## htnea2025009

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### Introduction and purpose
- Climate change threatens macroeconomic and financial stability through rising temperatures, shifting precipitation patterns, sea level rise, and more frequent and intense extreme weather.
- Purpose: show how to include the effect of rising temperatures into long-term GDP projections using a three-step method:
  - (1) estimating macroeconomic effects of rising temperatures from historical data,
  - (2) building temperature change scenarios from climate model simulations,
  - (3) integrating impacts into long-term GDP projections.
- Scope and availability:
  - Impact assessments for 171 countries are available in an online Data Appendix.
  - Focuses on rising temperatures; abstracts from precipitation changes, extreme weather events, tropical cyclones, sea level rise, and mitigation/transition risks.

### Three-step methodological approach (overview)
- Step 1: Select empirical model of climate change impacts.
  - Note adopts Kahn and others (2021) methodology with enhancements: use of latest climate scenarios, calculation of confidence intervals for all impact projections, and inclusion of a very slow adaptation scenario.
- Step 2: Select climate scenarios.
  - Uses CMIP6 climate model outputs and Shared Socio-Economic Pathways (SSPs) from IPCC AR6.
- Step 3: Introduce estimated impacts into macro-fiscal projections.
  - Illustrative example adjusts GDP series and projects public debt using a simple macro-fiscal framework.
- Adaptation assumptions considered: m = 20, 30, 40, 50 years (reference m = 30 aligns with climatological normals).

### Empirical approach and identification challenges
- Data and estimator:
  - Panel of 174 countries from 1960 to 2014.
  - Key estimator: ARDL specification in first differences relating GDP growth to contemporaneous and lagged first differences of temperature deviations from their m-year moving average.
- Main empirical findings:
  - Persistently higher temperatures above their long-term averages lead to cumulatively lower GDP levels in rich and poor countries, and in hot and cold countries.
  - The critical driver is the change in the trend of temperature (deviations from the moving climate average), not the absolute temperature level.
- Identification and extrapolation issues:
  - Regressing stationary growth on trended temperature levels creates non-stationarity and bias unless trends cancel exactly.
  - Empirical estimates derived from random anomalies must be carefully translated to permanent trend shifts because adaptation, behavior, and technology may change.
- Preferred specification advantages:
  - ARDL in first differences with moving-average-based temperature deviations avoids linking stationary growth to trended temperature levels, addresses serial correlation, and models adaptation via the choice of m.

### Model mechanics and calculation procedure
- Baseline FE and ARDL forms:
  - Baseline FE (Dell, Jones, and Olken (2012)): r_{i,t} = Δ ln(y_{i,t}) = α_i + θ_{r,t} + β T_{i,t} + ε_{i,t}
  - Kahn et al. (2021) formulation (first-difference ARDL): Δ ln(y_{i,t}) = α_i + Σ_{j=1}^{p} φ_j Δ ln(y_{i,t-j}) + β Σ_{l=0}^{2m} Δ |T_{i,t} − (1/m) Σ_{l=1}^{m} T_{i,t-l}| + Δ ε_{i,t}
- Long-run multiplier and steady-state:
  - Long-run multiplier = (Σ β_j) / (1 − Σ φ_j)
  - Steady-state expected growth: E[Δ ln(y_{i,t})] = α_i / (1 − Σ φ_j)
- Procedure to calculate country impacts (2015–2100):
  1. Use median ensemble projection for selected emission scenario to compute country temperature change 2015–2100.
  2. Smoothly perturb historical trend using constant acceleration/deceleration to match scenario warming (avoids abrupt change in 2016).
  3. Calculate annual impacts on growth using ARDL and the long-run multiplier.
- Numerical example from model mechanics:
  - Historical trend δ_{1,i} = 0.01 °C per year → temperature increase 2015–2099 = 0.85 °C.
  - Scenario predicts temperature increase = 1.7 °C → δ_{1,i}^1 = 0.02; then d_i = 0.000233; δ_{1,i,2015}^1 = 0.010233; δ_{1,i,2057}^1 = 0.02; δ_{1,i,2099}^1 = 0.0298.
- Adaptation parameter m determines speed of adaptation and magnitude of GDP impact (larger m → slower adaptation → larger impacts).

### Climate scenarios used and physical assumptions
- Core SSP scenarios and median global outcomes (relative to pre-industrial averages reported in source):
  - SSP1-2.6: global mean temperature stabilizes around 2°C.
  - SSP2-4.5: global mean temperature increases by approximately 2.7°C in 2100.
  - SSP3-7.0: temperature increases by 3.6°C in 2100.
  - SSP3-7.0 90th percentile: pessimistic/high-warming sensitivity; summary pessimistic case increases by approximately 4.4°C by end-century.
- Data processing:
  - Model outputs processed with a 31-year moving average filter; anomalies relative to 1985–2014 average calculated.
  - Temperature projections conclude in 2099; from 2084 onward the 31-year moving average uses repeated 2099 values for missing subsequent years; GDP impacts for 2100 are based on 2099 climate data.

### Scenario patterns, adaptation role, and geographic heterogeneity
- Scenario-specific GDP impact tendencies:
  - SSP1-2.6: often yields positive impacts on per capita GDP growth relative to the Present Trend reference because mitigation reduces warming relative to historical trend.
  - SSP2-4.5: temperature trends similar to past observations → almost no impact on GDP relative to Present Trend.
  - SSP3-7.0 and SSP3-7.0 90th: produce larger negative GDP impacts as warming continues or accelerates.
- Adaptation sensitivity:
  - Reference m = 30 years; comparisons include m = 20, 40, 50 years.
  - Longer m implies slower adaptation and larger, more persistent GDP losses.
  - Even with adaptation, losses relative to a no-climate-change counterfactual are not fully recovered.
- Geographic heterogeneity:
  - All countries are negatively affected by acceleration in their warming trend and positively affected by reduction.
  - Impacts driven by deviations from expected temperatures rather than an absolute global optimal temperature.
  - Cold countries suffer more than temperate or hot countries only if they warm faster.

### Key statistics: distribution of real GDP impacts across countries (percent deviations relative to reference)
- SSP1-2.6 (percent deviations of real GDP relative to reference scenario)
  - Min: -0.04 (2030), -0.16 (2050), -0.49 (2075), -0.93 (2100)
  - p25: 0.01 (2030), 0.02 (2050), 0.04 (2075), 0.06 (2100)
  - Median: 0.07 (2030), 0.17 (2050), 0.27 (2075), 0.33 (2100)
  - p75: 0.15 (2030), 0.34 (2050), 0.50 (2075), 0.58 (2100)
  - Max: 0.45 (2030), 1.01 (2050), 1.38 (2075), 1.33 (2100)
- SSP2-4.5 (percent deviations)
  - Min: -0.22 (2030), -0.67 (2050), -1.67 (2075), -2.88 (2100)
  - p25: -0.10 (2030), -0.31 (2050), -0.64 (2075), -1.00 (2100)
  - Median: -0.05 (2030), -0.16 (2050), -0.30 (2075), -0.46 (2100)
  - p75: 0.00 (2030), 0.00 (2050), -0.01 (2075), -0.01 (2100)
  - Max: 0.24 (2030), 0.58 (2050), 0.94 (2075), 1.20 (2100)
- SSP3-7.0 (percent deviations)
  - Min: -0.5 (2030), -1.6 (2050), -3.4 (2075), -5.4 (2100)
  - p25: -0.3 (2030), -0.9 (2050), -1.9 (2075), -3.0 (2100)
  - Median: -0.2 (2030), -0.7 (2050), -1.5 (2075), -2.3 (2100)
  - p75: -0.2 (2030), -0.5 (2050), -1.0 (2075), -1.5 (2100)
  - Max: 0.1 (2030), 0.1 (2050), 0.3 (2075), 0.4 (2100)
- SSP3-7.0 90th (percent deviations)
  - Min: -0.9 (2030), -2.4 (2050), -5.1 (2075), -8.0 (2100)
  - p25: -0.6 (2030), -1.8 (2050), -3.7 (2075), -5.5 (2100)
  - Median: -0.5 (2030), -1.5 (2050), -3.0 (2075), -4.6 (2100)
  - p75: -0.4 (2030), -1.2 (2050), -2.5 (2075), -3.8 (2100)
  - Max: -0.1 (2030), -0.3 (2050), -0.6 (2075), -0.8 (2100)

### Selected country-level illustrative impacts (m = 30; percent deviations with 95 percent bootstrap confidence intervals in brackets)
- Afghanistan (AFG)
  - SSP1-2.6: 2050 = 0.86 [0.36 1.39]; 2100 = 1.13 [0.48 1.82]
  - SSP2-4.5: 2050 = 0.51 [0.21 0.82]; 2100 = 1.02 [0.43 1.65]
  - SSP3-7.0: 2050 = -0.34 [-0.56 -0.14]; 2100 = -0.91 [-1.48 -0.39]
  - SSP3-7.0 90th p.: 2050 = -1.19 [-1.93 -0.5]; 2100 = -3.32 [-5.39 -1.41]
- Bangladesh (BGD)
  - SSP1-2.6: 2050 = -0.16 [-0.25 -0.06]; 2100 = -0.93 [-1.52 -0.39]
  - SSP2-4.5: 2050 = -0.51 [-0.82 -0.21]; 2100 = -2.43 [-3.96 -1.03]
  - SSP3-7.0: 2050 = -1.08 [-1.75 -0.45]; 2100 = -4.28 [-6.95 -1.81]
  - SSP3-7.0 90th p.: 2050 = -1.91 [-3.11 -0.79]; 2100 = -6.53 [-10.61 -2.76]
- China (CHN)
  - SSP1-2.6: 2050 = 0.34 [0.14 0.55]; 2100 = 0.69 [0.29 1.12]
  - SSP2-4.5: 2050 = -0.3 [-0.49 -0.13]; 2100 = -0.8 [-1.29 -0.34]
  - SSP3-7.0: 2050 = -1.12 [-1.81 -0.47]; 2100 = -3 [-4.88 -1.27]
  - SSP3-7.0 90th p.: 2050 = -2.22 [-3.6 -0.93]; 2100 = -5.82 [-9.46 -2.47]
- India (IND)
  - SSP1-2.6: 2050 = -0.1 [-0.17 -0.04]; 2100 = -0.29 [-0.47 -0.12]
  - SSP2-4.5: 2050 = -0.5 [-0.81 -0.21]; 2100 = -1.58 [-2.57 -0.67]
  - SSP3-7.0: 2050 = -1.26 [-2.05 -0.52]; 2100 = -3.79 [-6.16 -1.6]
  - SSP3-7.0 90th p.: 2050 = -2.15 [-3.49 -0.89]; 2100 = -6.09 [-9.89 -2.58]
- United States (USA)
  - SSP1-2.6: 2050 = -0.02 [-0.04 -0.01]; 2100 = -0.06 [-0.1 -0.03]
  - SSP2-4.5: 2050 = -0.67 [-1.09 -0.28]; 2100 = -2.08 [-3.38 -0.88]
  - SSP3-7.0: 2050 = -1.61 [-2.61 -0.67]; 2100 = -4.81 [-7.82 -2.04]
  - SSP3-7.0 90th p.: 2050 = -2.31 [-3.74 -0.96]; 2100 = -6.67 [-10.83 -2.82]

### Incorporating warming impacts into macroeconomic and fiscal projections
- Two equivalent ways to introduce impacts:
  - Level adjustment: Y_{i,t,s}^1 = (1 + α_{i,t,s}/100) Y_{i,t}^0 where α_{i,t,s} is the percentage impact of scenario s on GDP.
  - Growth adjustment: Y_{i,t+1,s}^1 = (1 + r_{i,t} + η_{i,t,s}) Y_{i,t}^1 where η_{i,t,s} measures the scenario impact on growth rate in percentage points.
- Illustrative example (Figure 9):
  - Starting GDP: 10 Billion LCU in 2025
  - Reference growth: 3 percent constant until 2050
  - Under an acceleration of warming, GDP is approximately 6 percent lower in 2050 than in the reference scenario.
- Fiscal illustration:
  - Balanced budget initially, no public debt.
  - Government expenditure and fiscal revenues equal to 25 percent of GDP.
  - Public debt grows from zero to approximately 15 percent of (climate adjusted) GDP in 2050 as a result of GDP losses.
- Tools:
  - IMF Q-CRAFT operationalizes methods for long-term climate fiscal risk scenarios.

### Uncertainty, worst-case construction, and data availability
- Statistical uncertainty:
  - Dotted lines indicate 95 percent bootstrap confidence intervals around central estimates.
  - Uncertainty grows over time and becomes large at the end of the century for fast-warming scenarios with slow adaptation.
- Worst-case scenario can be constructed by combining:
  - very high emissions: SSP3-7.0
  - very fast warming: 90th percentile
  - very slow adaptation: 50 years
  - the lower bound of the confidence intervals
- All country-year data (temperature scenarios, GDP impacts, confidence intervals, percentiles across climate models, and adaptation assumptions) available in the companion data set for all years until 2099 (GDP impacts for 2100 based on 2099 climate data).

### Policy relevance, cautions, and recommended extensions
- Policy relevance:
  - Integrating climate impacts into long-term macroeconomic projections avoids optimistic biases in planning and debt sustainability analysis.
  - Adaptation materially reduces estimated losses; models with gradual adaptation yield much smaller losses than models with little or no adaptation.
- Cautions and limitations:
  - Spillovers through trade, financial flows, and migration are not included.
  - Inference about future damages based on past data is uncertain.
  - Estimates likely conservative because many impacts are excluded: global climate tipping points, societal tipping points, non-market damages, sea-level rise, ocean acidification.
- Recommended extensions:
  - Account for heterogeneity in impacts and spillover effects.
  - Incorporate direct impacts of climate change on fiscal variables (revenue and expenditure) beyond indirect GDP effects.
  - Combine GDP losses from rising temperatures with macroeconomic losses from other climate impacts where available.

*Source: htnea2025009 — IMF | How to Note NOTE/2025/009*

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

### Introduction

### Summary and purpose
- Climate change threatens macroeconomic and financial stability through rising temperatures, shifting precipitation patterns, sea level rise, and more frequent and intense extreme weather, in addition to other factors.
- To better assess vulnerabilities and future risks, climate change effects should be integrated in long-term macroeconomic projections.
- This note shows how to include the effect of rising temperatures into long-term GDP projections using a three-step method:
  - (1) estimating macroeconomic effects of rising temperatures from historical data,
  - (2) building temperature change scenarios from climate model simulations, and
  - (3) integrating impacts into long-term GDP projections.
- The methodology addresses key empirical challenges and can be leveraged to assess the effects of temperature increases on fiscal variables, including public debt.
- Impact assessments for 171 countries are available in an online Data Appendix.

### Structure of the How-to Note (contents list)
- Introduction
- The Empirical Literature on the Macroeconomic Impact of Rising Temperatures
- Unbiased Macroeconomic Estimates of Trend Temperature Increases
- Impacts of Trend Temperature Increase on GDP Using Climate Scenarios
- Introducing the Impacts of Trend Temperature Increases in Macroeconomic Projections
- Conclusion
- Appendix 1. Model Specification
- Appendix 2. Data on Temperature Scenarios and Their Impacts on GDP in All Countries
- References
- Box 1. A Schematic Description
- Figures: 1–9 (titles listed in source)
- Table 1. Key Statistics for the Distribution Across Countries of Impacts of Warming Trends on Real GDP in 2100

### Key methodological elements highlighted
- A three-step approach to include climate impacts in macroeconomic frameworks (Figure 1).
- Empirical challenges are acknowledged and addressed in the methodology (see "Unbiased Macroeconomic Estimates of Trend Temperature Increases" and Appendix 1. Model Specification).
- Temperature change scenarios are constructed from climate model simulations (see "Building temperature change scenarios from climate model simulations").
- Integration of impacts into long-term GDP projections enables assessment of effects on fiscal variables, including public debt (see "Introducing the Impacts of Trend Temperature Increases in Macroeconomic Projections" and Figure 9).

### Availability and scope
- Impact assessments cover 171 countries and are provided in an online Data Appendix.
- The note includes figures that illustrate:
  - Growth and Temperature (Figure 2)
  - Additional Global Temperature Increase Under Different Scenarios (2014–2100) (Figure 3)
  - Country-level temperature scenarios and GDP impacts using 30-year historical norms and varying adaptation assumptions (Figures 4–7)
  - Cross-country distribution of GDP impacts in 2100 and representative scenarios for GDP, deficit, and debt (Figures 8–9)
- Table 1 reports key statistics for the distribution across countries of impacts of warming trends on real GDP in 2100.

*IMF | How to Note NOTE/2025/009 — How to Include the Effects of Rising Temperatures in Long-Term GDP Projections*

### Introduction

### Introduction

### Climate change channels and macroeconomic relevance
- Climate change affects both supply and demand:
  - Supply-side: reduced agricultural crop yields; diminished labor productivity due to impaired physical and cognitive performance; increased mortality and morbidity; more severe droughts affecting agriculture and hydropower electricity generation; more frequent and intense extreme weather accelerating capital depreciation and slowing capital accumulation; sea level rise impairing coastal infrastructure and causing permanent inundation of coastal land.
  - Demand-side: changes in consumption and investment decisions; higher temperatures increasing energy demand for cooling; higher uncertainty impacting business investment decisions.
- Combined effects can produce significant long-term impacts on economic growth.
- Integrating climate change effects into long-term macroeconomic projections is crucial to avoid optimistic biases in planning and debt sustainability analysis (for example, projecting optimistic debt-to-GDP ratios and underestimating debt risks if climate change reduces future output, increases debt, or both).

### Gap in literature and empirical approaches
- Substantial literature examines temperature–GDP links using econometric methods (examples cited: Dell, Jones, and Olken 2012; Burke, Hsiang, and Miguel 2015; Kalkuhl and Wenz 2020; Kahn and others 2021; Tol 2021; Kotz, Levermann, and Wenz 2024; Akyapi, Bellon, and Massetti 2025).
- Far less work evaluates climate change effects on broader macroeconomic variables beyond GDP (for example, government revenue, expenditure, financial conditions, and debt ratios).
- Empirical panel-data approaches directly estimate net impacts of temperature increases on macroeconomic variables without modeling sectoral interdependencies.
- Two empirical paradigms in the literature:
  - Temperature changes affect GDP levels but not long-run GDP growth (example: a 1°C shock reduces GDP by 0.5 percent → a 2°C permanent increase reduces GDP by 1 percent).
  - Temperature shocks affect the growth rate permanently (example: a 1°C shock reduces GDP growth by 0.1 percentage points → a 2°C permanent increase reduces growth by 0.2 percentage points).
- Differences in empirical methods, adaptation assumptions, and emissions scenarios produce widely varying impact estimates.

### Three-step practical approach adopted in this note
- Figure 1 summarizes a three-step approach:
  - Select empirical model of climate change impacts.
  - Use climate scenarios to project impacts.
  - Introduce estimated impacts in macro-fiscal projections.
- Implementation details in this note:
  - Step 1: Select a robust method. This note adopts the methodology of Kahn and others (2021) (grounded in growth theory, addresses econometric challenges, highlights role of adaptation). Enhancements include: (1) leveraging the latest climate scenarios, (2) calculating confidence intervals for all impact projections to display statistical uncertainty, (3) adding a scenario with very slow adaptation.
  - Step 2: Select climate scenarios. This note uses the latest warming scenarios drawn from dozens of climate models prepared for the Sixth Assessment Report of the IPCC (AR6).
  - Step 3: Modify long-term macroeconomic projections for temperature impacts under chosen climate scenarios. The note includes an illustrative example showing how to adjust a GDP series and project changes in public debt using a simple macro-fiscal framework.
- Data availability: Time series data on GDP impacts for three climate scenarios and a special high-warming scenario, under four alternative assumptions about adaptation, are available with empirical confidence intervals in the online Data Appendix for each year until 2100, for 171 countries.
- Scope limitations:
  - Focuses on rising temperatures as one dimension of climate change.
  - Abstracts from precipitation changes, extreme weather events, tropical cyclones, and sea level rise (noted as important risks to integrate where relevant).
  - Abstracts from catastrophic risks from passing global climate thresholds due to substantial uncertainty in quantification.
  - Macroeconomic implications of mitigation policy and transition risks are outside the scope.

### Empirical identification challenges and model choice
- Key empirical challenges:
  - Identification: causal effects of temperature on macro variables are complicated by empirical obstacles; if estimated effects differ from “true” effects, projections are flawed.
  - Extrapolation: empirical estimates use random temperature shocks (anomalies) but are applied to permanent shifts (climate change). Behavioral, technological, and institutional adaptation to persistent changes can alter long-run outcomes.
  - Non-stationarity: regressing GDP growth (stationary) on temperature levels (positively trended) leads to biased estimates unless time trends exactly cancel trend temperature increases.
- Illustration:
  - Example parameter interpretation: in regression r_{i,t} = α_i + θ_{r,t} + β T_{i,t} + ε_{i,t}, β measures effect of temperature on growth. If β = −0.2 and average temperature = 20°C, then a year with temperature = 20.5°C implies growth lower by 0.1 percentage points (−0.2×(20.5−20) = −0.1).
  - Using temperature scenarios: a projected 2°C increase by 2050 relative to past thirty years implies average annual growth 0.4 percentage points lower (−0.2×(22−20) = −0.4) in the example above, with exponentially larger cumulative GDP divergences over time.
- Preferred econometric specification:
  - The note favors an Auto-Regressive Distributed-Lags (ARDL) approach in first differences with lags of dependent and independent variables included. This model relates GDP growth rates to lagged growth and both contemporaneous and lagged first differences of temperature deviations from their averages, avoiding direct linkage of stationary growth to trended temperature levels and addressing serial correlation and non-stationarity.

### Use cases and policy relevance
- The econometric approach is relatively straightforward and widely applied; ready-to-use climate datasets are increasingly available.
- Applications:
  - The Network for Greening the Financial System (NGFS) uses econometric relationships between GDP growth and weather variables to predict economic costs of climate change.
  - The IMF’s Quantitative Climate Risk Fiscal Tool (Q-CRAFT) relies on results in this note and the Data Appendix to predict effects of increasing temperatures on fiscal accounts and debt-to-GDP dynamics in the long run.
- Adaptation matters: models that include gradual adaptation yield much smaller losses than models with little or no adaptation.

*Source: htnea2025009 - Introduction*

### 1.   Demeaned GDP Growth and Demeaned Temperature

### 1.   Demeaned GDP Growth and Demeaned Temperature

### Empirical evidence and econometric approach
- Panel: 174 countries from 1960 to 2014.
- Key estimator: ARDL specification of GDP growth as a function of deviations of annual temperature from its moving average during the previous thirty years.
- Main empirical finding: Persistently higher temperatures above their long-term averages lead to cumulatively lower GDP levels in rich and poor countries, and in hot and cold countries.
- Econometric advantages of the Kahn and others (2021) strategy:
  - Allows regression in level terms and estimates long-term macroeconomic impact via the Half-Panel Jackknife Fixed Effects estimator to correct small sample bias.
  - Implicitly models adaptation by varying the speed with which historical norms are formed.
  - Accounts for state-specific and time-varying climate thresholds (a form of nonlinearity).
  - Circumvents pitfalls of including trended variables like temperature in output growth equations.

### Dynamics of temperature deviations and GDP impacts
- Benchmark for temperature shocks: moving average temperature (30-year moving average is the reference).
- Critical factor: change in the trend of temperature, not the absolute level of temperature.
- Persistence vs permanence:
  - Negative effect of long-term warming on GDP growth is persistent but not permanent.
  - If temperature trend stays constant relative to a baseline (the gray/baseline), economic growth remains unaffected; if trend accelerates, growth declines further; if trend decelerates, growth improves.
- Comparators used:
  - This note compares future temperature impacts to a baseline where temperature in each country rises according to its historical trend of 1960–2014 (the “Present Trend” reference).
  - Prior literature often used a “no further warming” counterfactual; implicit GDP loss by end-century under that comparator estimated at about 1.5 percent (Mohaddes and Raissi (2025) exercise).

### Box 1 — Schematic description and illustrative numerical example
- Variables in schematic: Temperature (°C); Temperature deviation from norm (°C / year); Annual GDP growth rate (Percent); GDP Index (Year 1 = 1); GDP With Respect to Baseline (Percent); GDP With Respect to Present Trend (Percent).
- Illustrative baseline growth rate used for illustration: 3% per year.
- Present Trend illustrative trajectory:
  - Temperature stabilizes at 23°C.
  - Results in an annual 0.05°C deviation of temperature from its 30-year moving average prior to gradual decline.
  - Growth stabilizes at 2.5% per year (down from 3% baseline), persisting over time.
  - GDP is permanently lower relative to the Baseline scenario; illustrative income loss eventually stabilizes at about 25 percent of baseline GDP.
- Alternative illustrative scenarios:
  - High scenario: warming accelerates; after initial temporary stability at 2.5%, GDP growth declines again for 30 years before converging to 2% implied by temperature trend; GDP losses larger and continue increasing relative to baseline because temperature never stabilizes.
  - Low scenario: temperature stabilizes at 22.4°C instead of 23°C; decline in warming rate starts earlier; growth converges faster back to the 3% baseline equilibrium and GDP is higher than under Present Trend and High scenarios.
- Interpretation: Using Present Trend as reference aligns with macroeconomic projections based on past observations; if temperature trend slows, GDP will be higher than projected; if trend increases, GDP will be lower.

### Climate scenarios, temperature projections, and GDP impacts
- Climate data and scenarios used:
  - New vintage of emission scenarios: Shared Socio-Economic Pathways (SSPs) and CMIP6 climate model data.
  - Core scenarios: SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP3-7.0 90th percentile (pessimistic/high-warming sensitivity).
- Scenario-specific warming outcomes (relative to pre-industrial averages):
  - SSP1-2.6: global mean temperature stabilizes around 2°C.
  - SSP2-4.5: global mean temperature increases by approximately 2.7°C in 2100.
  - SSP3-7.0: temperature increases by 3.6°C in 2100.
  - SSP3-7.0 90th percentile: used to include a high-emission high-warming sensitivity case.
  - Pessimistic case summary: Global temperature with the pessimistic case increases by approximately 4.4°C with respect to pre-industrial average level by end-century.
- Historical context:
  - At the time of the Paris Agreement's adoption in 2015, global temperatures were estimated to be 0.98°C above pre-industrial levels.
  - The planet has already warmed by approximately 1.2°C compared to pre-industrial averages (noted earlier in text).
- Modeling practice:
  - For each emission scenario, consensus temperature projections are calculated using multiple climate models; median warming trajectory across model-scenario combinations is used for impact estimation.
  - Data processing: model-scenario combination outputs are processed with a 31-year moving average filter; anomalies relative to the 1985–2014 average are calculated.
  - Temperature projections conclude in 2099; from 2084 onward the 31-year moving average uses repeated temperature values from 2099 for missing subsequent years; GDP impacts for 2100 are based on 2099 climate data.

### GDP impact patterns across scenarios and role of adaptation
- Sign and magnitude of GDP impacts:
  - SSP1-2.6 yields positive impacts on per capita GDP growth (i.e., GDP increases relative to the Present Trend reference) because temperature stabilizes and the warming trend is smaller than past decades—this reflects reduction of damage thanks to sharp emissions reductions (benefits of mitigation).
  - SSP2-4.5 displays temperature trends similar to past observations and thus has almost no impact on GDP; GDP growth in this scenario is largely consistent with baseline macroeconomic projections.
  - SSP3-7.0 and SSP3-7.0 90th produce larger negative GDP impacts as warming continues or accelerates.
- Adaptation (choice of time horizon for establishing temperature norms):
  - The length of the window used to form climate norms determines speed of adaptation and how fast growth diverges from and returns to baseline.
  - Reference standard: 30-year window (aligns with IPCC and World Meteorological Organization’s recommended climatological normals).
  - Longer windows imply slower adaptation and larger impacts; examples: using 40 or 50 years leads to more lasting impacts than using 30 years.
  - Using 20 years implies faster adaptation and quicker response to changes in temperature trends.
  - Adaptation does not eliminate GDP losses relative to a no-climate-change scenario; losses during the adjustment period and relative to a no-warming counterfactual are never fully recovered.
- Illustration of adaptation sensitivity:
  - Figure 6 explores impacts assuming adaptation offsets warming trend after 20, 30, 40, or 50 years; impacts are expressed as percent deviations of real GDP relative to a reference scenario where warming follows historical pattern.

### Methodological notes relevant for projections and interpretation
- The econometric estimate of temperature effects on GDP follows Kahn and others (2021), with projections recalculated for all countries using CMIP6 and SSPs.
- Projection procedure: historical trend in each country is perturbed by a constant annual acceleration (or deceleration) to match the median temperature change from 2015 to 2100 projected by an ensemble of climate models for each SSP.
- Practical guidance: If interest is measuring warming impacts in macroeconomic projections (which are based on past observations), using Present Trend as reference means no further adjustments to GDP are necessary; deviations arise when temperature trends change relative to the historical trend.
- Data and processing caveats:
  - Country-level temperatures are calculated by averaging CRU grid cells within country boundaries using area weights and excluding sea.
  - Some methodological approximations (e.g., repeated use of 2099 values for years beyond 2099 in moving averages) may underestimate positive or negative trends; analysts concerned may restrict analysis to year 2084.

*Source: IMF — htnea2025009 - 1.   Demeaned GDP Growth and Demeaned Temperature (How to Note).*

### 1. SSP1-2.6 2. SSP2-4.5

### htnea2025009 - 1. SSP1-2.6 2. SSP2-4.5

### Impact estimates and statistical uncertainty
- Impacts are estimated using Kahn and others (2021) and CMIP6 data (processed by Massetti and Tagklis (2024)) under the assumption that adaptation can offset the warming trend after 30 years.
- Dotted lines indicate 95 percent bootstrap confidence intervals around central estimates.
- The SSP3-7.0 90th percentile of climate model runs is treated as an independent extreme scenario; its own confidence intervals are calculated and the upper bound provides a worst-emission, worst-warming, worst-vulnerability case.
- Uncertainty grows over time and becomes large at the end of the century for fast-warming scenarios with slow adaptation because uncertainty compounds over time.
- A worst-case scenario can be constructed by combining:
  - very high emissions: SSP3-7.0
  - very fast warming: 90th percentile
  - very slow adaptation: 50 years
  - the lower bound of the confidence intervals

### Role of adaptation and sensitivity to adaptation speed
- The slower the response to a change in the temperature trend, the larger the impact on GDP.
- If projected warming is slower than in the historical period, slower adaptation can lead to larger positive impacts because expectations are updated with longer delay.
- The companion data set includes different assumptions on the speed of adaptation: 20, 30, 40, and 50 years.

### Geographic heterogeneity of impacts
- All countries are negatively affected by an acceleration in their warming trend and positively affected by a reduction in their warming trend.
- Impacts are driven by deviations from expected temperatures (changes relative to historical trends) rather than by a globally optimal temperature level.
- Cold countries suffer more than temperate or hot countries only if they warm faster.
- The long-run steady state growth level is unaffected in this model; long-term GDP projections primarily depend on technological progress and other drivers of growth.
- When compared to a hypothetical world without climate change (temperatures remaining at pre-industrial levels), all countries in all scenarios would have experienced macroeconomic losses.

### Key statistics: distribution of impacts on real GDP in 2100 across countries (Table 1)
- SSP1-2.6 (percent deviations of real GDP relative to reference scenario)
  - Min: -0.04 (2030), -0.16 (2050), -0.49 (2075), -0.93 (2100)
  - p25: 0.01 (2030), 0.02 (2050), 0.04 (2075), 0.06 (2100)
  - Median: 0.07 (2030), 0.17 (2050), 0.27 (2075), 0.33 (2100)
  - p75: 0.15 (2030), 0.34 (2050), 0.50 (2075), 0.58 (2100)
  - Max: 0.45 (2030), 1.01 (2050), 1.38 (2075), 1.33 (2100)
- SSP2-4.5 (percent deviations)
  - Min: -0.22 (2030), -0.67 (2050), -1.67 (2075), -2.88 (2100)
  - p25: -0.10 (2030), -0.31 (2050), -0.64 (2075), -1.00 (2100)
  - Median: -0.05 (2030), -0.16 (2050), -0.30 (2075), -0.46 (2100)
  - p75: 0.00 (2030), 0.00 (2050), -0.01 (2075), -0.01 (2100)
  - Max: 0.24 (2030), 0.58 (2050), 0.94 (2075), 1.20 (2100)
- SSP3-7.0 (percent deviations)
  - Min: -0.5 (2030), -1.6 (2050), -3.4 (2075), -5.4 (2100)
  - p25: -0.3 (2030), -0.9 (2050), -1.9 (2075), -3.0 (2100)
  - Median: -0.2 (2030), -0.7 (2050), -1.5 (2075), -2.3 (2100)
  - p75: -0.2 (2030), -0.5 (2050), -1.0 (2075), -1.5 (2100)
  - Max: 0.1 (2030), 0.1 (2050), 0.3 (2075), 0.4 (2100)
- SSP3-7.0 90th (percent deviations)
  - Min: -0.9 (2030), -2.4 (2050), -5.1 (2075), -8.0 (2100)
  - p25: -0.6 (2030), -1.8 (2050), -3.7 (2075), -5.5 (2100)
  - Median: -0.5 (2030), -1.5 (2050), -3.0 (2075), -4.6 (2100)
  - p75: -0.4 (2030), -1.2 (2050), -2.5 (2075), -3.8 (2100)
  - Max: -0.1 (2030), -0.3 (2050), -0.6 (2075), -0.8 (2100)

### Incorporating warming impacts into macroeconomic projections
- GDP with climate change (country i, time t, scenario s) can be computed from a reference GDP as:
  - Y_{i,t,s}^1 = (1 + α_{i,t,s}/100) Y_{i,t}^0
  - where α_{i,t,s} is the percentage impact of scenario s on GDP (negative if warming trend is larger than historical).
- Alternatively the reference growth rate r_{i,t} can be altered:
  - Y_{i,t+1,s}^1 = (1 + r_{i,t} + η_{i,t,s}) Y_{i,t}^1
  - where η_{i,t,s} measures the impact of scenario s on the GDP growth rate in percentage points.
- Example illustrated in Figure 9:
  - Starting GDP: 10 Billion LCU in 2025
  - Reference growth: 3 percent constant until 2050
  - Under an acceleration of warming, GDP is approximately 6 percent lower in 2050 than in the reference scenario.
- The companion data set includes, for all years until 2099 and all 171 countries: temperature scenarios, temperature impacts on GDP growth and GDP levels, statistical confidence intervals, key statistics of temperature-change distributions across climate models (10th, 50th, and 90th percentiles), and adaptation-speed assumptions (20, 30, 40, 50 years).

### Fiscal implications and example scenario
- Mechanism: lower GDP reduces the denominator of the debt-to-GDP ratio; with revenue and expenditure paths unchanged as shares of GDP, lower GDP implies lower revenues and potentially rigid expenditures; compounding interest on growing debt can amplify fiscal pressures.
- Illustrative fiscal example:
  - Balanced budget initially, no public debt.
  - Government expenditure and fiscal revenues equal to 25 percent of GDP.
  - In the example, public debt grows from zero to approximately 15 percent of (climate adjusted) GDP in 2050 as a result of GDP losses (Figure 9).
- The IMF Q-CRAFT tool operationalizes these methods for country-level long-term climate fiscal risk scenarios and is already in use in multiple countries.

### Conclusions and cautions for policy use
- The note provides a practical method to estimate GDP effects of slow-moving temperature increases and to incorporate them into macroeconomic projections using the best available empirical foundations.
- Significant uncertainties and limitations warrant caution:
  - Spillovers through trade, financial flows, and migration are not included.
  - Inference about future damages based on past data is uncertain.
  - Loss estimates are likely conservative because many potential impacts are excluded: global climate tipping points (examples listed), societal tipping points, non-market damages, sea-level rise, and ocean acidification.
- Extensions recommended:
  - Account for heterogeneity in impacts and spillover effects.
  - Incorporate direct impacts of climate change on fiscal variables (revenue and expenditure) beyond indirect GDP effects.
  - Combine GDP losses from rising temperatures with macroeconomic losses from other climate impacts where available.

*Source: IMF | How to Note — htnea2025009 (figures, tables, and text excerpts as provided).*

### Appendix 1. Model Specification

### Appendix 1. Model Specification

### Model setup and baseline FE specification
- Baseline panel Fixed Effects (FE) model (Dell, Jones, and Olken (2012)):
  - r_{i,t} = Δ ln(y_{i,t}) = α_i + θ_{r,t} + β T_{i,t} + ε_{i,t}
  - ln(y_{i,t}) is the natural logarithm of real GDP per capita.
  - r_{i,t} is GDP per-capita growth in country i at time t.
  - α_i controls time-invariant country characteristics.
  - θ_{r,t} is a regional time fixed effect.
  - T_{i,t} is average annual temperature in country i.
  - ε_{i,t} is a random disturbance.

### Temperature decomposition and consequences for estimation
- Temperature decomposition due to global warming:
  - T_{i,t} = δ_{i,t} + ν_{i,t}
  - ν_{i,t} is iid, normally distributed random shock with mean zero and variance σ_i^2.
  - δ_{i,t} = δ_{0,i} + δ_{1,i} t is the deterministic warming observed at time t relative to the previous long-run equilibrium temperature.
- Distinction:
  - ν_{i,t} is a random weather shock.
  - δ_{1,i} is deterministic and affected by geography (e.g., correlated with latitude and inversely correlated with average temperature).
- Rewriting the FE model by separating deterministic trend and weather variation yields:
  - Δ ln(y_{i,t}) = α_i + θ_{r,t} + β (δ_{0,i} + δ_{1,i} t + ν_{i,t}) + ε_{i,t}
  - Implication: unless the restriction θ_{r,t} + β δ_{1,i} t = 0 holds, the specification can lead to non-stationary growth (Kahn et al. (2021)).
  - Similar specifications in Burke, Hsiang, and Miguel (2015), and Kalkuhl and Wenz (2020) face analogous problems.

### Kahn et al. (2021) formulation and interpretation
- Simplified model of ln(y_{i,t}):
  - ln(y_{i,t}) = y_{i,0} + α_i t + β Σ_{l=1}^{m} |T_{i,t} - (1/m) Σ_{l=1}^{m} T_{i,t-l}| + ε_{i,t}
  - y_{i,0} captures initial technological endowment, steady-state capital, and climate.
  - α_i is exogenous rate of growth of technology.
  - The temperature shock is defined as the deviation of temperature in year t from its average during the previous m years: (T_{i,t} − (1/m) Σ_{l=1}^{m} T_{i,t-l}).
  - Weather shocks enter in absolute value in the main specification (effects measured by absolute deviations).
  - Asymmetry tests: Kahn et al. (2021) consider asymmetrical effects but cannot reject the null of symmetrical effects.
  - Precipitation effects are omitted as they never have a significant effect on GDP per capita.

### First-difference ARDL transformation and dynamics
- To address serial correlation and non-stationary GDP levels, transform to first differences to obtain an ARDL in growth:
  - Δ ln(y_{i,t}) = α_i + Σ_{j=1}^{p} φ_j Δ ln(y_{i,t-j}) + β Σ_{l=0}^{2m} Δ |T_{i,t} − (1/m) Σ_{l=1}^{m} T_{i,t-l}| + Δ ε_{i,t}
  - Interpretation:
    - Growth at time t is affected by long-run determinants (α_i), dynamic effects via lagged growth (φ_j), absolute deviations of temperature from the moving m-year average, and other shocks (Δ ε_{i,t}).
    - Lagged temperature shocks capture persistence of temperature anomalies.
    - The level of temperature does not explain growth; its trend and random variations do.
- Under ν_{i,t} normality, expected contemporaneous absolute temperature deviation:
  - E[|T_{i,t} − (1/m) Σ_{l=1}^{m} T_{i,t-l}|] = δ_{1,i} (m+1)/2 [Φ(δ_{1,i}/(2 σ_i)) (m+1)/m − Φ(−δ_{1,i}/(2 σ_i)) (m+1)/m] + 2 σ_i [1 + (1/m) φ(δ_{1,i}/(2 σ_i)) (m+1)/m]
  - Where φ and Φ are the pdf and cdf of the standard normal distribution.
  - In steady state the expected absolute change of temperatures does not depend on t (expected difference equals zero in (6)).

### Steady-state implications and long-run effect of trend changes
- Steady-state expected growth:
  - E[Δ ln(y_{i,t})] = α_i / (1 − Σ φ_j)
- Long-run effect of a permanent change in the temperature trend:
  - Long-run multiplier = (Σ β_j) / (1 − Σ φ_j)
  - If expression (8) is negative, an acceleration of warming (positive trend change) reduces growth; a deceleration increases growth above the counterfactual that already includes the historical trend's negative effect.
- Adaptation interpretation:
  - The amount of warming that damages the economy is measured relative to a moving climate average; larger m (longer reference period) implies larger negative impacts (more adaptation means smaller m).
  - If temperature stabilizes (δ_{1,i} = 0), GDP per capita eventually converges to its reference level with only historical volatility and no temperature trend.

### Procedure to calculate impacts of future warming scenarios
- Steps followed for each country to calculate impacts from 2015 to 2100:
  1. Use the median ensemble projection for a given emission scenario to calculate the change of temperature in the country, from 2015 to 2100.
  2. To avoid an abrupt change of the trend in 2016, calculate a counterfactual trend assuming constant acceleration (or deceleration) from the historical trend to achieve the warming level implied by the selected scenario.
  3. Calculate the impact of the difference between projected and historical trend on growth for each year from 2015 to 2100 using the long-run multiplier (equation (8)).
- Definitions for the calculation period:
  - T and H denote the beginning and the number of years in the period over which climate change impacts are calculated (example: for 2015 to 2099, T = 2015 and H = 85).
  - Slope of the linear trend with climate change:
    - δ_{1,i}^1 = (T_{i,T+H} − T_{i,T}) / H
- Smooth acceleration/deceleration approach:
  - Assume the slope of the linear trend increases constantly by d_i each of the j years from T to T+H:
    - δ_{1,i,j}^1 = δ_{1,i} + j d_i
  - Requirement that using δ_{1,i}^1 or δ_{1,i,j}^1 yield the same temperature increase at time H:
    - δ_{1,i}^1 H = Σ_{j=1}^{H} (δ_{1,i} + j d_i)
    - δ_{1,i}^1 H = δ_{1,i} H + H(H+1)/2 d_i
    - d_i = 2 (δ_{1,i}^1 − δ_{1,i}) / (1 + H)
- Numerical example (preserving exact values from the source):
  - Assume historical trend δ_{1,i} = 0.01 ° C per year.
  - From 2015 to 2099 this yields temperature increase = 0.85 °C.
  - Scenario predicts temperature increase = 1.7 ° C from 2015 to 2099 ⇒ δ_{1,i}^1 = 0.02.
  - Then d_i = 0.000233.
  - δ_{1,i,2015}^1 = 0.010233.
  - δ_{1,i,2057}^1 = 0.02.
  - δ_{1,i,2099}^1 = 0.0298.
- Final computation:
  - The impact on growth is calculated using the ARDL (equation (5)) and the long-run multiplier (equation (8)).
  - The parameter m governs the speed of adaptation to the changing trend and the magnitude of GDP impact.

*IMF | How to Note NOTE/2025/009*

### Appendix 2. Data on Temperature Scenarios and Their Impacts on GDP in All

### Appendix 2. Data on Temperature Scenarios and Their Impacts on GDP in All Countries

### Summary
- All data on temperature scenarios and their impact on GDP in all years until 2100, all countries, under alternative assumptions on the speed of adaptation is available in an Excel file at this link.
- The following table provides a summary of results for 2050 and 2100 in the case in which adaptation can offset any negative climate impacts after 30 years (m=30).
- Brackets show 95 percent bootstrap confidence intervals.

### Scenario framework and presentation
- Scenarios reported: SSP1-2.6, SSP2-4.5, SSP3-7.0, and an SSP3-7.0 90th percentile column.
- Horizon years: 2050 and 2100.
- Units: reported impacts on GDP (percentage points) with 95 percent bootstrap confidence intervals in brackets.
- Adaptation assumption: m=30 (adaptation can offset negative climate impacts after 30 years).

### Illustrative country results (selected rows as presented)
- Afghanistan (AFG)
  - SSP1-2.6: 2050 = 0.86 [0.36 1.39]; 2100 = 1.13 [0.48 1.82]
  - SSP2-4.5: 2050 = 0.51 [0.21 0.82]; 2100 = 1.02 [0.43 1.65]
  - SSP3-7.0: 2050 = -0.34 [-0.56 -0.14]; 2100 = -0.91 [-1.48 -0.39]
  - SSP3-7.0 90th p.: 2050 = -1.19 [-1.93 -0.5]; 2100 = -3.32 [-5.39 -1.41]
- Bangladesh (BGD)
  - SSP1-2.6: 2050 = -0.16 [-0.25 -0.06]; 2100 = -0.93 [-1.52 -0.39]
  - SSP2-4.5: 2050 = -0.51 [-0.82 -0.21]; 2100 = -2.43 [-3.96 -1.03]
  - SSP3-7.0: 2050 = -1.08 [-1.75 -0.45]; 2100 = -4.28 [-6.95 -1.81]
  - SSP3-7.0 90th p.: 2050 = -1.91 [-3.11 -0.79]; 2100 = -6.53 [-10.61 -2.76]
- China (CHN)
  - SSP1-2.6: 2050 = 0.34 [0.14 0.55]; 2100 = 0.69 [0.29 1.12]
  - SSP2-4.5: 2050 = -0.3 [-0.49 -0.13]; 2100 = -0.8 [-1.29 -0.34]
  - SSP3-7.0: 2050 = -1.12 [-1.81 -0.47]; 2100 = -3 [-4.88 -1.27]
  - SSP3-7.0 90th p.: 2050 = -2.22 [-3.6 -0.93]; 2100 = -5.82 [-9.46 -2.47]
- India (IND)
  - SSP1-2.6: 2050 = -0.1 [-0.17 -0.04]; 2100 = -0.29 [-0.47 -0.12]
  - SSP2-4.5: 2050 = -0.5 [-0.81 -0.21]; 2100 = -1.58 [-2.57 -0.67]
  - SSP3-7.0: 2050 = -1.26 [-2.05 -0.52]; 2100 = -3.79 [-6.16 -1.6]
  - SSP3-7.0 90th p.: 2050 = -2.15 [-3.49 -0.89]; 2100 = -6.09 [-9.89 -2.58]
- United States (USA)
  - SSP1-2.6: 2050 = -0.02 [-0.04 -0.01]; 2100 = -0.06 [-0.1 -0.03]
  - SSP2-4.5: 2050 = -0.67 [-1.09 -0.28]; 2100 = -2.08 [-3.38 -0.88]
  - SSP3-7.0: 2050 = -1.61 [-2.61 -0.67]; 2100 = -4.81 [-7.82 -2.04]
  - SSP3-7.0 90th p.: 2050 = -2.31 [-3.74 -0.96]; 2100 = -6.67 [-10.83 -2.82]
- Small set of additional entries (as presented)
  - European countries such as Austria (AUT): SSP1-2.6 2050 = 0.05 [0.02 0.08]; SSP3-7.0 2100 = -2.78 [-4.52 -1.17].
  - African examples such as Nigeria (NGA): SSP1-2.6 2050 = 0.21 [0.09 0.34]; SSP3-7.0 2100 = -2.63 [-4.27 -1.11].
  - Latin American examples such as Brazil (BRA): SSP1-2.6 2050 = 0.19 [0.08 0.31]; SSP3-7.0 2100 = -3.68 [-5.98 -1.56].

### Cross-cutting patterns visible in the table
- Under SSP1-2.6 many countries show small positive GDP impacts by 2050 and 2100 (examples: Libya LBY 2050 = 1 [0.42 1.62], 2100 = 1.23 [0.52 1.99]; Tunisia TUN 2050 = 1.01 [0.42 1.64], 2100 = 1.33 [0.56 2.15]).
- Under higher-emissions scenarios (SSP2-4.5 and SSP3-7.0) many countries experience negative impacts by 2050 and substantially larger negative impacts by 2100 (examples: Pakistan PAK SSP3-7.0 2100 = -4.04 [-6.57 -1.71]; Peru PER SSP3-7.0 2100 = -4.26 [-6.91 -1.8]).
- The SSP3-7.0 90th percentile column shows larger-magnitude negative outcomes for many countries by 2100 (examples: Angola AGO 2100 = -5.99 [-9.73 -2.54]; South Africa ZAF 2100 = -7.12 [-11.57 -3.01]).

### Notes
- Table entries are country-specific percentage-point impacts on GDP with 95 percent bootstrap confidence intervals in brackets.
- Reported values reflect the case where adaptation is assumed able to offset negative climate impacts after 30 years (m=30).

*IMF | How to Note NOTE/2025/009*

### References

### References

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### Methods, econometrics, and reviews
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*htnea2025009 - References*

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_Source: https://www.imf.org/-/media/files/publications/howtonotes/2025/english/htnea2025009.pdf_