## wpiea2025077-print-pdf ## Source details **Canonical URL:** [wpiea2025077-print-pdf](https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025077-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2025/english/wpiea2025077-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2025/english/wpiea2025077-print-pdf.pdf.json) --- ### 2.1 Production — key features - IMF-ENV is a global multi-region, multi-sector recursive dynamic CGE with core data based on the GTAP database (features 160 countries and regions, along with 76 sectors). - Production: - Separate production functions for each economic sector/activity (a) using nested CES functions to capture substitution possibilities. - Sector-specific representative firms minimize production costs under constant returns to scale (perfect competition assumption, relaxable). - Activities can be separated from commodities (e.g., single electricity commodity produced by multiple technologies). - Factors: - Factors excluding capital are almost perfectly mobile across sectors within a region but not across countries. - Capital follows a putty-clay vintage specification: New capital (net-investment) is malleable; Old installed capital is fixed and cannot be reallocated without high costs. - Labor supply determined by working age population, labor participation and long-term unemployment rates, and adjusts endogenously to real wages via a reduced-form wage supply curve. - Land and natural resources included as production factors constraining agricultural and mining expansion. ### Box 1: Generic CES production function — formulations and calibrated elements - CES formulation and definitions: - Primal CES constraint: X = A [ Σ_i a_i (λ_i V_i)^ρ ]^{1/ρ}; ρ = (σ − 1) / σ - Optimal input demand: V_i = α_i^σ (A λ_i)^{σ−1} (P / P_i)^σ X_a - Composite price: P = (1/A) [ Σ_i α_i (P_i λ_i)^{1−σ} ]^{1/(1−σ)} - Production factors in IMF-ENV: - Four factor types: capital, labor, land, natural resources. - Capital vintages: Old and New; substitution elasticities lower with Old capital (sticky). - Labor: single type movable across activities within a region; future developments to allow skilled/unskilled split leveraging GTAP’s five labor occupation categories. - Land: single type for agricultural activities; possible extension using GTAP satellite data to 18 AEZs. - Natural resources: factor input for fossil and mineral extractive sectors, fisheries and forestry. - Default nested production structure (non-agricultural) — topology preserved: - Top: XP (gross output sector a) = aggregation over vintage outputs XPV (σ_xpv) - XPX combined with XGHG via CES (σ_emi) - XPX = CES between intermediate goods bundle (ND1: domestic vs imports) and domestic value-added (VA) (σ_p) - VA = CES between labor (LAB1) and capital, energy, natural resource bundle (VA1) (σ_v) - VA1 = CES between energy demand (XNRG) and capital & natural resource bundle (KF) (σ_n1 / σ_kef / σ_kf) - Production adjustments and policy levers: - Technological shifters A and λ exogenous and used to reflect structural change or policies. - Elasticity parameters σ differentiable across regions; specific values provided in Annex tables. ### Production structure for crops and livestock - Distinctions from default: - Inclusion of land as factor and fertilizer/feed removed from ND1 and coupled with land in VA2. - Crops: VA2 = land (extensive) and fertilizers (intensive); CH4 and N2O linked with land input and fertilizer application. - Livestock: VA2 uses feed for intensification; GHGs CH4 and N2O linked with land and manure; livestock capital generates CH4. ### Energy bundle (XNRG) architecture - XNRG: nested CES composite of ELY (electricity commodity bundle) and NELY (non-electricity energy bundle) with σ_e / σ_nely. - NELY: Oil & Gas bundle (OLG) nests natural gas with oil (σ_olg); Coal (COA) nested with oil-gas composition. - Coal and oil assumed easily traded internationally; natural gas less tradable. - Electricity (ELY): produced by eight generation sectors in conjunction with T&D; power sector captures regional cost differences and vintage aging. - Emissions: fossil fuel burning nodes flagged as GHG sources. --- ### 2.2 Domestic commodity supply — mapping and electricity specifics - Activity-to-commodity mapping via mapi: - Default: one activity produces one commodity (mapi diagonal), exception electricity (many-to-one). - Flexibility: one-to-many and many-to-one mappings supported. - Non-electricity goods: - Transformation uses CET supply allocation (ωs r,a default = 0 → one-to-one mapping). - Supply aggregation across activities for commodity i uses CES with αs and σs ri (default σs ri = 0). - Electricity supply — nested CES representation (key equations preserved): - Top nest aggregates T&D (Xetd ely) and power bundle (Xpow ely); default σel r,ely = 0 (Leontief). - Equations (6)–(8) define Xetd, Xpow and PS r,ely aggregation. - Power-bundle decomposed into four default bundles: FOSP, NUCP, HYDP, OTHP; λpow pb for efficiency; σpow for substitution (Equations (9)–(10)). - Technology nests: each bundle decomposed into component technologies (8 electricity generation technologies) with σpb intra-bundle elasticity (Equations (11)–(12)). - Modeling levers and caveats: - Output taxes and subsidies can be applied within nests (feebates, feed-in tariffs). - λ parameters adjust mixes/efficiency. - Aggregation into single electricity commodity limits end-user identification of generation technology; expansion to multiple electricity commodities possible but requires structural changes. - IMF-ENV lacks some country-specific technical and legal electricity aspects (grid integration, legal decisions on nuclear/hydro, electricity trade barriers). --- ### 2.4 Final demand — household consumption, government, investment - Final demand types: private consumption, public expenditure, investment. - Household consumption via Extended Linear Expenditure System (ELES): - Representative household maximizes U = Σk μk ln(Ck − θk) + μs ln(S/Ps) subject to YHd = Σk Pck Ck + S and Σk μk + μs = 1. - Consumption solution: Ck = Pop θk + μk / Pck Y∗ where Y∗ = Yd − Pop Σk Pck θk (equation 23). - Savings: S = Yd − Σk Pck Ck (equation 24). - Households save a constant proportion of income; forward-looking behavior absent; model requires exogenously specified savings rate. - Commodity mapping for consumers: - Transition matrix maps consumer goods k to produced commodities i; consumer goods set smaller than produced commodities. - Consumer goods split between energy and non-energy bundles; energy bundle follows energy structure with different elasticities for final consumption. - Government and investment: - Government and investment consumption use CES bundles (no subsistence nor savings). - Total demand equals sum of consumer demand, intermediate demands, government consumption, investment. --- ### 6 Export taxes, carbon taxes, and fiscal closures — implementation and recycling - Export taxes: - Revenue: YGOV_r,etx = Σ_d Σ_i τ_e_r,i,d PE_r,i,d XW_s_r,i,d (equation 55). - Trade volumes: iceberg trade cost generates wedge; model operates on pre-border export supply XW_s. - Carbon taxes: - Revenue: YGOV_r,ctx = Σ_em Σ_β Σ_aa τ_emi_r,em,β,aa Emi_r,em,β,aa (equation 56). - Revenue recycling options (menu of four main options): - Direct household transfers (TRG_r endogenized to offset YGOV_ctx increase). - Reduce taxes on wages or capital (factor tax rate κ_f endogenized). - Increase government expenditures (budget-neutral). - Increase government savings (not budget-neutral; increases S_g and total investment proportionally). - Combination allowed (e.g., 50% transfers + 50% labor tax reduction); predominant IMF-ENV practice: increase direct household transfers. - Direct taxes and standard fiscal closure: - Direct tax revenue: YGOV_r,dtx = (Σ_f Σ_a κ_f_r,f,a PF_r,f,a XF_r,f,a) + κ_h_r YH_r − TRG_r (equation 57). - Standard closure: government expenditures fixed to baseline; κ_h endogenized to match government balance; other tax rates fixed. - Investment and savings balance: - Gross investment financed by savings and depreciation: YFD_r,inv = S_h_r + S_g_r + PW_sav S_f_r + DeprY_r (equation 58). - Depreciation allowance: DeprY_r = δ_f_r PFD_r,inv K_s_r (equation 59). - Global foreign savings cancel: Σ_r PW_sav S_f_r = 0 (equation 60). - Default: investment is savings-driven; alternative closures available. - Macroeconomic closures (default): 1. Government budget balance follows exogenous projections; κ_h endogenized. 2. Current account balance (CAB) fixed to baseline; real exchange rate adjusts. 3. Domestic investment determined by total savings each year. - Model dynamics: - Labor supply growth driven by working-age population (working age defined 15 to 64 years). - Capital accumulation: K_t = K_{t−1} (1−δ) + I_{t−1} (equation 61). - Standard technology assumption: 1 percent annual improvement in energy efficiency across all regions and sectors. - Emissions accounting highlights: - GTAP-based GHGs: CO2, CH4, N2O, F-gases; IPCC AR6 100-year GWPs: CH4 (fossil and non-fossil) and N2O about 29.8, 27 and 273 respectively (values as presented). - Emission aggregation: Emi_{r,em,β,a} = χ_Emi_em ρ_Emi_{r,em,β,aa} B_{r,β,a} (equation 62); EmiTot and global totals in equations (63)–(64). --- ### 3.1 Data sources, calibration and outputs - Core database: - GTAP Power database version 11 with 2017 base year. - GTAP Power: 143 country-specific IO tables, 18 regions, 65 commodities, 76 activities; differentiates 4 fossil fuel sectors, 12 electricity generation technologies, and T&D. - Electricity activities specified: coal, gas (base and peak), oil (base and peak), nuclear, hydro, wind, solar, other power technologies, and TnD. - GHGs included: CO2, CH4, N2O, fluorinated gases (HFCs, PFCs, SF6). - Typical IMF-ENV aggregation: 25 regions (all G20 plus 5 regional groups); G-20 version differentiates 36 activities and 28 commodities. - Software: GAMS. - Calibration: - Two-step: static calibration to base year GTAP data; dynamic calibration to create baseline projected to 2040 (model calibrated until 2040). - Baseline drivers and targets: - Medium-term projections from IMF WEO; long-term projections from SSP-2 calibrated until 2040. - Electricity generation in baseline: Leontief specification targeting generation shares; policy simulations can allow endogenous CES electricity aggregation or use exogenous PE model projections. - GHG baseline projections targeted by calibrating emission-intensity parameters; LULUCF fixed to base year absent projections. - Energy efficiency baseline: assumed 1% annual growth in energy efficiency across fuels. - Model outputs and dashboard: - IMF-ENV dashboard (R-shiny) ingests GDX files; standardized chart panels include Baseline drivers, Emissions, Energy and prices, Real Sector, External sector, Fiscal sector. - Sensitivity analysis: - Parametric uncertainty: substitution elasticities, AEEIs, technology costs. - Structural uncertainty: aggregation, trade specification, closures. - Policy design sensitivity: revenue recycling can materially change global GDP costs (least GDP cost when revenues fund productive investments; largest cost when recycled as lump sum transfers). --- ### 6.1 Climate and energy policies — instruments and sectoral measures - Carbon and fossil fuel pricing: - Price-based carbon taxes and quantity-based ETS implementable by combinations of sectors, regions and GHGs. - Fossil fuel subsidy reform modeled by updating baseline subsidy rates and removing subsidies in scenarios with revenue recycling options. - Power sector instruments: - Clean energy standard: minimum share φ of non-fossil generation imposed (constraint form preserved). - Feed-in tariffs: renewable producers receive subsidy subs_a; representative price PP_a × (1 − subs_a) (equation 66). - Feebates: self-financing fees/rebates with p̃ determined to meet emission targets (equation 67). - Energy-intensive sectors: - Emission caps or CO2 intensity constraints θ_a applied as in equation (68). - Green industrial policies: - Output subsidies via tax rate adjustments; investment subsidies subsidize new capital vintages (equation 21 referenced). - Energy efficiency regulations: - Implemented via shifts in CES share parameters (α) and via investment-loss function when costs known (investment-loss function in equation 69). - AFOLU and LULUCF: - LULUCF emissions treated with marginal abatement cost (MAC) curves calibrated from MAGNET; allows reductions for carbon price but does not model full general equilibrium land transformation. - Emerging technologies: - EV adoption modeled by changing household CES α parameters to shift demand from diesel/gasoline to electricity. - CCUS modeled if year-by-year captured shares and capex available; CCUS investment reduces next period productive capital via K_{t+1} = K_t (1 − δ) + (1 − IL_t) I_t (equation 69). --- ### 7 Climate finance, damages, and transition opportunities - Climate finance: - IMF-ENV used to develop global and regional scenarios for pooling climate finance from advanced to emerging/developing economies and assess macro impacts. - Climate damages: - Model supports inclusion of NGFS scenario GDP reductions and detailed climate damage functions (labor productivity losses, crop yields, energy demand, land loss, capital losses). - Damage function sources include Roson and Sartori (2016) and country-specific studies; LULUCF and NGFS updates referenced. - Growth opportunities: - Regional applications show macro gains from renewable deployment when complemented by T&D and energy-efficiency investments; financing assumptions (domestic, external, mix) materially affect outcomes. - AI and energy demand: - IMF-ENV applied to study data-center-driven electricity demand increases and impacts on prices and emissions for U.S., China and Europe. --- ### 8 Future developments (selected) - 8.1 Endogenous technological change (R&D module): - Links R&D expenditures to knowledge stock proxied by patents; Gamma distributed lags; initial results show average lag ~ ten years. - 8.2 Labor split skilled/unskilled: - Plan to distinguish skilled and unskilled labor leveraging GTAP five labor types to capture skill-biased technological change. - 8.3 Outdoor air pollution module: - Planned accounting of air pollutant emissions and health co-benefits. - 8.4 Natural resource depletion: - Module to account for reserves, production costs and update supply elasticities; integrate Rystad UCube and Wood Mackenzie outputs. - 8.5 Endogenous current account balance: - Planned closures: GTAP closure (global investment allocation by expected returns) and wedge closure (domestic savings, reserves accumulation). - 8.6 Savings and investment modeling extensions: - (1) Private savings determinants by demographics and income level. - (2) Private savings responsive to expected returns to capital. - (3) Compatibility with endogenous CAB closures. - (4) Split investment between public and private where data available. --- ### 9 Summary — core takeaways - IMF-ENV is designed to examine medium- and long-term macroeconomic and sectoral impacts of structural policies (climate mitigation, energy transition, fiscal and trade policies). - Strengths: - Granularity across regions, sectors, production factors, and energy sources. - Consistency with resource constraints and macro/fiscal balances. - Flexibility to link with bottom-up PE energy models, gravity trade models, and micro-simulations. - Direct integration of sectoral GHG emissions and activity-level emission accounting. - Limitations: - Recursive-dynamic, not suitable for short-term business cycle or interest-rate/inflation dynamics (agents not forward-looking). - Embedding forward-looking intertemporal optimization would reduce some detailed features (e.g., capital vintages) and be computationally costly. - Documentation structure includes production, demand, trade, factor markets, inter-temporal linkages, GTAP-based data/calibration, outputs and dashboard, uncertainty and sensitivity analyses, simulated policies, and annexes with algebraic derivations and elasticity tables. *Source: wpiea2025077-print-pdf (IMF-ENV model documentation).* ### 2.1 Production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ### 2.1 Production ### Subsections and headings - 2.1.1 Production factors. 11 - 2.1.2 Default production structure. 13 - 2.1.3 Production structure for crops and livestock sectors. 14 - 2.1.4 Energy bundle. 16 *Source: wpiea2025077-print-pdf - 2.1 Production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (canonical URL provided separately)* ### 8.6 Savings and investment modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . ### 8.6 Savings and investment modeling. ### Overview - IMF-ENV is a global multi-region, multi-sector recursive dynamic computable general equilibrium (CGE) model developed to examine impacts of policies inducing structural economic changes on both the overall economy and specific sectors. - Core data are based on the GTAP database which "features 160 countries and regions, along with 76 sectors." - The model is recursive dynamic: solved as a sequence of comparative static equilibria where factors of production are exogenous within each period and linked between periods with accumulation expressions. - Investment is driven by savings; agents are not forward-looking and investment levels are determined by savings, which combine household savings, the government budget balance, and the current account balance. ### Production and factor markets - Production: - Separate production functions are defined for each economic sector or activity (denoted by a). - Sector-specific representative firms minimize production costs under constant returns to scale (perfect competition assumption, which can be relaxed). - Production is modeled via nested constant-elasticity-of-substitution (CES) functions to capture substitution possibilities across inputs and factors. - The model can separate production activities from commodities (e.g., a single electricity commodity produced by multiple generation technologies). - Factors: - Factors of production, excluding capital, are almost perfectly mobile across sectors but not across countries. - Capital follows a putty-clay specification: - New capital (net-investment) is malleable and allocated without friction such that the return to new capital equalizes across sectors. - Old installed capital is fixed and cannot be reallocated without high costs. - Labor supply is determined by working age population, labor participation and long-term unemployment rates, and adjusts endogenously to real wages via a reduced-form wage supply curve (accounts for leisure/work decisions at both intensive and extensive margins). - The model also includes land and natural resources as production factors constraining agricultural and mining expansion. ### Demand, trade, and closures - Household demand is non-homothetic. - International trade is modeled with the Armington specification (differentiation by region of origin) using full bilateral trade flows, prices, transportation and trade costs by commodity. - All commodity and factor markets clear through flexible price adjustments. - Countries exchange commodities and capital on international markets. - Model closures maintain resource constraints and macroeconomic and fiscal balances; model links to partial equilibrium sectoral models and micro-simulations are possible. ### Energy, emissions, and sectoral detail - The model directly links economic activities to greenhouse gas (GHG) emissions from energy, agriculture, transportation, industry, waste management, buildings, fugitive emissions, and LULUCF (land use, land-use change and forestry). - Sector-specific emission accounting enables analysis of GHG- and activity-specific policies. - Power sector representation captures regional variations in capital and operational expenses across generation technologies, investment in transmission and distribution (T&D) technologies, and capital vintage aging. - IMF-ENV can use data from bottom-up partial equilibrium (PE) energy models to guide the evolution of electricity generation. ### Policy instruments and applications - The model can simulate: - Carbon taxes (on flexible combinations of activities, emission sources, and GHGs). - National and regional emission trading schemes (ETS). - Feed-in tariffs, feebates, energy-efficiency regulations. - Incentives and programs encouraging technology adoption (e.g., heat pumps), production and investment subsidies. - Broader fiscal policy packages. - Trade policies: free trade agreements (FTAs), tariffs, non-tariff measures (NTMs), import quotas, sanctions, and disruptions. - Carbon border adjustment mechanisms (CBAM) and interactions between trade, energy, and mitigation policies. - The model is suitable for medium- to long-term structural policy analysis (climate mitigation, energy transition, fiscal and trade policies) and can implement concurrent or independent policies across countries and regions. ### Comparison with other modeling frameworks - Recursive dynamic CGE models (like IMF-ENV) versus New-Keynesian / DSGE: - IMF-ENV is not designed for short-term transition dynamics, business cycles, inflation dynamics, or interest rate fluctuations because nominal rigidities are not modeled and agents are not forward-looking. - DSGE models capture business cycle and short-term rigidities and typically include forward-looking agents, but at the cost of regional and sectoral granularity. - For medium- to long-term policies with political and technological uncertainties, recursive dynamic CGE models can yield similar energy-sector behavior and carbon price estimates as forward-looking models. - Partial equilibrium (PE) models: - PE models provide bottom-up, high-detail sectoral representation (e.g., plant-level, daily/seasonal load), but cannot capture economy-wide feedbacks or macroeconomic effects. - CGE models are often linked to PE models to leverage strengths of both approaches; IMF-ENV uses PE model data for electricity evolution. - Integrated Assessment Models (IAMs): - IAMs integrate human and environmental systems, focus on environmental feedbacks and physical dynamics, and often present cost-benefit frameworks for optimal policy pathways. - Embedding CGE models in IAMs is computationally expensive and often reduces model dimensionality and economic detail. - New Quantitative Trade (NQT) models: - NQT models are stylized CGE forms, parsimonious and analytically tractable, useful for structural estimation like trade elasticities. - CGE models include additional features (multiple production factors, non-homothetic demand, institutional detail, energy and environmental modules) enabling more detailed policy analysis. - Hybrid approaches and richer NQT models are emerging that narrow differences. ### Strengths and limitations - Strengths: - Granularity across countries, sectors, production factors, and energy sources. - Consistency with resource constraints and macro/fiscal balances. - Flexibility to link with partial equilibrium models, gravity trade models, and micro-simulations for distributional analysis. - Direct integration of sectoral GHG emissions and activity-level emission accounting. - Limitations: - Not designed for short-term business cycle or transition dynamics involving nominal rigidities. - Agents are not forward-looking, which affects intertemporal behavioral responses compared with DSGE models. - Embedding forward-looking intertemporal optimization would require removing some detailed features (e.g., capital vintages) and is computationally costly. ### Organization of the paper and model documentation pointers - The paper and model documentation cover: - Core components (production, demand, trade, factor markets, inter-temporal linkages). - Data and baseline calibration (GTAP-based). - Model outputs and IMF-ENV dashboard. - Modeling uncertainties and policy simulation options. - Recent model applications and ongoing developments. - Annexes include algebraic derivations of CES functions, production equations (default, energy, agriculture), main elasticity values, and model dimensions (as indicated in the table of contents). *Source: wpiea2025077-print-pdf (IMF-ENV model documentation).* ### Box 1: Generic CES production function. ### Box 1: Generic CES production function ### CES primal and optimization problem - Objective (aggregated production-cost minimization): - min Σ_i P_i V_i - Constraint (CES primal function): - X = A [ Σ_i a_i (λ_i V_i)^ρ ]^{1/ρ} - Definitions: - P_i is the price of input i. - V_i is the input quantity purchased for a given level of production X. - A is an aggregate technological parameter that shifts the overall production function. - a_i are the primal share coefficients. - λ_i are input-specific shifters used to implement input-specific productivity increases (e.g., biased technological change or labor productivity changes). - ρ is linked to the curvature of the CES function and is defined by the elasticity of substitution σ, such that: - ρ = (σ − 1) / σ ### Optimal input demand and composite price - Optimal demand functions (for given input prices P_i and production level X_a): - V_i = α_i^σ (A λ_i)^{σ−1} (P / P_i)^σ X_a - α_i are the dual share parameters typically fixed and calibrated to base year data. - Composite price of all inputs (P): - P = (1/A) [ Σ_i α_i (P_i λ_i)^{1−σ} ]^{1/(1−σ)} - Model feature: - Demand for intermediate inputs and production factors is mainly determined by changes in relative prices (P/P_i), conditional on the elasticity of substitution (σ). ### CES special cases - σ = 0 → Leontief (fixed proportions). - σ = 1 → Cobb-Douglas. ### Production factors in IMF-ENV - IMF-ENV incorporates four types of production factors: - capital - labor - land - natural resources - Capital vintages: - Two capital types via a vintage capital modeling approach: Old and New capital. - Old capital: cumulative sum of net capital allocated to the sector by the end of the previous year (accounts for depreciation). - New capital: determined by regional investments and allocated across sectors so as to equalize rates of returns. - Putty-clay specification: sectoral production is divided into old and new vintages; substitution elasticities among factors are lower with old capital relative to new capital (old capital is sticky), imposing adjustment costs that reflect frictions reallocating capital away from a sector once investment has been made. - Labor: - One type of labor input that can move freely across production activities within a region. - Note: upcoming developments will allow differentiation between skilled and unskilled labor types leveraging GTAP data (five distinct labor occupation categories) and potential geographic differentiation (rural vs. urban) if country-specific data are available. - Land: - Single type of land input necessary for production of agricultural activities only. - IMF-ENV could be extended to include different land use types using GTAP’s satellite data on Land Use and Land Cover to represent land endowment by 18 agro-ecological zones (AEZs) per region/country. - Natural resources: - Factor input in fossil and mineral extractive sectors, fisheries and forestry sectors; captures natural capital like fossil-fuel and mineral reserves, forests and fisheries necessary for production in these sectors. ### Notation used in production trees (Box 2) - Model dimensions: - r regions (or individual countries) - a economic activities (sectors) - i commodities - v capital vintages - Node color coding in production trees: - Maroon nodes: total sectoral output summed across capital vintages. - Dark blue nodes: CES functions; substitution elasticity at each node shown by σ parameters; some CES nodes have more than two branches (e.g., ND1 or XGHG). - Light blue nodes: Armington demand for intermediate inputs or demand for primary production factors (land, labor, capital, natural resources). - Green nodes: zero-emission production activities (renewable power generation sources in IMF-ENV). - Gray nodes: sources of GHG emissions at different production levels; single-GHG labels specify the GHG, otherwise the label GHG indicates multiple emitted GHGs. ### Default nested production structure (non-agricultural) - Top-level aggregation: - Gross output of sector a (XP) = sum of gross output by capital vintage (XPV). - Nesting sequence (Figure 1 description): - XP = aggregation over XPV (σ_xpv) - XPX (gross output by vintage excluding GHGs) combined with XGHG (process-related GHG emissions) via CES (σ_emi) - XPX = CES between intermediate goods bundle (ND1: domestically produced vs. imports) and domestic value-added (VA) (σ_p) - VA = CES between labor (LAB1) and capital, energy, and natural resource bundle (VA1) (σ_v) - VA1 = CES between energy demand (XNRG) and capital & natural resource bundle (KF) (σ_n1 / σ_kef / σ_kf) - Model capabilities: - Different substitution possibilities (σ parameters) at each node, differentiable across regions; specific elasticity values provided in Tables 2 and 3 in the source. - Technological shifters (A and λ parameters) are exogenous; can be changed to reflect structural change or explicit policies (e.g., renewable generation becoming cheaper, labor productivity increases). - Initial production levels calibrated using input-output information from the GTAP database to reflect cost structure and factor intensities; full calibration is explained in Section 3.2. - Annex B contains specific equations for each production node and specifies price wedges (taxes including carbon taxes, transport margins, international trade costs). ### Production structure for crops and livestock (modifications) - Two main distinctions from default function: - Inclusion of land as a factor of production. - Fertilizer inputs removed from ND1 and coupled with land demand in a new node VA2. - Implications: - Production functions permit differentiation between land use intensification (increase output by increasing fertilizer or feed inputs) and extensification (increase land input). - Provides richer responses of agricultural sectors to policy shocks. - Crops (Figure 2): - VA2 represents land (extensive use) and fertilizers (intensive use). - Demand for fertilizers can be domestically or internationally sourced. - GHG emissions of CH4 and N2O are linked with land input and cover direct soil emissions and emissions from application of fertilizers. - Rest of production structure follows default specification. - Livestock (Figure 3): - VA2 uses feed (instead of fertilizers) for intensification. - GHG emissions of CH4 and N2O are linked with land input covering direct soil emissions and manure management. - Capital (the livestock itself) generates GHG emissions, chiefly CH4 from livestock. ### Energy bundle (XNRG) structure - Energy bundle is a nested CES composite of: - Electricity commodity bundle (ELY) - Non-electricity energy commodity bundle (NELY) (σ_e / σ_nely) - Non-electricity bundle details: - Oil & Gas bundle (OLG) nests natural gas with oil (σ_olg) - Coal (COA) is nested with the oil-gas composition - Coal and oil are assumed easily traded internationally; natural gas is less tradable (requires pipelines or LNG facilities) - Total supply of energy commodities determined using the Armington specification - Electricity (ELY) supply: - Produced by eight electricity generation sectors in conjunction with the transmission and distribution sector (see Section 2.2.2 for detailed electricity supply determination) - Emissions: - Gray nodes indicate GHG emissions directly generated by burning fossil fuels. *Source: wpiea2025077-print-pdf - Box 1: Generic CES production function* ### 2.2 Domestic commodity supply ### 2.2 Domestic commodity supply ### General mapping of activities to commodities - Domestic production activities (a) are transformed into commodities (i) via the commodity transformation matrix (mapi), which specifies which activities produce which commodities. - IMF-ENV default: each economic activity produces a single commodity (mapi diagonal for all a values except electricity activities). - Exceptions and flexibility: - One activity can produce many commodities (e.g., an agricultural activity producing both crops and bio-fuels). - Many activities can produce a single commodity (e.g., electricity generated using different power sources). - IMF-ENV can capture one-to-one, one-to-many, and many-to-one mappings as defined by mapi. - Electricity generation is a many-to-one mapping: eight electricity generation technologies are distinguished (coal, gas, oil (diesel), nuclear, hydro, solar, wind and others (including geothermal, bio-fuels, tidal and waste technologies)) and all power generation activities produce a single electricity commodity. ### Non-electricity goods and services — transformation and supply functions - Transformation from activity a to commodity i uses a constant elasticity of transformation (CET) supply allocation (Equation (1)): - Variables and parameters: - XPr,a : aggregate gross output of activity a in region r. - Xr,a,i : allocation of output in region r from activity a to commodity i. - Pr,a,i : price of commodity i produced by activity a. - PXr,a : producer price before taxes for activity a. - γp r,a,i : CET share parameter in transformation matrix. For all non-electricity commodities γp r,a,i = 1. - λs r,a,i : efficiency parameter (default value is one; can simulate e.g., post-harvest losses). - ωs r,a : transformation elasticity; default ωs r,a = 0 (one-to-one matching Xr,a,i = XPr,a). Special cases: - ωs r,a = ∞ implies perfect transformation (law-of-one-price). - Equation (2) determines total gross output of activity a (XP r,a) needed to produce Xr,a,i and becomes an equilibrium condition when each activity produces a single commodity. - Supply of commodity i aggregates outputs of one or more activities using a CES aggregation (Equations (3)–(5)): - Variables and parameters: - XS ri : total supply of commodity i in region r. - PS ri : market price of commodity i in region r. - PPr,a,i : producer price including output taxes for activity a producing commodity i (Equation (5): PPr,a,i = (1 + ptax r,a,i) Pr,a,i). - αs r,a,i : CES share parameter; for all non-electricity commodities αs r,a,i = 1. - σs ri : substitution elasticity for activities producing commodity i; default σs ri = 0 (all activities produce a single commodity), with possibility σs ri = ∞ for perfect substitution (law-of-one-price). ### Domestic supply of electricity — nested CES representation - Electricity supply in region r: a representative electricity provider chooses an optimal generation mix across technologies using a nested CES structure (Figure 5 described in text). - Top nest (Equations (6)–(8)): - Aggregation between electricity transmission & distribution services (Xetd ely) and the power bundle (Xpow ely) to produce the electricity commodity (ely). - αetd r,ely : CES share parameter for T&D services. - σel r,ely : elasticity of substitution between T&D and power bundle. Default specification assumes Leontief technology: σel r,ely = 0 (T&D is a necessary input and scales proportionally). - PPetd r,ely and PPpow r,ely : producer prices (including output taxes) for T&D and power bundle, respectively. - Equations: - Xetd r,ely = αetd r,ely (PS r,ely / PPetd r,ely)^(σel r,ely) XS r,ely (Equation (6)) - Xpow r,ely = αpow r,ely (PS r,ely / PPpow r,ely)^(σel r,ely) XS r,ely (Equation (7)) - PS r,ely = [ αetd r,ely (PPetd r,ely)^(1−σel r,ely) + αpow r,ely (PPpow r,ely)^(1−σel r,ely) ]^(1/(1−σel r,ely)) (Equation (8)) - Power-bundle nest (Equations (9)–(10)): - Power is decomposed into four default power bundles (pb): - Fossil fuel power bundle (FOSP): coal, gas and oil (diesel) generation. - Nuclear (NUCP). - Hydro (HYDP). - Other (OTHP): solar, wind, and remaining sources (bio-fuels, geothermal, waste, tidal). - αpb pb : CES share parameters for power bundles. - λpow pb : power-specific efficiency parameter (user-adjustable; can be used to adjust electricity mix). - σpow : elasticity of substitution between power bundles. - Equations: - XPB pb = αpb pb (λpow pb)^(-σpow) (PPpow / PPB pb)^(σpow) Xpow (Equation (9)) - PPpow = [ Σ_pb αpb pb (λpow pb PPB pb)^(1−σpow) ]^(1/(1−σpow)) (Equation (10)) - Technology/activity nests (Equations (11)–(12)): - Each power bundle pb is decomposed into component power activities (elya) mapped to it; eight electricity generation technologies indexed by elya. - αs elya : CES share parameters for power activities within bundle pb. - λpb elya : activity-specific efficiency parameter. - σpb : elasticity of substitution within the power bundle. - Equations: - Xelya = αs elya (PPB pb / (λpb elya PP elya))^(σpb) XPB pb if elya ∈ pb (Equation (11)) - PPB pb = [ Σ_elya∈pb αs elya (λpb elya PP elya)^(1−σpb) ]^(1/(1−σpb)) (Equation (12)) - Modeling features and policy levers: - Output taxes and subsidies can be included in any producer price within nests to model feebates and other mitigation policies (further explained in Section 6.1.2). - λ parameters provide technology levers for adjusting mixes and representing efficiency or integration constraints. - Modeling limitations noted in the text: - Aggregation into a single electricity commodity means end-users cannot identify generation technology (reflects consumers usually cannot choose source). - The assumption can be relaxed by expanding ely to include more than one electricity commodity, requiring alterations to the production structure. - IMF-ENV’s electricity representation misses several technical and legal country-specific aspects important for policy assessment, e.g., potential for renewable deployment, political decisions on nuclear/hydro, legal and technical hurdles to electricity trade, grid-integration technical issues, renewable intermittency. ### Parameters, defaults, and special cases (selected) - Electricity technologies distinguished: 8 (coal, gas, oil (diesel), nuclear, hydro, solar, wind, others (including geothermal, bio-fuels, tidal and waste)). - Default CET transformation elasticity: ωs r,a = 0 (one-to-one activity → commodity). - Special CET case: ωs r,a = ∞ implies perfect transformation (law-of-one-price). - Default CES substitution for non-electricity commodities: σs ri = 0 (all activities produce a single commodity); electricity generation exceptions exist. - Default top-nest electricity substitution between T&D and power bundle: σel r,ely = 0 (Leontief). - Power bundles in default classification: 4 (FOSP, NUCP, HYDP, OTHP). - Efficiency parameters available as λs and λpow pb for calibrating technology-specific effects and policy levers. ### Cross-reference to subsequent modeling of factors (transition) - The chapter continues into factor supply (Section 2.3), where labor, capital, land, natural resources, and factor taxes are specified (Equations (13)–(21)). Notable numerical defaults and formulations in the subsequent section include: - Working age population definition: 15 to 64 years old. - Labor participation elasticity range for the real wage-labor supply curve: ηwl r standard values range from 0.05 to 0.2. - Aggregate land supply specifications: logistic (Equations (15)–(17)) and iso-elastic (Equations (18)–(19)). - Natural resource supply elasticities (standard values): fisheries 0.25, forestry 0.5, coal extraction 0.9, natural gas extraction 1.0. - Producers’ purchase price of factors: PFp r,f,a = (1 + τf r,f,a) PF r,f,a (Equation (20)). - Price of capital across vintages: PKp r,a,v = (1 + τf r,cap,a) PK r,a,v (Equation (21)). *Source: wpiea2025077-print-pdf — 2.2 Domestic commodity supply.* ### 2.4 Final demand ### wpiea2025077-print-pdf - 2.4 Final demand ### Overview of final demand types - IMF-ENV has three types of final demand: private consumption (by households), public expenditure (government) and investment. - Household consumption demand is implemented as an Extended Linear Expenditure System (ELES). - Investment is savings driven and equal to domestic saving adjusted by net international capital flows and changes in the government balance; alternatively, investment can be targeted (e.g., as a share of GDP) and μs endogenized to match targeted investment. ### Household consumption: ELES specification and properties - Representative, price-taking household in each region optimally allocates disposable income (Y) among consumption commodities (Ck) and savings (S). - Non-homothetic private demand functions are used. - ELES integrates savings with demand (Lluch, 1973; Howe, 1975) and assumes year-by-year maximization (not fully inter-temporal). Consumers save a constant proportion of income; forward-looking behavior is absent. - Formal utility maximization: - Max U = Σk μk ln(Ck − θk) + μs ln(S/Ps) - subject to: YHd = Σk Pck Ck + S - and Σk μk + μs = 1 - Definitions and parameters (as presented): - C is a vector of k consumer goods. - Pck is the vector of consumer prices (market prices plus any consumer excise or ad valorem tax and subsidies). - μk are marginal propensities to consume; μs is marginal propensity to save. - θk is subsistence consumption level for commodity k. - S represents value of saving; Ps set equal to average price of consumer goods. - YHd represents household disposable income (net-of-taxes) and is completely allocated between consumption and savings. - Note: "Since the model is dynamic, the absence of forward-looking households makes it necessary to exogenously specify a savings rate of households." ### ELES solution for consumption and savings (exact equations preserved) - Household private consumption (equation 23): - Ck = Pop θk + μk / Pck Y∗ , where Y∗ = Yd − Pop Σk Pck θk - Savings (equation 24): - S = Yd − Σk Pck Ck - Variable definitions in equations: - Pop represents population. - Y∗ is supernumerary income (income above subsistence level). - Households derive income by supplying factors of production; Yd is net-of-taxes income including direct transfers. ### Commodity mapping and consumer structure - A transition matrix converts household commodities into produced commodities. - In the core IMF-ENV the set of consumer goods k is smaller than the set of produced commodities i (see Table 7 in the Annex). - Advantages: more accurate picture of consumer demand (raw agricultural and manufacturing commodities often used as intermediate inputs), easier linkage of demand with consumer taxes, and easier integration with household surveys for distributional and poverty impacts. - Consumer goods are initially separated between energy and non-energy bundles. - Energy bundle follows structure in Figure 4 but with different elasticities (final consumption vs intermediate consumption). - Figure 6 (consumer demand structure) key elements (terms preserved): - Disposable income (YD) - Private savings (Sh) - Demand for consumer goods (XCk) - Demand for aggregate non-energy bundle (XCnnrgk) - Household demand for non-energy Armington goods (XAi,h) - Energy demand bundle (XNRG) - ELES, νc, νnnrg referenced in the diagram. ### Government and investment final demand - Government and investment sectors consume a bundle of final goods using a CES specification (simplified household demand: excludes savings and the subsistence bundle). - Total demand for a good equals sum of: - consumer demand, - intermediate demands from firms, - government consumption, - investment expenditures. ### Key modeling notes and options (methodological) - Alternative consumer preference systems can be used instead of ELES (LES, CDE, AIDADS) as noted in the source. - Investment closure: standard saving/investment rule (investment driven by savings) with option to target investment share and endogenize μs. - The model separates the national sourcing of consumer goods at the aggregate level using a transition matrix; option exists to source at agent level (requires GTAP MRIO specification and database). *Source: IMF working paper content unit "2.4 Final demand" from wpiea2025077-print-pdf* ### 6. Export taxes (etx). The export tax rateτ ### 6. Export taxes (etx). The export tax rateτ ### Export taxes (etx) - Export tax revenue in region r is applied to the producer price of exports (PE) times trade volumes (XW): - YGOV_r,etx = Σ_d Σ_i τ_e_r,i,d PE_r,i,d XW_s_r,i,d (equation 55) - Note on trade volume representation: - The iceberg trade cost parameter generates a wedge between import and export volumes. - Import volume is given by XW_d and export volume by XW_s; at equilibrium XW_d = λ_w / λ_x XW_s and the model substitutes out XW_d so the implementation carries XW (pre-border export supply). ### Carbon taxes (ctx) and revenue recycling options - Carbon tax revenue in region r is applied to emissions (Emi) by GHG (em), emission source (β) and economic agents (aa): - YGOV_r,ctx = Σ_em Σ_β Σ_aa τ_emi_r,em,β,aa Emi_r,em,β,aa (equation 56) - Emissions accounting details referenced: Section 2.9; alternatives to fiscal closure and targeted recycling: Section 2.6.3. - Revenue recycling options (IMF-ENV provides a menu of four main options): - Direct household transfers: - TRG_r is endogenized to reduce YGOV_dtx by the same amount as the increase in YGOV_ctx. - With a single representative household, equivalent to budget-neutral reduction in direct income tax rates. - Reduce taxes on wages (or capital income): - Factor tax rate κ_f for labor (or capital) is endogenized to match the revenue change (e.g., reduction in YGOV_vtx equals increase in YGOV_ctx). - For fossil fuel removals, the factor tax revenue decrease can be endogenized to match the increase in production and/or consumption tax revenue (YGOV_ptx and/or YGOV_itx). - Increase government expenditures: - All carbon tax revenues allocated to expand government spending on goods and services (budget-neutral). - Increase government savings: - Not budget-neutral; additional carbon tax revenue (or savings from fossil fuel subsidy removals) is used entirely to increase government savings (S_g). - Equivalent to a reduction in the government budget deficit and implies total savings increase and total investment increases proportionally. - Combination option: - The model allows combinations, e.g., 50% of carbon tax revenue to household transfers and 50% to reduce labor taxes. - Practical note: - Predominant recycling rule used in recent IMF-ENV work is to increase direct household transfers. ### Direct (income) taxes (dtx) and the standard fiscal closure - Direct taxes are imposed on: - Household factor incomes (using factor income tax rate κ_f applied on PF * XF). - Total household income after factor taxes (using net direct tax rate κ_h applied to YH). - Direct transfers to households (TRG_r) are deducted from these income tax revenues. - Direct tax revenue expression: - YGOV_r,dtx = (Σ_f Σ_a κ_f_r,f,a PF_r,f,a XF_r,f,a) + κ_h_r YH_r − TRG_r (equation 57) - Standard closure rule: - Government balance (for a given deficit level) is calibrated using net direct tax rate κ_h which is endogenously determined; all other tax rates fixed. - All tax rates can be determined at detailed levels: by region, activity/commodity, production factor, bilateral trade partner. - Allows simulation of very specific fiscal policies (e.g., differentiated carbon taxes by region, GHG, emission source, activity, and agent). - Production and consumption subsidies can be simulated as reductions in τ_p and τ_s or as negative values (pure subsidies). ### Investment and savings balance - Gross investment financed by sum of savings and depreciation allowance: - YFD_r,inv = S_h_r + S_g_r + PW_sav S_f_r + DeprY_r (equation 58) - YFD denotes final demand expenditures for agents (h, gov, inv). - PW_sav is the global price index for foreign savings. - Depreciation allowance: - DeprY_r = δ_f_r PFD_r,inv K_s_r (equation 59) - δ_f may differ from physical depreciation δ, but usually identical. - PFD_inv is unit cost of investment; K_s is non-normalized aggregate capital stock. - Foreign savings and global balancing: - Foreign savings S_f represent net capital inflow; global cancellation: Σ_r PW_sav S_f_r = 0 (equation 60) - Default closure implication: - Investment is savings-driven; equation (58) determines nominal investment. - Equation defined for all regions except one residual region (r_res) to maintain Walras’ Law. - Notes on interpretation: - If an alternate closure fixes investment, equation (58) could determine household or public savings instead. - Future development aims to provide richer interaction between savings and investment (see Section 8.6). ### Macroeconomic balances and closure rules (default) - All commodity and factor markets and income flows must balance each period. - Default closure rules in IMF-ENV: 1. Government budget balance follows exogenous projections: - Default: government expenditures fixed to baseline values (levels or share of GDP). - Tax revenues adjust so budget balance is fixed; all tax rates fixed except direct tax rate κ_h which is endogenously determined. - Standard approach uses budget balance projections from the most recent IMF World Economic Outlook (WEO); beyond WEO years, balance as a share of GDP remains the same as last available year. 2. Current account balance (CAB) kept fixed to baseline values (levels or share of GDP): - Real exchange rate adjusts to ensure CAB closure. 3. Domestic investment determined by total savings each year: - Total investments = household savings (from ELES demand system) + government savings (fixed exogenously) + foreign savings (from CAB closure). - Flexibility: - Closure rules can be changed: direct tax rate can be swapped with another tax, government expenditures or savings can adjust, revenues from carbon pricing/fossil fuel subsidy phaseouts can be recycled via multiple mechanisms (reduce other taxes, increase subsidies, increase transfers, increase government savings). - Planned extensions include endogenizing the CAB (Section 8.5) and modifying investment-saving closure (Section 8.6). - Modeling caveat: - Households are not forward-looking (no intertemporal optimization); this is less critical for policies with high uncertainty or gradual implementation. - Preferred approach if needed: use optimal investment path from a forward-looking model to adjust savings in IMF-ENV. ### Model dynamics - Recursive-dynamic structure driven by: - Total labor supply (LS) growth determined by equation 13; driven by working-age population shifts and endogenous participation via real wage-labor supply curve when active. - Aggregate capital evolution (stock/flow): - K_t = K_{t−1} (1−δ) + I_{t−1} (equation 61) - Technological change assumptions: - Standard version assumes labor-augmenting technological change calibrated to baseline GDP growth and inter-sectoral productivity differences. - Standard assumption: 1 percent annual improvement in energy efficiency across all regions and sectors. - In policy simulations, technology parameters typically fixed at calibrated or assumed baseline levels. ### Emissions accounting (Section 2.9) - GHG composition and data: - GHGs: CO2 and non-CO2 gases. Non-CO2 emissions roughly a quarter of total global GHG emissions. - Input data from GTAP emissions database: carbon in millions of metric tons of CO2; other GHGs available in physical units (metric tons) and in CO2-equivalent. - Standard GTAP database includes CO2 and three non-CO2 GHGs: methane (CH4), nitrous oxide (N2O) and fluorinated gases (F-gases). - GWP converters: IPCC AR6 estimates 100-year GWP of CH4 (fossil and non-fossil) and N2O to be about 29.8, 27 and 273 respectively. - Drivers and categories of emissions: - CO2 (fossil): burning fossil fuels and fugitive emissions. - CO2 (non-fossil): industrial process emissions and LULUCF. - CH4: rice cultivation, livestock, fugitive methane from coal, crude oil extraction, natural gas, services (landfills, sewage). - N2O: crops (fertilizers), livestock (manure), chemicals (non-combustion industrial processes), services (landfills). - Fluorinated gases: chemicals industry, aluminum, magnesium, semiconductor production. - Emissions modeling and decoupling: - Emissions become relatively decoupled from economic activity over time due to autonomous energy efficiency parameter (aeei). - For non-CO2 calibration: sectors with non-CO2 emissions have emission prices set to a small value based on a chosen carbon price; sectors without non-CO2 emissions have emission rate maintained at zero. - Emission aggregation formulas: - Emi_{r,em,β,a} = χ_Emi_em ρ_Emi_{r,em,β,aa} B_{r,β,a} (equation 62) - Set a includes all activities plus final demand by households, government and investment. - B is the matrix of emission sources linking sources to GHGs and economic activities (see Table 8 in Annex). - Emission sources: direct consumption (coalcomb, oilcomb, roilcomb, gascomb), factor-based (land, capital), industrial processes/fugitive (chemUse, act, fugitive, wasteld). - EmiTot_{r,em} = Σ_i Σ_aa Emi_{r,em,β,aa} + EmiOth_{r,em} (equation 63) - EmiOth includes LULUCF emissions which can be modeled via marginal abatement cost curves when mitigation policies active or follow exogenous pathways. - EmiGbl_em = Σ_r EmiTot_{r,em} (equation 64) *Source: IMF-ENV documentation (extracted text from content unit).* ### 3.1 Data sources and model dimensions ### 3.1 Data sources and model dimensions ### Data sources and core database - Primary input database: GTAP Power database, currently using version 11 with 2017 as the base year. - GTAP Power coverage and granularity: - Country-specific input-output tables for 143 countries, 18 regions, 65 commodities, and 76 economic activities. - Differentiation between four fossil fuel sectors, 12 electricity generation technologies, and an electricity transmission and distribution activity. - Electricity activities separated into coal, gas (base and peak load), oil (base and peak load), nuclear, hydro, wind, solar, other power technologies, and electricity transmission and distribution. - Global trade flows represented for 2017. - Greenhouse gases included: carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), and fluorinated gases – hydrofluorocarbons (HFCs), Perfluorocarbons (PFCs) and Sulphur hexafluoride (SF6). - Regional and sectoral aggregations: - Commonly used IMF-ENV calibration: all G20 countries plus 5 regional groups = total of 25 regions. - For the G20 version: differentiates between 36 economic activities and 28 commodities. - Model aggregation is flexible; recent aggregations created for Sub-Saharan African countries and Middle Eastern and Central Asian countries. - Software environment: IMF-ENV is coded and solved in GAMS (General Algebraic Modeling System), enabling set-based indices and high-dimensional non-linear optimization. ### Baseline emission and coefficients - Regional and fuel-based GHG emission coefficients are based on base year data from the GTAP Power database. - Electricity sector data sources referenced for baseline and projections include IRENA and other energy models (PRIMES, POLES, NGFS, EPM) or authorities’ projections. --- ### Calibration #### Overview - Two-step calibration process: - Static calibration: adjust model to match base year data from the GTAP Power database. - Dynamic calibration: create baseline scenario and project model dynamics to 2040 (model currently calibrated until 2040). #### Static calibration - Primary elasticities and technological parameters defined using empirical studies and data sources; key elasticities documented in Tables 2 and 3 in the Annex. - GTAP provides income elasticities of household demand and Armington trade elasticities. - Main calibrated parameters: share parameters of CES functions (α’s). Scale parameters (λ’s) are usually not calibrated and are used for policy experiments. - Calibration procedure for a generic CES function is explained in Section A.2 in the Annex. #### Dynamic calibration (baseline drivers and targets) - Baseline dynamics determined by macroeconomic and sectoral drivers; calibration aligns model progression between 2017 and 2040. - Historical data and projections sources: - Medium-term macroeconomic projections (real GDP, current account balance, government budget balance, investment shares) from IMF’s World Economic Outlook (WEO). - Long-term projections use SSPs, specifically the SSP-2 scenario, calibrated until 2040. - Historical energy and emissions: IMF Climate Indicators database (IMF, 2022). - Electricity sector: IRENA. - Medium- and long-term energy projections from several sources (PRIMES, POLES, NGFS, EPM, authorities’ projections). - Key drivers and how they are modeled in the baseline: - Real GDP projections: - External GDP growth rate and population projections target growth rates of real GDP per capita by endogenizing economy-wide labor productivity. - In policy simulations, real GDP is endogenous and overall labor productivity is kept fixed to the calibrated levels. - Labor supply: - Projections on working age population growth consistent with the SSP2 scenario. - Baseline: labor supply growth is exogenously determined using the growth rate of the working age population. - Policy scenarios: labor supply is endogenously determined by the real wage-labor supply curve. - Government budget balance: - External projections target government balance as a share of real GDP by endogenizing the direct tax rate. - Policy scenarios: budget balance assumed to remain fixed at baseline levels unless policy shock changes government savings; direct tax rate endogenized for each country. - Current account balance (CAB): - Projections exogenously determine CAB as a share of GDP in the baseline by changing inflow of foreign savings and ensuring global net savings are zero. - Policy scenarios: CAB remains fixed as a share of GDP; residual region’s foreign savings adjusts to balance global savings. - Electricity generation by technologies: - Baseline: Leontief specification targets generation shares of each electricity technology. - Policy simulations can use: - CES production function for electricity aggregation (allowing endogenous adjustments), or - Exogenous projections from bottom-up energy models incorporated by adjusting exogenous share parameters under Leontief specification. - Electricity prices and electricity demand are endogenously determined in both CES and Leontief specifications. - Each electricity technology has its own cost structure and production price, affecting regional electricity commodity prices via supply mixes. - GHG emissions: - Baseline: external projections on overall emissions targeted by calibrating emission-intensity parameters differentiated by region and GHG type. - External emission projections from national sources or NGFS scenarios (NGFS, 2024). - LULUCF emissions are fixed to base year levels in absence of projections. - Policy simulations: all GHG emissions endogenously determined unless policy instrument targets a certain reduction (e.g., emissions trading scheme). - Energy efficiency: - Assumed 1% annual growth rate in energy efficiency across all fuel types used in intermediate and final consumption. - Economic structure: - When recent IO tables are available, production values by activity can be targeted by endogenizing sector-specific TFP values in the baseline; sectoral TFP values are kept fixed in policy scenarios. - Trade patterns: - Bilateral trade patterns can be updated using UN COMTRADE. - For small sectoral trade adjustments, iceberg trade costs can be endogenized to target desired baseline trade values. #### Optional calibrated drivers (when data available) - Consumer preference convergence in developing countries toward OECD averages. - Autonomous efficiency gains for capital, land and specific natural resources. - Autonomous efficiency gains of fertilizers in crops sectors and of the food bundle in livestock rearing. - Supply of land and natural resources (except for fossil fuels sectors). - Aggregate average and sectoral labor productivity growth via calibration of technical progress coefficients embodied in labor. - Energy demands for all fuels except crude oil determined by calibrating Autonomous Energy Efficiency Improvements (AEEIs) in energy use, by sector and fuel type. - International prices of fossil fuels determined by calibrating potential supply of fossil fuel resources. - Investment to GDP ratios determined by calibration of the household marginal propensity to save. --- ### Model outputs and visualizations - Output files for each simulation include numerous variables for all regions and sectors. - Standardized visuals and dashboard: - IMF-ENV dashboard (R-shiny app) available to IMF staff; repository for model results with interactive visualization. - Six standardized chart panels can be generated by country: - Baseline drivers panel: projections on overall GHG emissions, real GDP, labor supply, value-added by sector, government finances, current account balance. - Emissions panel: changes to GHG emissions by source, gas and other emission-related results. - Energy and prices panel: changes in electricity generation, energy use, energy-related indicators, producer and consumer price changes. - Real Sector panel: impacts on real GDP, demand components (consumption, investment, net exports), supply components (changes in value-added by broad activity groups), sectoral employment, value-added and gross investments. - External sector panel: changes in sectoral exports/imports, international commodity prices, market shares, terms of trade, real effective exchange rate. - Fiscal sector panel: impacts on government finances and revenue sources, including carbon taxes and associated revenue. - Additional outputs provided project-by-project; bilateral support yields highly detailed results. - Dashboard usage (high-level): - Built in R-shiny with reactive programming and interactive filters. - Requires upload of GDX files (GAMS output): at least one baseline file plus policy scenario files. - Tabs for "Summary charts" and "Detailed charts"; charts update after clicking “Update”. - Export features include saving individual charts as PNG, saving data files, and exporting all data/charts or configurations. - Users can save and restore configurations; saved configurations must be used with compatible GDX files. --- ### Sensitivity analysis - Two types of uncertainty evaluated: parametric and structural. - Parametric uncertainty sources: - Behavioral parameters (substitution elasticities between primary factors, energy commodities, trade elasticities). - Autonomous efficiency assumptions for capital, land, natural resources. - Autonomous energy efficiency gains. - Parametrization of costs for new and emerging technologies. - Common sensitivity tests: key elasticity values and energy efficiency assumptions; values compared with existing literature and other CGE applications. - Structural uncertainty sources: - Static vs dynamic approaches. - Regional and sectoral aggregation differences. - Trade specification choices. - Inclusion of non-carbon technology. - Closure rule assumptions. - Policy design sensitivity: - Results sensitive to how policies are designed (e.g., carbon tax revenue recycling). - Example: global GDP costs vary by revenue recycling rule; least GDP cost when revenues fund productive investments, largest cost when recycled as lump sum transfers to households. - Revenue recycling variants referenced include: 2C-PublicInvst, 2C-Lumpsum, 2C-LabTax, and In2C-Mixall with country-specific allocations described. --- ### Policy design and transmission in IMF-ENV - Evaluation scope: comprehensive range of policies within a neo-classical framework. - Transmission mechanism: policy shocks operate primarily through changes in relative prices and substitution possibilities in consumption, production, and trade. - Behavioral response determined by relevant elasticities; example: - A carbon tax raises prices of emission-intensive inputs and final goods relative to low- or no-emission alternatives, with ultimate responses depending on production, consumption, and trade elasticities and substitution possibilities. *Source: IMF working paper section "3.1 Data sources and model dimensions" (IMF-ENV model documentation).* ### 6.1 Climate and energy policies ### 6.1 Climate and energy policies ### Overview - Globally, approximately three-quarters of greenhouse gas (GHG) emissions originate from energy use in industry, transport, and buildings; remaining emissions come from agriculture, forestry, and land-use, as well as process emissions from industry and waste. - IMF-ENV captures major sources of emissions for all major GHGs (i.e., CO2, CH4 and N2O) by economic activity, allowing flexibility to model several mitigation policy instruments. ### 6.1.1 Carbon and fossil fuel pricing - Carbon pricing approaches: - Price-based measures: direct carbon taxation charging producers per ton of CO2−eq emissions from fossil fuel combustion. Carbon content varies among coal, oil and gas, resulting in differing tax costs by fuel type. - Quantity-based measures: emission trading scheme (ETS) that caps total CO2−eq emissions from fossil fuel generation and induces an implicit carbon price. - IMF-ENV can apply carbon pricing by combinations of sectors, regions and GHG gases (examples: carbon tax on CO2−eq emissions on transportation services; methane emissions in agricultural activities; or an overall carbon tax for all GHGs in all economic activities). - Fossil fuel subsidy reforms: - Subsidies to fossil fuel consumption act as a negative carbon tax; removing these subsidies can yield substantial reductions in energy demand and emissions. - Modeling approach: update baseline subsidy rates (noting this can be challenging when subsidy values are not publicly available), then remove subsidies in the policy scenario and assume revenue recycling options (see Section 2.6.3). ### 6.1.2 Power sector - Regulation on clean energy standards: - Modelled as an additional constraint in the production optimization imposing a minimum share φ of non-fossil power generation in total electricity generation: - φ X_pow < F[X_solar + X_wind + X_hydro + X_nuclear + X_other] (65) - Feed-in tariff policy: - Producers of renewable power receive a subsidy per unit so they sell above their unit cost PP. Representative electricity provider price becomes: - PP_a × (1 − subs_a) (66) - Subsidy rate (subs) can differ by generation technology and vary over time. - Feebates (fees and rebates system): - Self-financing: rebates to renewable generation are compensated by fees on fossil generation, revenue neutral for government. - Mechanism: generation emitting more than target emissions per kWh (emi_ely) pays a fee (p̃ > 0); those emitting less receive a rebate (p̃ < 0). Price adjustment enters producer price PP_a with p̃ and is endogenously determined to meet total emission target: - PP_a + p̃ (emi_ely_a X_ely_a − P_a emi_ely_a P_a X_ely_a) (67) - p̃ is year- and country-specific depending on specification. ### 6.1.3 Energy-intensive sectors - Regulations typically impose emission caps or activity reduction paths via a CO2 intensity or total CO2 emissions constraint θ_a for each sector a: - emi_proc_CO2,a + Σ_f x_a(f). c_a(f) = CO2,a < θ_a Σ_v X_a,v (68) - Total CO2 emissions for sector a sum process CO2 emissions (emi_proc_CO2,a) and CO2 from fossil fuel combustion, where c(f) is fixed emission coefficient for fossil fuel f. ### 6.1.4 Green Industrial Policies - Policies incentivize development of targeted activities via output subsidies or investment subsidies: - Output subsidy implemented by altering tax rate in equation 5. - Subsidy on new investments modeled by subsidizing new capital vintages in targeted sectors in equation 21. ### 6.1.5 Energy efficiency regulations - Policies reduce energy use of activities (examples: IC vehicle emission standards, reduced heating energy use for buildings, replacement of gas boilers with heat pumps). - Modeling requires detailed information on energy savings and implementation costs. - Example: increase in share of heat pumps is implemented as a shift in CES share parameters (α values in Box 1) of household demand (shifting from gas to electricity) and a reduction in overall household energy demand. - Associated costs modeled using an investment-loss function (see equation 69). ### 6.1.6 Agriculture, Forestry and LULUCF - Drivers of agricultural GHG emissions include land, capital, fossil fuel use, and fertilizers. - Agricultural emissions drivers are tied to economic activity and respond endogenously in the CGE framework. - Land-use change and forestry emissions are estimated using predefined marginal abatement cost (MAC) curves because IMF-ENV does not model land transformation (current model has only one land type). - Regional MAC curves for LULUCF calibrated using MAGNET estimates. - Using an explicit MAC for LULUCF allows emission reductions for a given carbon price but does not capture full general equilibrium impacts of land-use changes (e.g., economic consequences of reduced agricultural output when reforesting). - Figure 15 in source is an illustrative MAC; IMF-ENV provides explicit MAC only for LULUCF while other activities reduce emissions based on structural and policy assumptions. ### 6.1.7 Emerging green technologies - New technologies can be included when represented in national accounts and input-output tables; delays occur because these tables are not frequently updated. - IMF-ENV can provide broad estimations for emerging technologies when provided with expected emission reductions, energy demand changes, and cost information. - Electrical vehicles (EVs): - Main effect: switch household demand from diesel and gasoline to electricity; modeled as change in CES share parameters (α values in Box 1) for household demand calibrated to EV penetration projections. - Results: increase in electricity demand and proportional reduction in fossil fuel demand. - Associated costs: charging station networks; can be privately or publicly financed and can be modeled via the investment-loss function (equation 69) when cost projections are available. - Carbon capture, utilization and storage (CCUS): - Modeled if year-by-year projections of captured share of economy-wide emissions and associated capex are available. - Estimated emission reductions are deducted from total emissions; costs modeled via investment-loss function where CCUS investment is a yearly share IL_t of total investment and reduces next period capital accumulation: - K_{t+1} = K_t (1 − δ) + (1 − IL_t) I_t (69) - Specification implies CCUS investment reduces GHG emissions but does not expand productive capital stock in the next period. *Source: IMF working paper chapter "6.1 Climate and energy policies" (IMF-ENV model description).* ### 7.5 Climate finance ### 7.5 Climate finance ### Key points - Meaningful climate action in several developing economies would require the flow of climate finance from advanced economies. - The model has been used to develop global (Black et al., 2022) and regional (Cai et al., 2024) scenarios that explore normative rules for pooling climate finance by advanced economies and redistributing it to emerging and developing economies and the resulting macroeconomic impacts. --- ### 7.6 Climate damages ### Findings and modeling approaches - The model’s granularity enables inclusion of various estimates of future climate change damages (climate physical risks). - Economy-wide assessments can use NGFS scenarios (NGFS, 2024) as expected reductions in real GDP (i.e., chronic physical risks). - More detailed damage estimations use climate damage functions linking changes in temperature and precipitation to productivity and other economic losses, including: - labor productivity reductions from worker exposure to extreme heat, - reduced agricultural productivity and lower yields for certain agricultural crops, - increased energy demand for air conditioning, - loss of arable land from rising sea levels, - capital losses from flooding, hurricanes and other extreme weather events. - Damage functions sources: - global reports (Roson and Sartori, 2016), - country- or region-specific studies. - Notes and cross-references: - Work is underway to update NGFS scenarios to the NGFS phase V. - An IMF-ENV application using the methodology is explained in the Technical Note from Japan’s FSAP. - Several World Bank Country Climate and Development Reports (CCDRs) employ detailed country-specific damage functions in their CGE assessments. --- ### 7.7 Growth opportunities from the green transition ### Findings from regional IMF-ENV applications - IMF-ENV sub-Saharan Africa version developed to assess macroeconomic gains of increasing deployment of renewable electricity (Cai et al., 2024). - Financing assumptions considered: - domestic sources, - external sources, - a mix of the two. - Complementary investments modeled: - transmission and distribution grid (T&D), - energy efficiency measures. --- ### 7.8 AI and energy demand ### Findings and applications - Increased electricity demand from drivers including artificial intelligence (AI) is an emerging topic of interest. - IMF-ENV applied to study impacts of increasing electricity demand from expansion in data centers on: - electricity prices, - emissions. - Geographic applications mentioned: U.S., China and Europe. --- ### Table 1: Selected IMF Applications of the IMF-ENV model ### Notable country, regional, and global applications (selection) - Country reports and FSAPs: Canada 2023, Indonesia 2023, Mexico 2023, Saudi Arabia 2023, USA 2023, Germany 2022, Mexico 2022, Japan 2024, Kazakhstan 2024, India 2025. - Country analysis working papers and staff publications include focused studies for the USA, China, Italy, India, Poland, South Africa, France, Australia. - Regional and global studies include G7+, Europe, North America, Sub-Saharan Africa, and Global analyses such as: - Global 2022 SCN: Getting on Track to Net Zero (Black et al., 2022). - Global 2024 WP: Energy Security and the Green Transition (Kim et al., 2025). - Forthcoming items include Commodity Special Feature 2025 WEOP: Power Hungry: How AI will drive Energy Demand; Canada 2025 FSAP; Egypt 2025 SIPA; Global 2025 WP: The ENV-FIBA Model for Climate Risk Analysis: Framework, Model Details, and Guide. --- ### 8 Future model developments ### Overview - IMF-ENV is continually updated to incorporate new policies, technologies and modeling features to improve country support and analytical scope. - Priorities shaped by feedback from bilateral and multilateral work. --- ### 8.1 Endogenous technological change (R&D module) - Purpose: assess impact of changes in R&D expenditures on growth and other macroeconomic and sectoral variables. - Mechanism: - Links R&D expenditures to a stock of knowledge proxied by number of patents that increases labor productivity and/or TFP growth. - Distributed lag structure of R&D impacts modeled using the Gamma distribution function to capture cross-country and cross-sector differences in lag shape. - Data and calibration: - Stock of knowledge proxied by cumulative number of patent applications received between 1980 and 2019. - Leverages INPACT-S project data (LaBelle, 2024). - Regress knowledge stock (patent applications) on R&D expenditure data from the World Bank’s World Development Indicators to calibrate Gamma distribution parameters. - Initial results: increasing the share of R&D expenditure has a positive effect on the stock of knowledge measured by patents with an average lag of around ten years. - Productivity linkage: - Two measures considered: - labor productivity from the World Bank’s Global Productivity Sectoral Database for 109 countries (World Bank, 2024), - TFP using EU-KLEMS data for 30 selected advanced economies (European Commission, 2024). - Planned additions: learning by doing and international technological spillovers based on CGE applications and literature. --- ### 8.2 Labor split between skilled and unskilled workers - Current limitation: IMF-ENV distinguishes a single labor type while GTAP provides information for five labor types based on occupations typically grouped into skilled and unskilled. - Planned extension: - Distinguish skilled and unskilled workers and their relations with capital, following literature on skill-biased technological change (Krusell et al., 2000). - Expected outcomes: - generate changes in economy-wide wages for each labor type, - provide information on functional distribution of income, - facilitate linkage with micro-simulation models using household-level data. - Note: GTAP split into five labor types; literature finding cited: Unskilled labor is found to be a relative substitute and skilled labor a relative complement to capital. --- ### 8.3 Outdoor air pollution and associated co-benefits - Current gap: greenhouse gas emissions included, but air pollutant emissions not yet part of model outputs. - Planned module: - detailed accounting of air pollutant emissions, - use pollutant concentrations to estimate health-related and environmental costs or benefits from changes in air pollution due to policies. --- ### 8.4 Natural resource depletion module - Basis: work applied to the ENVISAGE model (Peszko et al., 2020). - Functionality: - accounts for reserves and country-specific production costs of fossil fuels, - calculates and updates elasticities of the supply function for the fixed natural resource factor for fossil fuel extraction activities: coal, natural gas and oil (see Section 2.3.4). - Data integration: - detailed data on natural resource reserves and production costs, - integrates outputs of extractive models: oil and gas sectors from Rystad UCube, coal mining from Wood Mackenzie. --- ### 8.5 Endogenous current account balance - Current default CAB closure: fixed as a share of GDP or at a nominal value. - Planned additional endogenous CAB closure rules: - GTAP closure: Global investment allocated across regions depending on region-specific differentials on expected rates of return to capital and country-specific risk parameters (Corong et al., 2017). - Wedge closure: international investment flows driven by domestic savings and accumulation of international reserves (Gouirinchas and Jeanne, 2013), creating a “wedge” between historical CAB average values and expected capital flows from regional differences in rates of return to capital. - Reference: See Bekkers et al. (2020) for discussion regarding different CAB closures in CGE models. --- ### 8.6 Savings and investment modeling - Context: IMF-ENV’s recursive-dynamic setup determines aggregate investment each year from available savings (private, public, foreign savings/CAB). - Planned extensions to provide more structure and flexibility: 1. Private savings determinants: - new module adjusting private (household) savings by demographic factors (aging, dependency ratios), country income levels and other determinants selected from literature and CGE best practices. 2. Private savings and expected returns to capital: - option where private savings adjust to reflect changes in expected rates of return to capital driven by policy changes or technological shocks (e.g., artificial intelligence, new green technologies). - mechanism analogous to increases in foreign net savings under alternative CAB closure arising from shifts in expected returns to capital. 3. Compatibility with new CAB closure rules: - run new private savings determinants jointly with endogenous CAB closures to test results. 4. Split total investment between public and private investment: - GTAP provides overall investment only; explore splitting total investment where public and private investment data are available. --- ### 9 Summary ### Core takeaways - The working paper documents the IMF-ENV model designed to examine impacts of policies inducing structural economic changes on the overall economy and specific sectors. - Suitability: - examining medium- and long-term macroeconomic effects, - analyzing structural shifts from national and/or global climate mitigation, energy, fiscal and trade policies. - Structure of documentation: - technical description of core model blocks (production, consumption, trade), - explanation of macroeconomic balance preservation across demand and supply and income/expenditure accounts, - description of underlying data and calibration choices, - compilation of model outputs and IMF-ENV Dashboard utilities, - extensive compilation of simulated policies and applications across energy, climate, and trade policies. - Forward-looking developments target emerging topics: large-scale industrial policies and green technology subsidies, macroeconomic impacts of artificial intelligence (AI), trade disputes and agreements, and global fragmentation. *Source: IMF-ENV model documentation (working paper content provided).* ### 3. OECD Environment Directorate Working Papers 2021-14, Organisation for Economic Co-operation ### 3. OECD Environment Directorate Working Papers 2021-14, Organisation for Economic Co-operation and Development. ### Bibliographic and related citations (selected) - Chateau, J., Feng, A., Shabunina, A., Tolosa, G., and Zhang, Z. S. (2022b). Securing a smoot green transition. Selected Issues Paper 22/256, International Monetary Fund, Washington DC. - Chateau, J., Jaumotte, F., and Schwerhoff, G. (2022c). Climate policy options: A comparison of economic performance. IMF Working Paper WP/22/242, International Monetary Fund, Washington DC. - Chateau, J., Jaumotte, F., and Schwerhoff, G. (2022d). Economic and environmental benefits from international cooperation on climate policies. IMF Departmental Papers DP/2022/007, International Monetary Fund, Washington DC. - Chepeliev, M. (2020). Development of the non-CO2 GHG emissions database for the GTAP 10a database. GTAP Research Memorandum 30, Global Trade Analysis Project (GTAP), Center for Global Trade Analysis, Purdue University. - Chepeliev, M. (2023). GTAP-Power data base: Version 11. Journal of Global Economic Analysis, 8(2). - Corong, E., Hertel, T., McDougall, R., Tsigas, M., and van der Mensbrugghe, D. (2017). The standard GTAP model: Version 7. Journal of Global Economic Analysis, 2(1):1–119. - (Additional citations listed in the source include Dellink et al. (2017), Delzeit et al. (2020), Devarajan and Robinson (2005), Dixon and Jorgenson (2013), and many others.) ### Annex A — Algebraic derivations of CES function - A.1 Optimization problem of a CES production function - Lagrangian set up (notation preserved from source): - L = Σ_i P_i V_i + Λ ( X − A [ Σ_i a_i (λ_i V_i)^ρ ]^{1/ρ} ) - First-order conditions yield: - P_i = Λ a_i λ_i^ρ V_i^{ρ−1} A [ Σ_i a_i (λ_i V_i)^ρ ]^{(1−ρ)/ρ} - X = A [ Σ_i a_i (Λ_i V_i)^ρ ]^{1/ρ} - Aggregation result: - PX = Σ_i P_i V_i = Λ X - Hence Λ = P (aggregate price) - Optimal input demand (Λ replaced by P): - V_i = a_i^{1/(1−ρ)} A^{ρ/(1−ρ)} (P/P_i)^{1/(1−ρ)} λ_i^{ρ/(1−ρ)} X - Final expression (equation 70) using σ (elasticity of substitution) and dual share α_i: - V_i = α_i^σ (A λ_i)^{σ−1} (P/P_i)^σ X (equation 70) - Substitutions used: - σ = 1/(1−ρ) ⇔ ρ = (σ−1)/σ ⇔ ρ/(1−ρ) = σ−1 ⇔ ρ·σ = σ−1 - α_i = a_i^{1/(1−ρ)} = a_i^σ ⇔ a_i = α_i^{1/σ} - A.2 Calibration of the CES production function - Calibration notes: - Prices and volumes (P_i, P, X and V_i) normally initialized from a database or SAM. - Substitution elasticities are inputs (from econometrics, databases, or literature). - Technology parameters (λ_i and A) are normally initialized to unit value. - Remaining parameters to calibrate: α_i (from which primal share parameters s_i can be derived). - Calibration formula (inversion of equation 70): - α_i = (V_i / X) (P_i / P)^σ (A λ_i)^{1−σ} = (V_i / X) (P_i / P)^σ (equation 71) - Practical recommendation: - Explicitly initialize prices to 1 if excluding the price term; otherwise include the price term to avoid calibration bugs. - Test calibration by initializing prices to an arbitrary value and volumes accordingly; a counter-factual with no shocks should replicate the initial data solution (COMPSTAT option in IMF-ENV). ### Annex B — Derivation of production equations - B.1 Default production equations (notations and many indexed equations preserved) - Average unit price over capital vintages of total gross production: - PX_{r,a} = Σ_v PXv_{r,a,v} XPv_{r,a,v} / XP_{r,a} (equation 72) - Marginal unit cost of gross production by capital vintage under perfect competition (top-level production function): - UC_{r,a,v} = 1 / A xpv_{r,a,v} [ α_xp_{r,a,v} (PXP_{r,a,v}/λ_xp_{r,a,v})^{1−σ_xp_{r,a,v}} + α_ghg_{r,a,v} (PXGHG_{r,a,v}/λ_ghg_{r,a,v})^{1−σ_xp_{r,a,v}} ]^{1/(1−σ_xp_{r,a,v})} (equation 73) - Zero profit condition: - UC_{r,a,v} · XP_{r,a,v} = PXP_{r,a,v} · XPX_{r,a,v} + PXGHG_{r,a,v} · XGHG_{r,a} (equation 74) - Post-tax unit cost of production with τ_uc denoting the tax on the cost of production: - PXv_{r,a,v} = UC_{r,a,v} · (1 + τ_uc_{r,a,v}) (equation 75) - Market or output price equals unit cost adjusted by an output tax τ_p (markup π_m optional, default zero): - PP_{r,a} = (PX_{r,a} + π_m_{r,a}) · (1 + τ_p_{r,a}) (equation 76) - Gross production second level bundles: - XPX_{r,a,v} = α_xp_{r,a,v} (A xpv_{r,a,v} λ_xp_{r,a,v})^{σ_xp_{r,a,v}−1} (UC_{r,a,v}/PXP_{r,a,v})^{σ_xp_{r,a,v}} XPv_{r,a,v} (equation 77) - XGHG_{r,a,v} = α_ghg_{r,a,v} (A xpv_{r,a,v} λ_ghg_{r,a,v})^{σ_xp_{r,a,v}−1} (UC_{r,a,v}/PXGHG_{r,a,v})^{σ_xp_{r,a,v}} XPv_{r,a,v} (equation 78) - Price of second level production bundles: - PXP_{r,a,v} = [ α_nd1_{r,a,v} (PND1_{r,a})^{1−σ_p_{r,a,v}} + α_va_{r,a,v} (PVA_{r,a,v})^{1−σ_p_{r,a,v}} ]^{1/(1−σ_p_{r,a,v})} (equation 79) - PXGHG_{r,a,v} = XGHG_{r,a,v} [ α_emi_{r,a,v} (p_emi_PROD_{r,GHG,v} − ctax_pi_{r,GHG,v} λ_emi_{r,GHG,v})^{1/(1−σ_emi_{r,v})} ]^{1/(1−σ_emi_{r,v})} (equation 80) - Aggregate bundle of intermediate consumption (summed over vintages): - ND1_{r,a} = Σ_v α_nd1_{r,a,v} (PXP_{r,a,v}/PND1_{r,a})^{σ_p_{r,a,v}} XPX_{r,a,v} (equation 81) - Price of aggregate intermediate bundle: - PND1_{r,a} = [ Σ_{i∈{ND1}} α_io_{r,i,a} (PA_a_{r,i,a} / λ_io_{r,i,a})^{1−σ_n1_{r,a}} ]^{1/(1−σ_n1_{r,a})} (equation 82) - Intermediate demand (excluding energy inputs) of commodity i in sector a: - XA_{r,i,a} = α_io_{r,i,a} (λ_io_{r,i,a} PND1_{r,a} / PA_a_{r,i,a})^{σ_nd1_{r,a}} ND1_{r,a} λ_io_{r,i,a} if i ∈ {ND1} (equation 83) - Value added bundle and price: - VA_{r,a,v} = α_va_{r,a,v} (PXP_{r,a,v}/PVA_{r,a,v})^{σ_p_{r,a,v}} XPX_{r,a,v} (equation 84) - PVA_{r,a,v} = [ α_l1_{r,a,v} (PLAB1_{r,a})^{1−σ_v_{r,a,v}} + α_va1_{r,a,v} (PVA1_{r,a,v})^{1−σ_v_{r,a,v}} ]^{1/(1−σ_v_{r,a,v})} (equation 85) - Productivity adjusted demand for labor: - LAB1_{r,a} = Σ_v α_l1_{r,a,v} (PVA_{r,a,v} / PLAB1_{r,a})^{σ_v_{r,a,v}} VA_{r,a,v} (equation 86) - Labor demand in number of people: ld1_{r,a} = LAB1_{r,a} × λ_l_{r,a} (equation 87) - KEF and KF bundles: - KEF_{r,a,v} = α_kef_{r,a,v} (PVA1_{r,a,v}/PKEF_{r,a,v})^{σ_v_{r,a,v}} VA1_{r,a,v} (equation 88) - PKEF_{r,a,v} = [ α_kf_{r,a,v} (PKF_{r,a,v})^{1−σ_kef_{r,a,v}} + α_e_{r,a,v} (PNRG_{r,a,v})^{1−σ_kef_{r,a,v}} ]^{1/(1−σ_kef_{r,a,v})} (equation 89) - KF_{r,a,v} = α_kf_{r,a,v} (PKEF_{r,a,v}/PKF_{r,a,v})^{σ_kef_{r,a,v}} KEF_{r,a,v} (equation 90) - PKF_{r,a,v} = [ α_K_{r,a,v} (PK_{r,a,v})^{1−σ_kf_{r,a,v}} + α_nrf_{r,a,v} (PNRF_{r,a} λ_nrf_{r,a,v})^{1−σ_kf_{r,a,v}} ]^{1/(1−σ_kf_{r,a,v})} (equation 91) - XNRG bundle and NRF demand: - XNRG_{r,a,v} = α_e_{r,a,v} (PKEF_{r,a,v}/PNRG_{r,a,v})^{σ_kef_{r,a,v}} KEF_{r,a,v} (equation 92) - PNRG_{r,a,v} = [ α_ely_{r,a,v} (PA_ely_{r,a,v})^{1−σ_e_{r,a,v}} + α_nely_{r,a,v} (PNELY_{r,a,v})^{1−σ_e_{r,a,v}} ]^{1/(1−σ_e_{r,a,v})} (equation 93) - XNRF_d_{r,a} = Σ_v α_nrf_{r,a,v} λ_nrf_{r,a,v} (PKF_{r,a,v}/PNRF_p_{r,a})^{σ_kf_{r,a,v}} KF_{r,a,v} λ_nrf_{r,a,v} (equation 94) - Natural resource supply (iso-elastic) and equilibrium: - If η_nrf_{r,a} ≠ ∞: - XNRF_s_{r,a} = χ_nrf_{r,a} ( χ_nrfp_{r,a} PNRF_{r,a} / PGDPMP_{r} )^{η_nrf_{r,a}} (equation 95) - If η_nrf_{r,a} = ∞: - χ_nrfp_{r,a} PNRF_{r,a} = PGDPMP_{r} (equation 95) - Market clearing: - XNRF_s_{r,a} = XNRF_d_{r,a} (equations 96 and 97) - B.2 Energy Sector Equations - Demand for electric and non-electric bundles (σ_e substitution elasticity): - XA_ely_{r,a,v} = α_ely_{r,a,v} (PNRG_{r,a,v}/PA_ely_{r,a,v})^{σ_e_{r,a,v}} XNRG_{r,a,v} (equation 98) - XNELY_{r,a,v} = α_nely_{r,a,v} (PNRG_{r,a,v}/PNELY_{r,a,v})^{σ_e_{r,a,v}} XNRG_{r,a,v} (equation 99) - PNRG_{r,a,v} = [ α_ely_{r,a,v} (PA_ely_{r,a,v})^{1−σ_e_{r,a,v}} + α_nely_{r,a,v} (PNELY_{r,a,v})^{1−σ_e_{r,a,v}} ]^{1/(1−σ_e_{r,a,v})} (equation 100) - Coal and oil & gas decomposition (σ_nely substitution elasticity): - XA_coa_{r,a,v} = α_coa_{r,a,v} (PNELY_{r,a,v}/PA_coa_{r,a,v})^{σ_nely_{r,a,v}} XNELY_{r,a,v} (equation 101) - XOLG_{r,a,v} = α_olg_{r,a,v} (PNELY_{r,a,v}/POLG_{r,a,v})^{σ_nely_{r,a,v}} XNELY_{r,a,v} (equation 102) - PNELY_{r,a,v} = [ α_coa_{r,a,v} (PA_coa_{r,a,v})^{1−σ_nely_{r,a,v}} + α_olg_{r,a,v} (POLG_{r,a,v})^{1−σ_nely_{r,a,v}} ]^{1/(1−σ_nely_{r,a,v})} (equation 103) - Oil and gas nested (σ_olg substitution elasticity): - XA_oil_{r,a,v} = α_oil_{r,a,v} (POLG_{r,a,v}/PA_oil_{r,a,v})^{σ_olg_{r,a,v}} XOLG_{r,a,v} (equation 104) - XA_gas_{r,a,v} = α_gas_{r,a,v} (POLG_{r,a,v}/PA_gas_{r,a,v})^{σ_olg_{r,a,v}} XOLG_{r,a,v} (equation 105) - POLG_{r,a,v} = [ α_oil_{r,a,v} (PA_oil_{r,a,v})^{1−σ_olg_{r,a,v}} + α_gas_{r,a,v} (PA_gas_{r,a,v})^{1−σ_olg_{r,a,v}} ]^{1/(1−σ_olg_{r,a,v})} (equation 106) - Armington demand for energy commodities (σ_NRG substitution elasticity) and prices: - XA_{r,e,a} = Σ_v α_eio_{r,e,a,v} λ_e_{r,e,a,v} (PA_NRG_{r,a,v}/PA_{a,r,e,a})^{σ_NRG_{r,a,v}} XA_NRG_{r,a,v} λ_e_{r,e,a,v} if e ∈ {NRG} (equation 107) - PA_NRG_{r,a,v} = [ Σ_{e∈{NRG}} α_eio_{r,e,a,v} (PA_{a,r,e,a} / λ_e_{r,e,a,v})^{1−σ_NRG_{r,a,v}} ]^{1/(1−σ_NRG_{r,a,v})} (equation 108) - B.3 Agriculture Sector equations - Value-added nest including land (active only in agriculture activities cro-a and lvs-a): - VA1_{r,a,v} = α_va1_{r,a,v} (PVA_{r,a,v}/PVA1_{r,a,v})^{σ_v_{r,a,v}} VA_{r,a,v} (equation 109) - PVA1_{r,a,v} = [ α_land_{r,a,v} (PLand_p_{r,a} λ_t_{r,a,v})^{1−σ_v1_{r,a,v}} + α_kef_{r,a,v} (PKEF_{r,a,v})^{1−σ_v1_{r,a,v}} ]^{1/(1−σ_v1_{r,a,v})} (equation 110) ### Annex C — Main elasticity values (selected) - Table 2: Key production elasticities (excerpted entries preserved exactly as in source) - σ_xpv: Substitution between process emissions bundle and net-of-emissions gross output - Values and sources: - 0 for air pollutants (source: van der Mensbrugghe (2024)) - For GHGs: - 0.05 for agriculture - Old = 0.05; New = 0.25 for manufacturing *Source: Excerpt from wpiea2025077-print-pdf - 3. OECD Environment Directorate Working Papers 2021-14, Organisation for Economic Co-operation and Development.* ### 0.15 for cement ### wpiea2025077-print-pdf - 0.15 for cement ### Substitution and elasticity parameter values (sector and technology specific) - 0.15 for cement - Old = 0.14; New = 28 for chemicals - Old = 0.15; New = 0.3 for waste - Old = 0.1; New = 0.3 for extraction - σp Substitution between ND10.2 for agriculture Okagawa and Ban (2008) and VA bundle [0.4 , 1.0] for manufacturing and services - σp [0.35 , 0.42] for energy sectors - σp Always 0 for old vintage technologies - σn1 Substitution between intermediate goods and services 0 for agriculture Okagawa and Ban (2008) - σn1 [0.1 , 0.4] for manufacturing & services - σn1 0.2 for energy sectors - σv Substitution between Labor and KTE bundle Old = 0.06; New = 0.5 for agriculture Okagawa and Ban (2008) - σv Old = 0.1; New = 0.8 for manufacturing - σv Old = 0.15; New = [1.2 , 1.3] for services - σv Old = 0.1; New = 0.9 for energy sectors - σkef Substitution between capital and energy bundle 0.1 for agriculture Okagawa and Ban (2008) - σkef [0.1 , 0.4] for manufacturing - σkef [0.4 , 0.5] for services - σkef [0.1 , 0.5] for energy sectors - σkef Always 0 for old vintage technologies - σkf Substitution between capital and natural resource factor New = 0.2 van der Mensbrugghe (2024) - σkf 0 for old vintage technologies - σe Elasticity between electricity and non-electricity energy bundle Old = 0.125; New = 1 van der Mensbrugghe (2024) - σe 0.025 and 0.2 for oil, coal and gas sectors - σnely Elasticity between coal and non-coal bundle Old = 0.0625; New = 0.51 van der Mensbrugghe (2024) - σnely 0.025 and 0.2 for oil, coal and gas sectors - σolg Elasticity between energy inputs in liquids bundle Old = 0.125 ; New = 1 van der Mensbrugghe (2024) - σolg 0.025 and 0.2 for oil, coal and gas sectors - σel Elasticity between power generation and transmission and distribution 0.05 van der Mensbrugghe (2024) - σm Armington elasticity, domestic versus imports [0.9, 5 ] depending on commodity, identical across regions. Aguiar et al. (2022) - σw Armington elasticity, import origins [1.8, 10], generally twice higher than σm Aguiar et al. (2022) - Note: Following the putty or semi-putty technology specification, this table shows that the substitution possibilities among factors, inputs and production bundles are assumed to be higher with new vintage capital than with old vintage capital. Values in brackets denote a range of elasticities varying by specific sectors within the overall manufacturing and services sectors. ### Key sector-specific elasticities (Table 3) - ηnrf Elasticity of Supply of natural resource factor - [1 , 10] for coal depending on region Calibrated with IEA-WEM - [0 , 0.58] for oil depending on region - [0.1 , 1.8] for gas depending on region - 0.25 for fishing, 0.5 for forestry, 2 for mining - ηt Elasticity of Land Supply [0.01, 0.6] depending on the region Woltjer and Kuiper (2014) - ηwl Elasticity of Labor Supply [0.05, 0.2] depending on the region Evers et al. (2008) - ηh Income elasticities by consumption commodity [0.25, 1.25] depending on consumption commodity k and region r Aguiar et al. (2022) - σpow Elasticity of substitution between electricity technologies 5 Chateau et al. (2014) - σpb Elasticity of substitution between power bundles 2 Chateau et al. (2014) ### Model dimensions and concordances (Annex: IMF-ENV G-20 version) - Model aggregation: 25 regions, 36 activities and 28 commodities. - Table 4: Concordance for commodities (i) between IMF-ENV and the GTAP database — commodities 1 to 4 correspond to agriculture, 5 to 8 to mining, 9 to 20 to manufacturing, and 21 to 28 to services. - Examples: - 1 All Crops (cro) maps to Paddy Rice (pdr), Wheat (wht), Cereal grains nec (gro), Vegetables, fruits, nuts (vf), Oil Seeds (osd), Sugar cane, sugar beet (cb), Plant-based fibers (pfb), Crops nec (ocr) - 5 Coal extraction (coa) maps to Coal (coa) - 12 Petroleum and coal products (pc) maps to Petroleum, coal products (pc) - 21 Electricity (ELY) maps to a detailed list including Coal power baseload (CoalBL), Coal-based CCS (colccs), Oil power baseload (OilBL), Oil power peakload (OilP), Gas power baseload (GasBL), Gas power peakload (GasP), Gas-based CCS (gasccs), Nuclear power (NuclearBL), Advanced nuclear (advnuc), Hydro power baseload (HydroBL), Hydro power peakload (HydroP), Wind power (WindBL), Solar power (SolarP), Other baseload includes biofuels, waste, geothermal, and tidal technologies (OtherBL), Electricity transmission and distribution (TnD) - Table 5: Concordance for activities (a) between IMF-ENV and the GTAP database — activities 1 to 4 correspond to agriculture, 5 to 8 to mining, 9 to 20 to manufacturing, and 21 to 36 to services. - Examples: - 1 All Crops (cro) maps to same GTAP crop categories as commodities - 21 Coal powered electricity (clp) maps to Coal power baseload (CoalBL), Coal-based CCS (colccs) - 29 Electricity transmission and distribution (etd) maps to Electricity transmission and distribution (TnD) - 36 Other collective services (osg) maps to Public administration and defense (osg), Education (edu), Human health and social work activities (hht) - Table 6: Regional concordance between IMF-ENV and the GTAP database — 25 regions enumerated with GTAP codes. - Examples: - 1 Argentina (Argentina) Argentina (ARG) - 5 China (CHN) China (CHN) - 19 United States (USA) United States of America (USA) - 20 Rest of EU & EFTA (REU) includes Austria (AUT), Belgium (BEL), Cyprus (CYP), Czech Republic (CZE), Denmark (DNK), Estonia (EST), Finland (FIN), Greece (GRC), Hungary (HUN), Ireland (IRL), Latvia (LVA), Lithuania (LTU), Luxembourg (LUX), Malta (MLT), Netherlands (NLD), Poland (POL), Portugal (PRT), Slovakia (SVK), Slovenia (SVN), Spain (ESP), Sweden (SWE), Switzerland (CHE), Norway (NOR), Rest of EFTA (XEF), Bulgaria (BGR), Croatia (HRV), Romania (ROU) - Regions 21 to 25 defined as grouped country lists (Other Middle East countries (ROP), Other Asian countries & New Zealand (ODA), Other African countries (OAF), Other East European and Eurasian countries (OEA), Other Latin American countries (OLA)) with specific country constituents listed. ### Household consumption concordance (Table 7) - Table 7: Concordance for commodities that are consumed by households (k) between IMF-ENV and the GTAP database - Commodity groups 1–4 map to agriculture; 4 is Energy bundle: Electricity (ELY), Coal (coa), Oil (oil), Gas (gas), Gas manufacture, distribution (gdt) and Petroleum, coal products (pc) - Remaining groups map to manufacturing and services categories used for household consumption aggregation. ### Emission source matrix (Table 8) - Emission sources listed: Land, Capital, coalcomb, coilcomb, roilcomb, gascomb, chemUse, act, fugitive, lulucf, AgrBurn, wastesld - GHGs tracked: CO2, CH4, N2O (present in matrix for multiple sources) - Emission-source to activity mapping: entries marked with 1 indicate emissions association - Agriculture-related activities (cro-a, lvs-a, frs-a, fsh-a) have 1 across multiple emission sources including Land, Capital, coalcomb, coilcomb, roilcomb, gascomb, chemUse, act, fugitive, lulucf, AgrBurn, wastesld as shown. - Fossil fuel extraction activities (coa-a, oil-a, gas-a, omn-a) have 1 across relevant fossil-fuel-related emission sources. - Electricity generation activities (clp-a, olp-a, gsp-a, xel-a, etd-a) show 1 across related emission sources. - Energy-intensive manufacturing (ppp-a, nmm-a, is-a, crp-a, nfm-a, ele-a, fdp-a) show 1 across relevant emission sources. - Other manufacturing and services activities similarly mapped with 1s for the applicable sources (txt-a, mvh-a, fmp-a, oma-a, wtp-a, atp-a, otp-a, osg-a, osc-a, cns-a, wts-a, hhd). - Note: There are no GHG emissions associated with renewable power generation sources sol-a, wnd-a, hyd-a and nuc-a. *Source: wpiea2025077-print-pdf - 0.15 for cement* --- _Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025077-print-pdf.pdf_