## 2. Comparison of Projected Fuel Use and CO2 with IEA (2017a)

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### Major themes and analytical focus
- Framework: country-level fuel use projected to 2030 in a business-as-usual (BAU) scenario; environmental, fiscal, local health, economic welfare, and incidence impacts computed for carbon pricing and alternative instruments scaled to impose the same explicit or implicit CO2 price.
- Emphasis on:
  - Comprehensive carbon pricing versus alternative instruments (ETS, coal tax, electricity taxes, road fuel taxes, energy efficiency policies).
  - Domestic environmental co-benefits (premature deaths from outdoor air pollution) and fiscal revenue potential.
  - Incidence on households and industry for illustrative carbon tax levels ($20 in 2020; $35 and $70 in 2030 scenarios).
- Reference year and projection horizon: 2014 baseline data; projections to 2030; focus incidence year 2020 for $20/tCO2 analysis.

### Methodology and model structure
- Fuels and sectors modeled:
  - Five fossil fuels: COAL, NGAS, GAS, DIES, OIL.
  - Three sectors: power generation (E), road transport (T), other energy (O) (disaggregated LARGE, SMALL users).
- Key model mechanics:
  - Power sector: demand grows with GDP (income elasticity), responds to electricity prices; generation can switch among COAL, NGAS, OIL, NUC, BIO, HYD, REN; autonomous productivity growth fastest for renewables.
  - Road transport: gasoline (GAS) and diesel (DIES) demand driven by vehicle km and fuel consumption rates; fuel economy improvements modeled via autonomous decline in consumption rates.
  - Other energy: separates large industrial users (ETS coverage) from small users.
- Externalities and welfare metrics:
  - CO2 emissions, premature deaths from outdoor air pollution (PM2.5 driven), road-use externalities (congestion, accidents, road damage).
  - Economic welfare gains exclude global climate benefits and calculated using second-order public finance approximations (equations (A12)–(A14)).
- Parameterization highlights (values taken exactly as specified):
  - 2014 fuel use from IEA (2017b); projected GDP from IMF (2017) (growth after 2022 assumed to continue at the 2022 projected rate).
  - Real prices: coal and oil in 2030 are 31 and 42 percent higher compared with 2015 respectively; natural gas 0 to 30 percent higher in different regions (Table 1, Appendix 2).
  - Income elasticities for energy products between 0.5 and 0.8 with country-specific adjustments.
  - Price elasticities: electricity demand, road fuels, and other fuels set to -0.5; conditional price elasticities for fossil fuels in power sector set to -0.7. Elasticities constant across countries.
  - Electricity sector: usage and energy consumption rate elasticities assumed 0.25 for both (implying total electricity demand elasticity of -0.5).
  - Annual rate of efficiency improvement for electricity-using products: 1 percent a year.
  - Coal generation share of fuel costs: 0.25.
  - Autonomous productivity growth rates: Coal 0.5 percent; Natural gas, nuclear, hydro 1 percent; Renewables 5 percent.
  - Road transport: income elasticity for vehicle km generally 0.6; China and India 0.8. Fuel price elasticities for gasoline and diesel: -0.25 each (total -0.5). Annual autonomous decline in vehicle fuel consumption rates: 1 percent.
  - Other energy: 75 percent of industry fuel consumption assumed by large firms (ETS coverage). Income elasticities: coal, oil, biomass 0.5; natural gas and renewables 1.0.
  - Mortality adjustments: China and India mortality rates grow at 1.3 and 2.6 percent a year respectively to 2030 for urban exposure.
- Policy scenarios modeled (all prices in US $2015):
  - Carbon tax: full coverage rising in $5 per ton CO2 annual increments from 2017 to reach $70/tCO2 by 2030. “Modest” tax rises at $2.5 per ton per year to reach $35/tCO2 by 2030.
  - ETS: price set equal to carbon tax price, applied to power generators and other large users; allowances fully auctioned.
  - Coal excise: applies only to coal.
  - Electricity output tax: equals induced annual electricity price increase in carbon tax scenario.
  - Electricity emissions tax: charge on carbon content of power generation fuels.
  - Road fuel tax: gasoline and road diesel taxes equal CO2 emissions factors times CO2 price from carbon tax scenario.
  - Energy efficiency combination: shadow price rewarding CO2 reductions from efficiency improvements; incentives for renewables not modeled.

### Main quantitative results — BAU and Paris pledges (2030 comparisons)
- BAU CO2 drivers 2015–2030 (percent changes, drivers listed):
  - GDP-driven increases (holding energy/GDP and CO2/energy constant): China 140 percent, India 213 percent, Indonesia 121 percent; other countries between 11 percent (Japan) and 71 percent (Turkey).
  - Energy intensity of GDP falls causing CO2 reductions between 20 percent (Russia) and over 40 percent (Argentina, China, India, Indonesia).
  - Net BAU CO2 emissions changes: India 123 percent increase; nine countries increase between 0 and 42 percent; nine countries show reductions up to 17 percent.
- BAU primary fuel mix in 2030 (shares):
  - High coal shares: Australia 29 percent, China 59 percent, India 52 percent, South Africa 60 percent.
  - Intermediate coal shares (10–30 percent): Germany, Indonesia, Japan, Korea, Turkey, UK, US.
  - Low coal shares (≤10 percent): Argentina, Brazil, Canada, France, Italy, Mexico, Russia, Saudi Arabia.
  - Natural gas shares: <12 percent in Brazil, France, India, South Africa; about 30 percent or more in Argentina, Australia, Canada, Italy, Japan, Mexico, Russia, Saudi Arabia, Turkey, UK, US.
  - Oil shares: 23 percent in France to over 50 percent in Brazil, Mexico, Saudi Arabia.
  - Nuclear: about 30 percent in France; ≤10 percent in other G20 countries.
  - Renewables (including biomass): around 5-20 percent in most cases; about 30 percent in Brazil and 34 percent in France.
- BAU outdoor air pollution death rates in 2030:
  - Death rate highest in China at 900 per one million population.
  - South Africa about 50 per one million.
  - Russia about 400 per million, India 240, Korea 185, Germany 110; below 100 per million in other cases.
  - Absolute annual mortality: China about 680,000; India 380,000; Russia 55,000; United States 25,000.
- Emissions reductions implied by Paris pledges (2030 below BAU):
  - Over 40 percent in Australia and Canada.
  - Between 30 and 40 percent in European countries, Korea, South Africa, United States.
  - Between 20 and 30 percent in five cases.
  - Less than 20 percent in Argentina, China, India, Indonesia, Russia.
  - G20 aggregate pledges amount to about 21 percent below BAU levels in 2030 (2030 BAU emissions share-weighted average).

### Main quantitative results — Carbon tax impacts (2030 focus)
- CO2 reductions under $70/tCO2 by 2030 (country groupings and magnitudes):
  - Seven countries meet or exceed NDC CO2 components: Argentina, China, India, Indonesia, Russia, South Africa, Turkey.
  - Six countries would need up to 10 percent further reductions: Brazil, Germany, Japan, Korea, Mexico, United States.
  - Six countries would need above 10 percent further reductions: Australia, Canada, France, Italy, Saudi Arabia, United Kingdom.
  - Emissions reductions under $70 tax vary:
    - >30 percent reductions in coal-intensive China, India, South Africa.
    - ~15–25 percent in Argentina, Brazil, Canada, Indonesia, Japan, Mexico, Russia, Turkey, UK, US.
    - <15 percent in France and Saudi Arabia.
  - Marginal diminishing returns: $70 tax reductions less than double those under $35 tax; example: in China $35 tax raises coal prices 116 percent relative to BAU cutting emissions 30 percent; raising from $35 to $70 increases coal prices by a further 54 percent cutting emissions by a further 12 percent.
  - Fuel contributions to CO2 reductions:
    - Coal accounts for >2/3 of CO2 reductions in nine countries and >4/5 in six cases (Australia, China, Germany, India, Korea, South Africa).
    - Oil reductions account for ≤30 percent of CO2 reductions in all but Brazil, France, Saudi Arabia.
    - Natural gas accounts for ≤30 percent in all but Argentina, Canada, Italy, Mexico, Russia, Saudi Arabia.
  - G20 aggregate: a $35/tCO2 price in 2030 is consistent with the total of current NDCs (owing to China and India’s weight).
- Revenue from carbon tax (2030):
  - Revenues typically around 1-2.5 percent of GDP for the $70 tax; substantially higher in India, Russia, Saudi Arabia, South Africa.
  - Revenues about 70-85 percent higher under $70 tax compared with $35 tax (less than double due to reduced fuel demand).
  - Revenues as percent of GDP decline over time with declining emissions intensity of GDP (example: China $70 tax 2020 revenues 3.7 percent of GDP vs 3.2 percent in 2030).
- Health co-benefits (air pollution deaths reduction):
  - Percent reductions in air pollution deaths moderately larger than percent CO2 reductions where coal share in deaths is larger than in CO2.
  - Lives saved per 1 million tons CO2 reduced: about 5-20 in nine cases; 4 or less in Argentina, Australia, Canada, Mexico, Saudi Arabia; about 50 and 80 in China and India respectively.
  - Illustrative valuation: if value of a statistical life in China is $1 million, domestic environmental benefit per ton CO2 reduced in China ~ $100.
- Economic welfare impacts (percent of GDP, domestic-only, excluding global climate benefits):
  - Welfare costs (loss in consumer surplus less government revenue):
    - <0.5 percent of GDP under the modest tax ($35).
    - <0.8 percent of GDP under $70 tax in all but three cases (China, India, South Africa where costs 1.0–1.6 percent of GDP).
  - Net domestic welfare gains (domestic environmental benefits minus welfare costs):
    - For modest carbon tax domestic environmental benefits about as large as, or larger than, costs in all cases (net gains zero or positive).
    - For $70 tax net welfare losses in three cases (two cases 0.1 percent of GDP loss; South Africa 0.7 percent of GDP loss).
    - Large net welfare gains in some cases: Korea 0.7 percent of GDP, India 2.3 percent, Russia 3.7 percent, China 6.7 percent.

### Comparison of alternative mitigation policies relative to $70 carbon tax (2030)
- CO2 reduction effectiveness (relative to $70 carbon tax):
  - Coal tax: ~75 percent or more of carbon tax reductions in Australia, China, Germany, India, Korea, South Africa; >60 percent in Indonesia, Japan, Turkey.
  - ETS (limited coverage): ~40–75 percent of carbon tax reductions in 16 cases; 27 percent in France; ~80 percent or more in Australia and India.
  - Electricity CO2 emissions tax: ≥80 percent of ETS reductions in all but two cases.
  - Electricity output tax: substantially less effective than electricity emissions tax (does not promote fuel switching).
  - Road fuel taxes: well below 10 percent of carbon tax reductions in all but one case.
  - Energy efficiency combination: typically 25–40 percent of carbon tax reductions.
- Revenue relative to carbon tax:
  - Coal tax revenues ~30 percent or less of carbon tax revenues in 16 cases; exceptions China, India, South Africa where revenues are 63–76 percent of carbon tax revenue.
  - ETS revenue generally ~20–60 percent of carbon tax revenue.
  - Taxes on electricity or electricity emissions moderately less than ETS revenues.
  - Road fuel taxes raise ~15–30 percent of carbon tax revenues.
  - Energy efficiency combination slightly erodes pre-existing fuel tax bases but revenue losses are very small.
- Air pollution death reductions generally mirror CO2 reduction patterns; coal tax sometimes performs better relative to carbon tax for mortality reductions.
- Welfare example comparisons (percent of GDP):
  - India: carbon tax 2.3; coal tax 1.8; ETS 1.5; electricity output tax 0.5; electricity CO2 tax 1.3; road fuel tax 0.3; energy efficiency combination 0.8.
  - United States: carbon tax, road fuel tax, energy efficiency combination generate modest net benefits (0.04–0.06 percent of GDP); other policies generate modest net costs (0.02–0.05 percent of GDP). Only the carbon tax approaches meeting the Paris pledge.

### Sensitivity analysis (parameter variations and impacts)
- Parameters varied by ±50 percent to test robustness.
- Sensitivity of required percent CO2 reductions and policy effects:
  - For Argentina, Indonesia, Korea, Mexico, and Turkey, Paris pledges specified as percent reductions below BAU in 2030 are unaffected by absolute 2030 BAU emission changes from parameter variations.
  - For countries with Paris pledges relative to historical emissions, increases in 2030 BAU emissions increase required percent reduction and vice versa.
  - Parameters noticeably affecting required percent reductions: GDP growth rates, income elasticities, fuel price elasticities.
  - Parameters with smaller effects: rates of autonomous technological change, international energy prices.
  - China (and to a lesser extent India) especially sensitive to GDP and income elasticity assumptions; higher GDP growth combined with low income elasticities can lower emissions intensity of GDP and may make China’s Paris pledge met in BAU.
- Sensitivity of CO2 reductions from $70 tax:
  - Not very sensitive to GDP growth, income elasticities, or autonomous technological change.
  - Sensitive to fuel price elasticities:
    - Percent CO2 reductions fall by about two-fifths when elasticities are 50 percent smaller.
    - Percent CO2 reductions increase by around one-third when elasticities are 50 percent larger.
  - Also sensitive to international energy price scenarios because these affect proportionate price increases induced by carbon charges.

### Incidence analysis — methodology and key results (2020, $20/tCO2)
- Method: first-order approximation using input-output tables and household expenditure surveys; assumption of full pass-through of taxes into consumer prices in domestic markets; behavioral responses abstracted from for first-order burdens.
- Focus countries: Canada, China, India, United States.
- Household burdens measured relative to consumption (proxy for permanent/lifetime income).
- Household burdens (bottom decile and top decile burdens as percent of total household consumption):
  - China: bottom decile 4.5 percent, top decile 3.3 percent.
  - United States: bottom decile 2.8 percent, top decile 1.4 percent.
  - India: bottom decile 1.9 percent, top decile 2.6 percent.
  - Canada: bottom decile 1.1 percent, top decile 1.3 percent.
- Drivers of distributional outcomes:
  - China and United States: electricity budget shares decline for higher consumption households (contributes to regressivity).
  - India: electricity budget shares rise for higher consumption households (contributes to mild progressivity) reflecting higher grid access.
  - Indirect burdens (higher consumer goods prices) larger in China and India than in Canada and United States and approximately proportional to expenditure across quintiles—this proportionality moderates regressivity/progressivity.
- Fiscal cost of full compensation of bottom income quintile (share of carbon tax revenues required):
  - Canada: about 11 percent of carbon tax revenues.
  - United States: about 13 percent of carbon tax revenues.
  - India: about 5 percent of carbon tax revenues.
  - China: about 8 percent of carbon tax revenues.
- Notes: full compensation becomes increasingly challenging as carbon price ramps up; targeted social safety nets and well-designed transfers are recommended.

### Industry incidence (2020, $20/tCO2) — exporter cost impacts
- Industry cost increases reported as weighted average percent cost increases for exporter quintiles (vulnerability ranking by export share and intensity).
- India:
  - Top 20 percent of most vulnerable exporters: weighted average cost increases 5.4 percent.
  - Largest increase 10 percent for non-ferrous basic metal exports (account for 1.8 percent of total exports).
  - Top 40 percent of most vulnerable exporters: weighted average cost increases 3.8 percent.
  - Across all exports weighted average cost increase 2.2 percent.
- Cross-country weighted average cost increase across all exporters for $20 tax in 2020:
  - China: 8.2 percent (largest increase reported).
  - Canada: 0.7 percent (smallest increase reported).
- Note: fuel exporters excluded as they would not be subject to carbon pricing.

### Practical policy implications and recommended elements to advance carbon pricing
- Environmental, fiscal, and welfare advantages:
  - Comprehensive carbon taxes (or equivalents) generally outperform alternative instruments across G20 when domestic environmental benefits are considered.
  - In many countries, carbon pricing can be in national interest once domestic benefits (health, congestion, road damage) are included.
- Practical elements to advance domestic carbon pricing (informed by energy price reform experience):
  - Comprehensive plan addressing stakeholder concerns with clear objectives, timetables, and revenue use specifics.
  - Effective communications on global and national benefits (environmental, health, fiscal).
  - Gradual reforms to allow time for firm and household adjustment.
  - Measures to address burdens on vulnerable groups:
    - Improve targeting of social safety nets.
    - Displaced worker programs.
    - Possible temporary tax reliefs for energy-intensive industries (to be phased out progressively).
- International coordination opportunities:
  - Cross-country dispersion in required prices suggests cost-effectiveness gains from international price coordination.
  - An explicit carbon price floor arrangement among large emitters could:
    - Provide protection against competitiveness concerns.
    - Allow flexibility for countries to set higher prices.
    - Permit sale of Internationally Transferred Mitigation Outcomes for countries over-achieving NDCs under Article 6.2.
  - Analogues: provincial/territorial carbon price floors in Canada; incorporation of indirect taxes into national legislation for EU member states.
- Role of modeling:
  - Provides consistent, transparent comparisons across policies, metrics, countries, and parameter scenarios to inform domestic and international design of carbon pricing and related policies (subject to stated caveats and uncertainties).

### BAU comparisons with IEA (2017a) — projection ratios to 2030
- Using the paper’s averaged prices, BAU CO2 emissions for 2030 are 7–36 percent higher across countries compared with IEA (2017a).
- When IEA (2017a) energy price projections are used, BAU tends to be about the same or moderately higher than IEA (2017a) (selected country ratio examples to IEA 2017a):
  - Brazil CO2: Current analysis 1.07; with IEA (2017a) prices 0.91.
  - China CO2: Current analysis 1.36; with IEA (2017a) prices 1.20.
  - India CO2: Current analysis 1.28; with IEA (2017a) prices 0.98.
  - Japan CO2: Current analysis 1.30; with IEA (2017a) prices 1.17.
  - Russia CO2: Current analysis 1.16; with IEA (2017a) prices 1.09.
  - South Africa CO2: Current analysis 1.16; with IEA (2017a) prices 1.05.
  - United States CO2: Current analysis 1.27; with IEA (2017a) prices 1.14.

*Source: wp18193 — "2. Comparison of Projected Fuel Use and CO2 with IEA (2017a)" (IMF Working Paper).*

### 1. Paris Mitigation Pledges, Emissions Intensity and Emissions Per Capita, 2014 ................................. 24

### 1. Paris Mitigation Pledges, Emissions Intensity and Emissions Per Capita, 2014

### Major themes and analytical focus
- Comparison of Paris mitigation pledges against baseline (BAU) emissions projections.
- Metrics emphasized:
  - Emissions intensity.
  - Emissions per capita.
  - Reference year: 2014.

### Related sections in the same content unit
- "Impacts of Other Policies Relative to Carbon Tax, 2030" — comparative assessment of non–carbon-tax policies versus a carbon tax by 2030.
- "Sensitivity of CO2 Reductions from Paris Pledge and $70 Carbon Tax, 2030" — sensitivity analysis for two policy scenarios by 2030.

### Figures and what they cover (as listed)
- Figure 1. Change in BAU CO2 Emissions, 2015-2030
- Figure 2. BAU Primary Fuel Mix, 2030
- Figure 3. Outdoor Air Pollution Death Rates from Fossil Fuels, 2030
- Figure 4. Percent Reduction in BAU CO2 Emissions Implied by Paris Pledge, 2030
- Figure 5. Reduction in CO2 Emissions from Carbon Taxes, 2030
- Figure 6. Revenue from Carbon Taxes, 2030
- Figure 7. Reductions in Air Pollution Deaths from Carbon Taxes, 2030
- Figure 8. Domestic Welfare Effect of Carbon Taxes, 2030
- Figure 9. Burden of $20 Carbon Tax on Household Consumption Quintiles, 2020
- Figure 10. Cost Increases from $20 Carbon Tax by Exporter Quintile, 2020

### Appendixes and supporting material
- Appendix 1. Analytical Model
- Appendix 2. Model Parametrization
- Appendix 3. Incidence Analysis
- Appendix Tables
  - Table 1. Comparison of Future Fuel Price Assumptions

*Source: wp18193 - 1. Paris Mitigation Pledges, Emissions Intensity and Emissions Per Capita, 2014 (PDF chapter/section).*

### 2. Comparison of Projected Fuel Use and CO2 with IEA (2017a) ...........................................................

### 2. Comparison of Projected Fuel Use and CO2 with IEA (2017a)

### I. Introduction and summary
- Framework: model projects country-level fuel use by sector in a business-as-usual (BAU) scenario assuming no new mitigation policies; computes environmental, fiscal, local health, economic welfare, and incidence impacts of carbon pricing and alternative instruments scaled to impose the same explicit or implicit CO2 price.
- Role of carbon pricing:
  - Comprehensive carbon pricing provides across-the-board incentives for reducing energy use and shifting to cleaner fuels and raises significant revenues for fiscal policy options.
  - Political challenges exist due to first-order impacts on energy prices; complementary measures may be needed to compensate vulnerable groups and facilitate clean technology investment.
- Main illustrative quantitative findings:
  - Under a carbon tax with full coverage reaching a price of $70 per ton of CO2 by 2030:
    - Seven countries meet or exceed CO2 component targets implied by their NDCs: Argentina, China, India, Indonesia, Russia, South Africa, and Turkey.
    - Six countries would need further emissions reductions of up to 10 percent: Brazil, Germany, Japan, Korea, Mexico, and United States.
    - Six countries would need further emissions reductions of above 10 percent: Australia, Canada, France, Italy, Saudi Arabia, and United Kingdom.
  - For the whole G20, a carbon price of $35 per ton in 2030 is consistent with the total of current NDCs (owing to China and India’s weight).
  - Revenue potential: around 1-2.5 percent of GDP in most cases for the $70 per ton tax in 2030, and considerably more in a few cases.
  - Local air pollution co-benefits: value of the reduction in local pollution deaths per ton of CO2 reduced in China is estimated at $100 (illustrative).
  - Pure welfare costs of the $70 per ton tax are generally less than 0.8 percent of GDP in all but three cases; accounting for local environmental benefits (excluding global warming) yields net welfare impacts around zero to strongly positive in all but three cases.
- Relative performance of other instruments (same explicit/implicit CO2 price):
  - Coal taxes can achieve over 75 percent of the CO2 reductions under the carbon tax in six countries.
  - ETSs (limited coverage to large stationary sources) typically reduce emissions by about 40 to 75 percent of the reductions under an equally priced carbon tax.
  - Tax on CO2 emissions from power generation typically achieves 80 percent or more of emissions reductions under ETSs.
  - Energy efficiency policies typically reduce emissions by 25 to 40 percent of that under the carbon tax (even if implemented nationwide).
  - Road fuel taxes typically reduce emissions by less than 10 percent of that under the carbon tax.
  - Revenue from other instruments is generally well below carbon tax revenues: around 40-80 percent lower for ETSs and power sector taxes; more than 70 percent lower for road fuel taxes and (in most cases) coal taxes.

### II. Methodology (analytical framework and caveats)
- Model scope:
  - Five fossil fuels: coal, natural gas, gasoline, road diesel, and other oil products.
  - Three sectors projected to 2030: power generation, road transport, and an “other energy” sector (households, firms, non-road transport, industry disaggregated by large vs small users).
  - Externalities included: CO2 emissions, premature deaths from outdoor air pollution, and road-use externalities (congestion, accidents, road damage).
- Key model mechanics:
  - Power sector: demand grows with GDP (income elasticity), responds to electricity prices; generation can switch among coal, natural gas, oil, nuclear, biomass, hydro, and other renewables; autonomous technological progress reduces unit generation costs (fastest for renewables).
  - Road transport: gasoline (light-duty) and diesel (heavy and some light-duty) fuel use varies with GDP and fuel prices; fuel economy improvements captured by autonomous improvements or fleet composition shifts.
  - Other energy: disaggregates small users from large industrial users to reflect ETS coverage differences.
- Caveats:
  - BAU excludes new mitigation policies beyond those already implicit in observed energy use and prices.
  - Fuel price responses may be less reliable for dramatic price changes that could induce major technological shifts (e.g., CCS); global average CO2 price currently about $1 per ton.
  - Model is comparative static, de-coupled from broader economy and inter-sector feedbacks; assumes perfectly elastic fuel supply curves and ignores international trade effects.
  - Welfare calculations omit broader fiscal linkages, transitory adjustment costs, and possible macroeconomic impacts.
- Parameterization highlights:
  - 2014 fuel use from IEA (2017b); projected GDP from IMF (2017) (growth after 2022 assumed to continue at the 2022 projected rate).
  - Real prices: coal and oil in 2030 are 31 and 42 percent higher compared with 2015 respectively (average of EIA (2018) rising projections and IMF (2017) generally flat projections); natural gas 0 to 30 percent higher in different regions (Table 1, Appendix 2).
  - Income elasticities for energy products between 0.5 and 0.8 with country-specific adjustments.
  - Price elasticities: electricity demand, road fuels, and other fuels set to -0.5; conditional price elasticities for fossil fuels in power sector set to -0.7. Elasticities constant across countries.
  - CO2 emissions per unit of fuel use from the International Energy Agency; local air pollution mortality rates updated from detailed country-by-country estimates.
- Policy scenarios:
  - Carbon tax: full coverage on carbon content of fossil fuel supply, rising in annual increments of $5 per ton of CO2 each year from 2017 to reach $70 per ton by 2030. A “modest” tax rises at $2.5 per ton a year to reach $35 per ton by 2030. All prices in US $2015.
  - ETS: modeled as cap-set price equal to carbon tax price, applied to carbon content of fuels used by power generators and other large energy users; allowances fully auctioned.
  - Coal excise: mimics coal charge portion of broader carbon tax.
  - Electricity output tax: equals induced annual electricity price increase in the carbon tax scenario; electricity emissions tax (charge on carbon content of power generation fuels) also considered.
  - Road fuel tax: gasoline and road diesel tax increases set equal to CO2 emissions factors times the CO2 price in the carbon tax scenario.
  - Energy efficiency combination: shadow price rewarding CO2 reductions from efficiency improvements across all sectors (practical implementation challenges acknowledged).
  - Incentives for renewables are not modeled.

### III. Results

#### A. BAU scenarios (to 2030)
- CO2 emissions percent changes 2015–2030 (drivers):
  - GDP-driven increases (holding energy/GDP and CO2/energy constant): China 140 percent, India 213 percent, Indonesia 121 percent; other countries between 11 percent (Japan) and 71 percent (Turkey).
  - Energy intensity of GDP falls causing CO2 reductions between 20 percent (Russia) and over 40 percent (Argentina, China, India, Indonesia).
  - Net BAU CO2 emissions changes: India 123 percent increase; nine countries increase between 0 and 42 percent; nine countries show reductions up to 17 percent.
- BAU primary fuel mix in 2030 (shares):
  - High coal shares: Australia 29 percent, China 59 percent, India 52 percent, South Africa 60 percent.
  - Intermediate coal shares (10–30 percent): Germany, Indonesia, Japan, Korea, Turkey, UK, US.
  - Low coal shares (≤10 percent): Argentina, Brazil, Canada, France, Italy, Mexico, Russia, Saudi Arabia.
  - Natural gas shares: <12 percent in Brazil, France, India, South Africa; about 30 percent or more in Argentina, Australia, Canada, Italy, Japan, Mexico, Russia, Saudi Arabia, Turkey, UK, US.
  - Oil shares: 23 percent in France to over 50 percent in Brazil, Mexico, Saudi Arabia.
  - Nuclear: about 30 percent in France; ≤10 percent in other G20 countries.
  - Renewables (including biomass): around 5-20 percent in most cases; about 30 percent in Brazil and 34 percent in France.
- BAU air pollution mortality in 2030:
  - Death rate highest in China at 900 per one million population.
  - South Africa about 50 per one million.
  - Russia about 400 per million, India 240, Korea 185, Germany 110; below 100 per million in other cases.
  - Absolute annual mortality: China about 680,000; India 380,000; Russia 55,000; United States 25,000.
- Emissions reductions implied by Paris pledges (2030 below BAU):
  - Over 40 percent in Australia and Canada.
  - Between 30 and 40 percent in European countries, Korea, South Africa, United States.
  - Between 20 and 30 percent in five cases.
  - Less than 20 percent in Argentina, China, India, Indonesia, Russia.
  - G20 aggregate pledges amount to about 21 percent below BAU levels in 2030 (2030 BAU emissions share-weighted average).

#### B. Impacts of carbon taxes (2030 focus)
- CO2 emissions reductions:
  - Under $70 per ton tax by 2030:
    - Seven countries meet/exceed NDC CO2 components: Argentina, China, India, Indonesia, Russia, South Africa, Turkey.
    - Six countries need up to 10 percent further reductions: Brazil, Germany, Japan, Korea, Mexico, Turkey, United States.
    - Six countries need above 10 percent further reductions: Australia, Canada, France, Italy, Saudi Arabia, United Kingdom.
  - Emissions reductions under $70 tax vary:
    - >30 percent reductions in coal-intensive China, India, South Africa.
    - ~15-25 percent in Argentina, Brazil, Canada, Indonesia, Japan, Mexico, Russia, Turkey, UK, US.
    - <15 percent in France and Saudi Arabia.
  - Marginal diminishing returns: $70 tax reductions less than double those under $35 tax; e.g., in China $35 tax raises coal prices 116 percent relative to BAU cutting emissions 30 percent; raising from $35 to $70 increases coal prices by a further 54 percent cutting emissions by a further 12 percent.
  - Fuel contributions to CO2 reductions:
    - Coal accounts for >2/3 of CO2 reductions in nine countries and >4/5 in six cases (Australia, China, Germany, India, Korea, South Africa).
    - Oil reductions account for ≤30 percent of CO2 reductions in all but Brazil, France, Saudi Arabia.
    - Natural gas accounts for ≤30 percent in all but Argentina, Canada, Italy, Mexico, Russia, Saudi Arabia.
  - G20 aggregate: $35 per ton price sufficient to meet Paris pledges (due to China and India’s weight).
- Revenue from carbon tax (2030):
  - Revenues typically around 1-2.5 percent of GDP for the $70 tax; substantially higher in India, Russia, Saudi Arabia, South Africa.
  - Revenues about 70-85 percent higher under $70 tax compared with $35 tax (less than double due to reduced fuel demand).
  - Revenues as percent of GDP decline over time with declining emissions intensity of GDP (example: China $70 tax 2020 revenues 3.7 percent of GDP vs 3.2 percent in 2030).
- Health co-benefits (air pollution deaths reduction):
  - Percent reductions in air pollution deaths moderately larger than percent CO2 reductions where coal share in deaths is larger than in CO2.
  - Lives saved per 1 million tons CO2 reduced: about 5-20 in nine cases; 4 or less in Argentina, Australia, Canada, Mexico, Saudi Arabia; about 50 and 80 in China and India respectively.
  - Illustrative valuation: if value of a statistical life in China is $1 million, domestic environmental benefit per ton CO2 reduced in China ~ $100.
- Economic welfare impacts (2030, percent of GDP):
  - Economic welfare costs (loss in consumer surplus less government revenue) are:
    - <0.5 percent of GDP under the modest tax ($35).
    - <0.8 percent of GDP under $70 tax in all but three cases (China, India, South Africa where costs 1.0-1.6 percent of GDP).
  - Net domestic welfare gains (domestic environmental benefits excluding global warming minus welfare costs):
    - For the modest carbon tax domestic environmental benefits about as large as, or larger than, costs in all cases (net gains zero or positive).
    - For $70 tax net welfare losses in three cases (two cases 0.1 percent of GDP loss; South Africa 0.7 percent of GDP loss).
    - Large net welfare gains in some cases: Korea 0.7 percent of GDP, India 2.3 percent, Russia 3.7 percent, China 6.7 percent.

#### C. Comparison of alternative mitigation policies (relative to $70 carbon tax)
- CO2 reductions relative to $70 carbon tax:
  - Coal tax: ~75 percent or more of carbon tax reductions in Australia, China, Germany, India, Korea, South Africa; >60 percent in Indonesia, Japan, Turkey.
  - ETS (limited coverage): reduces emissions by ~40–75 percent of carbon tax reductions in 16 cases; 27 percent in France; ~80 percent or more in Australia and India.
  - Electricity CO2 emissions tax: achieves ≥80 percent of ETS reductions in all but two cases.
  - Electricity output tax: substantially less effective than electricity emissions tax (does not promote fuel switching).
  - Road fuel taxes: weak effectiveness, well below 10 percent of carbon tax reductions in all but one case.
  - Energy efficiency combination: typically reduces emissions by 25–40 percent of carbon tax reductions.
- Revenue relative to carbon tax:
  - Coal tax revenues ~30 percent or less of carbon tax revenues in 16 cases; exceptions China, India, South Africa where revenues are 63-76 percent of carbon tax revenue.
  - ETS revenue generally ~20–60 percent of carbon tax revenue.
  - Taxes on electricity or electricity emissions moderately less than ETS revenues.
  - Road fuel taxes raise ~15–30 percent of carbon tax revenues.
  - Energy efficiency combination slightly erodes pre-existing fuel tax bases but revenue losses are very small.
- Air pollution death reductions: generally mirror CO2 reduction patterns; coal tax sometimes performs better relative to carbon tax for mortality reductions.
- Welfare outcomes (examples):
  - India: welfare gains (% of GDP) from carbon tax 2.3; coal tax 1.8; ETS 1.5; electricity output tax 0.5; electricity CO2 tax 1.3; road fuel tax 0.3; energy efficiency combination 0.8.
  - United States: carbon tax, road fuel tax, energy efficiency combination generate modest net benefits (0.04-0.06 percent of GDP); other policies generate modest net costs (0.02-0.05 percent of GDP). Only the carbon tax approaches meeting the Paris pledge.

#### D. Sensitivity analysis
- Main uncertain parameters varied by ±50 percent.
- Relative impacts of other mitigation policies are approximately robust or change in predictable ways (e.g., increasing road fuel price elasticities increases effectiveness of road fuel taxes proportionately).
- Emissions impacts of carbon pricing and comparisons with Paris targets sensitive to parameter choices; specific sensitivity outcomes discussed in Section III.D. (full parameter sensitivity explored in paper appendices).

*Source: wp18193 - 2. Comparison of Projected Fuel Use and CO2 with IEA (2017a) - IMF Working Paper*

### Appendix 2).

### Appendix 2)

### Sensitivity of Required Percent CO2 Reductions and Policy Effects
- For Argentina, Indonesia, Korea, Mexico, and Turkey, Paris pledges specify percent reductions below BAU levels in 2030; changes in absolute 2030 BAU emissions due to parameter variations do not affect the required percent reductions in 2030.
- For countries with Paris pledges relative to historical emissions, increases in 2030 BAU emissions increase the required percent reduction in 2030 and vice versa.
- Parameters that noticeably affect required percent reductions in 2030:
  - GDP growth rates
  - Income elasticities
  - Fuel price elasticities
- Parameters with smaller effects on required percent reductions in 2030:
  - Rates of autonomous technological change
  - International energy prices
- China (and to a lesser extent India) are especially sensitive to GDP and income elasticity assumptions:
  - Example: higher GDP growth combined with the baseline assumption of low income elasticities for energy products lowers the emissions intensity of GDP and China’s Paris pledge is met in the BAU.
- Percent reductions in CO2 below 2030 BAU levels induced by the $70 carbon tax:
  - Not very sensitive to assumptions about GDP growth, income elasticities, or autonomous rates of technological change.
  - Sensitive to fuel price elasticities:
    - Percent CO2 reductions fall by about two-fifths when elasticities are 50 percent smaller in size than in the baseline.
    - Percent CO2 reductions increase by around one-third when elasticities are 50 percent larger.
  - Almost as sensitive to different scenarios for international energy prices, because these affect the proportionate increase in prices from BAU levels induced by carbon charges.
- Footnote: "These factors have no, or at best modest, impacts on the percent change in fuel prices induced by carbon charges and fuel price elasticities."

### Incidence Analyses — Methodology
- Standard procedures involving input-output tables and household expenditure surveys (described in Appendix 3) are used to obtain first order approximations of incidence effects (abstracting from behavioral responses).
- Assumption: full pass-through of taxes into consumer prices in domestic markets.
- Focus countries for incidence analysis: Canada, China, India, and the United States.
- Focus year: 2020 (impacts of immediate concern as the tax is phased in).
- Carbon tax level analyzed: $20 per ton of CO2.
- Footnote references:
  - Fabrizio et al. (2016) for discussion of an online tool using the same general approach.
  - The framework would predict burdens about three times as large in 2030 (due to higher tax rates), but this overstates incidence by failing to account for medium-term behavioral responses.

### Incidence Analyses — Households (2020, $20/ton CO2)
- Burdens are defined relative to consumption (proxy for permanent/lifetime income).
- Key findings on regressivity/progressivity (burdens as percent of total household consumption for bottom and top income deciles):
  - China: bottom decile 4.5 percent, top decile 3.3 percent.
  - United States: bottom decile 2.8 percent, top decile 1.4 percent.
  - India: bottom decile 1.9 percent, top decile 2.6 percent.
  - Canada: bottom decile 1.1 percent, top decile 1.3 percent.
- Drivers of distributional outcomes:
  - China and the United States: budget shares for electricity decline for higher consumption households (contributes to regressivity).
  - India: budget shares for electricity rise for higher consumption households (partly reflecting higher rates of grid access), contributing to mild progressivity.
  - Indirect burdens from higher consumer goods prices induced by higher energy prices are larger in China and India than in Canada and the United States, and are approximately proportional to expenditure across household quintiles—this proportionality moderates overall regressivity/progressivity.
- Fiscal cost of compensating the bottom income quintile (share of carbon tax revenues required for full compensation):
  - Canada: about 11 percent of carbon tax revenues.
  - United States: about 13 percent of carbon tax revenues.
  - India: about 5 percent of carbon tax revenues.
  - China: about 8 percent of carbon tax revenues.
- Notes:
  - Compensating low-income households is most realistic where adjustments to fiscal and social safety net systems can be carefully targeted.
  - Even poorly targeted measures (e.g., a poll subsidy) might do much to protect the poorest without absorbing all available revenues.
  - Full compensation becomes increasingly challenging as the carbon price is progressively ramped up.

### Incidence Analyses — Industry (2020, $20/ton CO2)
- Figure 10 analysis: average percent cost increases for most vulnerable exporting industries (weighted by each industry’s share in total exports).
- India:
  - The 20 percent of most vulnerable exporters face weighted average cost increases of 5.4 percent.
  - The largest increase is 10 percent for non-ferrous basic metal exports (which account for 1.8 percent of total exports).
  - The 40 percent of most vulnerable exporters face weighted average cost increases of 3.8 percent.
  - Across all exports the weighted average cost increase is 2.2 percent.
- Cross-country comparison of weighted average cost increase across all exporters (for $20 tax in 2020):
  - China: 8.2 percent (largest increase across countries reported), reflecting high energy-intensity of exports and carbon intensity of energy.
  - Canada: 0.7 percent (smallest increase), given limited use of coal.
- Note: fuel exporters excluded as they would not be subject to carbon pricing.

### Conclusion — Main Themes and Policy Implications
- Theme 1: Environmental, fiscal, and welfare advantage of comprehensive carbon taxes (or equivalent instruments) over other mitigation policies across G20 countries.
  - Such taxes can be in many countries’ national interests when accounting for domestic environmental benefits (before global climate benefits).
  - Raises issue of how to advance carbon pricing domestically.
- Theme 2: Practical elements to advance domestic carbon pricing (informed by previous experience with energy price reform):
  - Have a comprehensive plan addressing stakeholder concerns, with clearly stated objectives, timetables, and specifics (e.g., on revenue use).
  - An effective communications plan about global and national (environmental, health, fiscal) benefits.
  - Gradual reforms to provide time for firms and households to adjust.
  - Address burdens on vulnerable groups via:
    - Improved targeting of social safety nets
    - Displaced worker programs
    - Possible temporary tax reliefs for energy-intensive industries (should be progressively phased out on efficiency grounds, especially if other countries are acting on Paris pledges)
- Theme 3: High carbon prices may be needed to meet NDCs in some cases:
  - Given evidence on fuel price responsiveness and assuming no other mitigation policies, required prices might produce energy price increases and burdens on vulnerable groups that push political acceptability bounds.
  - Need to complement carbon pricing with other policies to enhance environmental effectiveness, e.g., infrastructure upgrades for renewable generation, carbon capture and storage, electric vehicles.
- Theme 4: Cross-country dispersion in required prices suggests opportunities for cost-effectiveness gains through some international price coordination:
  - Relative tightening of lax NDCs would promote carbon price convergence.
  - An explicit carbon price floor arrangement (among large emitters and as reinforcement, not substitute, for the NDC process) could help:
    - Provides protection against competitiveness concerns.
    - Allows countries flexibility to set prices higher than the floor.
    - Could benefit all participants.
  - Analogues cited: carbon price floor requirements at the provincial/territorial level in Canada and incorporation of indirect taxes into national legislation for EU member states.
  - Countries for which the price floor over-achieves their NDC could sell "Internationally Transferred Mitigation Outcomes" to others falling short via Article 6.2 of the Paris Agreement.
- Role of modeling:
  - The model developed provides consistent and transparent comparisons across policies, metrics, countries, and parameter scenarios and can inform dialogue on domestic and international design of carbon pricing and related mitigation policies (subject to caveats and uncertainties).

### Key Tables and Figures — Notable Quantities and Metrics (as reported)
- Table 1: Paris Mitigation Pledges, Emissions Intensity and Emissions Per Capita, 2014 (selected entries)
  - Argentina: Mitigation pledge "Reduce GHGs 15% below BAU in 2030 by 2030"; 2014 share of global CO2 0.6; tons CO2/$1,000 GDP 0.39; tons CO2 per capita 4.7.
  - China: Mitigation pledge "Reduce CO2/GDP 60-65% below 2005 by 2030"; 2014 share of global CO2 28.5; tons CO2/$1,000 GDP 0.98; tons CO2 per capita 7.5.
  - India: Mitigation pledge "Reduce GHG/GDP 33-35% below 2005 by 2030"; 2014 share of global CO2 6.2; tons CO2/$1,000 GDP 1.10; tons CO2 per capita 1.7.
  - United States: Mitigation pledge "Reduce GHGs 26-28% below 2005 by 2025"; 2014 share of global CO2 14.5; tons CO2/$1,000 GDP 0.30; tons CO2 per capita 16.5.
  - Saudi Arabia: Mitigation pledge "Reduce GHGs 130 million tons below BAU in 2030 by 2030"; 2014 share of global CO2 1.7; tons CO2/$1,000 GDP 0.79; tons CO2 per capita 19.5.
- Table 2: Impacts of Other Policies Relative to Carbon Tax, 2030
  - Reports multiple relative ratios and percent changes (revenue under alternative policies relative to $70 carbon tax; CO2 reductions under other policies relative to $70 carbon tax; welfare impacts percent GDP; reductions in air pollution deaths relative to $70 carbon tax).
  - Example values (selected): China row shows CO2 reduction under carbon tax = 1.00 baseline; revenue under alternative policies relative to $70 carb. tax includes values 0.67, 0.42, 0.29, 0.23, 0.09, 0.00 (across policy columns).
  - Welfare impacts, percent GDP for China include 6.67, 6.38, 3.86, 1.05, 3.32, 0.15, 2.20 (across policy columns).
- Table 3: Sensitivity of CO2 Reductions from Paris Pledge and $70 Carbon Tax, 2030
  - Presents percent CO2 reduction from baseline across parameter variations (GDP growth rate, income elasticities, autonomous rate of technological change, international energy prices, fuel/electricity price elasticities) with "decreased 50%" and "increased 50%" columns for each parameter.
  - Example entries (selected): United States baseline Paris pledge % CO2 reduction = 15; corresponding $70 CO2 tax baseline = 20. Under fuel/electricity price elasticities increased 50% the $70 CO2 tax value for the United States is 25.
- Figures (described):
  - Figure 1: Change in BAU CO2 Emissions, 2015-2030 (In percent) — bars indicate changes from GDP, energy intensity of GDP, and CO2 intensity of energy; boxes indicate net effect.
  - Figure 2: BAU Primary Fuel Mix, 2030 (In percent).
  - Figure 3: BAU Outdoor Air Pollution Death Rates from Fossil Fuels, 2030 (In units per million people) — excludes deaths from indoor air pollution and non-fossil pollution.
  - Figure 4: Percent Reduction in BAU CO2 Emissions Implied by Paris Pledge, 2030 (In percent).
  - Figure 5: Reduction in CO2 Emissions from Carbon Taxes, 2030 (In percent) — blue bars $35 tax, brown bars additional reductions under $70 tax; black squares indicate target CO2 reductions from Figure 4.
  - Figure 6: Revenue from Carbon Taxes, 2030 (In percent of GDP).
  - Figure 7: Reductions in Air Pollution Deaths from Carbon Taxes, 2030 (In percent).
  - Figure 8: Domestic Welfare Effect of Carbon Taxes, 2030 (In percent of GDP) — environmental benefits include reduced domestic air pollution mortality, traffic congestion, traffic accidents, and road damage; exclude global climate benefits.
  - Figure 9: Burden of $20 Carbon Tax on Household Consumption Quintiles, 2020 (In percent of total household consumption).
  - Figure 10: Cost Increases from $20 Carbon Tax by Exporter Quintile, 2020 (In percent of total costs).

*Source: wp18193 - Appendix 2).*

### Appendix 1. Analytical Model

### Appendix 1. Analytical Model

### (i) Fossil Fuels
- Fuel types: i = COAL, NGAS, GAS, DIES, OIL.
- User fuel price at time t:
  - (A1) 푝푡푖 = 휏푡푖 + 푝̂푡푖
    - 휏푡푖 is the tax or subsidy (if negative) on fuel i reflecting (a) the combined effect of any pre-existing excises, favorable treatment under general sales tax for household fuels, and distortions from regulated or monopoly pricing and (b) any carbon charge.
    - 푝̂푡푖 is the pre-tax fuel price or supply cost (the international commodity price adjusted for processing/distribution margins).
    - For most countries, 휏푡푖 is large for road fuels and zero for coal and gas (or a small positive for the latter two fuels in countries covered by the EU ETS).
    - For fuel products used in multiple sectors, pre-tax prices and taxes are taken to be the same for all fuel users (for non-road oil products taxes are zero, except for EU countries to the extent they are covered by the ETS).

### (ii) Power Sector
- Aggregate electricity demand: 푌푡퐸 determined by:
  - (A2) 푌푡퐸 = ( (푈푡퐸 / 푈0퐸) · (ℎ푡퐸 / ℎ0퐸) ) · 푌0퐸,  
    where
    - 푈푡퐸 / 푈0퐸 = (퐺퐷푃푡 / 퐺퐷푃0)^휐퐸 · ( (ℎ푡퐸 · 푝푡퐸) / (ℎ0퐸 · 푝0퐸) )^휂𝑈𝐸,
    - ℎ푡퐸 / ℎ0퐸 = (1 + 훼퐸)^{−t} · ( (푝푡퐸 / 푝0퐸) )^{휂ℎ𝐸 }.
  - Definitions:
    - 푈푡퐸: usage of electricity-consuming products or capital (stock × intensity of use).
    - ℎ푡퐸: electricity consumption rate (kWh per unit of capital usage) — inverse of energy efficiency.
    - 휐퐸: income elasticity of demand for electricity-using products (constant).
    - 휂𝑈𝐸 < 0: elasticity of demand for use of electricity-consuming products w.r.t. unit energy costs.
    - 훼퐸 ≥ 0: fixed annual rate of autonomous decline in electricity consumption rate.
    - 휂ℎ𝐸: elasticity of the energy consumption rate with respect to energy prices.
  - Note: (A2) can be implemented with 푈0퐸 and ℎ0퐸 normalized to unity.

- Generation fuels: i = COAL, NGAS, OIL, NUC, HYD, BIO, REN.
- Generation share of fuel i:
  - (A3) 휃푡퐸푖 = 휃0퐸푖 { ( (푔푡푖 / 푔0푖)^{ε̃퐸푖} ) + ∑_{j} 휃0퐸푗 [ 1 − ( (푔푡푗 / 푔0푗)^{ε̃퐸푗} ) ] · ( 휃0퐸푖 / ∑_{l≠j} 휃0퐸𝑙 ) }
    - 푔푡푖: full cost of generating a unit of electricity using fuel i (fuel, labor, capital, transmission/distribution costs).
    - ε̃퐸푖 < 0: conditional own-price elasticity of generation from fuel i with respect to generation cost.
    - Interpretation: fuel i’s generation share decreases in its own generation cost and increases when other fuels’ generation costs rise; share-shifts are allocated proportional to initial shares among alternatives.

- Fuel use in power generation:
  - (A4) 퐹푡퐸푖 = 휃푡퐸푖 · 푌푡퐸 / 휌푡퐸푖
    - 휌푡퐸푖: productivity of fuel use (electricity generated per unit of 퐹푡퐸푖).

- Unit generation costs:
  - (A5) For i = COAL, NGAS, OIL:
      - 푔푡퐸푖 = 푝푡푖 + 푘푡퐸푖 / 휌푡퐸푖
    For i = NUC, HYD, BIO, REN:
      - 푔푡퐸푖 = 푘푡퐸푖 / 휌푡퐸푖
    And:
      - 휌푡퐸푖 = (1 + 훼휌𝑖)^{t} · 휌0퐸푖
    - 푘푡퐸푖: non-fossil fuel costs per unit.
    - Productivity increases at rate 훼휌𝑖 ≥ 0 per year (reflecting autonomous improvements).

- User price of electricity:
  - (A6) 푝푡퐸 = ∑_{i} 휃푡퐸푖 · 푔푡퐸푖 + 휏푡퐸
    - User electricity price equals weighted sum of unit generation costs plus an electricity tax 휏푡퐸 (pre-existing electricity taxes are taken to be zero in the baseline).

### (iii) Road Transport Sector
- Fuel types for road: i = GAS (gasoline), DIES (road diesel).
- Fuel demand in period t:
  - (A7) 퐹푡푇푖 = ( (푈푡푇푖 / 푈0푇푖) · (ℎ푡푇푖 / ℎ0푇푖) ) · 퐹0푇푖,
    where
    - 푈푡푇푖 / 푈0푇푖 = (퐺퐷푃푡 / 퐺퐷푃0)^휐𝑇푖 · ( (ℎ푡푇푖 · 푝푡푖) / (ℎ0푇푖 · 푝0𝑖) )^휂𝑈𝑇𝑖,
    - ℎ푡푇푖 / ℎ0푇푖 = (1 + 훼ℎ𝑇푖)^{−t} · ( (푝푡𝑖 / 푝0𝑖) )^{휂ℎ𝑇𝑖 }.
  - Definitions:
    - 푈푡푇푖: kilometers (km) driven by vehicles with fuel type i.
    - ℎ푡푇푖: average fuel use per vehicle km (inverse of fuel economy).
    - 휐𝑇푖: income elasticity for km driven.
    - 휂𝑈𝑇𝑖 < 0: elasticity of vehicle km driven w.r.t. per-km fuel costs.
    - 훼𝑇𝑖 ≥ 0: annual autonomous reduction in fuel consumption rate (fuel economy improvements).
    - 휂ℎ𝑇𝑖 ≤ 0: elasticity of the fuel consumption rate to fuel prices (includes shift to electric/hybrid vehicles and other efficiency improvements).
  - Note: model abstracts from formal substitution between gasoline and diesel vehicles.

### (iv) Other Energy Sector
- Groups q = LARGE, SMALL (households and small firms).
- Fuels i = COAL, NGAS, OIL, BIO, REN.
- Fuel use by group q at time t:
  - (A8) 퐹푡푂푞푖 = ( (푈푡푂푞푖 / 푈0푂푞푖) · (ℎ푡푂푞푖 / ℎ0푂푞푖) ) · 퐹0푂푞푖,
    where
    - 푈푡푂푞푖 / 푈0푂푞푖 = (퐺퐷푃푡 / 퐺퐷푃0)^휐𝑂𝑖 · ( (ℎ푡푂푞푖 · 푝푡𝑖) / (ℎ0푂푞푖 · 푝0𝑖) )^휂𝑈𝑂𝑖,
    - ℎ푡푂푞푖 / ℎ0푂푞푖 = (1 + 훼𝑂𝑖)^{−t} · ( (푝푡𝑖 / 푝0𝑖) )^{휂ℎ𝑂𝑖 }.
  - Interpretation analogous to (A2) and (A7).
  - Parameters 휐𝑂𝑖, 휂𝑈𝑂𝑖, 휂ℎ𝑂𝑖, 훼𝑂𝑖 have analogous interpretations and are taken to be the same across LARGE and SMALL users.

### (v) Modelling Policies
- Carbon tax:
  - Implemented by adding to 휏푡푖 a charge 휏푡𝐶𝑂2 · 휇𝐶𝑂2푖 for i = COAL, NGAS, GAS, DIES, OIL.
    - 휏푡𝐶𝑂2: uniform tax on CO2 emissions in period t.
    - 휇𝐶𝑂2푖: fuel i’s CO2 emissions factor (positive for fossil fuels; zero for renewables, hydro, biomass, nuclear).
- ETS:
  - Modelled similarly to carbon tax but charges apply only to fuels used by power generators and large users in the other energy sector.
- Coal tax:
  - Same structure as carbon tax but applies only to coal use.
- Road fuel tax:
  - Applies carbon charges to road fuels only.
- Electricity tax (휏푡퐸):
  - Increases electricity prices by the same amount as they increase in the carbon tax scenario.
- Electricity emissions tax:
  - Same as ETS but charges applied to power generation fuels only (not large industrial users).
- Energy efficiency policy:
  - Applies a ‘virtual’ carbon charge to fuel prices in the equations governing energy efficiency, but not to fuel prices in the equations governing usage of energy-consuming products.

### (vi) Metrics for Comparing Policies
- CO2 emissions from fossil fuel use at time t:
  - (A9) ∑_{j=E,T,O} ∑_{i} 퐹푡_{ji} · 휇𝐶𝑂2푖
    - j = E (electricity), T (road transport), O (other energy sector).
- Revenue from fuel and electricity taxes:
  - (A10) ∑_{j,i} 퐹푡_{ji} · 휏푡𝑖 + 푌푡𝐸 · 휏푡𝐸
- Deaths from fossil fuel air pollution at time t:
  - (A11) ∑_{j,i} 퐹푡_{ji} · 푚푡_{ji}
    - 푚푡_{ji}: mortality per unit of (fossil) fuel i used in sector j; may differ by sector due to emissions controls and population exposure.

- Economic welfare gains (excluding global climate benefits):
  - Calculated using second-order approximations from public finance formulas, requiring:
    - size of price distortions in fuel and electricity markets (difference between social and private costs due to domestic environmental costs net of any fuel taxes),
    - induced quantity changes in markets affected by these distortions (outputs of the model),
    - any new source of distortions created by carbon policies.
  - Welfare change from a carbon tax in period t:
    - (A12) ∑_{j,i} ( Γ푡_{ji} − (휇𝐶𝑂2푖 · 휏푡𝐶𝑂2 / 2) ) · (−∆퐹푡_{ji} )
    - (A13) Γ푡_{ji} = V M O R T 푡 · 푚푡_{ji} − 휏̂푡𝑖, for j ≠ T, i = COAL, NGAS, OIL
      - Γ푡_{T𝑖} = V M O R T 푡 · 푚푡_{T𝑖} + ( (휂𝑈𝑇𝑖 / (휂ℎ𝑇𝑖 + 휂𝑈𝑇𝑖)) · 훽푡_{T𝑖} ) − 휏̂푡𝑖
        - V M O R T 푡: value per premature mortality.
        - 훽푡_{T𝑖}: external costs of traffic congestion, accidents, and road damage per unit of fuel use.
        - 휏̂푡𝑖: pre-existing fuel tax (Γ푡_{ji} is defined net of any pre-existing fuel taxes).
    - (A14) ∆퐹푡_{ji} = 퐹푡_{ji} − 퐹̂푡_{ji} (change in fuel use relative to BAU).
  - Interpretation of (A12):
    - Welfare change equals (i) reduction in fuel use times pre-existing price distortion associated with that product/sector (aggregated over fuels/sectors) minus (ii) the Harberger triangle equal to reduction in fuel use times one-half of the tax increase (product of fuel’s CO2 emissions factor and the CO2 price at time t).
  - Same formula applied to ETS, coal tax, road fuel taxes, and energy efficiency policies with charges applied to relevant fuels/sectors or virtually to energy efficiency.

*Source: Appendix 1. Analytical Model (wp18193 - Appendix 1. Analytical Model).*

### 0.25 are assumed for both the usage and energy consumption rate elasticities for all countries,

### wp18193 - 0.25 are assumed for both the usage and energy consumption rate elasticities for all countries,

### Electricity sector: demand and efficiency assumptions
- 0.25 are assumed for both the usage and energy consumption rate elasticities for all countries, implying a total electricity demand elasticity of -0.5.
- Annual rate of efficiency improvement for electricity-using products is taken to be 1 percent a year.
- Generation shares are obtained from IEA (2017c) by the electricity produced from each fuel type divided by total electricity generation.
- Own-price elasticities for generation fuels (conditional on total electricity output): empirical survey evidence places coal price elasticity at -0.15 to -0.6 in various studies; a coal price elasticity of -0.7 is assumed here for all countries (with the same elasticity assumed for other fossil generation fuels).

### Fuel-cost and generation-cost relationships
- Elasticities in equation (A3) are defined with respect to generation costs rather than fuel costs and can be obtained by dividing the fuel price elasticity by the share of fuel costs in generation costs.
- For coal generation, the share of fuel costs in generation costs is taken to be 0.25.
- Fossil fuel consumption (coal, natural gas, oil used in power generation) is taken from IEA (2017c) for 2014.
- Productivity of a fuel is electricity generated from that fuel divided by input of that fuel.

### Autonomous productivity and non-fuel generation cost assumptions
- Annual rate of autonomous productivity improvement:
  - Coal: 0.5 percent annual average productivity growth (based approximately on IEA (2015), Figure 2.16).
  - Natural gas, nuclear, and hydro: baseline annual growth rate of 1 percent.
  - Renewables: productivity growth rate of 5 percent (i.e., costs halve every 15 years).
- Non-fuel generation costs:
  - For coal and oil plants: non-fuel generation costs are taken to be three times 2014 fuel costs.
  - For natural gas plants: non-fuel generation costs are taken to be 50 percent of fuel costs.
  - Generation costs for nuclear, biofuels, and renewables (implicitly including any subsidies) in 2014 are taken to be 100 percent of those for coal.
  - For hydro: 90 percent of those for coal.

### Road transport sector: demand, elasticities, and efficiency
- Fuel use: consumption of road gasoline and diesel in 2014 taken from IEA (2017c).
- Income elasticity of demand for vehicle km:
  - A value of 0.6 is used generally.
  - For China and India, values of 0.8 are assumed.
- Fuel price elasticities for road fuels:
  - A value of -0.25 is used for each elasticity and for both gasoline and diesel — the total price elasticities for each fuel are therefore -0.5.
- Annual rate of autonomous decline in vehicle fuel consumption rates (from technological improvements) is set at 1 percent a year (and implicitly encompasses progressive penetration of electric and hybrid vehicles).

### Other energy sector (industry, residential)
- Fuel use: assume 75 percent of fuel consumption by industry is by large firms that would be covered by the ETS.
- Income elasticities for products using fuels:
  - Coal, oil, and biomass: 0.5.
  - Natural gas and renewables: 1.0.
- These income elasticity assumptions imply BAU projections of these fuels outside power and transport in 2030 broadly consistent with corresponding country data in IEA (2017a) when using comparable price projections.
- Price elasticities for fuels used in the other energy sector are taken to be the same as for electricity and road fuels.
- Annual rate of autonomous productivity improvements for other energy products are assumed to follow those for the same fuel as used in the power sector.

### Mortality, air pollution, and health damage assumptions
- Major pollutant from power plant coal combustion causing premature mortality is PM2.5.
- Air pollution emissions, mortality, and damage estimates by country are taken from Parry and others (2014), with adjustments:
  - Parry and others (2014) provide data for representative coal plants with emissions control technologies and industry-wide damages averaging over plants with and without control technologies for 2010.
  - Air emission rates from power plant coal combustion are assumed to converge linearly from the industry average in 2010 to the emission rate from plants with control technologies by 2030.
  - A linear upward adjustment in the annual mortality rate is made for China and India, growing at 1.3 and 2.6 percent a year respectively, to account for rising urban population exposure.
- For large industrial coal users, the same mortality rates as for coal power plants in each year are assumed.
- For small-scale coal users, mortality rates in 2010 are assumed equal to the industry average for coal plant emissions.
- For natural gas, gasoline, diesel, and oil products, rates are based on Parry and others (2014); for China and India these rates rise with urban population.
- For gasoline and road diesel, emission rates are assumed to linearly converge between 2010 and 2030 from the vehicle fleet average in 2010 to the emission rates for representative vehicles in 2010 with advanced emission control technologies.
- Mortality rates for other oil products (not estimated by Parry and others 2014) are taken to be the same as for road diesel.
- Caveat: analysis ignores possible saturation of physical absorption channels at very high outdoor pollution concentrations which could reduce marginal health benefits of pollution reductions at high pollution levels.

### Miscellaneous macro and emissions assumptions
- GDP growth: projected GDP out to 2022 is from IMF (2017) and annual GDP growth between 2023 and 2030 is assumed equal to the projected growth rate for 2022.
- CO2 emissions factors: calculated by dividing, for 2014, CO2 emissions by fuel use from IEA (2016) by fuel use (from IEA 2017b).

### BAU comparisons with IEA (2017a) (2030 projections expressed relative to IEA 2017a)
- Using the paper’s averaged prices, BAU CO2 emissions for 2030 are 7-36 percent higher across countries compared with IEA (2017a).
- When IEA (2017a) energy price projections are used, BAU projections tend to be about the same or moderately higher than IEA (2017a); examples given:
  - CO2 projections are 20 percent higher for China, about the same for India, and lower for Brazil.
- Table 2: Current analysis and Current analysis with IEA (2017a) prices, 2030 projections expressed relative to IEA 2017a (values listed as ratios):

  - Brazil
    - Current analysis: coal 0.97, oil 1.56, natural gas 1.09, CO2 1.07
    - Current analysis with IEA (2017a) prices: coal 0.89, oil 1.35, natural gas 1.08, CO2 0.91

  - China
    - Current analysis: coal 1.41, oil 1.55, natural gas 1.05, CO2 1.36
    - Current analysis with IEA (2017a) prices: coal 1.24, oil 1.32, natural gas 1.07, CO2 1.20

  - India
    - Current analysis: coal 1.40, oil 1.62, natural gas 1.07, CO2 1.28
    - Current analysis with IEA (2017a) prices: coal 1.03, oil 1.49, natural gas 1.20, CO2 0.98

  - Japan
    - Current analysis: coal 0.86, oil 1.64, natural gas 1.73, CO2 1.30
    - Current analysis with IEA (2017a) prices: coal 0.79, oil 1.33, natural gas 1.72, CO2 1.17

  - Russia
    - Current analysis: coal 0.72, oil 1.46, natural gas 1.30, CO2 1.16
    - Current analysis with IEA (2017a) prices: coal 0.66, oil 1.18, natural gas 1.28, CO2 1.09

  - South Africa
    - Current analysis: coal 1.21, oil 1.59, natural gas 1.09, CO2 1.16
    - Current analysis with IEA (2017a) prices: coal 1.11, oil 1.39, natural gas 1.08, CO2 1.05

  - United States
    - Current analysis: coal 1.27, oil 1.37, natural gas 1.25, CO2 1.27
    - Current analysis with IEA (2017a) prices: coal 1.12, oil 1.12, natural gas 1.25, CO2 1.14

*Source: wp18193 (excerpt).*

### Appendix 3. Incidence Analysis

### Appendix 3. Incidence Analysis

### Household incidence: first-order approximation and implementation
- First-order approximation of the burden on household income group h = 1...H from higher consumer prices induced by carbon taxes is given by:
  - 100 * ∑_g π_t_hg · ρ_t_hg  (Equation (C1))
  - g denotes major categories of consumer goods, π_t_hg is the share of household h’s budget spent on good g at time t, and ρ_t_hg is the percent increase in price of good g induced by the carbon tax.
- Illustrative numeric example preserved from the source:
  - If the budget share for a product is, say, 5 percent, this formula implies a 10 percent increase in its price will decrease the household group’s consumption by the equivalent of 0.5 percent.
- Policy-induced impacts on fuel and electricity prices are taken from the model.
- Indirect price increases for other consumer goods are calculated assuming full pass through of the burden from producers to consumers in domestic markets (i.e. horizontal supply curves), using input/output tables with more granular product classifications than in the household data.
- In projecting to 2020:
  - Shares of different industries in total output, and their energy intensity of production, are assumed to be the same as in the years of the input/output data.
  - Household budget shares for electricity and direct fuel consumption are scaled by the corresponding 2020 energy prices relative to prices in the year of the household survey.

### Household and input data (country-specific details)
- Canada:
  - Household survey: Survey of Household Spending; distinguishes 20 aggregated categories; interviewed 16,758 households in 2009.
  - Input-output table: national input-output table for 2013; disaggregates 230 industries.
- China:
  - Household survey: China Family Panel Studies; data on household expenditures for 25 aggregated categories; latest year available is 2012; nationally representative sample of more than 13,000 households across 25 provinces.
  - Input-output table: 2012; covering 139 industries.
- India:
  - Household survey: 68th Round of the National Sample Survey (NSS); distinguishes 39 categories of goods; interviewed 101,724 households (59,700 rural and 42,024 urban) between July 2011 and June 2012.
  - Input-output table: 2007-2008; covering 130 industries.
- United States:
  - Household survey: Consumer Expenditure Survey (CEX); 2015 survey used; nationally representative sample of 24,617 households.
  - Input-output table: 2007; covering 389 industries.
- Note on input-output alternatives:
  - More recent standardized input-output tables (e.g., World Input-Output database) cover 43 countries over 2000-2014 and a standardized set of (56) industries, but do not provide necessary disaggregation (e.g., separate categories for coal, oil, natural gas, electricity and road fuels).

### Caveats, approximation limits, and incidence channels
- Overstatement risks from input-output use:
  - Energy intensity of production in different sectors will tend to fall in response to higher energy prices, implying use of input/output tables overstates the consumer price increases. The source judges this overstatement likely modest for the policy scenarios considered.
  - The formula overstates consumer surplus loss by ignoring the reduction in household quantity demanded for energy-intensive products caused by higher energy prices; this effect should be modest.
  - Numerical example from the source: the first-order approximation (a rectangle equal to initial consumption times the price change) overstates the loss of consumer surplus (a trapezoid to the left of the demand curve between the pre- and post-tax price) by only about 5 percent when demand for a fuel product falls by 10 percent.
- Pass-through and distributional complications:
  - Some fraction of the burden of fuel taxes may be passed backwards in lower producer prices if fuel supply curves remain upward sloping in the medium to longer term.
  - If net-of-tax return to capital falls, some incidence may be borne by owners of capital; if net tax returns are largely determined in world capital markets, the burden of lower producer prices should be largely borne by workers in the form of lower wages.
  - Resulting incidence effects depend on whether energy-intensive firms disproportionately hire high- or low-wage workers, and substitution elasticities between energy and other inputs.
  - Some studies for advanced countries suggest these incidence effects are not that large and may disproportionately harm higher income groups.
  - Alternatively, policy costs may not be fully passed forward in energy markets with regulated pricing; who ultimately bears the burden of resulting losses to state-owned enterprises and government budgets is unclear.

### Industry impacts
- The percent increases in unit production costs for different industries caused by carbon taxes are assumed equal to the percent price increases obtained from the input-output calculations described above.

*Source: wp18193 - Appendix 3. Incidence Analysis*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18193.pdf_