## Getting to Know GMMET (wpiea2023269-print-pdf)

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### Purpose and scope
- GMMET analyzes short- and medium-term macroeconomic implications of reducing GHG emissions, focusing on costs of mitigation policies for output, employment, inflation, the external sector, and fiscal accounts.
- GMMET is a large-scale non-linear structural New-Keynesian dynamic general equilibrium model building on the IMF’s Global Integrated Monetary and Fiscal model (GIMF).
- Four-region calibration: China, the euro area, the United States, and a “rest-of-the-world” bloc.
- Annual, multi-region, stock-flow consistent model with perfect-foresight rational expectations; omits warming-damage benefits and prospective long-term productivity gains from abatement technologies.

### Model architecture and major extensions
- Fossil fuel mining
  - Resource input factor (“mines”) whose volume adjusts to fuel output price to match empirical short- and long-run supply elasticities.
  - Effective price elasticities of fossil fuel supply in the United States:
    - Coal: After 1 year 0.17; After 7 years 0.4; Long term 0.6
    - Fossil Gas: After 1 year 0.18; After 7 years 0.3; Long term 0.5
    - Oil: After 1 year 0.14; After 7 years 0.5; Long term 1.3
- Electricity generation
  - Five technologies: Coal, fossil gas, nuclear, hydroelectric, renewables. Nuclear and hydroelectric grouped; investment exogenous.
  - Renewables treated as intermittent and paired with fossil-gas backup; optimal backup and renewable capacity determined by cost minimization (M*, L, curtailed generation C).
  - Grid-scale storage not considered (short- and medium-term focus).
- Renewable-plus-backup utilities
  - Renewable generation G(x)=M x^γ; output L expressed as Cobb-Douglas of backup B (share γ/(γ+1)) and gross renewables R̄ (share 1/(γ+1)).
- Transportation
  - Two vehicle types: combustion engine cars (CCs) and electric vehicles (EVs); fleet stock-flow accounting M_t = N_t + (1−δ) M_{t−1}.
  - EV vs CC elasticity of substitution: 5.5
  - Network externalities between EV adoption and charger deployment; charger growth driver: Li and others (2017); relative EV price data: American Automobile Association (2021).
- Non-fossil-fuel emissions
  - Sector-specific reduced-form abatement technologies calibrated to marginal abatement cost curves; abatement increases sectoral total factor productivity costs nonlinearly.
- Households
  - Two types: OLG households (can accumulate domestic and US dollar bonds) and LIQ households (consume all income each period).
  - LIQ household shares: China 7.3, Euro Area 7.5, United States 8.4, Rest of the World 12.2, Global Average 9.7 (note: LIQ household share also described as set at 40 percent for rest-of-the-world and 25 percent for United States, euro area, and China in household behavior description).
  - OLG households share: China 44.9, Euro Area 47.2, United States 57.3, Rest of the World 45.7, Global Average 48.6.
- Fiscal and monetary policy features
  - Monetary policy: inflation-forecast-based interest rate rule; weight on forward-looking core inflation: 1.5 for the euro area, 1 elsewhere; core inflation measure: contemporaneous weight 0.25 and one-year-ahead weight 0.75.
  - Fiscal instruments: subsidies for green technologies and EV purchases; public investment in nuclear; sectoral GHG taxes; regulatory shadow-price instruments; “feebates.”
  - Government targets long-term debt-to-GDP; benchmark fiscal rule uses automatic stabilizer with lumpsum transfers negatively correlated with the output gap.

### Calibration highlights and steady-state figures
- Regions’ GDP shares (percent of world): China 16.3, Euro Area 15.5, United States 24.4, Rest of the World 43.8, Global 100.0.
- Household consumption shares (percent of region’s GDP): China 52.2, Euro Area 54.7, United States 65.7, Rest of the World 57.9, Global Average 58.4.
- Private Investment (percent of region’s GDP): China 22.3, Euro Area 20.7, United States 16.6, Rest of the World 21.6, Global Average 20.4.
- Energy use in aggregate (percent of region’s GDP): China 7.4, Euro Area 4.3, United States 3.9, Rest of the World 6.8, Global Average 5.8.
- Fossil fuel extraction (percent of region’s GDP): China 3.3, Euro Area 0.2, United States 2.6, Rest of the World 6.1, Global Average 3.9.
- Fossil fuel in electricity (percent of region’s GDP): China 1.8, Euro Area 0.3, United States 0.6, Rest of the World 1.1, Global Average 1.0.
- Energy in household consumption (percent of region’s GDP): China 1.3, Euro Area 1.5, United States 1.8, Rest of the World 2.1, Global Average 1.8.
- GHG emissions steady-state (billions of metric tons of CO2 equivalent):
  - China: 13.0 billion tCO2e
  - Euro area: 2.8 billion tCO2e
  - United States: 6.3 billion tCO2e
  - Rest-of-the-world bloc: 25.5 billion tCO2e
- Elasticities (selected):
  - Four types of generation in electricity: 20.0
  - Four types of energy in tradables: 0.5
  - Energy and other factors in tradables: 0.4
  - Electricity and other factors in nontradables: 0.5
  - Electricity and fossil gas in residential energy: 1.5
- Depreciation rates (percent):
  - Non-energy tradables: 10.00
  - Nontradables: 10.00
  - Infrastructure stock: 4.00
  - Mining sectors (Coal / Fossil gas / Oil max / min): 3 (10/2)
  - Electricity generation (Coal / Fossil gas max / min): 3 (5/2)
  - Nuclear and hydroelectric: 2.00
  - Renewables: 3.00
  - Transmission: 3.33
  - All vehicles: 12.50
- Short-term nominal rigidities and markups:
  - Regional nominal-rigidity normalization: China 0.25; Euro Area 0.55; United States 0.32; Rest of the World 0.50.
  - Sectoral markups (percent) and nominal rigidities (relative): Final consumption goods — Markup (%) 10 10 10 10; Nominal rigidity 1.00 1.50 1.00 1.00 (China, Euro Area, United States, Rest of the World).

### Principal simulation insights — economy-wide GHG pricing (US$50/tCO2e examples)
- Policy design simulated: gradual introduction of a US$50/tCO2e GHG price phased in over 8 years (global or unilateral US implementation); revenue recycling via lowering the labor income tax or increasing general lumpsum transfers.
- Macroeconomic outcomes:
  - Negative impact on real GDP weaker when revenues recycled through labor income tax cuts due to higher net-of-tax wages and labor supply.
  - Investment decline is dampened under labor income tax cuts compared to lumpsum transfers.
  - Inflation impact similar across recycling options; headline CPI impacts limited given gradual implementation.
  - Under symmetric global shock: no significant adjustment of real effective exchange rate and current account.
- Emissions and sectoral adjustment (United States, global US$50/tCO2e, revenues recycled via labor income tax unless noted):
  - Total US GHG emissions reduced by close to 30 percent.
  - Electricity generation: coal generation crowded out almost entirely; coal-based electricity emissions decline almost 100 percent; fossil gas used as backup and picks up mildly; renewables generation rises; electricity price rises gradually; overall generation volume barely declines.
  - Transportation: fuel costs over car life cycle increase for EVs and CCs (higher electricity price; tax on oil); oil price increases more than electricity price; modest shift to EVs in new purchases; increased EV charging stations create positive feedback increasing EV share.
  - Tax incidence: fossil gas and oil tax burden mostly on consumers; coal burden roughly split between miners and consumers.
  - Non-fossil-fuel abatement: tradables — around 20 percent abatable at less than US$50/tCO2e; nontradables — US$50/tCO2e reduces non-fossil-fuel emissions by about 5 percent.
  - Gas for home heating emissions decline by about 40 percent.
- Global vs unilateral effects:
  - US current account increases when US acts alone (decline in US investment).
  - Under global implementation, rest-of-the-world (more energy-intensive) experiences larger investment decline and can become net capital exporter, lowering US current account and causing US dollar appreciation.
  - Producer prices of oil and fossil gas fall more in global scenario; oil affected more due to integrated market.
  - US total emissions decline slightly more when US acts alone; global emissions decline smaller absent global response.

### Nonlinearities and long-term trade-offs
- Emissions vs GHG price:
  - Total GHG emissions fall rapidly as price rises from US$0/tCO2e to US$50/tCO2e; marginal impact decreases beyond about US$50/tCO2e.
  - Up to about US$50/tCO2e: large reduction driven by eliminating coal in electricity generation.
  - Beyond about US$50/tCO2e: reductions driven mainly by electrification of transport and expansion of EV charging network; abatement of non-fossil-fuel emissions becomes more costly.
- Revenue dynamics:
  - As emissions shrink, marginal GHG tax revenues diminish, reducing fiscal space for labor income tax cuts and muting labor supply responses.
- Sectoral reallocations:
  - Tradables: lower energy input use reduces demand for capital services and labor, lowering tradables production and capital stock.
  - Nontradables: sees shallower capital decline and milder reduction of labor productivity; nontradables employment can increase and nontradables output can rise.
  - Net foreign asset position increases due to fall in domestic capital stock combined with mild wealth adjustment.
- Electricity effects:
  - Electricity price rises with GHG price; generated electricity volume starts to increase at about US$40/tCO2e.
  - Electricity price increase smaller than fossil fuel price increases, inducing substitution toward electricity.

### Sectoral mitigation instrument comparisons and key sectoral experiments
- Electricity sector (three policy options calibrated to same long-term renewables share):
  - GHG price (US$50/tCO2e over 8 years, revenues used to lower labor income tax).
  - Feebate mimicking GHG tax relative-price effects with revenues used to subsidize final electricity price.
  - Portfolio regulatory standard interpreted as subsidy on renewables financed by equal taxes on other generation.
- Findings:
  - Long-term emissions: GHG tax and feebates — decline in emissions of about 15 percent (Panel E); regulation yields smaller emissions decline.
  - Mechanisms: GHG tax and feebates produce roughly identical relative fuel price effects; regulation crowds out more expensive gas than cheaper coal, yielding smaller emissions decline.
  - Electricity price: declines under regulation; feebates mitigate electricity price rise via implicit subsidies.
  - Investment: rises under both GHG tax and feebates; investment increase greater under feebates.
  - GDP and inflation: differences negligible over transition; long-term outcomes depend on labor supply elasticity and complementarity of capital and electricity.
- Transportation interventions:
  - EV purchase subsidy: 17 percent subsidy in the United States, financed by reduction in general lumpsum transfers. Long-term subsidy cost converges to 0.15 percent of output. EV fleet share rises to about a quarter in the long term. Overall emissions decline by about 4 percent.
  - Increase in EV charging stations: permanent exogenous increase of 50 percent in chargers. Overall GHG emissions reduced by about 1.5 percent in the long term. Fiscal costs negligible.
- Renewables and nuclear:
  - Subsidy on renewable generation capital: reduces renewable capital price by 80 percent in the United States. Fiscal cost peaks at more than 0.3 percent of GDP, converges to 0.15 percent of GDP long term. Policy reduces overall GHG emissions by about 8 percent.
  - Public investment in nuclear: exogenous increase in US nuclear investment by 180 percent; fiscal cost equal to 0.15 percent of output. Total emissions decline by about 10 percent.
  - Sectoral effects: renewables expansion crowds out other sources; fossil gas share declines more than coal despite gas being backup; domestic coal price rises more than fossil gas price due to trade structure.

### Energy price shock experiments and model responses
- Temporary increase in oil price:
  - Oil production in rest-of-the-world cut by 25 percent in first year, returning to initial level over four years.
  - Global oil price increases by 100 percent in the first year and returns to initial level by year 3.
  - Headline inflation rises in year 1: around 1 percent in China to close to 2 percent in the rest-of-the-world; core inflation rises by about 0.1 percent.
  - Real GDP declines by less than or close to 1 percent in the United States, China, and the euro area; rest-of-the-world suffers largest real GDP decrease.
- Permanent increase in oil price:
  - Oil production falls by 6 percent in rest-of-the-world causing a 10 percent oil price increase.
  - Long-term: permanent drop in non-energy investment; aggregate investment declines in all regions except the United States.
  - GDP and consumption permanently lower; GDP decline about twice as large as comparable temporary decrease.
  - Headline CPI increases by roughly 0.2 percentage points in the euro area and the United States in year 1; core inflation not noticeably affected.
- Temporary increase in fossil gas prices:
  - Gas production in rest-of-the-world cut by 30 percent in year 1, returning to pre-cut levels by year 4.
  - Price increases vary by region: close to 80 percent in euro area and rest-of-the-world; around 60 percent in China; around 40 percent in the United States.
  - Headline inflation increases in year 1: around 0.3 percent in China to 1 percent in rest-of-the-world; core inflation rises by less than 0.1 percent.
  - Electricity prices increase temporarily by 20 percent or more where fossil gas is used heavily; by 6 percent or less where reliance on renewables or coal is greater.
  - Short-term declines in labor demand and investment; larger consumption impacts for LIQ households.
- Permanent increase in fossil gas prices:
  - Permanent decrease in fossil gas supply in rest-of-the-world leads to immediate, permanent 10 percent rise in fossil gas price in that region.
  - Regional heterogeneity: euro area similar increase; China and United States around 8 percent increases initially, with domestic production rising over time.
  - Negative impacts on electricity sector: higher electricity prices and lower electricity use across regions.
  - Permanent reductions in real GDP in most regions: euro area and China about 0.1 percent; rest-of-the-world about 0.3 percent; United States an exception due to increased fossil gas production investment.
  - Initial spike in headline CPI in all regions; no material change in core inflation.

### Annex and numerical solution methods
- Annex I: mathematical derivations for mining sectors, renewables-plus-backup utilities, tradables/nontradables abatement, transportation.
- Annex II: standard model properties with canonical shock responses (monetary policy, productivity, demand, risk premium, fiscal) including specific numerical outcomes (examples: temporary 100 basis point US policy rate hike reduces real GDP by 0.6 percent on impact; permanent non-energy productivity increase raises long-term GDP by 1 percent).
- Annex III: simulation techniques for GMMET including linearization methods.
  - Marginal numeric linearization method: uses exact solution for rescaled shock (example: 50 percent) plus derivative to approximate remaining shock; shown to improve accuracy versus full numeric linearization for macro aggregates, marginal propensity to consume, emissions, and GHG tax revenues.

### Key policy-relevant takeaways
- Revenue recycling matters: labor income tax cuts mitigate GDP and labor-supply effects relative to lump-sum transfers by increasing net-of-tax wages and labor supply.
- Nonlinearities: large initial emissions gains from phasing out coal up to about US$50/tCO2e; beyond that, marginal emissions reductions become smaller and costlier, relying on transport electrification and abatement of non-fossil emissions.
- Global coordination matters: unilateral versus global implementation yields different external sector, price, and incentive dynamics; global implementation lowers fossil-fuel prices more but can weaken incentives for energy transition.
- Instrument choice matters: economy-wide GHG prices generally yield greater emissions reductions for a given fiscal envelope than sectoral subsidies or regulation calibrated to the same renewables share; feebates can combine emissions effects with softer electricity price increases and stronger investment responses.
- Transition interactions: electrification of transport increases electricity demand and prices; renewables and nuclear investment choices have distinct fiscal profiles and differing macroeconomic short- and long-term effects.

*Source: wpiea2023269-print-pdf — IMF Working Paper “Getting to Know GMMET” (Introduction, Model Description, Calibrations, Policy Experiments, Annexes).*

### Introduction ...........................................................................................................

### Introduction

### Major themes covered
- Model Description (page 8)
  - Supply Side
  - Fossil Fuel and Non-Fossil Fuel Emission Abatement
  - Electricity Generation
  - Renewable-Plus-Backup Utility
  - Fossil Fuel Mining and Trade
  - Household Sector
    - Household Consumption
    - Transportation
  - Monetary Policy
  - Fiscal Policy
- Model Calibration (page 17)
  - Domestic Economy
  - External Sector
  - GHG Emissions
  - Energy and Electricity Sectors
  - Transportation
  - Fiscal and Monetary Policy and Prices

### Policy experiments, scenarios, and simulations
- Economy-wide mitigation policies
  - Global Increase in the GHG Price with Different Recycling Options (page 26)
  - Global vs. Unilateral Increase in the GHG Price (page 32)
  - Long-Term Impacts of GHG Prices (page 35)
- Sectoral mitigation policies (page 38)
  - Comparison of GHG Prices, Feebates, and Portfolio Standards in Electricity Generation (page 39)
  - Subsidy for the Purchase of Electric Vehicles (page 41)
  - Increase in the Number of EV Charging Stations (page 43)
  - Subsidy on Investment in Renewable Electricity Generation (page 45)
  - Increase in Public Investment in Nuclear Electricity Generation (page 47)

### Energy price shock experiments
- Model Properties for Global Energy Price Shocks (page 49)
  - Temporary Increase in the Oil Price (page 49)
  - Permanent Increase in the Oil Price (page 52)
  - Temporary Increase in Fossil Gas Prices (page 55)
  - Permanent Increase in Fossil Gas Prices (page 58)

### Figures and illustrative scenarios (selected)
- Figure 1: Production Sector (page 9)
- Figure 2. Electricity Generation Sector (page 11)
- Figure 3. Illustration of Cost-Minimization Problem of Renewable-plus-Backup utilities (page 12)
- Figure 6. Initial GHG Emissions (page 20)
- Figures illustrating policy experiments with a US$50/tCO2e GHG price:
  - Figure 7: Gradual Introduction of a US$50/tCO2e Global GHG Price — Macroeconomic Impact in the United States
  - Figure 8: Gradual Introduction of a US$50/tCO2e Global GHG Price — Emitting Sectors in the United States
  - Figure 9: Gradual Introduction of a US$50/tCO2e Global GHG Price — Emissions in the United States
- Comparative figures for US only vs. global introduction of the GHG price:
  - Figure 10, Figure 11
- Long-term impacts: Figure 12, Figure 13
- Sectoral policy comparison and specific interventions: Figures 14–18
- Energy shock figures: Figures 19–26

### Calibration tables and parameters (selected)
- Table 1. Domestic Sector Calibration (page 17)
- Table 2. Depreciation Rates for Investment (page 18)
- Table 3. External Sector Calibration (page 19)
- Table 4. Fossil Fuel Supply and Use (page 21)
- Table 5. Energy Use (page 22)
- Table 6. Elasticities of Substitution for Energy and Electricity (page 22)
- Table 7. Effective Price Elasticities of Fossil Fuel Supply in the United States (page 23)
- Table 8. Automatic Stabilizer for the Output Gap (page 24)
- Table 9. Steady-State Markups and Short-Term Nominal Rigidities (page 25)

### Annexes and methodological material
- Annex I. Mathematical Derivations for Specific Sectors (page 62)
  - Mining Sectors
  - Renewables-Plus-Backup Utilities
  - Tradables and Nontradables Production and the Abatement of Non-Fossil-Fuel GHG Emissions
  - Transportation Sector
- Annex II. Standard Model Properties (page 69)
  - Several canonical shocks (monetary policy, productivity, demand, risk premium, fiscal)
- Annex III. Simulation Techniques for GMMET (page 80)
- References (page 83)

*Source: wpiea2023269-print-pdf - Introduction*

### Introduction

### Introduction — Getting to Know GMMET (wpiea2023269-print-pdf)

### Purpose and focus
- GMMET analyzes short- and medium-term macroeconomic implications of reducing GHG emissions, focusing on costs of mitigation policies for output, employment, inflation, the external sector, and fiscal accounts.
- GMMET is a large-scale non-linear structural New-Keynesian dynamic general equilibrium model building on the IMF’s Global Integrated Monetary and Fiscal model (GIMF).

### Major model extensions (energy, emissions, transport, fiscal)
- Fossil fuel mining
  - Features resource input factors (“mines”) whose volumes adjust to the price of fuel output so fossil-fuel-specific supply elasticities align with empirical estimates.
- Electricity generation
  - Five technologies with differing cost structures and emission intensities: Coal, fossil gas, nuclear power, hydroelectric power, and renewables.
  - Nuclear and hydroelectric grouped together; investment in these is decided exogenously.
- Renewable-plus-backup utilities
  - Renewables paired with flexible fossil-gas backup to manage intermittency; backup size determined endogenously by cost minimization that accounts for variable and fixed costs and distribution of weather regimes.
- Transportation
  - Distinguishes combustion engine cars (CCs) and electric vehicles (EVs); fleet stock-flow accounting; models charging/fueling stations and network externalities between EV adoption and charging station deployment.
- Non-fossil-fuel emissions
  - Sector-specific reduced-form emission abatement technologies calibrated to estimated marginal abatement cost curves; abatement increases sectoral total factor productivity costs nonlinearly.

### Policy levers modeled
- Wide set of GHG mitigation policies: subsidies, regulatory measures, sector-specific GHG taxes proportional to sectors’ GHG emission intensities.
- Regulatory instruments implemented as revenue-neutral tax-subsidy combinations and via “shadow prices.”
- Revenue recycling options explicitly modeled (e.g., lump-sum transfers, labor income tax cuts).
- Government targets a long-term debt-to-GDP level; short-term automatic stabilizers included.

### Key analytical scope and exclusions
- GMMET abstracts from benefits of avoided warming damages; the model takes emissions decline targets (e.g., Paris Agreement) as given and focuses on how to achieve them.
- Excludes prospective long-term increases in firm/sectoral productivity from improving abatement technologies.
- Annual, multi-region model with stock-flow consistency and a well-articulated steady state.

### Principal insights from simulations
- Distinction between sectoral and macro effects
  - Sectoral effects drive emissions reductions via relative price changes; macro costs depend crucially on macroeconomic policy responses and revenue recycling.
  - Example: Coal and fossil gas decline in electricity generation due to higher GHG prices is insensitive to recycling option, but labor supply and real GDP responses differ markedly between lump-sum transfers and labor income tax cuts.
  - Labor income tax cuts raise net-of-tax wages and consumption relative to lump-sum transfers, dampening negative GDP impact.
- Non-linearities in policy impact
  - Example: In the United States, up to about US$50 per metric ton of CO2 equivalent (tCO2e), total GHG emissions fall rapidly as high-emitting coal is phased out; beyond this point marginal emissions impact of higher GHG price becomes smaller and reductions rely more on transport electrification and costly abatement of non-fossil emissions.
  - As emissions shrink, the marginal increase in GHG tax revenues diminishes, reducing fiscal space for labor income tax cuts and muting labor supply responses.
- Global dimension and spillovers
  - If the United States raises GHG prices alone, its current account balance increases as aggregate investment falls.
  - Under global implementation, production outside the United States (more energy-intensive) faces larger investment impacts, can become net capital exporters, lowering the US current account and causing US dollar appreciation.
  - Producer prices of oil and fossil gas fall less when the United States acts alone than under global implementation.

### Model class comparisons
- Compared to IAMs (e.g., DICE, WITCH, REMIND): GMMET is annual, includes Keynesian aggregate demand channels, and is suited to short- and medium-term cyclical analysis.
- Compared to CGE models (e.g., GTAP, ICES): GMMET simplifies sectoral breakdown but emphasizes forward-looking expectations, fiscal instrument detail for emitting sectors, and perfect-foresight rational expectations.
- Closest large-scale macroeconomic cousins: G-CUBED and E-QUEST; GMMET differs in sector modeling and uses solution techniques that do not require full linearization.

### Model structure — regions and high-level design
- Four-region calibration: China, the euro area, the United States, and a “rest-of-the-world” bloc.
- Trade and assets: incomplete international asset markets; international non-contingent US dollar-denominated bonds only; no international trade in coal in this version.
- Supply side: tradables and nontradables firms use capital-labor bundles; energy-related inputs introduced — nontradables consume electricity, tradables use an energy bundle (electricity plus fossil gas, coal, oil).
- Emissions treatment:
  - Fossil-fuel-related emissions tracked via fuel volumes and input-specific emission intensities.
  - Non-fossil emissions linked to output of non-energy tradables and nontradables and abated via sector-specific abatement cost functions calibrated to marginal abatement cost curves.

### Calibration highlights and steady-state figures
- Regions’ GDP shares (percent of world): China 16.3, Euro Area 15.5, United States 24.4, Rest of the World 43.8, Global 100.0.
- Household consumption shares (percent of region’s GDP): China 52.2, Euro Area 54.7, United States 65.7, Rest of the World 57.9, Global Average 58.4.
- LIQ households share: China 7.3, Euro Area 7.5, United States 8.4, Rest of the World 12.2, Global Average 9.7.
- OLG households share: China 44.9, Euro Area 47.2, United States 57.3, Rest of the World 45.7, Global Average 48.6.
- Private Investment (percent of region’s GDP): China 22.3, Euro Area 20.7, United States 16.6, Rest of the World 21.6, Global Average 20.4.
- Energy use in aggregate (percent of region’s GDP): China 7.4, Euro Area 4.3, United States 3.9, Rest of the World 6.8, Global Average 5.8.
- Fossil fuel extraction (percent of region’s GDP): China 3.3, Euro Area 0.2, United States 2.6, Rest of the World 6.1, Global Average 3.9.
- Fossil fuel in electricity (percent of region’s GDP): China 1.8, Euro Area 0.3, United States 0.6, Rest of the World 1.1, Global Average 1.0.
- Energy in household consumption (percent of region’s GDP): China 1.3, Euro Area 1.5, United States 1.8, Rest of the World 2.1, Global Average 1.8.
- Elasticities (selected)
  - Four types of generation in electricity: 20.0
  - Four types of energy in tradables: 0.5
  - Energy and other factors in tradables: 0.4
  - Electricity and other factors in nontradables: 0.5
  - Electricity and fossil gas in residential energy: 1.5
- Depreciation rates (percent)
  - Non-energy tradables: 10.00
  - Nontradables: 10.00
  - Infrastructure stock: 4.00
  - Mining sectors (Coal / Fossil gas / Oil max / min): 3 (10/2)
  - Electricity generation (Coal / Fossil gas max / min): 3 (5/2)
  - Nuclear and hydroelectric: 2.00
  - Renewables: 3.00
  - Transmission: 3.33
  - All vehicles: 12.50

### GHG emissions steady-state (billions of metric tons of CO2 equivalent)
- China: 13.0 billion tCO2e
- Euro area: 2.8 billion tCO2e
- United States: 6.3 billion tCO2e
- Rest-of-the-world bloc: 25.5 billion tCO2e

### Electricity sector and renewables-plus-backup mechanics
- Five generation technologies combined into a final electricity bundle; renewables are modeled as intermittent and paired with gas backup.
- Renewables-backup tradeoff solved by cost minimization: optimal renewable capacity M* generally implies some overcapacity (M* − L) due to curtailment; additional renewable capacity raises expected curtailment area C and flattens marginal variable-cost savings, yielding a cost-minimizing M* where marginal cost savings equal installation costs.
- Grid-scale storage is not considered (focus on short and medium term, current technology).

### Fossil fuel mining and supply elasticities
- Mining sectors combine capital services, labor, and a resource factor (“mines”) whose volume is governed by a backward-looking moving average of output price, calibrated to match short- and long-run supply elasticities from empirical estimates.
- Oil traded on a global market; fossil gas traded bilaterally; coal not traded across regions in this version.

### Household and consumption details
- Two household types: OLG households (can accumulate domestic bonds and internationally traded US bonds) and LIQ households (consume all income each period).
- OLG share and LIQ share heterogeneity across regions; LIQ share set at 40 percent for rest-of-the-world and 25 percent for United States, euro area, and China.
- Household consumption bundle extended to include residential heating (electricity + fossil gas) and individual transportation (cars as final investment goods plus oil and electricity as fuels).
- CPI components: only cars (final investment goods) and final consumption goods included in core inflation; alternative core inflation measure can include GHG taxes.

### Fiscal and monetary policy treatment (relevant for mitigation)
- Monetary policy: inflation-forecast-based interest rate rule under flexible exchange rate (fixed exchange rate possible); output gap can be included.
- Fiscal policy: government has standard instruments from GIMF plus:
  - Subsidies for green technologies and EV purchases; public investment in nuclear power; sectoral GHG taxes; regulatory shadow-price instruments; “feebates” linking GHG prices to sectoral input subsidies.
  - Adjustment of lump-sum transfers typically used to target long-run debt-to-GDP.
- Revenue recycling matters for macro outcomes (e.g., labor tax cuts vs. lump-sum transfers).

### Simulations and documentation
- Paper documents model structure, calibration (four regions), and simulations on economy-wide mitigation policies, sectoral mitigation policies, global energy shocks, and standard macro shocks (Annex II).
- Simulations are illustrative of model properties and not policy recommendations.

*Source: IMF Working Paper — “Getting to Know GMMET” (Introduction and Model Description sections).*

### 1.3 percent in the long term (labor, the capital stock, and the number of active oilfields) are flexible.

### wpiea2023269-print-pdf - 1.3 percent in the long term (labor, the capital stock, and the number of active oilfields) are flexible.

### Model calibration and supply elasticities
- Effective price elasticities of fossil fuel supply in the United States (outcomes of model parameters):
  - Coal: After 1 year 0.17; After 7 years 0.4; Long term 0.6
  - Fossil Gas: After 1 year 0.18; After 7 years 0.3; Long term 0.5
  - Oil: After 1 year 0.14; After 7 years 0.5; Long term 1.3
- Transportation calibration:
  - EV vs CC elasticity of substitution: 5.5
  - Relative EV price data source: American Automobile Association (2021)
  - Charging-station network growth driver: Li and others (2017)
- Short-term nominal rigidities and steady-state markups (percent over price for markups; relative strength of adjustment for nominal rigidities):
  - Regional nominal-rigidity normalization and values:
    - China: 0.25
    - Euro Area: 0.55
    - United States: 0.32
    - Rest of the World: 0.50
  - Sectoral steady-state markups and nominal rigidities (selected entries):
    - Final consumption goods — Markup (%) 10 10 10 10; Nominal rigidity 1.00 1.50 1.00 1.00 (China, Euro Area, United States, Rest of the World)
    - Final investment goods — Markup (%) 5 5 5 5; Nominal rigidity 1.00 1.50 1.00 1.00
    - Tradable intermediate goods — Markup (%) 20 20 20 20; Nominal rigidity 1.00 1.50 1.00 1.00
    - Imported consumption/investment/intermediate goods — Markup (%) 5 5 5 5; Nominal rigidity 0.33 0.50 1.00 0.10
    - Nontradable intermediate goods — Markup (%) 20 20 20 20; Nominal rigidity 1.00 1.50 1.00 1.00
    - Wages — Markup (%) 10 10 10 10; Nominal rigidity 2.50 3.75 2.50 2.50

### Fiscal and monetary policy specification
- Benchmark fiscal rule:
  - Primary function: stabilize debt-to-GDP ratio at targeted level based on 2021 data
  - Contains automatic stabilizer: general lumpsum transfers negatively correlated with the output gap (derived from Price, Dang and Botev (2015))
- Benchmark monetary policy rule:
  - Weight on forward-looking core inflation: 1.5 for the euro area, 1 elsewhere
  - Core inflation measure: contemporaneous core inflation weight 0.25 and one-year-ahead core inflation weight 0.75
- Regional differences:
  - Euro area price adjustment rigidity parameters are 1.5 times higher than those of the United States
  - Remaining countries bloc (mostly small open economies): nominal rigidity 0.1 for imports

### Economy-wide GHG-pricing policies — design and macroeconomic impact (United States illustrative)
- Policy shock analyzed: gradual introduction of a US$50/tCO2e GHG price phased in over 8 years in all regions (global) or only in the United States (unilateral)
- Revenue recycling options compared:
  - Lowering the labor income tax (revenue recycled through labor tax cuts)
  - Increasing general lumpsum transfers to households
- Key macroeconomic and sectoral findings (global US$50/tCO2e, revenues recycled via labor income tax unless noted):
  - Macroeconomic responses:
    - Negative impact on real GDP is weaker when revenues are rebated through labor income tax cuts (increases net-of-tax wages and labor supply)
    - Investment decline is dampened under labor income tax cuts compared to lumpsum transfers
    - Inflation impact similar across recycling options due to central bank response; headline CPI impacts limited given gradual implementation
    - No significant adjustment of real effective exchange rate and current account under symmetric global shock
  - Emission and sectoral adjustment:
    - Total US GHG emissions reduced by close to 30 percent under global US$50/tCO2e
    - Electricity generation:
      - Coal generation is crowded out almost entirely; emissions from coal-based electricity decline almost 100 percent
      - Fossil gas generation is used as backup and picks up mildly
      - Nuclear generation exogenous; renewables generation rises
      - Electricity price rises gradually; overall generation volume barely declines (stabilized by higher EV demand)
    - Transportation:
      - Fuel costs over car life cycle increase for EVs and CCs (higher electricity price; tax on oil)
      - Oil price increases more than electricity price
      - Shift towards EVs in new purchases modest; but increased EV charging stations create positive feedback increasing EV share
    - Incidence of tax burdens:
      - For fossil gas and oil, most tax burden borne by consumers
      - For coal, burden roughly split between miners and consumers
    - Abatement of non-fossil-fuel emissions:
      - Tradables: around 20 percent of non-fossil-fuel emissions abatable at less than US$50/tCO2e
      - Nontradables: US$50/tCO2e reduces non-fossil-fuel emissions by about 5 percent
    - Specific sectoral reductions:
      - Gas for home heating emissions decline by about 40 percent (substitution to electricity)
      - The largest absolute emission reduction comes from eliminating coal in electricity generation

### Global vs unilateral GHG price — comparative effects
- Scenario definitions:
  - Global: US$50/tCO2e introduced globally over 8 years; revenues recycled via labor income tax cuts
  - Unilateral: US implements same US$50/tCO2e policy alone; revenues recycled via labor income tax cuts
- Key comparative findings:
  - External sector and current account:
    - US current account increases when US acts alone (decline in US investment in fossil fuels)
    - Under global policy, rest-of-the-world bloc (more energy intensive) experiences larger investment decline and becomes net capital exporter, lowering US current account and appreciating US dollar
  - Inflation and monetary policy:
    - When US acts alone: direct effect on headline inflation; no visible impact on core inflation
    - When global: large reduction in world fossil fuel prices (especially oil) reduces US core inflation and elicits monetary easing; can produce a short-lived expansionary GDP effect
  - Sectoral and emission outcomes:
    - Producer prices of oil and fossil gas fall more in global scenario; effect stronger for oil (fully integrated market)
    - Global decline in high-emission fossil fuel prices reduces incentives for energy transition (slightly smaller increase in renewable electricity share under global policy)
    - US total emissions decline slightly more when US acts alone; global emissions decline is smaller absent global response

### Long-term impacts and nonlinearities of GHG prices
- Long-term comparative statics consider different GHG price levels (horizontal axis) and marginal long-term impacts (vertical axis)
- Nonlinear responses:
  - Total GHG emissions fall rapidly as price rises from US$0/tCO2e to US$50/tCO2e; marginal impact decreases beyond about US$50/tCO2e
  - Main drivers by price range:
    - Up to about US$50/tCO2e: large reduction driven by eliminating coal in electricity generation
    - Beyond about US$50/tCO2e: further reductions driven mainly by electrification of transport and expansion of EV charging network
  - Abatement of non-fossil-fuel emissions is nonlinear: lower-cost options implemented first, making additional abatement more costly
- Electricity and energy bundle effects:
  - Electricity price rises with the GHG price; generated electricity volume starts to increase at about US$40/tCO2e
  - Electricity price increase is smaller than fossil fuel price increases, inducing substitution of fossil fuels by electricity in production and household use
- Macroeconomic long-term trade-offs:
  - As emissions decline, marginal tax revenues fall, leading to smaller reductions in labor income tax rate
  - Tradables sector: lower energy input use reduces demand for capital services and labor, lowering tradables production and capital stock
  - Nontradables sector: less reliant on fossil fuels, sees shallower capital decline and milder reduction of labor productivity; nontradables employment can increase and nontradables output can rise
  - Net foreign asset position increases due to fall in domestic capital stock combined with mild wealth adjustment
- Note on welfare: model omits warming damages; decline in output and consumption from mitigation policies is not balanced by avoided climate damages within the model

### Sectoral mitigation instruments (overview)
- Three instrument categories analyzed:
  - Economy-wide GHG prices (taxes)
  - Sector-specific subsidies for green investment (renewables, nuclear, hydro, EVs)
    - When subsidy fiscal envelope matches GHG tax revenues, induced emission reduction usually lower than direct GHG taxation
  - Regulatory measures (portfolio standards, emissions-intensity limits)
    - Implemented as shadow prices in the model; induce expenditure shifting without explicit price signals
- Sectoral focus examples previewed:
  - Electricity sector: comparison of GHG prices, feebates, and portfolio standards
  - Transportation sector: EV purchase subsidies and expansion of EV charging network
  - Electricity generation: subsidy on renewables capital and nuclear expansion

*Source: IMF Working Paper "Getting to Know GMMET" — authors' calculations and tabulated model calibrations.*

### introduction over 8 years of a US$50/tCO2e tax on fossil fuels used in electricity generation, with revenues

### introduction over 8 years of a US$50/tCO2e tax on fossil fuels used in electricity generation, with revenues

### Policy scenarios compared
- Three gradual policies in the electricity sector are modeled:
  - GHG price: gradual introduction of a US$50/tCO2e tax on fossil fuels used in electricity generation over 8 years, with revenues recycled by lowering the labor income tax.
  - Feebate structure: gradual introduction of a feebate that mimics the impact on relative prices from the GHG tax; resulting tax revenues are used to subsidize the final electricity price instead.
  - Portfolio regulatory standard (regulation): gradual increase in the share of renewables, interpreted as a subsidy on renewable generation financed by equal taxes on all other generation technologies.
- The three policies are calibrated to bring about the same long-term increase in the share of renewables in the electricity mix.

### Emissions and electricity-mix outcomes
- Long-term emissions:
  - GHG tax and feebates: decline in emissions of about 15 percent (Panel E).
  - Regulation: smaller decline in emissions than under GHG tax and feebates (no single percentage given in text for regulation's emissions decline here).
- Mechanisms:
  - GHG tax and feebates impose per-unit burdens proportional to emission content (e.g., per-unit tax on coal is twice as large as on gas), producing roughly identical effects on relative fuel prices and the electricity mix (Panels H, I, J).
  - Regulation does not affect the relative price between fossil gas and coal; increasing renewables then crowds out more expensive gas rather than cheaper coal, yielding a smaller emissions decline.
- Electricity prices:
  - The electricity price declines under regulation due to the adjustment in the electricity mix (Panel G).
  - Under feebates, the rise in electricity price is mitigated by implicit subsidies (Panel G).

### Macroeconomic impacts and channels
- Investment and capital:
  - Investment rises under both GHG tax and feebates due in part to ramping-up renewable generation capacity (Panel C).
  - Increase in investment is greater under feebates because muted electricity price increases reduce the negative effect of higher electricity prices on desired capital stock.
- Household consumption and GDP:
  - Relative to feebates, the GHG tax supports household consumption during the transition period (Panel B).
  - Differences in GDP and inflation responses are negligible over the transition period due to offsetting effects on private investment and household consumption (Panels A and D).
  - Long-term impacts on household consumption and output depend on assumed labor supply elasticity and complementarity of capital and electricity in production; fostering investment under feebates can be more productive than reducing distortionary labor income taxes under the GHG price.
- Regulation-specific macro effects:
  - Lower electricity price under regulation increases electricity use (Panel F), which raises private investment (Panel C) and the economy’s production potential, raising output (Panel A) and household consumption (Panel B) but yielding a smaller emissions reduction.
  - Headline inflation remains practically constant under regulation (Panel D).

### Subsidy for the purchase of electric vehicles (EVs)
- Policy simulated: a 17 percent subsidy on EV purchases in the United States, financed by a reduction in general lumpsum transfers to households (Panel B).
- Immediate and long-term effects:
  - Immediate uptick in new EV purchases (Panel E); deployment of charging stations increases (Panel F).
  - Subsidy costs converge to 0.15 percent of output in the long term (Panel A).
  - EV share in newly purchased cars rises, and the EV share of the total fleet gradually increases to about a quarter in the long term (Panel G).
- Macroeconomic and emissions impacts:
  - General macro effects are very small on real GDP and inflation (Panels C and D).
  - Rising EV share boosts electricity demand and its price (Panel I).
  - Overall emissions decline by about 4 percent (Panel K), as additional electricity generation (predominantly from fossil fuel-based technologies) partly offsets gasoline reductions (Panel J).
- Electricity mix adjustments:
  - Fixed volume of nuclear generation declines as a share of rising overall production; renewables expand most, constrained by climbing fossil fuel prices to the extent gas is used as backup.
  - Differences between coal and fossil gas responses relate to gas being used as backup and to trade in fossil gas, increasing its price elasticity of supply.

### Increase in the number of EV charging stations (exogenous)
- Policy simulated: permanent exogenous increase in EV chargers by 50 percent; fiscal costs negligible as share of GDP.
- Dynamics:
  - Policy-induced rise in chargers makes EVs more attractive, endogenously increasing EV purchases and further charging deployment, creating a positive feedback loop (Panels D, E, A).
- Impacts:
  - Electricity demand and price rise; gasoline demand falls, lowering fuel costs of CCs (Panel G).
  - Aggregate transportation costs increase mildly and aggregate transportation services volume falls (Panel F) because EV purchase price remains above CCs.
  - Overall GHG emissions reduced by about 1.5 percent in the long term (Panel I).
  - Negligible effects on real GDP and inflation as policy affects a small sector (Panels B and C).

### Subsidy on investment in renewable electricity generation
- Policy simulated: subsidy that reduces the price of renewable electricity generation capital by 80 percent in the United States.
- Fiscal profile:
  - Subsidy volume peaks at more than 0.3 percent of GDP when renewables capacity deployment is fastest, converging to 0.15 percent of GDP in the long term (Panel A).
  - Funded by reduction in general lumpsum transfers to LIQ and OLG households.
- Investment and prices:
  - Surge in renewable investment expands capital stock and drives down technology-specific rental rate (Panels E and D).
  - Tobin’s Q declines by about 80 percent to match lower cost of the investment good (Panel D).
- Electricity mix and emissions:
  - Additional renewable generation crowds out other sources; share of fossil gas declines more than coal despite gas as backup (Panel F).
  - Domestic coal price rises more than fossil gas price due to trade structure; fossil gas price cushioned by foreign trading partners (Panel I).
  - Policy reduces overall GHG emissions by about 8 percent (Panel K); decline mainly driven by reduced fossil gas use in electricity generation (Panel L).
  - Expansion of output raises tradable-sector GHG emissions, partially offsetting emissions decline; lower electricity price from renewables further limits emissions reductions.
- Macroeconomic impacts:
  - Reduction in transfers depresses household consumption, causing short-term decline in real GDP (Panel B).
  - Medium- and long-term effects: surge in investment and lower electricity prices raise real GDP and household consumption permanently.
  - Inflation and interest rate not appreciably affected (Panel C).
  - EV share rises mildly as lower EV fuel costs have limited effect relative to purchase price (Panel J).

### Increase in public investment in nuclear electricity generation
- Policy simulated: exogenous increase in US nuclear power investment by 180 percent; fiscal costs equal to 0.15 percent of output and funded by decline in household transfers (Panel A).
- Electricity mix and elasticities:
  - Nuclear generation rises and crowds out other sources; coal generation declines substantially less than renewables and fossil gas due to relative price-elasticities of supply (Panel F).
  - Supply elasticities ranking: renewables highest long-term elasticity, gas intermediate, coal lowest.
- Macroeconomic and emissions impacts:
  - Additional generation capacity lowers electricity price and boosts output in the long term (Panel E).
  - Short-term real GDP initially rises because government subsidization constitutes immediate investment; contrasts with renewables subsidy where private adjustment costs make expansion gradual (Panel B).
  - Mild impact on EV share and negligible impact on inflation (Panel C).
  - Total emissions decline by about 10 percent, mainly driven by reduced use of fossil gas in electricity generation (Panels I and J).

### Global energy price shock scenarios: oil and fossil gas
- Temporary increase in oil price:
  - Assumed oil production in the rest-of-the-world bloc cut by 25 percent in the first year, returning to initial level over four years (Figure 19, Panel B).
  - Global oil price increases by 100 percent in the first year (Panel A) and returns to initial level by year 3.
  - Headline inflation rises sharply in year 1 (Figure 20, Panel E): around one percent in China to close to 2 percent in the rest-of-the-world bloc; core inflation rises by about 0.1 percent (Panel F).
  - Real GDP declines by less than or close to one percent in the United States, China, and the euro area (Panel A); rest-of-the-world bloc suffers largest real GDP decrease.
  - Energy price interactions: first-year drops in coal, fossil gas, and electricity prices due to lower aggregate demand (Figure 19, Panel C); then substitution pushes up other energy prices in year 2.
  - EV share rises modestly due to divergent gasoline and electricity prices, with modest lasting effect on electricity demand for transport (Panel H).
- Permanent increase in oil price:
  - Oil production falls by 6 percent in the rest-of-the-world bloc leading to a 10 percent increase in the price of oil (Figures 21 and 22).
  - Long-term structural effects: permanent drop in non-energy investment; aggregate investment declines in all regions except the United States, which increases oil production investment (Panel J).
  - GDP and consumption permanently lower; decline in GDP about twice as large as comparable temporary decrease (Figure 22, Panel A).
  - Headline CPI increases by roughly 0.2 percentage points in the euro area and the United States in year 1 (Panel E); core inflation does not increase noticeably (Panel F).
  - Real exchange rate and external accounts adjust heterogeneously across regions (Panels B, I, J).
- Temporary increase in fossil gas prices:
  - Gas production in rest-of-the-world bloc cut by 30 percent in year 1, returning to pre-cut levels by year 4.
  - Price increases vary by region: close to 80 percent in euro area and rest-of-the-world bloc; around 60 percent in China; around 40 percent in the United States (Figure 23, Panel A).
  - Headline inflation increases in year 1: around 0.3 percent in China to 1 percent in rest-of-the-world bloc; core inflation increases by less than 0.1 percent (Figure 24, Panels E and F).
  - Electricity prices increase temporarily, by 20 percent or more in regions that use fossil gas more heavily and by 6 percent or less in regions relying more on renewables or coal (Panel C).
  - Coal demand for electricity generation increases, pushing up coal price (Panel E).
  - Short-term declines in labor demand and investment; larger consumption impacts for LIQ households (Panels C and D).
  - Real GDP falls in the rest-of-the-world bloc by around 0.3 percent; other regions experience mild GDP increases due to shifts in external demand (Panel A).
- Permanent increase in fossil gas prices:
  - Permanent decrease in fossil gas supply in rest-of-the-world bloc leads to immediate, permanent 10 percent rise in fossil gas price in that region (Figure 25, Panel A).
  - Regional heterogeneity: euro area similar increase; China and United States around 8 percent increases initially, with domestic production rising over time to stabilize prices (Panel C).
  - Negative impacts on electricity sector: higher electricity prices and lower electricity use across regions (Panels E and F).
  - Permanent reductions in real GDP in most regions: euro area and China about 0.1 percent; rest-of-the-world bloc about 0.3 percent; United States the exception due to increased fossil gas production investment (Figure 26, Panel A).
  - Initial spike in headline CPI inflation in all regions (Panel E); no material change in core inflation (Panel F).

*Source: Authors’ calculations; IMF Working Papers – Getting to Know GMMET*

### Conclusion

### Conclusion

### Model overview
- Presents the Global Macroeconomic Model for the Energy Transition, GMMET: a large-scale, dynamic, nonlinear, microfounded, multiregion, general equilibrium model designed to analyze the short- and medium-term macroeconomic impact of climate policies.
- Documents model structure, data sources, and model properties through an extensive set of simulations to form a reference guide.
- Features granular, sector-specific modeling to better capture real-world obstacles to the energy transition:
  - Electricity generation (capturing the intermittency of renewables).
  - Transportation (capturing network externalities between EV charging stations and EV adoption).
  - Fossil fuel mining (replicating estimated supply elasticities at various time horizons).
- Includes a rich set of policy tools: taxation of GHG emissions, various subsidies, and regulations.

### Key insights from the model
- The micro and macro effects of climate policies (for example, the gradual implementation of a GHG tax as a source of revenue for the government) are conditioned on how revenues are spent (for example through lump-sum transfers or a reduction in the labor income tax).
- Important nonlinearities exist in the impact of climate policies:
  - In initial stages of a GHG price rise, total GHG emissions fall rapidly as the use of high-emitting coal in electricity generation is phased out.
  - After this initial reduction is exhausted, emission reductions slow and the marginal impact of a GHG price rise lessens.
- The global dimension matters: macro and micro effects depend crucially on whether a region implements policies unilaterally or many regions act simultaneously.

### Model features and sectoral mechanics (summary)
- Mining sectors:
  - Fossil fuel extraction uses mines, labor, and specific capital in a CES production function with elasticity of substitution 휎.
  - Mines input evolves via an initial volume multiplied by a time-varying scaling factor 휓 with parameters 휙 and persistence 휌 governing adjustment dynamics and supply elasticities across horizons.
  - Short-term and long-term price-elasticities of commodity supply are functions of factor-specific elasticities 휂_i, factor shares 훼_i, and 휎, yielding distinct short- and long-term supply elasticities.
- Renewables-plus-backup utilities:
  - Treats generation technologies as close to perfect substitutes by compensating intermittency within the renewables-plus-backup utility.
  - Renewable generation follows a generation-duration curve G(x)=M x^γ with intermittency parameter γ; backup fills gaps to maintain a constant generation level L.
  - Defines gross renewables generation R̄, curtailed generation C, fraction of regimes requiring backup p, and backup average generation B; varying p defines the production frontier.
  - Output L can be expressed as a Cobb-Douglas function of backup generation B (share γ/(γ+1)) and intermittent gross generation R̄ (share 1/(γ+1)).
  - Cost minimization yields demand schedules for R̄ and B and an expression for average cost of electricity generation C as a function of component costs.
- Tradables and nontradables abatement:
  - Fossil-fuel-related emissions tracked via fossil fuel inputs; non-fossil-fuel-related emissions linked to output and abated at sectoral productivity cost.
  - Firms choose abatement share φ* equating marginal productivity cost A'(φ*)λ with marginal tax savings τκ, where A'(φ) is the marginal abatement cost curve (MACC).
  - Functional forms and parameters (σ̄, γ, φ̄) for A'(φ) are calibrated to converted MACC estimates to align φ*(τ) with empirical abatement cost data.
- Transportation sector:
  - Transportation modeled as a household service provided by vehicle fleet capital; two vehicle types (EV, CC) differ in purchase price Pt_i, fuel intensity κt_i, and fuel cost PFt_i.
  - Households choose vehicle types based on expected life-cycle real costs Ct_i including purchase and discounted expected fuel costs; scrappage rate δ and real discount factor ℱ enter cost calculations.
  - New-car average cost C_t is a share-weighted average of type-specific costs; fleet rental rate RT_t covers new purchases and fuel costs.
  - Fleet accumulation follows M_t = N_t + (1−δ) M_{t−1}; new purchases split across types via relative life-cycle-costs and preference shifters α_t^i that incorporate network effects.
  - EV adoption endogenously interacts with charger deployment C H_t^j via symmetric network effects: charger stock evolves with fleet size (elasticity ε_ch) and stations influence purchase decisions (elasticity ε_net), amplifying policy impacts.
  - Transportation emissions tracked as oil consumption for CCs and electricity consumption for EVs; emissions reduction from EVs depends on electricity generation GHG intensity.

### Future development priorities
- GMMET will remain a living model for ongoing analysis of macroeconomic implications of GHG mitigation in the global economy.
- Recent documented development: introduction of a metal sector to explore impacts of metals mining and use on renewable energy and EVs (IMF (2023)).
- Further development plans include:
  - (i) Introduce Emissions Intensive Trade Exposed Industries (EITEs) for more granular sector-specific abatement options and trade implications of unilateral policies.
  - (ii) Model abatement costs as sector-specific capital accumulation (industrial retrofit).
  - (iii) Introduce endogenous sector-specific productivity (learning-by-doing) to capture technological progress and economies of scale for new technologies.
  - (iv) Expand the transportation sector to include the transport of goods.
- Different model versions with more regions are under development to provide greater insights into cross-country interactions of climate policies and country-specific outcomes.

*Source: wpiea2023269-print-pdf - Conclusion*

### Annex II. Standard Model Properties

### Annex II. Standard Model Properties

### Temporary Increase in the Monetary Policy Rate
- Shock: one-year 100 basis point increase in the monetary policy rate in the United States, surprise to firms and households.
- Real GDP: decreases by 0.6 percent on impact (Panel A).
- Inflation: decreases by less than 0.2 percentage point at its trough in the first year (Panel H).
- Private investment and household consumption: both reduced (Panels D and C) due to higher cost of capital and higher real interest rates.
- Wealth and labor income: firm profitability falls, reducing household wealth; lower production reduces demand for factor inputs and labor income.
- External sector:
  - US dollar appreciates (Panel G) with higher real interest rates than foreign rates.
  - Foreign demand for US goods weakens (Panel E).
  - Import prices facing US households decline; households substitute toward foreign goods.
  - Imports decline by more than exports (Panel F).
  - Net impact: small increase in the current account surplus in the short term (Panel B).
- Fiscal response:
  - Government increases transfers to households to stabilize activity, raising the fiscal deficit in the short term.
  - Eventually government reduces transfers to return public debt-to-GDP to its long-term target.
- Monetary policy reaction:
  - Downward pressure on CPI inflation (exacerbated by declining import prices) leads monetary policy to ease.
  - Monetary authority reduces the monetary policy rate to achieve a period with real interest rates below their long-term level (Panel J), temporarily stimulating aggregate demand and re-anchoring inflation at the target.

### Permanent Increase in the Level of Non-Energy Productivity
- Scenarios: increase in productivity either in the entire non-energy economy (blue lines) or only in non-energy tradable goods (red lines).
- Long-term output: each scenario raises the level of real GDP by 1 percent in the long term (Panel A).
- Sectoral definition: non-energy economy includes non-energy tradable and nontradable goods sectors, but excludes the electricity sector, the transportation sector and the mining sectors.
- Investment and capital: higher productivity leads to more investment and a higher capital stock (Panel D); higher return to capital.
- Labor and consumption:
  - Increased labor demand, higher household labor income and wealth.
  - Households consume more permanently; OLG households partially anticipate higher future wealth so consumption can increase rapidly in the short term (Panel C).
- Real Effective Exchange Rate (REER) behavior (Panel B):
  - Productivity increase only in tradable goods: REER appreciates in the long term (Balassa-Samuelson effect).
  - Productivity increase across tradables and nontradables: REER depreciates in the long term, as relative price of tradable to nontradable goods does not fall and higher domestic demand raises imports requiring currency depreciation to maintain external balance.
- Dynamics:
  - Most key components of real GDP reach new steady-state levels within ten years.
  - Rapid and fully anticipated productivity increase: aggregate demand adjusts upward more quickly than aggregate supply (capital accumulation is slower).
  - Inflation falls (Panel H); monetary authority eases interest rates (Panel G).
- Global spillovers:
  - US shock raises real global GDP by about 0.3 percent permanently (Panel I).
  - Increases global demand for oil and fossil gas, permanently increasing both prices by about 0.2 percent (Panel J).
  - Higher fuel prices act as automatic global stabilizers, dampening global demand slightly by increasing production costs.

### Temporary Increase in Aggregate Demand
- Shock: one-year US private domestic demand shock calibrated to raise real GDP by almost one percent relative to baseline (Panel A); private investment increase roughly three times larger than household consumption increase.
- Investment and output:
  - Increased private investment raises private capital stock and capital services, contributing to a persistent increase in production (Panel D).
- Inflation and monetary response:
  - Short-term upward pressure on inflation: inflation rises about 0.2 percentage point above target (Panel B).
  - Monetary policy rate increased by monetary authority (Panel E), raising real interest rates (Panel F).
  - Higher real interest rates raise cost of capital and dampen private investment demand; OLG households increase private saving, reducing consumption after year 4 (Panel C).
- External sector:
  - REER appreciates in the short term (Panel H) due to higher real interest rates relative to foreign rates.
  - Appreciation reduces import prices and boosts import demand; weakens US exports and current account (Panel G).
- Fiscal side:
  - Increased domestic activity raises tax revenues and improves fiscal balance (Panel B).
  - Government decreases general lumpsum transfers in short term to close output gap (automatic stabilizer), dampening private consumption.
  - In medium term government stabilizes deficit and gradually restore debt-to-GDP to target by increasing general lumpsum transfers, putting upward pressure on private consumption.
- Global spillovers:
  - Raises real global GDP by more than 0.2 percent (Panel I).
  - Temporarily boosts global oil price by about 1.4 percent (Panel J).
  - Higher fuel prices act as automatic global stabilizers, temporarily increasing production costs and damping global demand slightly.

### Temporary But Persistent Increase in the Corporate Risk Premium
- Shock: increase in corporate risk premium by 1 percentage point on impact, declining by 40 percent each year thereafter (Panel B).
- Output and inflation:
  - Real GDP declines by approximately 0.25 percent on impact (Panel A).
  - Inflation falls by less than 0.1 percentage point (Panel G).
- Borrowing and investment:
  - In GMMET, only tradable and nontradable goods firms borrow; energy-related firms use Tobin’s Q model.
  - Increased perceived corporate risk raises borrowing costs only for tradable and nontradable firms.
  - Immediate increase in cost of capital leads to an immediate rise in leverage (Panel E), then corporate debt falls (Panel F) as leverage unwinds.
  - Private investment significantly lower for several years (Panel D).
- Consumption and wealth:
  - Household consumption declines from lower dividends (reduced firm profitability) and lower labor income (firms demand less labor), affecting OLG and LIQ households differently (Panels C).
  - Consumption decline smaller in magnitude than investment decline.
- Monetary and external response:
  - Weaker activity reduces inflation slightly; monetary authority decreases policy interest rate (Panel H) to stimulate demand.
  - Small fall in short-term real interest rate yields small real depreciation in short term (Panel J).
  - Exports increase slightly, imports fall, and current account improves modestly in short term (Panel I).

### Temporary Fiscal Stimulus
- Definition: fiscal multiplier measured as average deviation of real GDP from steady state during two years of fiscal stimulus.
- Fiscal stimulus design: 1 percent of GDP increase in one of GMMET’s four fiscal spending instruments, or a cut in one tax rate, financed by a concurrent increase in government deficit.
- Multiplier magnitudes and ranking:
  - Largest multipliers: public consumption and public investment (enter directly into real GDP; public investment has higher value due to productivity-enhancing properties).
  - Next largest: instruments that directly impact LIQ households’ consumption (cuts in consumption and labor income taxes; increases in transfers targeted to LIQ households).
  - Smallest impact: lumpsum transfers distributed to all households (OLG households do not respond with higher consumption as transfers are subsumed in their wealth stock).
- Monetary accommodation effects:
  - If significant slack exists, monetary authority may not respond; holding interest rates unchanged lowers real interest rates and stimulates the economy.
  - Monetary accommodation magnifies fiscal multipliers; longer accommodation increases the multiplier further as households expect more inflation and lower real interest rates.
  - Example outcomes from Annex Table II.1 (Average GDP Impact After the First Two Years, percent deviation from the steady state):
    - Public Consumption: Normal Conduct of Policy 0.86; Two Years of Accomodation 1.65
    - Public Investment: Normal Conduct of Policy 0.97; Two Years of Accomodation 2.05
    - General Transfers: Normal Conduct of Policy 0.25; Two Years of Accomodation 0.30
    - Targeted Transfers to LIQ Households: Normal Conduct of Policy 0.96; Two Years of Accomodation 1.87
    - Consumption Tax: Normal Conduct of Policy 0.41; Two Years of Accomodation 0.57
    - Labor Income Tax: Normal Conduct of Policy 0.31; Two Years of Accomodation 2.00
  - Numerical example: with two years of monetary accommodation for fiscal stimulus through higher public consumption, real GDP is over 0.8 percentage points higher on average; with only one year of accommodation the additional impact on real GDP would be about 0.3 percentage points.

### Permanent Fiscal Consolidation
- Experiment design: three fiscal consolidation experiments each reduce the United States’ fiscal deficit permanently by 1 percent of GDP (Panel A).
- Debt outcome: permanent reduction in public debt-to-GDP of roughly 20 percentage points (Panel G).
- Instruments considered: reduction in public consumption (blue), increase in effective labor income tax rate (red), reduction in general lumpsum transfers (green).
- Reversion rule: as debt service costs fall, the initially changed instrument is allowed to revert toward its original value to confine deficit improvement to 1 percent of GDP.
- New steady state outcomes:
  - Real GDP is higher relative to baseline in the new steady state under all consolidations.
  - Reasons:
    - Gradual reduction in debt burden yields permanently lower debt service costs, allowing tightening to be partially unwound long term.
    - Higher public saving in the United States raises global supply of savings and lowers global real interest rate, raising desired capital and production.
  - Global real interest rate effect: about a 3-basis-point decline relative to a 10 percent of GDP public debt consolidation.
  - US size: United States is nearly a quarter of global GDP, so its consolidation materially affects global real interest rates.
- Asset and external adjustments:
  - Domestic public bond stock falls; households substitute foreign assets for government bonds; net foreign asset position improves markedly in the new steady state (Panel J).
  - Net export position can deteriorate given improvement in income balance; REER appreciates slightly in long term (Panel H).
- Transition path:
  - Real GDP initially falls in all cases (Panel A); largest initial decline when public consumption reduced, followed by labor income tax rise and general lumpsum transfer cut.
  - Private investment (Panel D) and net exports drive the bounce back as firms respond to permanently lower real interest rates and REER depreciation.
  - Household consumption falls most in short term with general transfer cuts, closely followed by labor income tax increases (Panel C).
  - To accumulate net foreign assets, REER initially depreciates (Panel J), reducing imports and raising exports.
  - Greater negative effect of consolidation on domestic demand requires larger depreciation to achieve required net foreign asset accumulation (Panel I).
  - Most depreciation occurs with government consumption cuts; least depreciation occurs when general lumpsum taxes rise.
  - Paths for current account and net foreign assets are similar across the three instruments.

*Source: Annex II. Standard Model Properties, wpiea2023269-print-pdf.*

### Annex Figure III.1 presents the solution of two types of variables 푣 in the model, either specified in level terms,

### Annex Figure III.1. Linearization Methods

### Description of linearization approaches
- The figure presents the solution of two types of variables 푣 in the model, either specified in level terms, or in natural logarithms (logs).
- Red lines: the fully solved answer (if 100 percent of the shock was solved).
- Green lines: the full numeric linearization method using the solution from 50 percent of the shock.
- Blue lines: the "marginal numeric linearization" method, an alternative that can give a more accurate approximation.

### Marginal numeric linearization method (procedure)
- Marginal linearization uses the exact solution (fully nonlinear) for a rescaled shock (50 percent of the full shock in this example) and the first derivative of the exact solution at the same point.
- The left panel in the figure illustrates a variable in levels (example: GHG tax revenue); the right panel illustrates a variable in natural logarithms (example: coal extraction).
- The method relies on an approximation more closely related to the first simulation, instead of the model’s steady-state solution.
- Steps described:
  - Obtain 푣ุ from the first simulation of the model (50 percent of the shock in this example).
  - Conduct a second simulation for 1 percentage point less of the solution than in the first simulation (in this example, 49 percent of the GHG price increase), producing the variable 푣෤.
  - In the final solution of 푣, 50 percent (푣ุ) is provided by the first simulation, while the remaining 50 percent (the remaining portion of the shock) is the difference between the second and first simulations multiplied by the remaining portion of the shock – in this case, 50 percent.
- The marginal numeric linearization method solves for the variable 푣 as follows:
- 푣 = 푣ุ+ (
(1−휔)
)
100(푣ุ−푣෤)

### Comparative performance and applications (Annex Figure III.2 summary)
- Annex Figure III.1: the marginal linearization method would produce the blue lines, which is a more accurate solution.
- Annex Figure III.2 quantifies accuracy across ten variables in the United States from the permanent and immediate increase in the global GHG price to US$50/tCO2e:
  - Red lines: exact solution.
  - Green lines: full numeric linearization method.
  - Blue lines: marginal linearization at 50 percent of the shock.
- The marginal numeric linearization method is closer to the correct solution for some variables, including:
  - Macro aggregates (Panels A, B, and C).
  - Important components such as the marginal propensity to consume (Panel D).
  - Measures related to climate policy (at least in the short term): measures of emissions (Panels E and F).
  - Emissions related to the marginal abatement curves in tradables (Panel G) and nontradables.
  - GHG tax revenues (Panel H).
  - Price and volume of electricity (Panels I and J).

*Source: Authors’ calculations (Annex Figures III.1 and III.2, Getting to Know GMMET, IMF Working Paper WP/2023/269)*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023269-print-pdf.pdf_