## 3.1–5.2 Benefits, Costs, and Climate Finance to Phase Out Coal (wpiea2022107-print-pdf) ## Source details **Canonical URL:** [3.1–5.2 Benefits, Costs, and Climate Finance to Phase Out Coal (wpiea2022107-print-pdf)](https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022107-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2022/english/wpiea2022107-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2022/english/wpiea2022107-print-pdf.pdf.json) --- ### Major quantitative findings and headline results - Baseline global net social gain from beginning a phase-out in 2024 in line with the NGFS Net Zero 2050 scenario (always replacing coal with renewable energy): $85.01 trillion (present value, discounted to 2022, through 2100). - Present value of benefits of phasing out coal (baseline parameters): 114.04 trillion dollars. - Present value of costs of phasing out coal (baseline): 29.03 trillion dollars. - Opportunity costs: 0.05 trillion dollars. - Investment costs in replacement renewables: 28.98 trillion dollars. - Carbon arbitrage expressed relative to world GDP: 1.3 percent of current world GDP every year until 2100 (world GDP in 2020 = 84.705 trillion US Dollars). - Carbon arbitrage per unit: - Per tonne of coal production prevented: $136. - Per tCO2 avoided: $60. - Total coal production prevented (Giga Tonnes): 623.62. - Total emissions prevented (GtCO2): 1425.55. - Prevented further temperature increase (on top of 1.1◦C already observed): 2.14◦C (Matthews et al. (2009) best estimate 1.5◦C per trillion tonnes of carbon; 5th–95th percentiles: 1.0◦C and 2.1◦C per trillion tonnes carbon corresponding to prevented further increase 1.43◦C and 2.99◦C respectively). ### Baseline parameterization and scenarios analyzed - Baseline mean SCC θ: $80/tCO2 (Pindyck (2019) lower-bound justification). - SCC sensitivity range considered: minimum $61.4/tCO2 to maximum $268.4/tCO2 (Rennert et al. (2021) and survey evidence). - At θ = $268.4/tCO2 baseline net social benefit rises from $85 trillion to $211 trillion (present-value comparisons reported). - Carbon arbitrage disappears only if SCC ≤ $20.4/tCO2. - Time horizons: - Primary horizon: [t+2 = 2024, T = 2100] (two-year lag to set up carbon arbitrage). - Additional horizons studied: T = 2050 and T = 2070. - Example: T = 2050 (θ = $80/tCO2) → carbon arbitrage ≈ $18 trillion (GCAM5.3-NGFS). - Replacement energy mixes (sr) and impacts: - Baseline sr: 50% solar, 25% wind‑onshore, 25% wind‑offshore (in other sections simplified as 50% solar, 50% wind where wind split on/offshore 50/50). - NGFS Net Zero 2050 consistent weights: 56% solar, 42% wind‑onshore, 2% wind‑offshore → carbon arbitrage = $92 trillion. - Replacement with natural gas scenarios reduce or reverse arbitrage: - 100% natural gas → carbon arbitrage = −62 (trillion dollars). - 33% solar / 33% wind / 33% natural gas → carbon arbitrage = −32 (trillion dollars). - 45% solar / 45% wind / 10% natural gas → carbon arbitrage = 29 (trillion dollars). - 100% nuclear replacement → carbon arbitrage = 26 (trillion dollars). - Other sensitivities: - Renewable plant lifetime: 30Y (baseline) → carbon arbitrage = 85; 50Y → 106; lifetime dictated by depreciation → 222. - No experience-curve learning (30Y): carbon arbitrage = 70. - Including storage and grid extension: baseline + storage/grid → carbon arbitrage = 61–78 (various inclusions). - Discount rates: baseline WACC ρ = 2.8% → 85; ρ = 3.6% → 90; ρ = 5% → 68. ### Methodology and key model structure - Benefit calculation: - B_{s1,s2,θ}_{t,T} = θ × Σ_{i∈C} Σ_{τ=t+2}^T ΔE^{s1,s2}_{i,τ}, where ΔE^{s1,s2}_{i,τ} = E^{s1}_{i,τ} − E^{s2}_{i,τ}. - Avoided emissions priced at mean SCC θ (average SCC chosen instead of marginal SCC to value large, non-marginal emission reductions). - Cost decomposition: - C_{s1,s2,sr}_{t,T} = O_{s1,s2}_{t,T} + I_{s1,s2,sr}_{t,T}. - Opportunity costs O computed from missed free cash flow: O_{i,τ} = ΔP_{i,τ} × π_{i,τ}, discounted by firm WACC ρ_i (baseline ρ = 2.8%). - Investment costs I computed from country-level required renewable capacity additions, using capacity factors f_q, technology lifetimes l_q, depreciation d_q, and Wright’s-law experience curves for i_{q,τ}. - Learning-by-doing (experience curves): - i_{q,τ} = α_q × (global cumulative installed capacity up to τ−1)^{−γ_q}. - Learning rates Θ_q and implied γ_q: - Solar Θ = 20% → γ = 0.32. - Wind‑onshore Θ = 5% → γ = 0.07. - Wind‑offshore Θ = 3% → γ = 0.04. - Renewable technical parameters (baseline): - f_solar = 16.1%, f_wind‑onshore = 36%, f_wind‑offshore = 40%. - Baseline renewable lifetime l_q = 30 years; alternative 50 years and degradation-only lifetimes considered. - Storage and grid: - Short-term storage α = 0.2/365 (20% daily storage); battery baseline cost $86,111/GJ ($310/kWh), battery learning Θ_b = 25.3% (γ_b = 0.42), battery lifetime 12 years. - Long-term storage (electrolyzers): unit cost $1,313,000,000/GW ($1,313/kW), learning Θ_e = 8.6%, conversion efficiency ψ = 0.7, σ = 1/12. - Grid unit cost proxy c_g = $4.14/GJ ($14.9 billion/PWh). ### Data sources, coverage, and empirical inputs - Asset Resolution (AR) coal dataset coverage and aggregates: - Coal companies: 2027; ultimate parent companies: 1549. - Coal plants: 6590 (4466 linked to ultimate parent; 2124 owned by subsidiaries). - AR estimate global coal production in 2020: 6.41 Gt. - AR scope I and III coal emissions in 2020: 14.53 GtCO2e. - AR coal power capacity in 2020: 1938 GW. - AR covers at least 85% of global coal production (per AR). - Financial and operating inputs: - Median free cash flow per tonne of coal (top-10 pure coal companies, 2010–2020): 0.34 dollars per tonne of coal (baseline); top‑100 median: 0.58 dollars/tonne (robustness). - Discounting parameters: ρ_f = 2.08%, χ = 15%, λ = 52%, β = 0.9, E[R_M] = 1.99% → implied ρ = 2.8%; alternative E[R_M] yields ρ = 3.6%; robustness uses ρ = 5%. - BAU and phase-out coal scenarios: - Business-as-usual: Current Policy Scenario (GCAM5.3‑NGFS). - Phase-out: NGFS Net Zero 2050 scenario (GCAM5.3‑NGFS). - Projection method: quinquennial NGFS projections linearly interpolated for annual values; AR plant projections used to 2026 then NGFS trends applied from 2027 with two-year lag t+2. ### Climate finance needs and regional distribution - Present value of global financing needed to end coal (C_{s1,s2,sr}_{t,T}): around $29 trillion. - Approximately $18 trillion needed up to T = 2050. - Front-loaded investment this decade estimated to reach up to around $3 trillion annually (text phrasing: "between 1 2 a trillion and 2 trillion dollars, with a front-loaded investment this decade, which we estimate reaches up to around 3 trillion"). - Regional distribution of the ~$29 trillion: - Asia: 46% - Europe: 18% - North America: 13% - Australia and New Zealand: 13% - Africa: 8% - Latin America and the Caribbean: 2% - Accounting for private financing via de‑risking and blended finance would reduce governments’ total fiscal commitments to roughly $50 billion to $200 billion per year. - Example blended-finance leverage (IFC‑Amundi deal): first‑loss tranche $125 million in a $2 billion deal; typical public:private leverage ratios at 1:9 or 1:10. - If 10% public junior tranche (α = 10%), governments would commit ≈ $2.9 trillion (PV) into junior tranches; applying marginal cost of public funds (MCPF) 1.6 raises public PV cost to ≈ $4.5 trillion and reduces global net gain from ≈ $85 trillion to ≈ $80 trillion. ### Country-level heterogeneity, Coasian bargaining, and policy implications - Country-level SCC allocation: - Country share θ_y = θ × (ˆθ_y / ˆθ) using Ricke et al. (2018) estimates so that Σ_y θ_y = θ. - Country benefit: B_{y} = θ_y × Σ_{i∈C} Σ_{τ=t+2}^T ΔE_{i,τ}^{s1,s2}. - Country cost: C_{y} = O_{y} + I_{y}. - Heterogeneity outcomes: - Most countries gain from joining a global phase-out even if they bear their own costs. - Some developing countries require small compensatory transfers to be net winners; rich countries are often net beneficiaries and can rationally pay transfers. - Block-by-block deals targeting top coal‑reliant countries are efficient: top‑9 coal‑reliant countries account for around 1210 GtCO2 of the 1425 GtCO2 avoidable by phasing out coal under Net Zero 2050. - Policy design principles and recommendations: - Use Coasian bargaining: compensate coal owners and finance replacement renewables to create Pareto‑improving outcomes. - Prioritize blended climate finance to leverage private capital (e.g., 1:9 junior:senior tranche structures). - Make climate finance conditional on credible coal phase‑out commitments and concurrent renewable deployment to avoid carbon leakage. - Target initial deals at the largest coal‑polluting countries (block approach) to capture the majority of global benefits. - For countries with fiscal constraints, use blended finance instruments and, where required, sovereign debt restructuring to create fiscal space. ### Robustness, caveats, and co‑benefits - Carbon arbitrage robust across alternative integrated assessment and energy models (MESSAGEix‑GLOBIOM and REMIND‑MAgPIE yield similar orders of magnitude). - Opportunity costs are small relative to benefits; broader opportunity‑cost accounting (five years wage compensation + retraining) raises O from $50 billion to $331 billion but does not meaningfully change net gain. - Health co‑benefits: back‑of‑envelope present‑value health benefits from reduced air pollution ≈ $52 trillion over 2022–2050 (discounted at ρ = 2.8%). - Limits and caveats: - Analysis does not incorporate general equilibrium effects (e.g., coal price changes from supply reduction). - Emission intensities ε_{i,l} assumed constant at 2020 values; future coal abatement could reduce benefits slightly. - Replacement renewables and storage learning calibrated conservatively (only count learning from capacity built to replace coal). - Investment cost proxies (LCOE) can overstate PV investment needs; LCOE captures O&M and financing and thus yields higher PV estimates in sensitivity checks. - CCUS at high cost (e.g., $1200/tCO2) is economically infeasible for this replacement; CCUS must fall below $266/tCO2 for positive net gain under baseline settings. *Italic: Content derived from the specified IMF working paper section (wpiea2022107-print-pdf — 3.1–5.2).* ### 3.1 Benefits of Avoiding Coal Emissions . . . . . . . . . . . . . . . . . . . . . . . . .7 ### wpiea2022107-print-pdf - 3.1 Benefits of Avoiding Coal Emissions ### Overview and framing - Paper adopts a Coasian approach (Coase (1960)) to evaluate the total net benefit from replacing coal with renewable energy rather than a marginal Pigouvian SCC-only approach. - Focus: quantify the net social benefit of phasing out coal and replacing its energy with renewables (wind, solar), using plant-level coal production and emissions aggregated from the plant level. - Coal emits roughly 2 times as much carbon per unit of energy as natural gas, and roughly 1.5 times as much as oil. - The size of the carbon arbitrage is defined as the present value at time t of benefits from avoided carbon emissions minus the present value of costs of replacing coal with renewable energy. ### Key quantitative findings - Baseline global net social gain from beginning a phase-out in 2024 in line with the NGFS Net Zero 2050 scenario (always replacing coal with renewable energy): $85 trillion. - This $85 trillion represents an increase of around 1.3% of current world GDP every year until 2100. - Net gain per unit: - Per ton of coal: around $136. - Per ton of avoided CO2 emissions: $60. - Baseline assumes an average SCC of $80 per ton of CO2 (tCO2) from Pindyck (2019). - Sensitivity on SCC: - Range examined includes a minimum of $61.4/tCO2 to a maximum of $268.4/tCO2 (Rennert et al. (2021)). - At $268.4/tCO2 the net social benefit rises from $85 trillion to $211 trillion. - Estimated avoided emissions from phasing out coal discussed on the order of around 1425 Gt (context: a large emission reduction of around 1425 Gt resulting from phasing out coal is referenced). ### Climate finance needs and regional breakdown - Present value of financing needed to end coal globally: around $29 trillion. - Annual global climate financing need described in the source text as: - "between 1 2 a trillion and 2 trillion dollars, with a front-loaded investment this decade, which we estimate reaches up to around 3 trillion." - (Elsewhere phrased as) "between$1 2 trillion and$2 trillion dollars (up to$3 trillion)" - Front-loaded investment this decade estimated to reach up to around $3 trillion. - Regional distribution of the ~$29 trillion: - 46% in Asia - 18% in Europe - 13% in North America - 13% in Australia and New Zealand - 8% in Africa - 2% in Latin America and the Caribbean - Accounting for private financing (via de-risking and blended finance) would reduce governments’ total fiscal commitments for renewables to replace coal to between roughly $50 billion and $200 billion per year. ### Policy implications and Coasian bargaining - From a Coasian perspective, compensating coal companies for losses and accounting for capital expenditures to replace coal with renewables can produce a Pareto-improving bargain: paying polluters to stop polluting can make the world better off. - The paper argues that the climate financing needs (~$29 trillion PV; annual flows between the figures above) are large but small relative to the conservatively estimated social benefits (over $104 trillion referenced in the text). - Many countries would gain from participating in a global deal to end coal even without cross-country compensatory transfers; some (mostly developing) countries require small compensatory transfers to benefit. - Rich countries are self-interested in making transfers because they are main beneficiaries from eliminating coal. - Most replacement renewable investment can come from the private sector once investments are de-risked through public co-investments via blended finance. ### Methodology, scenarios, and timing - Benefits B and costs C are computed as present values over a phase-out horizon; the carbon arbitrage A = B − C. - Avoided emissions measured as difference in plant-level coal production between Current Policy Scenario (CPS), s1, and the Net Zero 2050 scenario, s2. - Primary phase-out horizon analyzed: t+2 = 2024 up to T = 2100 (the NGFS Net Zero 2050 gradual phase-out horizon); the two-year lag gives time to set up the carbon arbitrage. - Additional horizons studied: T = 2050 and T = 2070 (to capture shorter transition horizons and net-zero targets of various country groups). - Replacement scenarios sr specify the mix of renewables substituted for phased-out coal. - The baseline average SCC parameter θ is set to $80/tCO2; sensitivity analysis spans $61.4/tCO2 to $268.4/tCO2. - The analysis does not incorporate general equilibrium effects (e.g., potential coal price increases from supply reduction), which could raise opportunity costs but are judged unlikely to erase the net social benefit. *Source: wpiea2022107-print-pdf - 3.1 Benefits of Avoiding Coal Emissions (canonical PDF).* ### 3.1 Benefits of Avoiding Coal Emissions ### 3.1 Benefits of Avoiding Coal Emissions ### Present value of global benefits from coal-phase-out - The present value of global benefits B_{s1,s2,θ}_{t,T} from each coal company i ∈ C (where C is the set of coal companies) reducing its CO2 emissions by an amount ΔE^{s1,s2}_{i,τ} each year τ ∈ [t+ 2,T] is given by: - B_{s1,s2,θ}_{t,T} = θ × ∑_{i∈C} ∑_{τ=t+2}^T ΔE^{s1,s2}_{i,τ}, - where avoided emissions are priced at the mean SCC θ. - The emission reduction in year τ is ΔE^{s1,s2}_{i,τ} = E^{s1}_{i,τ} − E^{s2}_{i,τ}, the difference in coal emissions in year τ between business-as-usual scenario s1 and phase-out scenario s2. - Coal company i’s emissions in year τ under scenario s are given by: - E^{s}_{i,τ} = ∑_{l∈L_i} P^{s}_{i,l,τ} ε_{i,l}, - where P^{s}_{i,l,τ} is coal production in plant l ∈ L_i under scenario s and ε_{i,l} is the plant emission intensity. - Coal company i thus reduces emissions by reducing coal production in each plant l from P^{s1}_{i,l,τ} to P^{s2}_{i,l,τ} as specified by phase-out scenarios s2. ### Rationale for using the average SCC rather than the marginal SCC - The marginal SCC is applicable to a one-tonne deviation from a business-as-usual pathway s1 and is expected to change (in particular, grow) over time as more CO2 accumulates (references: Daniel et al. (2016), Dietz and Stern (2015)). - For large, non-marginal emission reductions (moving from s1 to a net-zero-2050 pathway s2), the marginal SCC is not suitable because the applicable marginal SCC at a given time depends on cumulative emissions up to that date. - To capture time-varying applicable marginal SCCs over a large emission reduction, the analysis uses the average SCC corresponding to the average marginal SCC that applies over the course of emission reductions from s1 to s2. ### Pindyck (2019) average SCC and its application here - Pindyck (2019) defines the average SCC θ as the ratio of the present value of lost GDP due to direct or indirect climate damages from an extreme climate outcome (causing GDP reductions of at least 20%) to the total emission reduction needed to avert that outcome. - In Pindyck’s formulation: S = B_0 / ΔE, where - B_0 = β [E_0(z1) − E_1(z1)] / ((R−g)(R+β−g)(1−exp^{−βT_1})), - ΔE = (m_0 − m_1) E_0 (R−m_0)(R−m_1). - E_0(z1) = expected future damages to GDP under business as usual; E_1(z1) = expected future damages once emissions are reduced sufficiently to avoid worst catastrophes (≥ 20% GDP loss). - Parameters: R = discount rate, g = projected growth rate of GDP, β captures how climate damages change over time, m_0 and m_1 are growth rates of emissions. - The average SCC already embeds a discount rate R; thus no explicit discount rate appears in equation 2. ### Choice of baseline mean SCC and sensitivity ranges - Consistent with a cautious approach, the baseline estimate for the mean SCC is θ = $80/tCO2 (from Pindyck (2019) lower-bound justification). - Pindyck (2019) survey findings (selected): - Economists’ mean SCC estimates: $153 to $203 (depending on distribution). - Climate scientists’ mean SCC estimates: $291 to $326. - A democratic treatment of all respondents yields a mean closer to $200/tCO2. - If one trims outliers and weights economists or more confident respondents more heavily, Pindyck suggests around $80/tCO2. - Rennert et al. (2021) central estimates suggest a range for the marginal SCC as high as $168.4 and as low as $61.4 per tonne of carbon; this range is used for sensitivity analysis. ### Scale of avoided emissions and comparability to Pindyck’s catastrophe-avoidance framing - The emission reduction needed to avoid a climate catastrophe (Pindyck’s lower bound mean SCC of $80/tCO2) is similar to the 1425.55 GtCO2 emission reduction from phasing out coal along the NGFS Net Zero 2050 scenarios relative to business as usual. - The benchmark scenario for future emissions from coal under business-as-usual is s1; the alternative scenario s2 is the NGFS net zero 2050 scenario under which coal production is gradually phased out. ### Caveats, assumptions, and modelling notes - Plant definition: a coal company’s plant is defined as any unique combination of energy use, coal technology, coal sub-technology and plant country; emissions are summed across these unique combinations. - Assumption on emission intensities: the analysis assumes future emission intensity at the plant level remains equal to current values. If coal companies invest in abating emissions (reducing ε_{i,l} at future τ ∈ (t,T]), the global benefits of reducing coal production may be slightly overestimated. - Abatement of coal emissions is currently cost ineffective (see Section 5), partly due to high costs of early-demonstration projects and barriers in emerging and developing economies (regulatory uncertainties, lack of public financial support, risks around long-term ownership and liability of stored CO2, complex capture-transport-storage chains). - Nordhaus (2017) estimate: the SCC is likely to grow in real terms at 3% every year up to 2050; the SCC may grow non-linearly as climate tipping points approach. ### Temporal extent of benefits from building renewables - Social benefits of building renewable capacity over [t+2,T] extend beyond time T because renewable plants with lifetime l years built after time T−l will be operational beyond T and can avoid coal emissions after year T. - Truncating benefits at T would drastically underestimate benefits of replacing coal with renewable capacity. - The Appendix describes in detail how benefits that accrue beyond T are captured. *Source: wpiea2022107-print-pdf - 3.1 Benefits of Avoiding Coal Emissions* ### 3.2 Costs of Avoiding Coal Emissions ### 3.2 Costs of Avoiding Coal Emissions ### Aggregate decomposition - The present value of global costs C_{s1,s2,sr}_{t,T} of avoiding coal emissions under scenario set {s1,s2,sr} and over time horizon [t+2,T] is given by: - C_{s1,s2,sr}_{t,T} = O_{s1,s2}_{t,T} + I_{s1,s2,sr}_{t,T}. (4) - Where: - O_{s1,s2}_{t,T} = present value of opportunity costs associated with avoiding coal emissions. - I_{s1,s2,sr}_{t,T} = present value of investment costs in replacement renewables. ### 3.2.1 Opportunity Costs of Coal — definitions and valuation - Present value of global opportunity costs: - O_{s1,s2}_{t,T} = sum_{i∈C} sum_{τ=t+2}^{T} O_{s1,s2}_{i,τ} / (1+ρ_i)^{(τ−t)}. (5) - Missed free cash flow per coal company i in year τ: - O_{s1,s2}_{i,τ} = ΔP_{s1,s2}_{i,τ} × π_{i,τ}. (6) - ΔP_{s1,s2}_{i,τ} = P^{s1}_{i,τ} − P^{s2}_{i,τ}. - P^{s}_{i,τ} = sum_{l∈L_i} P^{s}_{i,l,τ}. - Profit margin assumptions: - π_{i,τ} is assumed constant across firms and time and equal to the median coal profit of the top 10 pure coal companies averaged over the last ten years. - Sensitivity analysis uses the median of the top 100 coal companies. - Discounting missed cash flows: - Company i’s discount rate (WACC) ρ_i is given by: - ρ_i = λ_i ρ_f (1−χ_i) + (1−λ_i)(ρ_f + β_i E[R_M]). (7) - Baseline parameter values and implied rate: - ρ_f = 2.08%, χ_i = 15%, λ_i = 52%, β_i = 0.9, E[R_M] = 1.99% → ρ_i = ρ = 2.8%. - Sensitivity analyses: - ρ = 3.6% (E[R_M] = 3.87% average risk-premium over last 100 years). - ρ = 5%. - Geographic decomposition: - O_{s1,s2}_{t,T} = sum_{y∈Y} O_{s1,s2}_{y,t,T}. - O_{s1,s2}_{y,t,T} = sum_{i∈C} sum_{τ=t+2}^{T} O_{s1,s2,i,y,τ} / (1+ρ_i)^{(τ−t)}. - O_{s1,s2,i,y,τ} = ΔP_{s1,s2,i,y,τ} × π. - ΔP_{s1,s2,i,y,τ} = P^{s1}_{i,y,τ} − P^{s2}_{i,y,τ}, with P^{s}_{i,y,τ} = sum_{l∈L^y_i} P^{s}_{i,y,l,τ}. - Broader interpretation of opportunity costs: - Includes lost wages of coal workers and retraining costs; present value of compensation for lost wages and retraining costs is calculated (referenced in Appendix A) as an alternative, broader measure. - Additional modeling assumptions: - Opportunity costs are attributed to the country y where the coal plant is located (alternative assumption of attribution to parent company headquarters is feasible with the data). - Variable costs of renewables are ignored for simplicity. (Footnote: renewables’ emissions are omitted as negligible relative to coal.) ### 3.2.2 Investment Costs in Renewable Energy — structure and accounting - Present value of investment costs to replace phased-out coal in renewable mix s_r: - I_{s1,s2,sr}_{t,T} = sum_{y∈Y} I_{s1,s2,sr}_{y,t,T}. (8) - Country-level discounted investments: - I_{s1,s2,sr}_{y,t,T} = sum_{τ=t+2}^{T} I_{s1,s2,sr}_{y,τ} / (1+ρ)^{(τ−t)}. (9) - Assumption: discount rate ρ for renewables equals that applying to coal companies (robustness checks consider a 50 basis point higher climate-risk premium for coal companies). - Country-level investment cost in year τ: - I_{s1,s2,sr}_{y,τ} = sum_{q∈R} G_{s1,s2,sr,q}_{y,τ} × i_{q,s1,s2,sr,τ}. (10) - G_{s1,s2,sr,q}_{y,τ} = ω_{q,sr,τ} × h^{−1}(D_{s1,s2,sr}_{y,τ}) × (1 / f_q). (11) - Energy shortfall and renewable stock: - D_{s1,s2,sr}_{y,τ} = max{ g(ΔP_{s1,s2,y,τ}) − R_{s1,s2,sr}_{y,τ}, 0 }. (12) - R_{s1,s2,sr}_{y,τ} = sum_{q∈R} R_{s1,s2,sr,q}_{y,τ}. (13) - R_{s1,s2,sr,q}_{y,τ} = h(S_{s1,s2,sr,q}_{y,τ}) × f_q. (14) - Capacity factor assumptions (2020 global averages from IRENA (2021b)): - f_solar = 16.1%, f_wind−onshore = 36%, f_wind−offshore = 40% (assumed constant over time and regions). - Renewable stock accumulation and depreciation: - S_{s1,s2,sr,q}_{y,τ} = sum_{τ_d=t+2}^{τ−1} G_{s1,s2,sr,q}_{y,τ_d} × (1−d_q)^{(τ−τ_d)} I_{ {τ−τ_d ≤ l_q} }. (15) - Parameters: - Depreciation rate d_q and lifetime l_q vary by technology. - Baseline lifetime commonly used: l_q = 30 years for solar and wind; alternative lifetimes considered: l_q = 50 years and l_q large (degradation only). - Empirical depreciation estimates: d_q^{solar} = 0.5% per year, d_q^{wind} = 0.48% per year. - Rationale for country-level replacement: - Replacing lost coal production with renewables is modeled at the country level (not per coal plant) due to local energy security considerations and transmission constraints. ### Renewable mix scenarios and baseline choices - Baseline renewable technology set R = {Solar PV, Wind Onshore, Wind Offshore}. - Baseline replacement scenario s_r weights: - ω_{solar,sr,τ} = 50%, ω_{wind−onshore,sr,τ} = 25%, ω_{wind−offshore,sr,τ} = 25%. - Reasons: policy support in over 130 countries; current competitiveness; trend of falling costs. - Robustness / alternative (NGFS Net Zero 2050 consistency) weights: - ω_{solar,sr,τ} = 56%, ω_{wind−onshore,sr,τ} = 42%, ω_{wind−offshore,sr,τ} = 2%. - Model flexibility: - The model can accommodate other choices for R and s_r in sensitivity analysis. ### 3.2.2.1 Experience Curves for Renewable Energy — Wright’s law and learning - Wright’s law specification for investment cost decline: - i_{s1,s2,sr,q,τ} = α_q ( sum_{y∈Y} ( sum_{τ_d ≤ t−1} G^{q}_{y,τ_d} + sum_{τ_d=t+2}^{τ−1} G_{s1,s2,sr,q}_{y,τ_d} ) )^{−γ_q}. (16) - The bracket term = global cumulative installed capacity of technology q up to time τ−1. - Learning rate definitions: - Cost reduction per doubling Θ_q = 1 − 2^{−γ_q}. (17) - Literature-based empirical values (Samadi (2018) synthesis) used: - Θ_q^{solar} = 20% → γ_q^{solar} = 0.32. - Θ_q^{wind−onshore} = 5% → γ_q^{wind−onshore} = 0.07. - Θ_q^{wind−offshore} = 3% → γ_q^{wind−offshore} = 0.04. - Calibration of α_q: - Global cumulative installed capacity of technology q at t−1 = 2021 set equal to 2020 IRENA (2021b) values. - Investment costs i_{q,t} at t = 2022 set equal to average 2020 investment costs from IRENA (2021b). - α_q is solved by equating both sides of equation (16) at these calibration points. - Scope and conservatism: - Equation (16) captures learning-by-doing only from capacity built to replace coal under {s1,s2,sr}, not from other deployments; thus estimates are conservative. - Empirical depiction and complementary storage: - The average drop of investment costs under the Net Zero 2050 scenario (s2), accounting only for learning from replacing coal, is depicted in Figure 1 (referenced). - Investment costs in complementary short- and long-duration electricity storage are also projected as functions of cumulative installed capacity (Figure 1). - Note: projected drop in storage costs is somewhat conservative because only storage built to replace coal is counted, not storage for broader electrification. - Additional notes: - Investment costs for renewables are expected to fall exponentially with cumulative build; storage learning is calibrated similarly (details in Appendix A). - A drop in investment costs from learning-by-doing does not reduce the profitable lifetime of renewable plants because maintenance costs are insignificant relative to capex; once capex is incurred, keeping plants operating is sensible. *Source: 3.2 Costs of Avoiding Coal Emissions (wpiea2022107-print-pdf).* ### 3.3 Climate Finance to Phase Out Coal ### 3.3 Climate Finance to Phase Out Coal ### Estimation framework - The financing needed to phase out coal production according to phase-out scenarios s1, s2 relative to a business-as-usual scenario s1 and to replace coal energy with renewable energy mixes sr is given by the present value of the costs C_{s1,s2,sr}_{t,T} of phasing out coal along this trajectory. - The present value of global climate financing is the sum across countries: - C_{s1,s2,sr}_{t,T} = ∑_{y∈Y} [ O_{s1,s2}_{y,t,T} + I_{s1,s2,sr}_{y,t,T} ] - Country y’s climate financing: C_{s1,s2}_{y,t,T} = O_{s1,s2}_{y,t,T} + I_{s1,s2,sr}_{y,t,T} - Annual, non-discounted climate financing need of country y: - O_{s1,s2}_{y,τ} + I_{s1,s2,sr}_{y,τ} - Global annual climate financing need: - ∑_{y∈Y} [ O_{s1,s2}_{y,τ} + I_{s1,s2,sr}_{y,τ} ] - Footnote summary: Global climate financing F should be at least equal to the opportunity cost of coal and investment cost in renewables (i.e., F = C_{s1,s2,sr}_{t,T} = I_{s1,s2,sr}_{t,T} + O_{s1,s2,sr}_{t,T}). The paper estimates the carbon arbitrage based on a climate financing cost of F = C_{s1,s2,sr}_{t,T}, noting a carbon arbitrage can be reaped as long as provided climate financing remains less than the social gain from phasing out coal: C_{s1,s2,sr}_{t,T} ≤ F < B_{s1,s2,sr}_{t,T}. ### Data (Asset Resolution and validation) - Asset Resolution (AR) plant- and company-level coal dataset: - Total number of coal companies: 2027 - Ultimate parent companies: 1549 - Total number of coal plants: 6590 - Plants directly linked to ultimate parent company: 4466 - Plants owned by subsidiaries: 2124 - For each coal plant the AR data include: - Emission intensity (tonnes of CO2 per tonnes of coal) as of 2020 (scope I and III) - Historical production 2013-2021 (tonnes of coal) - Projected production 2022-2026 (tonnes of coal) - Ownership structure (direct owner to ultimate parent) - Geolocation, plant country, sector (power or non-power), coal technology and sub-type - Coverage and aggregate values: - AR data cover at least 85% of global coal production (according to AR) - AR estimate of global coal production in 2020: 6.41 Giga tonnes (Gt) - AR estimate of global scope I and III emissions from coal in 2020: 14.53 Giga tonnes of CO2e - Comparison note: 2020 global carbon emissions from fossil fuels estimated at 34.81 GtCO2e by the Global Carbon Project; coal scope I and III emissions accounted for around 41.7% of fossil fuel emissions. - Coal power sector: - Total capacity in coal power sector in 2020: 1938 GW - Note: AR coal power data include 3534 coal power companies with 7735 plants; for each plant scope I and II emission intensity is captured. - Emissions terminology: - Scope 1: direct emissions from owned or controlled sources. - Scope 3: all other indirect emissions in a company’s value chain (vast majority for coal mining is combustion of coal in end use). - AR data do not cover Scope 2 emissions; these are negligible for coal mining companies. ### Coal production scenarios and methodology - Scenario sources and baseline: - Use quinquennial global NGFS projections (GCAM5.3-NGFS) of annual coal production over 2020-2100 for both Current Policy and Net Zero 2050 scenarios. - Linear interpolation of quinquennial projections to obtain annual estimates. - Extrapolation beyond AR plant projections: - AR provides plant-level projections up to 2026; from 2027 onwards assume percentage change in plant-level coal production follows annualized NGFS Current Policy trend for business-as-usual and follows Net Zero 2050 trend for the phase-out pathway. - A two-year lag is added (t+2) to allow for time to implement the carbon arbitrage; Net Zero 2050 pathway applied from t+2 onward. - Additional scenario considered: - Halt to Coal Production scenario: complete phase-out from t+2 onwards (included as a theoretical maximum for avoided emissions; noted as unlikely feasible in practice). - Scenario sensitivity analyses: - Apply regional NGFS projections based on GCAM5.3-NGFS to capture regional differences. - Apply MESSAGEix-GLOBIOM 1.1 and REMIND-MAgPIE 2.1-4.2 models of NGFS instead of GCAM5.3-NGFS. - Assumptions on replacement: - Any coal use NGFS projects to be feasibly phased out in Net Zero 2050 is assumed to be replaceable with renewables. - Acknowledged that Net Zero 2050 does not drop below 2 Gt of coal annually even by 2050, reflecting hard-to-abate sectors (e.g., steel). - Outcome visualization reported: - Figure 2 (described): left plot shows global coal production under different scenarios; right plot shows associated annual global emissions assuming emission intensity of each coal plant remains equal to its 2020 value. - Difference between Current Policy and Net Zero 2050 in a given year represents annual coal phased out and corresponding avoided emissions (illustrated with dotted grey lines for 2040). ### Opportunity costs of coal (method and parameter values) - Financial data source for operating metrics: Orbis (operating revenue, profit margin, taxes, interest payments, depreciation allowances) for 2010-2020. - Free cash flow computation: - Free cash flow for a coal company in a year = operating revenue × profit margin + depreciation allowances net of taxes and interest payments. - Unit coal profit assumption: - Future coal profit per tonne assumed constant and equal to median unit coal profit averaged over [2010-2020] of the top-10 coal companies by 2020 coal production. - Median free cash flow per tonne of coal production obtained: 0.34 dollars per tonne of coal. - Robustness check: median of top 100 pure coal companies yields free cash flow of 0.58 dollars per tonne of coal. - The median is applied to state-owned coal companies lacking Orbis data. - Discounting and WACC inputs: - Discount expected free cash flows with WACC, assuming constant beta, constant risk premium, constant risk-free rate. - Risk-free rate: nominal 30Y US treasury yield = 2.08%. - Global risk premium (baseline): average excess CAPE yield over last decade ≈ 3% minus 1% = (3% - 1%) (text describes average excess CAPE around 3% minus 1% to account for greater diversification benefits). - Alternative global risk premium (robustness): average excess CAPE yield over 1922-2022 minus 1% = 3.87%. - Coal company beta: regression of MSCI World/Metal & Mining Index vs MSCI World Index (Jan 1 2017 to Jan 1 2022) → beta = 0.91. - Target leverage (debt/enterprise value): 52% (weighed-average leverage of MSCI World/Metal & Mining index as of 2021). - Corporate income tax rate assumed: 15%. - Obtained discount rates: - Baseline discount rate: 2.8% - With average risk premium: 3.6% - Note on magnitude: authors state the opportunity cost of coal is roughly three magnitudes smaller than the benefits of phasing out coal and the investment costs in renewables (see Section 5 reference). ### Investment costs in renewables (data and approach) - Renewable technologies considered: solar PV, wind onshore, wind offshore. - Data sources for investment costs and cumulative installed capacity up to 2020: IRENA (2021b) and IRENA (2021a). - Assumption: investment costs at start date t = 2022 equal latest observed data of 2020. - Rationale for global averages: investment costs driven down by global cumulative installed capacity via global “learning” / “experience”; global average used as robust proxy despite regional differences. - Figure 3 (described): left plot shows investment costs in renewables (USD/KW) over 2010-2020; right plot shows cumulative installed capacity in renewables (GW) over 2010-2020. ### Key statistics and model scope - AR-based estimates (2020): - Global coal production: 6.41 Gt - Coal scope I and III emissions: 14.53 GtCO2e - Coal power capacity: 1938 GW - Comparative figures referenced: - NGFS, IEA, BP, Global Energy Monitor estimates broadly consistent with AR values (see Table 1 referenced). - 2020 global carbon emissions from fossil fuels: 34.81 GtCO2e (Global Carbon Project) - Coal accounted for around 41.7% of fossil fuel emissions in 2020. - Modeling scope: - Units and standard definitions of conversion functions for the detailed cost-benefit model summarized in Appendix Table 8. - Results to follow in Section 5. *Source: wpiea2022107-print-pdf - 3.3 Climate Finance to Phase Out Coal (IMF PDF chapter content).* ### 5.1 The Great Carbon Arbitrage ### 5.1 The Great Carbon Arbitrage ### Baseline assumptions and parameter settings - Social cost of carbon (θpindyck): $80/tCO2 - Time horizon [t+2, T]: t = 2022, T = 2100 - Coal BAU scenario, s1: Stated policy scenario (GCAM5.3-NGFS) - Coal phaseout scenario, s2: Net zero 2050 scenario (GCAM5.3-NGFS) - Coal replacement scenario, sr: 50% solar, 50% wind (of which 50% onshore and 50% offshore) - Investment costs, I: 30Y lifetime of renewable plants with depreciation and investment-cost experience curve - Opportunity costs, O: Median unit coal profit of top 10 pure coal companies ($0.34 per tonne of coal) - Discount rate, ρ: WACC (ρ = 2.8%) ### Main quantitative results (present values discounted to 2022, through 2100) - Present value of benefits of phasing out coal (in trillion dollars): 114.04 - Present value of costs of phasing out coal (in trillion dollars): 29.03 - Opportunity costs: 0.05 - Investment costs: 28.98 - Carbon arbitrage (in trillion dollars): 85.01 (114.04 - 29.03 = 85.01) - Carbon arbitrage relative to world GDP (%)*: 1.3 - Carbon arbitrage (in dollars) per tonne of coal production: 136 - Carbon arbitrage (in dollars) per tCO2: 60 - Total coal production prevented (Giga Tonnes): 623.62 - Total emissions prevented (GtCO2): 1425.55 - Further temperature increase – on top of 1.1◦C already observed – prevented: 2.14◦C - Note: Matthews et al. (2009) best estimate: 1.5◦C per trillion tonnes of carbon; 5th–95th percentiles: 1.0◦C and 2.1◦C per trillion tonnes of carbon, yielding prevented further temperature increase of 1.43◦C and 2.99◦C respectively. *The world GDP in 2020 is 84.705 trillion US Dollars according to the World Bank.* ### Decomposition and interpretation - The lion share of costs is investment costs at $28.98 trillion; opportunity costs are $0.05 trillion. - Net carbon arbitrage of $85.01 trillion represents a net benefit equivalent to 1.3% of current world GDP every year until 2100 (measured over cumulative discounted world GDP 2024–2100 using 2020 GDP levels). - Per-unit estimates: $136 per tonne of coal avoided; $60 per tCO2 avoided. - The prevented further temperature increase of 2.14◦C (on top of observed 1.1◦C) indicates major climate impact reduction from the coal phase out. ### Sensitivity analysis — social cost of carbon and time horizon - Carbon arbitrage disappears only if SCC ≤ $20.4/tCO2. - Alternative SCC values and headline impacts: - θlower = $61.4/tCO2 → net carbon arbitrage (baseline T=2100) ≈ $59 trillion - θpindyck = $80/tCO2 → net carbon arbitrage (baseline T=2100) = $85 trillion - θhigher = $168.4/tCO2 → net carbon arbitrage (baseline T=2100) ≈ $211 trillion - Time-horizon effects (examples from Table 4): - T = 2050 (baseline SCC = $80/tCO2): carbon arbitrage ≈ $18 trillion (GCAM5.3-NGFS) - T = 2100 (baseline SCC = $80/tCO2): carbon arbitrage = $85 trillion (baseline) ### Sensitivity analysis — replacement energy mixes and alternatives - Baseline replacement (50% solar, 50% wind) → carbon arbitrage = $85 trillion. - Net Zero 2050 replacement mix (56% solar, 44% wind) → carbon arbitrage = $92 trillion. - Replacement with natural gas and mixed scenarios (θ = $80/tCO2): - 100% natural gas → carbon arbitrage = -62 (θpindyck column shows -62) - 33% solar / 33% wind / 33% natural gas → carbon arbitrage = -32 (θpindyck column shows -32) and baseline example shows a drop from $85 trillion to $6 trillion when using that mix - 45% solar / 45% wind / 10% natural gas → carbon arbitrage = 29 (θpindyck column shows 29) - 100% nuclear replacement → carbon arbitrage = 26 (θpindyck column shows 26) - CCUS (direct air capture example): at $1200/tCO2, net gain = -372 trillion (net loss). Positive net gain only if CCUS costs drop below $266/tCO2 under baseline settings. ### Sensitivity analysis — investment costs, plant lifetimes, storage, grid, and discounting - Renewable plant lifetime assumptions (θ = $80/tCO2): - 30Y lifetime (baseline): carbon arbitrage = 85 - 50Y lifetime: carbon arbitrage = 106 - Lifetime dictated by depreciation: carbon arbitrage = 222 - No experience-curve learning (30Y, no experience curve): carbon arbitrage = 70 - Proxying investment costs by LCOE (with experience curve): carbon arbitrage = 48 - Including storage and grid extension (baseline plus storage/grid): - Including short-term and long-term storage (experience curve): carbon arbitrage = 78 - Including short-term + long-term storage + grid extension (experience curve): carbon arbitrage = 61 - Global price tag for investments in storage when replacing coal with renewables is estimated at around $7 trillion (assumes 20% daily electricity stored in short-term Li-ion; one month stored long-term in green hydrogen via electrolyzers). - Discount rate variations: - Baseline WACC (ρ = 2.8%): carbon arbitrage = 85 - WACC with climate-risk premium (ρ = 3.3%): carbon arbitrage = 85 (5985 and ∗211 entries show baseline robustness) - Average risk premium over 1922–2022 (ρ = 3.6%): carbon arbitrage = 90 - Benchmark (ρ = 5%): carbon arbitrage = 68 ### Robustness across min–max parameter settings (Table 6 summary) - For θpindyck = $80/tCO2 and T = 2100: carbon arbitrage range (min, max) = (70, 132) trillion dollars, central preferred estimate ≈ $85 trillion. - Combining lower/higher SCC with alternative parameters widens range to (43, 310) trillion dollars across θlower/θhigher and T up to 2100. - Expressed as percent of GDP, the baseline range corresponds to approximately 1.1–2.0 percentage points of GDP for θpindyck; combined SCC extremes give 0.7–4.6 percentage points. ### Additional notes on opportunity costs, co-benefits, and assumptions - Broader opportunity-cost accounting (compensation for lost wages for five years + retraining) raises global opportunity costs from $50 billion to $331 billion (of which $275 billion for lost wages and $7 billion for retraining), but does not materially change the large net gain ($85 trillion). - Back-of-the-envelope estimate of health benefits from reduced air pollution (Rauner et al. (2020) inputs) yields present value ≈ $52 trillion over 2022–2050 (discounted at ρ = 2.8%). - Results are generally robust to alternative BAU projections (MESSAGEix-GLOBIOM 1.1 and REMIND-MAgPIE 2.1-4.2): for θpindyck = $80/tCO2 and T = 2050, carbon arbitrage ≈ $18–21 trillion across models. - Immediate halt to coal production as of 2022 (alternative phase-out scenario) yields a baseline net carbon arbitrage slightly higher at $96 trillion (though noted as unrealistic). *Source: wpiea2022107-print-pdf — https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022107-print-pdf.pdf* ### 5.2 Climate Finance to Phase Out Coal ### 5.2 Climate Finance to Phase Out Coal ### Present value and time profile of global financing needs - The present value of the required global climate financing is around 29 trillion dollars. - Approximately 18 trillion dollars is needed up to T= 2050. - The majority of climate financing needs occur between 2024 and 2050, with relatively lesser investment needs in the far future. - Front-loading of investments is required this decade to reach net zero by 2050; investment peaks and then declines in 30 year cycles under the assumption of full depreciation after 30 years. ### Breakdown by development status and region - Financing needs are largest for emerging markets, and particularly those in Asia. - Financing needs to replace coal with renewables exist across all levels of development (developed countries, developing countries, and emerging market countries). - Geographic breakdowns noted: Asia, Africa, North America, Latin America and Caribbean, Europe, and Australia and New Zealand. - Financing needs per GDP tend to be higher for countries with lower GDP per capita; notable outliers concentrated in Asia and Africa. - A handful of countries have significantly higher financing needs than the average country; for many countries financing needs represent a significant fraction of GDP. ### Time-series pattern and investment cycles - Under the Net Zero 2050 scenario, more coal is phased out every year, creating an incremental annual need to build up more renewable capacity. - Investment cycles reflect assumed asset lifetimes: renewable capacity built in the first year produces energy for 30 years (baseline) with depreciation reducing output each year; subsequent cycles require additional capacity as coal is phased out further. ### Sensitivity analysis of climate financing - Baseline and alternative assumptions examined include effective lifetime of renewables, presence or absence of “experience” (learning-by-doing) driving declines in investment costs, and alternative cost proxies such as LCOE. - If assumed renewable lifetime lengthens from 30 to 50 years, the investment cycle lengthens to 50 years. - If renewable lifetime is dictated only by its depreciation (D) rate, the investment cycle disappears over the time horizon up to 2100. - Allowing for experience effects leads later investment cycles to have lower capex costs. - LCOE is a misleading proxy for investment costs as it does not capture the front loading of capex investments. - The assumption on lifetime of renewables does not materially change the present value of global climate financing; what matters more is the degree of learning (E/no E) and the resulting fall in future investment costs. - By construction, the present value is higher with the LCOE proxy since LCOE also captures operational and financing costs. - Including complementary investment needs in short-term storage (S), long-term storage (L), and compensation for lost wages and retraining increases annual costs by around 200 billion annually at most and barely changes present value estimates. ### Scenario comparison (global vs regional NGFS) - Global NGFS scenario assumes homogeneous coal production trajectories across countries; regional NGFS scenarios capture heterogeneous regional demand and phase-out speeds. - Annual climate financing in certain regions is higher (e.g., emerging countries, developing countries, in particular Asia) and lower in others (e.g., developed countries, in particular America and Europe) under regional scenarios versus the global NGFS scenario. - The present value of climate financing does not drastically differ between regional and global NGFS scenarios; estimates sit close to the diagonal when plotted against each other. ### Coasian rationale and blended finance policy recommendations - From a Coasian perspective, it is economically sound to provide climate financing to compensate losses from phasing out coal and to fund capital expenditures needed to replace coal energy with renewables, linking social benefits of avoided emissions to these costs. - Total funding costs to globally phase out coal are estimated at around 29 trillion dollars. - It is not desirable or often possible to finance all investments through public funds alone; blended finance is proposed to leverage public funds to catalyze capital market investments. - Advantages of blended finance: - Reduces reliance on public funds that have a higher marginal cost. - Limits increases in public-debt-to-GDP, relevant for countries with sovereign debt sustainability vulnerabilities. - Frees public funds for other purposes (e.g., education). - Example model: an asset backed security (ABS) fund where a development institution (IFC) took the first-loss tranche of 125 million dollars and the total deal size was about 2 billion dollars; the senior tranche was 90% of the fund value, indicating potential public:private leverage ratios typically at 1:9 or even 1:10. - Using the IFC-Amundi deal as representative, approximately 10% of public funds worldwide would have to be committed to finance the renewable energy capacity required to replace coal: - Governments would have to commit around 2.9 trillion dollars (in present value terms) into junior tranches. - The remaining 90% would be financed by private capital markets. - Consideration of marginal cost of public funds (MCPF): - MCPF tends to range between 1.1 and 1.6. - If applying 1.6 to the public investments of 2.9 trillion dollars, the present value of public’s costs rises to around 4.5 trillion dollars. - This would reduce the global net gain from phasing out coal and phasing in renewables from the conservative baseline estimate of around 85 trillion dollars to around 80 trillion dollars. - For countries with weak fiscal positions or debt distress, taking on more climate financing could be problematic; mechanisms such as sovereign debt restructuring can create fiscal space for climate financing. *Source: wpiea2022107-print-pdf - 5.2 Climate Finance to Phase Out Coal* ### 26.1 trillion dollars) would come from capital markets. Importantly, this blended finance model ### Country Costs and Benefits: An Economic Basis for Coasian Bargaining on Climate Finance ### Country-level social cost of carbon (SCC) and benefit calculation - Country-level SCC estimates ˆθy of Ricke et al. (2018) are used to allocate the global mean SCC θ across countries such that the sum of country-level mean SCCs θy equals the global mean SCC θ. - Benchmark global mean SCC: θ = $80/tCO2. - Country share: θy = θ × (ˆθy / ˆθ). - Present value of benefits to country y in a global coal phase-out: - Bs1,s2,θy y,t,T = θy × ∑_{i∈C} ∑_{τ=t+2}^{T} ∆E s1,s2 i,τ (Equation 18). - Present value of costs to country y is C s1,s2,s r y,t,T (defined in Section 3.2). - Baseline Coasian bargaining position: each country pays its own costs C s1,s2,s r y,t,T to replace coal with renewables. ### Heterogeneity of country-level costs and benefits; implications for financing - Most countries lie above the diagonal in the country-level cost–benefit plot (Figure 10) and are better off joining a global phase-out even if they must cover all their country-level costs. - Countries that gain substantially from others’ emission reductions can rationally offer foreign finance F y,w to pay part or all of other countries’ replacement costs while retaining net benefit, provided: - B s1,s2,θy y,t,T − C s1,s2,s r y,t,T − ∑_{w∈Y\y} F y,w > 0. - Example statistics from regional/country illustrations: - Africa’s investment need to replace coal with renewables: $2.3 trillion. - Africa’s benefits from its own avoided emissions (collective SCC of Africa): $0.5 trillion. - Benefits to North America if Africa phases out coal: around $3.0 trillion. - Emerging-market country A: costs to replace coal with renewables = $6.1 trillion; benefits from its own emission reductions = $2.9 trillion (open dot). - Benefits to developed country B if country A phases out coal: $7.6 trillion. - Country A’s benefit in a global deal (solid dot): $12.8 trillion. - These examples show it can be in the enlightened self-interest of wealthier regions to fully or partially finance coal phase-outs elsewhere. ### Regional climate clubs and scaling of benefits - Regional deals (climate clubs) lower transaction costs and bargaining obstacles and can deliver tangible benefits even if not global. - Present value of benefits to countries y ∈ YU from a climate club W: - Bs1,s2,θU,W U,t,T = θU × ∑_{y∈YW} ∑_{i∈C} ∑_{τ=t+2}^{T} ∆E s1,s2 i,y,τ (Equation 19), - where θU = ∑_{y∈YU} θy (collective SCC). - Larger climate clubs (in terms of avoided coal emissions) approach the magnitude of benefits of a global deal. ### Blended finance, leverage parameters, and practical deal design - Blended finance can change governments’ calculus: if only 10% of costs come from public funds via a 1:9 arrangement, it is much easier to justify a phase-out. - Parameter α = 10% for a 1:9 blended finance arrangement: - Foreign contributed amount F U,W would typically satisfy F U,W ≤ α × C s1,s2,s r W,t,T (example: F U,W ≤ $0.23 trillion). - Example: Indonesia Just Energy Transition Partnership: - $20 billion in climate finance promised to help Indonesia build out renewables, conditional on commitment to phase out coal. - Deal structure: blended finance in which 50% of financing comes from capital markets. - The deal is framed as “just” by offering compensation for the opportunity cost of coal. - Financing needs quantified across countries; blended climate finance is highlighted as a promising avenue to catalyze public investments and crowd in private capital. ### Carbon leakage and conditionality - Carbon leakage (emission increases elsewhere after reductions in one set of countries) is a concern absent global agreement. - The analysis reduces carbon leakage risk by matching reductions in coal with energy-equivalent additions in renewables. - Critical design feature: climate finance to expand renewable energy capacity must be conditional on phasing out coal to ensure emission reductions occur and to avoid leakage. - Phasing in renewables concurrently with phasing out coal is critical to ensure sufficient energy supply. ### Coasian rationale and normative implications - Coasean logic: pay the polluter to stop polluting if doing so makes the payer better off. - From a Coasian perspective, cross-country transfers to cover costs of building renewables in developing countries can be self-interested for rich countries if the transfers yield significant emission reductions and avoided climate damages. - Even coal-focused, block-by-block deals (targeting the most coal-polluting countries first) can quickly realize most of the global benefits: - From approximately 1425 GtCO2 avoidable by phasing out coal under a net zero 2050 scenario, around 1210 GtCO2 are in the top-9 coal-reliant countries. - Strategy: strike conditional blended financing deals with each of these top-9 countries to capture large net benefits. ### Quantified global conclusion and policy takeaways - Main quantitative conclusion: phasing out coal and replacing it with renewables yields large net economic and social gain. - Estimated global net economic gain (conservative): around $85 trillion. - Benchmark average social cost of carbon used: $80/tCO2. - Costs: investment costs to build replacement renewable energy and compensate for opportunity costs of coal. - Practical impediments: obstacles to bargaining and poorly defined property rights can prevent Coasian global bargaining; perceived limited benefits and political hurdles impede mobilization of finance. - Example shortfall: difficulty in garnering a mere $100 billion a year in climate finance for developing countries, far less than the 1 2 to 2 trillion dollars a year necessary to phase out coal around the world. - Policy recommendations and design principles: - Prioritize blended climate finance to leverage private capital and limit public fiscal exposure (e.g., 1:9 junior equity tranche arrangements). - Make climate finance conditional on credible coal phase-out commitments and concurrent renewable deployment to avoid carbon leakage. - Pursue deals by blocks — focus on top coal-polluting countries first — to capture the bulk of avoidable emissions (top-9 countries account for around 1210 GtCO2 of the 1425 GtCO2 total). - Use Coasian bargaining logic to justify cross-border transfers: rich countries can be better off by paying to avert foreign emissions that damage them. *Italic: Content derived from the specified IMF working paper section.* ### References ### wpiea2022107-print-pdf - References ### Coal replacement benefits and residual emissions accounting - Present value of residual benefits from renewables built over [t+2, T] that accrue in [T+1, T̄] is B^{s1,s2,sr,θ}_{t,T+1,T̄} = θ × Σ_{τ=T+1}^{T̄} Σ_{y∈Y} ΔE^{s1,s2,sr}_{y,t,T,τ}. - Baseline renewable lifetime used: 30 years. - Example: horizon [t+2, T] with T = 2070; a solar plant built in 2069 with a 30-year lifetime yields residual avoidance of coal emissions in 2069–2099. - Numerical illustration: carbon arbitrage gain underestimated by $44 − $23 = $21 trillion using θ_{pindyck} = $80/tCO2 if benefits truncated at T = 2070 instead of accruing to 2099. ### Investment needs: overview and conservative framing - Baseline captures investment costs to expand renewable capacity but initially excludes additional investments in storage and grid extensions; authors present conservative (high) upper-bound estimates for storage and grid. - Assumption for reliable grid in high-renewable scenarios (following Way et al. (2021)): - Short-term storage capacity must store 20% of daily renewable generation. - Long-term storage must store one month of annual renewable generation (σ = 1/12). - Alpha for short-term storage in baseline: α = 0.2/365 (i.e., 20% of daily generation). ### Short-term battery storage (Li‑ion) — quantities, costs, learning - Shortfall in storage D^{...}_{b,y,τ} = max{R^{...}_{y,τ} × α − R^{...}_{b,y,τ}, 0}. - Unit investment cost normalization and baseline unit costs: - Global cumulative installed battery storage up to t−1 = 2021: 4,222,800 GJ (1173 GWh). - Unit investment cost at t = 2021/2022: $86,111/GJ ($310/kWh). - Estimated learning parameter and learning rate for batteries: - Θ_b = 25.3% reduction in investment costs per doubling of installed capacity. - Corresponding learning rate γ_b = 0.42. - Battery lifetime and depreciation assumptions: - Depreciation rate d_b = 0. - Estimated lifetime l_b = 12 years (assuming one charge/discharge cycle per day). ### Long-term storage (Power-to-X / electrolyzers) — capacities, efficiencies, costs, learning - Storage technology focus: PEM electrolyzer used as representative for P2X long-term storage. - Required electrolyzer capacity formula: G^{...}_{e,y,τ} = max{ h^{-1}(R^{...}_{y,τ}) × σ / (f_e) × ψ − S^{...}_{e,y,τ}, 0 }. - Parameters and assumptions: - σ = 1/12 (one month of annual generated renewable energy). - Conversion efficiency ψ = 0.7 (around 30% loss when converting hydrogen back to electricity). - Electrolyzer capacity factor f_e = 0.5. - Electrolyzer lifetime l_e = 16 years. - Electrolyzer depreciation rate d_e = 0. - Electrolyzer unit investment cost and experience-base: - Global cumulative electrolyzer capacity at t−1 = 2021: 0.08024 GW (80.24 MW). - Unit investment cost at t = 2022: $1,313,000,000/GW ($1,313/kW). - Electrolyzer learning rate Θ_e = 8.6%. ### Investment costs to power electrolyzers with renewables - Extra renewables must be installed to compensate for ψ < 1. Present value of these investment costs is I^{...}_{pe,y,t,T} = Σ_{τ=t+2}^{T} (1+ρ)^{−(τ−t)} I^{...}_{pe,y,τ}. - Shortfall for renewables powering electrolyzers: - D^{...}_{pe,y,τ} = max{ R^{...}_{y,τ} × σ × (1/ψ − 1) − R^{...}_{pe,y,τ}, 0 }. - Learning effects: additional renewable capacity built for electrolyzers accelerates cumulative experience and drives down renewable i^{...}_{q,τ} per equation 25. ### Grid extension costs: empirical proxies and conservative upper bounds - Historical averages (2012–2021): - Average global annual investments in electricity networks: ≈ $280 billion/year. - Average annual electricity generation: ≈ 26.9 PWh. - Implied annual investment per unit generation: ≈ $10.4 billion/PWh. - Unit cost assumed for grid extension (triple-voltage lines, transmission + distribution): $14.9 billion/PWh. - Conversion used: c_g = $4.14/GJ (equals $14.9 billion/PWh). - Grid investment cost in year τ: I^{...}_{g,y,τ} = c_g × R^{...}_{y,τ}. - Present-value aggregation: I^{...}_{g,y,t,T} = Σ_{τ=t+2}^{T} (1+ρ)^{−(τ−t)} I^{...}_{g,y,τ}. - Authors note this estimate is an upper bound for at least three reasons: - Only incremental grid investments above business-as-usual (~$280 billion/year) should be considered. - Replacing coal in power sector alone may not increase overall electrification materially. - Built storage capacity can reduce peak loads and thus grid expansion needs. ### LCOE as proxy for renewable investment costs — values and learning - Proxy present value of renewable investment costs by discounted sum of phased-out coal energy g(ΔP^{...}_{τ}) × weighted average LCOE. - Baseline 2020 LCOE global averages (dollars per GJ): - L_{solar,2020} = 10.83 $/GJ. - L_{wind-onshore,2020} = 15.83 $/GJ. - L_{wind-offshore,2020} = 23.33 $/GJ. - Same learning rate γ_q applied to LCOE as to investment costs; mapping L_{q,τ} = L_{q,t2020} × [i^{...}_{q,τ} / i^{...}_{q,t2020}]. - 2020 LCOE values expressed per MWh (for reference in the text): - L_{solar,2020} = 39 $/MWh. - L_{wind-onshore,2020} = 57 $/MWh. - L_{wind-offshore,2020} = 84 $/MWh. ### Fossil and nuclear replacement variants - Coal replacement with natural gas: - If ω_{gas,sr}% of replacement is natural gas, benefits must be reduced by θ × ω_{gas,sr} × ̃φ_{gas} × Σ_{i∈C} Σ_{τ=t+2}^{T} g(ΔP^{...}_{i,τ}), where ̃φ_G is global weighted-average emission intensity of natural gas (tCO2/GJ). - Proxy investment costs for natural gas using LCOE: 2020 global average L_{gas,2020} = $19.4/GJ ($70/MWh). - Coal replacement with nuclear: - Benefits treated same as renewables (both are non-emitting). - Proxy investment costs for nuclear using LCOE; authors take 2020 IEA estimate around L_{nuclear,2020} = $19.4/GJ ($70/MWh) as used in the appendix. ### Broader opportunity costs of coal: jobs, wages, retraining - Global coal employment baseline: W^{2019}_t = 4.6 million workers in 2019. - Job loss projection under phase-out: - Coal job losses in country y at time t: j^{s2}_{y,t} = W^{2022}_{y,t} × (P^{s2}_{y,t−1} − P^{s2}_{y,t}) / P^{2022}_y. - Wage-compensation baseline assumptions: - Average coal miner wage data assembled for 2022; where unavailable, average mining wages used and converted using October 22, 2022 exchange rates. - Baseline compensation duration l = 5 years (authors note l = 5 is consistent with some policy examples). - Present value of wage-compensation for lost coal jobs in country y: - O^{s2,J}_{y,t,T} = Σ_{τ=t+2}^{T} j^{s2}_{y,τ} × w̄_{y,τ} × l × (1+ρ)^{−(τ−t)}. - Retraining costs per worker: - Louie and Pearce (2016) U.S. 2012 retraining estimates (per coal worker): - Best case, low: $2,014.60 - Best case, high: $7,231 - Worst case, low: $6,009 - Worst case, high: $20,863.18 - Baseline adopted for conservatism: $7,231 (best case, high). - Retraining cost scaling to other countries via wage ratio: - ī^{R}_{y,t} = (w̄_{y,t} / w̄_{USA,t}) × ī^{R}_{USA,t}. - Present value of retraining costs in country y: - O^{s2,R}_{y,t,T} = Σ_{τ=t+2}^{T} j^{s2}_{y,τ} × ī^{R}_{y,τ} × (1+ρ)^{−(τ−t)}. - Baseline assumption: retraining costs in future years equal to 2012 values scaled by wages. ### Units and conversion factors (as reported in the appendix Table 8) - Social cost of carbon θ: dollars per tonne of CO2 ($/tCO2). - Emissions E: tonnes of CO2 (tCO2). - Coal production P: tonnes of coal. - Unit coal profit π: dollars per tonne of coal ($/tonne of coal). - Renewable capacity S and capacity additions G: Gigawatt (GW). - Unit investment costs i: dollars per Gigawatt ($/GW). - Renewable energy per year R: GJ/year. - Conversion functions and constants: - h(x): GW → GJ/year by x × [# seconds per year]. - h^{-1}(y): GJ/year → GW by y / [# seconds per year]. - g(P): tonnes of coal → GJ, using P × 29.3076 (1 tonne of coal equivalent = 29.3076 GJ). - f(y): MWh → GJ by y × 3.6. - # seconds per year = 365.25 × 24 × 3600. _Italic: Source — The Great Carbon Arbitrage, Working Paper No. WP/2022/107 (Appendix A and References section)._ --- _Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022107-print-pdf.pdf_