group the lower the cash transfers it gets under this scenario. Similarly, the high-income group's consumption of welfare services that includes education, healthcare etc., decreases in all tax revenue recycling cases except when the tax revenue is recycled to households as a cash transfer in proportion to their income (Scenario 2a) or used for cutting personal income taxes (Scenario 3). In these two revenue recycling schemes, high-income group of households receives relatively higher transfers of carbon tax revenue either directly (Scenario 2a) or through their personal income tax cuts (Scenario 3). Thus, their real income increases, which in turn increases their consumption of welfare services. When tax revenue is recycled to households equally, the carbon tax causes an increase in the household consumption of textiles and leather for household income groups 1 and 2, whereas it decreases for the rest of the group (Appendix A). 7

Distributional impacts versus economic impacts
One of the key concerns regarding the impacts of the carbon tax is the trade-off between the equity (i.e., distribution by income) and efficiency effects of a carbon tax. This issue is prominent in developing economies like Ethiopia because they would like to achieve rapid and, at the same time, equitable economic growth. Therefore, it is important to investigate how a carbon tax's efficiency and distributional effects interact. Figure 4 presents the impacts of the carbon tax on GDP to illustrate the efficiency effects of the carbon tax. While the carbon tax with revenue transferred to households either equally or inversely proportional to their incomes is progressive (Table 3), the cash transfer scheme is found inferior to other schemes in terms of their economic impacts ( Figure 4). The cash transfer options cause the highest reduction of GDP compared to other options. Moreover, the 'Reverse income' cash transfer scheme, where carbon tax revenue is transferred to households inversely proportional to their incomes and which is progressive from the distributional perspective, is the worst scheme in terms of its impact to the economy (i.e., highest reduction of GDP). The contradicting findings between the distributional and economic impacts are also observed under other revenue recycling schemes. For example, the carbon tax with revenues recycled to investment is regressive in terms of distributional effect (Table 3), but it is more efficient in terms of economic impacts compared to several revenue recycling options considered. The same is true when carbon tax revenue is recycled to cut existing personal income tax rates. Under this case, there is a slight rise of GDP, but this revenue recycling option is also favorable to richer households if we ignore its anomalous impact on the poorest households.

Figure 4. Impacts of carbon tax on GDP (% change from the base case)
Which revenue recycling scheme is the most appropriate for a given economy depends upon the specific economic conditions of that economy. For example, Timilsina et al. (2022) find that recycling carbon tax revenue to cut the corporate income tax rate of non-fossil fuel industries would be best for China when the carbon tax revenue is recycled based on export intensities of the industries. Since the Chinese economy is a highly export-based economy, the finding seems intuitive. However, the Ethiopian economy is not like the Chinese economy, therefore, the best revenue recycling scheme is different for Ethiopia from that for China. Figure 3 illustrates that recycling the carbon tax revenue to cut personal income taxes would be the best (or most efficient) revenue recycling scheme for Ethiopia from an economic perspective as it can increase the GDP.  impacts for a given revenue recycling scheme would differ due to differences in their fossil fuel inputs. Emission-intensive sectors, such as transportation, chemicals (including pulps and paper), metallic products & machinery, would experience more than 4% output loss under all scenarios.
Less emission sector, such as agriculture, livestock, and welfare services, would experience relatively lower losses in their outputs. The sectoral output of a given sector differs across the scenarios because of different interactions of recycled revenues in the production process in that sector. For example, the output from the agricultural sector increases under Scenarios 2 and 3, but it decreases under Scenarios 1 and 4. This is because households receive cash transfers under Scenario 2 and a cut in their income tax under Scenario 3. It leads to an increase in their real income, which could result in increased consumption of agricultural products, which ultimately causes an increase in agriculture production. This phenomenon does not occur under the rest of the two scenarios. Another example is the chemical/pulp/paper sector. This sector receives the lowest carbon tax rebate because of its high CO2 emission intensity when carbon tax revenue is recycled to non-energy production sectors inversely proportional to their emission intensity (Scenario 4a). The negative impacts on its output under Scenario 4b would be lower than that under Scenario 4a because carbon tax revenue is recycled in proportion to capital account shares in the total capital account under former case, and the capital account share of chemical/pulp/paper is relatively high. It causes the sector to receive a higher carbon tax revenue to cut its corporate income taxes.

Distributional impacts versus environmental impacts
Since one of the main objectives of a carbon tax is reducing CO2 emissions, it is therefore important to examine how the distributional impacts of carbon tax interact with CO2 reductions. have been smaller further, as reported by Timilsina et al. (2022).
One of the most important findings is that the carbon tax scheme, which is progressive from the distributional perspective (when the tax revenue is recycled to households as a cash transfer under Scenarios 2b and 2c) causes higher reductions of CO2 emissions. It implies that the distributional (equity) and environmental objectives are aligned in Ethiopia. Emission reductions are relatively smaller when the carbon tax revenue is used for investment or cutting corporate income taxes. Note that these schemes are more efficient economically (increased GDP or lower GDP loss). Recycling carbon tax revenues to cut personal income tax, which causes GDP increase, also causes relatively higher reductions of CO2 emissions.   As indicated by the sensitivity analysis results, there is slight change in GDP impacts and household income impacts when values of elasticities of substitution are increased by 20%. The key findings, however, hold. First, the direction of the impacts does not change, and secondly, the order or ranking of alternative revenue recycling schemes does not change. The GDP impacts presented in Table 4(a) indicate that the ranking or ordering of the revenue recycling schemes are the same both in the main analysis and the sensitivity analysis. The same is true in the case of household income (Table 4b). Based on the results from sensitivity analysis we gain the confidence that the findings of the study are robust.

Conclusions and Policy Implications
This study analyzes the distributional impacts of a hypothetical carbon tax in Ethiopia using a static CGE model. It is one of the very few studies examining the distributional impacts of a carbon tax in the context of developing economies. It also examines the interactions of the distributional impacts with the economic efficiency and environmental performance of the carbon tax. It derives some interesting policy implications which are not available in the existing literature.
First, the distributional impacts of a carbon tax are highly sensitive to its design architectures, particularly the schemes to recycle the revenue to the economy. Our study finds that all household groups gain income from the carbon tax under some schemes for revenue recycling (e.g., recycling the tax revenues for investment), whereas the income impacts are uneven not only in magnitude but also in direction under other schemes of revenue recycling. The carbon tax would be regressive unless it is made progressive by recycling the tax revenue to households either equally (relatively higher transfers to low-income households) or inversely proportional to their income (transferring higher revenues in absolute term to low-income households).
The distributional impacts (i.e., equity implications) of the carbon tax are aligned with its environmental performance in Ethiopia. When the tax revenue is recycled to households either equally or inversely proportional to their incomes, the carbon tax benefits low-income households more than high-income households. The same schemes also cause higher reductions of CO2 emissions ensuring better environmental performance. Our study also finds that the efficiency objective of a carbon tax contradicts its equity and environmental objectives. The carbon tax design architecture, which is economically efficient by either increasing GDP (when tax revenue is recycled to cut personal income tax rate), is regressive as well as environmentally inferior (i.e., low reduction of CO2 emissions).
While our findingcarbon tax could result in a GDP increase when the carbon tax revenue is recycled to cut the personal income tax rateis consistent with the findings from existing studies, such as McKitrick (1997), van Heerden et al. (2006), the gain is very small. Moreover, one could argue that in many countries with the predominant existence of an informal economy, recycling tax revenues to cut indirect tax may not necessarily help a large segment of the population. On the other hand, a carbon tax with revenue used to further incentivize the formal economy could contribute to reducing the economic informality as demonstrated in Timilsina et al. (2021). Further investigations and debates are welcome on these issues.