## 1. INTRODUCTION

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---

### Overview and motivation
- Quantifying economic impacts of climate change is critical for policy issues including estimating the Social Cost of Carbon (Rennert et al., 2022), potential impacts on the financial system (Ranger et al., 2022), and implications of overshooting the 1.5 degree target (Drouet et al., 2021).
- Empirical approaches complement Integrated Assessment Models (IAMs) (Barrage and Nordhaus, 2024) by estimating links between economic growth and weather shocks (e.g., Dell et al., 2012; Burke et al., 2015; Kalkuhl and Wenz, 2020; Newell et al., 2021; Nath et al., 2024; Desbordes and Eberhardt, 2024; Bilal and Känzig, 2026; Kahn et al., 2021).
- Literature diverges dramatically on estimated impacts (IPCC, 2022; Tol, 2024; Howard and Sterner, 2025), with Social Cost of Carbon (SCC) estimates ranging up to over 1,000 US-$ per ton of CO2 in some climate-econometric specifications (Ricke et al., 2018; Bilal and Känzig, 2026).

### Key empirical and validation challenges
- Forward-looking validation (e.g., end-of-century under “business as usual”) is difficult because small annual impacts can compound over time (Piontek et al., 2021).
- Backward-looking validation using historical data is complicated by:
  - Unknown true counterfactual growth path without climate impacts.
  - Regression models linking growth to climate explain only a small fraction of growth variation; cross-validation has low power to distinguish models (Newell et al., 2021).
  - Identification concerns: temperature-growth relationships with country fixed effects may reflect omitted country-specific trends correlated with temperature rather than causal climate impacts (Kahn et al., 2021).

### Contribution and approach of this study
- Use IMF World Economic Outlook (WEO) economic growth forecasts as a baseline counterfactual for historical climate impact estimation and comparison of a large set of damage functions.
- Rationale: WEO forecasts cover each country over a five-year window, are updated every six months, and incorporate extensive economic fundamentals but do not account for future weather shocks or their expected impacts; therefore they serve as a climate-naïve counterfactual for short- and medium-term analysis.
- Combine WEO forecasts with a consistent implementation of available damage functions to:
  - Test whether forecasted GDP per capita growth is unrelated to climate variables (placebo test).
  - Calculate historical country-level climate impacts for multiple five-year evaluation windows between 2011–2019 using historical climate data, add them to corresponding WEO growth forecasts, and assess reduction in forecast error.
  - Provide meta-estimates of “baked-in” climate impacts into current (2023) GDP in Europe by weighting damage functions according to relative performance in reducing forecast errors.

### Time windows and exclusions
- Focus on the 2011–2019 period as the most recent window that excludes widespread crisis years such as the COVID-19 pandemic.
- Exclude the 2008–2010 financial crisis period and 2020–2023 pandemic period to avoid confounding from extreme non-climate shocks.

### Preview of main results
- Placebo test supports that temperature shifts affect actual GDP per capita growth rather than IMF forecasts, validating the WEO forecasts as a climate-naïve counterfactual.
- Different climate damage functions explain a low but positive share of IMF forecast errors. The best-performing damage functions:
  - Reduce the WEO’s mean absolute error over a five-year horizon by 0.1–0.4 percentage points of GDP per capita growth rates.
  - This reduction represents up to 6% of the total forecast error or at most 3% of average annual growth.
- Most forecasting error is due to the WEO’s systematic positive bias; some damage functions perform well because they predict systematic damages on average across countries.
- A few damage functions also reduce the dispersion of forecast errors around the average error.
- Country-specific reality check: the most severe damage functions would have predicted GDP per capita contractions in several countries over the last decade that are inconsistent with observed growth patterns, indicating limitations in short-term validity for some specifications and countries.
- European aggregate estimate: using a weighted average of impacts from best-performing damage functions, European GDP is approximately 1.0% lower in 2023 compared to a counterfactual with no additional warming after 2010.

### Data (relevant features and sample statistics)
- WEO dataset: country-level GDP forecasts and actual growth rates covering 1990–2023; published twice per year (April and October), using the Fall edition for each year.
- Forecast horizon: forecasts cover the ongoing year plus five subsequent years for more than 180 countries.
- Forecast performance characteristics:
  - WEO forecasts typically over-predict GDP growth and underestimate inflation.
  - Forecast errors depend on global and country cycles; highest for emerging-market and low-income economies.
  - Predictive accuracy drops as forecasting horizon lengthens; errors increase more steeply over the three-month to two-year horizons.
- Climate and other data:
  - Convert WEO GDP growth forecasts into GDP per capita growth forecasts using observed population growth rates from WEO Spring 2024 edition.
  - Climate variables: population-weighted annual averages for mean temperature and annual precipitation from ERA5 reanalysis via Gortan et al., 2024.
  - For Bilal and Känzig (2026) damage function driven by GMST change, use Berkeley Earth dataset (Rohde and Hausfather, 2020).
  - For Akyapı et al. (2025) LASSO-informed damage function, use authors’ original ERA5-based dataset.
- Key sample statistics (preserved exactly):
  - Country-level population-weighted temperatures range between -2 and 30°C.
  - Annual precipitation ranges between less than 10 mm and over 5,000 mm.
  - Global warming, measured as the change of GMST relative to the pre-industrial 1850–1900 baseline, averages approximately 0.98°C during the sample period and reaches 1.5°C in 2023.
  - Real GDP growth averages 3.1%.
  - Compared to observed growth rates, the one-year-ahead IMF forecast is, on average, about 0.9 percentage points higher and exhibits far less extreme lower tails (the worst forecast being only -10% during the sample period).
  - Table 1 excerpt:
    - Annual mean temperature (°C): N = 62,081; Mean = 9.8057; St. Dev. = 7.114; Min = -1.841; Max = 29.843
    - GMST change over 1850–1900 (°C): N = 6,252; Mean = 0.999; St. Dev. = 0.233; Min = 0.551; Max = 1.535
    - Real GDP per capita growth: N = 61,240; Mean = 0.017; St. Dev. = 0.056; Min = -0.613; Max = 0.928
    - IMF per-capita growth forecast (1 yr ahead): N = 58,860; Mean = 0.026; St. Dev. = 0.036; Min = -0.246; Max = 0.851
    - Annual growth rate MAE (1 yr ahead, pp): N = 58,860; Mean = 0.028; St. Dev. = 0.043; Min = 0.000; Max = 0.925

### Empirical strategy (conceptual)
- Notation and counterfactual construction:
  - git: actual growth rate of real GDP per capita for country i in year t.
  - ˆgτit: IMF forecast made in year τ, adjusted for actual population growth.
  - Counterfactual GDP per capita path predicted by IMF in year τ:
    - ˆyτit = yiτ ∏k=τ+1^t (1 + ˆgτik).
  - Weather-augmented (ex-post) forecast using damage function s:
    - ˆyτs it = ˆyτit (1 + ∆τs it).
  - Damage functions: ∆τs it = f(Cit) − f(Ciτ), with mathematical expressions provided in Appendix B.
  - Forecast error definitions (normalized by base-year GDP per capita):
    - eτit ≡ (ˆyτit − yit) / yiτ.
    - eτs it ≡ (ˆyτs it − yit) / yiτ.
  - Interpretation example: eτit = 0.05 means WEO fall edition from year τ overestimated actual GDP per capita in year t by 5% relative to the base year’s GDP per capita. If eτs it = 0.03, incorporating climate impacts reduced the error by three percentage points compared to the baseline forecast.

---

### 3.1 Climate damage function implementations

### Purpose and implementation approach
- Aim: estimate growth effects of climate impacts by applying empirical and model-based damage functions from recent studies.
- Implemented specifications: nine widely used studies (summarized in Table 2).
- Implementation approach: use the original coefficients and specifications and implement all functions on the compiled dataset applied to the quasi counterfactual GDP per capita trajectory ˆy^s_it as “Reference” or no-climate baseline.

### Types of damage functions
- Level-based specifications (express GDP impacts directly in levels) modeled as quadratic functions of GMST:
  - DICE 2023
  - COACCH (bottom-up impact estimates implemented in a CGE model)
  - HS 2025 (downscaled version of a global meta study by Howard and Sterner (2025))
- Growth-rate-based specifications (estimated using GDP per capita growth rates) incorporate various climatic drivers, including local annual temperature, precipitation, and indices of climate extremes.

### Implemented specifications (reported in Table 2)
- ABM 2025 — Impact on: growth; Climate drivers: Heat (Tx35), drought (PDSI), mean temperature; Reference: Akyapı et al. (2025)
- BK 2026 — Impact on: growth; Climate drivers: GMST; Reference: Bilal and Känzig (2026)
- BHM 2015 — Impact on: growth; Climate drivers: Mean temperature; Reference: Burke et al. (2015)
- COACCH — Impact on: level; Climate drivers: GMST; Reference: van der Wijst et al. (2023)
- DICE 2023 — Impact on: level; Climate drivers: GMST; Reference: Barrage and Nordhaus (2024)
- HS 2025 — Impact on: level; Climate drivers: GMST; Reference: Howard and Sterner (2025); Tol (2024)
- KW 2020 — Impact on: growth; Climate drivers: Mean temperature; Reference: Kalkuhl and Wenz (2020)
- KLW 2022 — Impact on: growth; Climate drivers: Mean temperature (others omitted); Reference: Kotz et al. (2022)
- KMNPRY 2021 — Impact on: growth; Climate drivers: Mean temperature; Reference: Kahn et al. (2021)

---

### 3.2 Forecast error and climate impact evaluation measures

### Sign matching and directional accuracy
- SignMatch τs = (1/NT) Σ_{i=1}^N Σ_{t=τ+1}^{τ+T} 1{ sgn(−∆^τs_it) = sgn(e^τ_it) } (Equation 7).
- Interpretation: value above 0.5 indicates climate impacts explain the direction of forecast errors better than chance.

### Forecast accuracy metrics
- Metrics computed for each specification s and evaluation window τ:
  - MAE τs = (1/NT) Σ_{i=1}^N Σ_{t=τ+1}^{τ+T} |e^τs_it| (Equation 8).
  - MSE τs = (1/NT) Σ_{i=1}^N Σ_{t=τ+1}^{τ+T} (e^τs_it)^2 (Equation 9).
  - RMSE τs = √MSE τs (Equation 10).
- Forecast improvement measures (relative to baseline without impacts):
  - ∆MAE τs = MAE τ − MAE τs (Equation 11).
  - ∆RMSE τs = RMSE τ − RMSE τs.
  - Positive values indicate improved forecast accuracy when climate impacts are included.

### Forecast window selection and averaging
- Base years: τ = 2010 to τ = 2014 (five base years); forecasts up to five years out.
- Average improvement across five evaluation windows:
  - ∆MAE_s = (1/5) Σ_{τ=2010}^{2014} ∆MAE τs (Equation 12).

### Forecast error decomposition
- Global component (MAE τs_GLOBAL) computed from global averages ˆy^s_t and y_t (Equation 13).
- Country-level deviation component (MAE τs_COUNTRY) computed using deviations fˆy^s_it = ˆy^s_it − ˆy^s_t and fy_it = y_it − y_t (Equation 14).
- Improvements decomposed as:
  - ∆MAE τs_GLOBAL = MAE τ_GLOBAL − MAE τs_GLOBAL (Equation 15).
  - ∆MAE τs_COUNTRY = MAE τ_COUNTRY − MAE τs_COUNTRY.
- Note: components sum to total error for MSE but not for MAE; decomposition isolates global-average growth errors vs. country-specific deviations.

### Placebo test for validation of climate-naïve forecasts
- Logic: regressions of actual GDP growth on climate variables can be biased by omitted correlated factors X_it. IMF forecasts ˆg^τ_it incorporate country-specific and global trends but (empirically) do not systematically account for climate projections.
- Representations:
  - True DGP: g_it = f(C_it) + g(X_it) + γ_i + α_t + ε_it (Equation 16).
  - Forecast (idealized): ˆg^τ_it = g(X_it) + γ_i + α_t + η_it (Equation 17).
  - Forecast error isolates climate shock: g_it − ˆg^τ_it = f(C_it) + (ε_it − η_it) (Equation 18).
  - Placebo regression: ˆg^τ_it = f(C_it) + γ_i + α_t + ν_it (Equation 19).
- Empirical result: using Burke et al. (2015) specification, the temperature-growth relationship is significant in actual data but not present when forecasted growth is used. Similar results for Kahn et al. (2021) specification.
- Implications:
  - IMF forecasts are empirically climate-naïve, supporting use as counterfactuals.
  - Identifying variation in climate-growth regressions likely stems from deviations from expected growth paths rather than predictable country-specific trends.

### Comparison of impact specifications using forecast errors (key quantitative findings)
- Nine impact functions evaluated across five validation windows (2011-2015 through 2015-2019).
- Typical MAE improvements from most climate damage functions: 0.1–0.4 percentage points (pp).
- Context and benchmarks:
  - Average annual climate impacts over the five-year evaluation window ≈ 1–3% of the average annual growth rate of 1.7%.
  - Debiased forecast (removing average WEO forecast error of −0.88 pp) yields an improvement of 0.56 pp.
  - A “PERFECT” forecast (matching actual outcomes) would improve the baseline forecast by 6.25 pp on average.
  - Thus, most damage functions achieve roughly 1–6% of the gain attainable under a perfect forecast.
- Error magnitudes and sample statistics:
  - Average annual WEO GDP forecast MAE of 2.5 pp between 2011 and 2019.
  - Average error of 2.8% observed over the full sample from 1990 to 2023.
  - Over each five-year horizon, error accumulates to an average of approximately 10.5% of base-year GDP.
- Model performance patterns:
  - Best consistent performers across windows: COACCH, HS 2025, DICE 2023, KMNPRY 2021.
  - BK 2026 is an outlier that deteriorates forecast performance in three out of five windows (but may improve for cumulative five-year forecast in some tests).
  - RMSE-based performance tends to favor damage functions implying larger global GDP losses; MAE preferred to limit influence of outliers (e.g., Libya in 2011).

### Heterogeneity and decomposition results
- Share of country-year observations with MAE improvements is highest for functions predicting negative impacts for all countries (HS 2025, COACCH, DICE 2023, KMNPRY 2021).
- High-impact functions (KLW 2022, BK 2026, BHM 2015) show dispersed performance: large gains for some countries, large deteriorations for others.
- Decomposition: forecast improvements are driven primarily by reductions in the average error across countries (global component), not by improved country-specific performance. Several functions reduce performance in the country-deviation dimension even while improving global average error.

### Country-level reality check (examples)
- Example period 2015–2019 (using 2014 WEO forecasts):
  - Global mean surface temperature increased from approximately 0.9°C above pre-industrial levels in 2014 to 1.1°C in 2019.
  - BK 2026 predicts substantial GDP per capita reductions for several industrialized and lower-income countries (e.g., Canada, Japan, Egypt, Eritrea, Madagascar) inconsistent with observed positive growth—suggesting possible overstatement of near-term impacts.
  - BHM 2015 predicts smaller annual impacts but more pronounced accumulation over longer horizons.
  - Damage functions using annual country-level temperature variation (KW 2020, KLW 2022) can yield volatile GDP projections for high-income countries that exceed observed trajectory volatility.

### Performance-weighted ensemble (Europe, 2010–2023)
- Performance weight construction:
  - For each damage function s compute R_s = (1/5) Σ_{τ=2010}^{2014} (MAE_{τ,baseline} − MAE_{τ,s}) / MAE_{τ,baseline} (Equation 20).
  - Exclude functions with R_s ≤ 0 and those showing clear deterioration in country-deviation dimension.
  - Weights: w_s = R_s / Σ_{j∈S*} R_j (Equation 21).
- Retained specifications and weights (R_s > 0; no country-deviation deterioration):
  - HS 2025: 0.55
  - COACCH: 0.24
  - DICE 2023: 0.10
  - BHM 2015: 0.06
  - KMNPRY 2021: 0.06
- Chaining one-year-ahead forecasts to 2023 and applying weighted damages yields:
  - ∆^2023_EU = −1.0%. (Equation 22)
- Geographic pattern (EU27): pronounced north–south gradient; Southern European countries experience the largest negative impacts; Northern Europe shows much smaller losses. BHM 2015 can imply large positive impacts in northern countries but receives a lower weight.

### Discussion — implications and limitations
- Methodological contribution: professional forecasts (WEO) serve as climate-naïve counterfactuals allowing validation of damage functions while mitigating omitted-variable bias from predictable country-specific trends.
- Main empirical implication: climate damage functions can explain meaningful but modest portions of IMF forecast errors; best-performing functions reduce MAE by 0.1–0.4 pp (≈1–6% of baseline forecast error; at most 3% of average annual growth).
- Heterogeneity across specifications:
  - Bottom-up models (COACCH) and specifications smoothing climate variation perform more consistently.
  - Some high-SCC implying functions (e.g., Bilal and Känzig (BK 2026) with SCC exceeding $1,000 per ton CO2) predict near-term contractions inconsistent with professional forecasts and observed data—suggesting potentially upward-biased short-term sensitivity.
- Main limitations:
  - Cannot definitively decompose forecast errors into climate vs. non-climate components; coincidentally signed non-climate shocks could contribute.
  - Validation period (2011–2019) covers modest warming (~0.2°C globally) — results pertain to near-term impacts and may not generalize to larger warming.
  - Cannot fully adjudicate functional forms governing long-term damage accumulation; accumulated small annual biases can compound over decades.
  - Exclusion of crisis years (2008–2010, 2020–2023) avoids contamination but may miss periods of salient climate impacts.
  - Focuses on GDP growth impacts and excludes non-market/non-use values (health, ecosystems, well-being).

### Conclusion (concise)
- Using WEO forecasts as climate-naïve counterfactuals, damage functions can modestly improve forecast accuracy (MAE reductions of 0.1–0.4 pp), indicating climate variables add information beyond standard economic indicators.
- Substantial heterogeneity exists across damage functions; several widely used high-impact functions imply near-term outcomes difficult to reconcile with professional forecasts and observed data.
- For near- to medium-term policy analysis, more moderate damage functions that align better with historical experience may provide more reliable guidance, while extreme damage estimates (e.g., implying SCC > $1,000 per ton) warrant cautious interpretation.

---

### Appendix B — Additional information on implementing damage functions (summary of implementation choices and parameters)

- BHM (Burke et al. 2015)
  - Regression: ln(y_it) − ln(y_i,t−1) = β1 T_it + β2 T_it^2 + β3 P_it + β4 P_it^2 + γ_i + α_t + θ_i,1 t + θ_i,2 t^2 + ε_it (Equation 23).
  - Parameters: β1 = 0.012718353 and β2 = −0.00048709.
  - Baseline choice: 2006–2010 average mean temperature.
  - Conversion: ∆_BHM_it = exp(Σ_{s=τ+1}^t δ_BHM_is) − 1 (Equations 24–27).

- COACCH
  - Region-specific quadratic in ∆T_{global,t,1986−2005}: ∆_COACCH_it = a_r [ b_{r,1} ∆T + b_{r,2} ∆T^2 ] (Equation 28).
  - 26 IMAGE regions; central a_r = 1; use region-specific b parameters and isolate post-forecast warming (Equation 29).
  - Units: % of GDP (assumed ≡ % of GDPpc).

- KW 2020
  - Use temperature first-difference terms: δ_KW_it = β1 ∆T_it + β2 ∆T_it T_{i,t−1} + β3 ∆T_{i,t−1} + β4 ∆T_{i,t−1} T_{i,t−1} (Equation 31).
  - Coefficients: β1 = 0.00641, β2 = −0.00109, β3 = 0.00345, β4 = −0.000718.
  - Conversion: ∆_KW_it = exp(Σ δ_KW_is) − 1 (Equation 32).

- KLW 2022
  - Use temperature-only projection analog to KW 2020 with coefficients:
    - β_{T1} = 0.000960192, β_{T2} = −0.002273751, β_{T3} = −0.0010594136, β_{T4} = −0.0006545396 (Equation 34).
  - Conversion: ∆_KLW22_it = exp(Σ δ_KLW22_is) − 1 (Equation 35).

- ABM 2025
  - LASSO-selected standardized climate variables: δ_ABM_it = β1 ∆Tx35 + β2 ∆T9to12 + β3 ∆PDSI (Equation 37).
  - Coefficients: β1 = −0.00168, β2 = 0.00144, β3 = −0.00225.
  - Conversion: ∆_ABM_it = exp(Σ δ_ABM_is) − 1 (Equation 38).

- BK 2026
  - Regional impulse-response using past 10 years of global temperature shocks:
    - δ_BK_it = Σ_{l=0}^{10} β_{r,l} T^{shock}_{global,t−l} (Equation 39).
  - Conversion: ∆_BK_it = exp(δ_BK_it) − 1 (Equation 40).

- DICE 2023
  - Global quadratic damage: ∆_DICE_global,t = β1 * ∆T_{global,t,1850−1900}^2 with β1 = −0.003467 (Equation 41).
  - Isolate post-forecast warming: ∆_DICE_global,t = β1 * [∆T_{global,t,1850−1900}^2 − ∆T_{global,τ,1850−1900}^2] (Equation 42).

- HS 2025
  - Meta-analytic global damage f(·); isolate post-forecast warming and downscale to countries following OECD/Tol approach (Equation 43).

- KMNPRY 2021
  - Half-panel jackknife estimator and deviation-from-norm projection using m = 30 and replication-package ψ(L) terms (Equations 44–51).
  - Use Berkeley Earth GMST trends and RCP8.5 d_{RCP} for 2011–2019 alignment.

- Appendix C sample and exclusions:
  - WEO data covers N = 196 economies.
  - Macao SAR and Hong Kong SAR not included in climate data; additional 27 economies omitted from forecast error evaluation due to implementation/mapping constraints.

_Italic source attribution: When Forecasts Meet Reality: Assessing Climate Damage Functions — Working Paper No. WP/2026/085 (Appendix B)_

### 1. INTRODUCTION ........................................................................................................

### 1. INTRODUCTION

### Overview and motivation
- Quantifying economic impacts of climate change is critical for policy issues including estimating the Social Cost of Carbon (Rennert et al., 2022), potential impacts on the financial system (Ranger et al., 2022), and implications of overshooting the 1.5 degree target (Drouet et al., 2021).
- Empirical approaches complement Integrated Assessment Models (IAMs) (Barrage and Nordhaus, 2024) by estimating links between economic growth and weather shocks (e.g., Dell et al., 2012; Burke et al., 2015; Kalkuhl and Wenz, 2020; Newell et al., 2021; Nath et al., 2024; Desbordes and Eberhardt, 2024; Bilal and Känzig, 2026; Kahn et al., 2021).
- Literature diverges dramatically on estimated impacts (IPCC, 2022; Tol, 2024; Howard and Sterner, 2025), with Social Cost of Carbon (SCC) estimates ranging up to over 1,000 US-$ per ton of CO2 in some climate-econometric specifications (Ricke et al., 2018; Bilal and Känzig, 2026).

### Key empirical and validation challenges
- Forward-looking validation (e.g., end-of-century under “business as usual”) is difficult because small annual impacts can compound over time (Piontek et al., 2021).
- Backward-looking validation using historical data is complicated by:
  - Unknown true counterfactual growth path without climate impacts.
  - Regression models linking growth to climate explain only a small fraction of growth variation; cross-validation has low power to distinguish models (Newell et al., 2021).
  - Identification concerns: temperature-growth relationships with country fixed effects may reflect omitted country-specific trends correlated with temperature rather than causal climate impacts (Kahn et al., 2021).

### Contribution and approach of this study
- Use IMF World Economic Outlook (WEO) economic growth forecasts as a baseline counterfactual for historical climate impact estimation and comparison of a large set of damage functions.
- Rationale: WEO forecasts cover each country over a five-year window, are updated every six months, and incorporate extensive economic fundamentals but do not account for future weather shocks or their expected impacts; therefore they serve as a climate-naïve counterfactual for short- and medium-term analysis.
- Combine WEO forecasts with a consistent implementation of available damage functions to:
  1. Test whether forecasted GDP per capita growth is unrelated to climate variables (placebo test).
  2. Calculate historical country-level climate impacts for multiple five-year evaluation windows between 2011–2019 using historical climate data, add them to corresponding WEO growth forecasts, and assess reduction in forecast error.
  3. Provide meta-estimates of “baked-in” climate impacts into current (2023) GDP in Europe by weighting damage functions according to relative performance in reducing forecast errors.

### Time windows and exclusions
- Focus on the 2011–2019 period as the most recent window that excludes widespread crisis years such as the COVID-19 pandemic.
- Exclude the 2008–2010 financial crisis period and 2020–2023 pandemic period to avoid confounding from extreme non-climate shocks.

### Preview of main results
- Placebo test supports that temperature shifts affect actual GDP per capita growth rather than IMF forecasts, validating the WEO forecasts as a climate-naïve counterfactual.
- Different climate damage functions explain a low but positive share of IMF forecast errors. The best-performing damage functions:
  - Reduce the WEO’s mean absolute error over a five-year horizon by 0.1–0.4 percentage points of GDP per capita growth rates.
  - This reduction represents up to 6% of the total forecast error or at most 3% of average annual growth.
- Most forecasting error is due to the WEO’s systematic positive bias; some damage functions perform well because they predict systematic damages on average across countries.
- A few damage functions also reduce the dispersion of forecast errors around the average error.
- Country-specific reality check: the most severe damage functions would have predicted GDP per capita contractions in several countries over the last decade that are inconsistent with observed growth patterns, indicating limitations in short-term validity for some specifications and countries.
- European aggregate estimate: using a weighted average of impacts from best-performing damage functions, European GDP is approximately 1.0% lower in 2023 compared to a counterfactual with no additional warming after 2010.

---

### Data (summary of relevant features)
- WEO dataset: country-level GDP forecasts and actual growth rates covering 1990–2023; published twice per year (April and October), using the Fall edition for each year.
- Forecast horizon: forecasts cover the ongoing year plus five subsequent years for more than 180 countries.
- WEO forecasting process: combines “top-down” and “bottom-up” approaches (Genberg et al., 2014a); methodology varies across countries; forecasts for low-income countries and at longer horizons tend to rely on less sophisticated approaches.
- No evidence of systematic use of country-level climate projections, especially before 2016; IMF guidance (IMF, 2016) addresses natural disasters but not systematic climate projections.
- Forecast performance characteristics:
  - WEO forecasts typically over-predict GDP growth and underestimate inflation.
  - Forecast errors depend on global and country cycles; highest for emerging-market and low-income economies.
  - Predictive accuracy drops as forecasting horizon lengthens; errors increase more steeply over the three-month to two-year horizons.

### Climate and other data
- Convert WEO GDP growth forecasts into GDP per capita growth forecasts using observed population growth rates from WEO Spring 2024 edition.
- Climate variables: population-weighted annual averages for mean temperature and annual precipitation from ERA5 reanalysis via Gortan et al., 2024.
- For Bilal and Känzig (2026) damage function driven by GMST change, use Berkeley Earth dataset (Rohde and Hausfather, 2020).
- For Akyapı et al. (2025) LASSO-informed damage function, use authors’ original ERA5-based dataset.

### Key sample statistics (preserved exactly as provided)
- Country-level population-weighted temperatures range between -2 and 30°C.
- Annual precipitation ranges between less than 10 mm and over 5,000 mm.
- Global warming, measured as the change of GMST relative to the pre-industrial 1850–1900 baseline, averages approximately 0.98°C during the sample period and reaches 1.5°C in 2023.
- Real GDP growth averages 3.1%.
- Compared to observed growth rates, the one-year-ahead IMF forecast is, on average, about 0.9 percentage points higher and exhibits far less extreme lower tails (the worst forecast being only -10% during the sample period).
- Table 1 (summary statistics excerpt):
  - Annual mean temperature (°C): N = 62,081; Mean = 9.8057; St. Dev. = 7.114; Min = -1.841; Max = 29.843
  - GMST change over 1850–1900 (°C): N = 6,252; Mean = 0.999; St. Dev. = 0.233; Min = 0.551; Max = 1.535
  - Real GDP per capita growth: N = 61,240; Mean = 0.017; St. Dev. = 0.056; Min = -0.613; Max = 0.928
  - IMF per-capita growth forecast (1 yr ahead): N = 58,860; Mean = 0.026; St. Dev. = 0.036; Min = -0.246; Max = 0.851
  - Annual growth rate MAE (1 yr ahead, pp): N = 58,860; Mean = 0.028; St. Dev. = 0.043; Min = 0.000; Max = 0.925

### Empirical strategy (conceptual summary)
- Notation:
  - git: actual growth rate of real GDP per capita for country i in year t.
  - ˆgτit: IMF forecast made in year τ, adjusted for actual population growth.
- For each year t up to 2020 there are five different Fall WEO forecasts from previous years (τ = t−1,...,τ = t−5) and one same-year forecast (τ = t).
- Counterfactual GDP per capita path predicted by IMF in year τ:
  - ˆyτit = yiτ ∏k=τ+1^t (1 + ˆgτik). (Equation reproduced exactly as presented)
- Weather-augmented (ex-post) forecast using damage function s:
  - ˆyτs it = ˆyτit (1 + ∆τs it). (Equation reproduced exactly as presented)
- Damage functions: annual country-specific GDP per capita impact of weather shocks from year τ to t is ∆τs it = f(Cit) − f(Ciτ), where f and its coefficients are as used by each study and Ciτ is the “reference” climate in the forecast year (mathematical expressions for ∆τs it for each damage function are provided in Appendix B).
- Forecast error definitions (normalized by base-year GDP per capita):
  - eτit ≡ (ˆyτit − yit) / yiτ. (Equation reproduced exactly as presented)
  - eτs it ≡ (ˆyτs it − yit) / yiτ. (Equation reproduced exactly as presented)
- Interpretation: eτit = 0.05 means WEO fall edition from year τ overestimated actual GDP per capita in year t by 5% relative to the base year’s GDP per capita. If eτs it = 0.03, incorporating climate impacts reduced the error by three percentage points compared to the baseline forecast.

*Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026085-source-pdf.pdf*

### 3.1    Climate damage function implementations

### 3.1    Climate damage function implementations

### Overview and purpose
- Aim: estimate the growth effects of climate impacts by applying empirical and model-based damage functions from recent studies.
- Implemented specifications: nine widely used studies (summarized in Table 2).
- Implementation approach: use the original coefficients and specifications and implement all functions on the compiled dataset applied to the quasi counterfactual GDP per capita trajectory ˆy^s_it as “Reference” or no-climate baseline.

### Types of damage functions and modeling choices
- Level-based specifications (express GDP impacts directly in levels) modeled as quadratic functions of GMST:
  - DICE 2023
  - COACCH (bottom-up impact estimates implemented in a CGE model)
  - HS 2025 (downscaled version of a global meta study by Howard and Sterner (2025))
- Growth-rate-based specifications (estimated using GDP per capita growth rates) incorporate various climatic drivers, including local annual temperature, precipitation, and indices of climate extremes.

### Forecast error definitions and temporal considerations
- Rationale: examine whether the reduction in forecast errors from adding damage functions increases over time, as expected if omitted climate impacts are persistent (Nath et al., 2024).
- Two alternative definitions of the forecast error implemented:
  - Error computed only for the last period (e.g., when τ = t−5): evaluates the forecast error in the last year and captures the full cumulative effect.
  - Simple forecast error in terms of growth rates, defined as
    ee^τs_it = (ˆy^τs_it − ˆy^τs_it−1)/ˆy^τs_it−1 − (y_it − y_it−1)/y_it−1,
    which represents the annual forecast error including climate impacts of damage specifications.

### Implemented specifications (as reported in Table 2)
- ABM 2025 — Impact on: growth; Climate drivers: Heat (Tx35), drought (PDSI), mean temperature; Reference: Akyapı et al. (2025)
- BK 2026 — Impact on: growth; Climate drivers: GMST; Reference: Bilal and Känzig (2026)
- BHM 2015 — Impact on: growth; Climate drivers: Mean temperature; Reference: Burke et al. (2015)
- COACCH — Impact on: level; Climate drivers: GMST; Reference: van der Wijst et al. (2023)
- DICE 2023 — Impact on: level; Climate drivers: GMST; Reference: Barrage and Nordhaus (2024)
- HS 2025 — Impact on: level; Climate drivers: GMST; Reference: Howard and Sterner (2025); Tol (2024)
- KW 2020 — Impact on: growth; Climate drivers: Mean temperature; Reference: Kalkuhl and Wenz (2020)
- KLW 2022 — Impact on: growth; Climate drivers: Mean temperature (others omitted); Reference: Kotz et al. (2022)
- KMNPRY 2021 — Impact on: growth; Climate drivers: Mean temperature; Reference: Kahn et al. (2021)

*Source: IMF staff compilation from the content unit "3.1    Climate damage function implementations".*

### 3.2    Forecast error and climate impact evaluation measures

### 3.2    Forecast error and climate impact evaluation measures

### Sign matching and directional accuracy
- Metric: SignMatch τs = (1/NT) Σ_{i=1}^N Σ_{t=τ+1}^{τ+T} 1{ sgn(−∆^τs_it) = sgn(e^τ_it) } (Equation 7).
- Interpretation: captures whether climate impacts move forecasts toward actual GDP per capita (direction only). A value above 0.5 indicates climate impacts explain the direction of forecast errors better than chance.

### Forecast accuracy metrics
- Metrics computed for each specification s and evaluation window τ:
  - MAE τs = (1/NT) Σ_{i=1}^N Σ_{t=τ+1}^{τ+T} |e^τs_it| (Equation 8).
  - MSE τs = (1/NT) Σ_{i=1}^N Σ_{t=τ+1}^{τ+T} (e^τs_it)^2 (Equation 9).
  - RMSE τs = √MSE τs (Equation 10).
- Forecast improvement measures (relative to standard forecast without impacts):
  - ∆MAE τs = MAE τ − MAE τs (Equation 11).
  - ∆RMSE τs = RMSE τ − RMSE τs.
  - Positive values indicate improved forecast accuracy when climate impacts are included.

### Forecast window selection and averaging
- Base years: τ = 2010 to τ = 2014 (five base years); forecasts up to five years out.
- Average improvement across five evaluation windows:
  - ∆MAE_s = (1/5) Σ_{τ=2010}^{2014} ∆MAE τs (Equation 12).

### Forecast error decomposition
- Global component (MAE τs_GLOBAL) computed from global averages ˆy^s_t and y_t (Equation 13).
- Country-level deviation component (MAE τs_COUNTRY) computed using deviations fˆy^s_it = ˆy^s_it − ˆy^s_t and fy_it = y_it − y_t (Equation 14).
- Improvements decomposed as:
  - ∆MAE τs_GLOBAL = MAE τ_GLOBAL − MAE τs_GLOBAL (Equation 15).
  - ∆MAE τs_COUNTRY = MAE τ_COUNTRY − MAE τs_COUNTRY.
- Note: components sum to total error for MSE but not for MAE; decomposition isolates global-average growth errors vs. country-specific deviations.

### Placebo test for climate impact regressions (validation of climate-naïve forecasts)
- Logic: regressions of actual GDP growth on climate variables can be biased by omitted correlated factors X_it. IMF forecasts ˆg^τ_it incorporate country-specific and global trends but (empirically) do not systematically account for climate projections.
- Representations:
  - True DGP: g_it = f(C_it) + g(X_it) + γ_i + α_t + ε_it (Equation 16).
  - Forecast (idealized): ˆg^τ_it = g(X_it) + γ_i + α_t + η_it (Equation 17).
  - Forecast error isolates climate shock: g_it − ˆg^τ_it = f(C_it) + (ε_it − η_it) (Equation 18).
  - Placebo regression: ˆg^τ_it = f(C_it) + γ_i + α_t + ν_it (Equation 19).
- Empirical result: using Burke et al. (2015) specification, the temperature-growth relationship is significant in actual data but not present when forecasted growth is used (Table 3). Similar results for Kahn et al. (2021) specification (Table 4).
- Implications:
  - IMF forecasts are empirically climate-naïve (do not systematically incorporate climate shocks), supporting their use as counterfactuals.
  - The identifying variation in climate-growth regressions likely stems from deviations from expected growth paths rather than predictable country-specific trends.

### Comparison of impact specifications using forecast errors (key quantitative findings)
- Nine impact functions evaluated across five validation windows (2011-2015 through 2015-2019).
- Typical MAE improvements from most climate damage functions: 0.1–0.4 percentage points (pp).
- Context and benchmarks:
  - Average annual climate impacts over the five-year evaluation window ≈ 1–3% of the average annual growth rate of 1.7%.
  - Debiased forecast (removing average WEO forecast error of −0.88 pp) yields an improvement of 0.56 pp.
  - A “PERFECT” forecast (matching actual outcomes) would improve the baseline forecast by 6.25 pp on average.
  - Thus, most damage functions achieve roughly 1–6% of the gain attainable under a perfect forecast.
- Error magnitudes and sample statistics:
  - Average annual WEO GDP forecast MAE of 2.5 pp between 2011 and 2019.
  - Average error of 2.8% observed over the full sample from 1990 to 2023.
  - Over each five-year horizon, error accumulates to an average of approximately 10.5% of base-year GDP.
- Model performance patterns:
  - Best consistent performers across windows: COACCH, HS 2025 (meta-study with country-level downscaling), DICE 2023, KMNPRY 2021.
  - BK 2026 is an outlier that deteriorates forecast performance in three out of five windows (but may improve for cumulative five-year forecast in some tests).
  - RMSE-based performance tends to favor damage functions implying larger global GDP losses; MAE preferred to limit influence of outliers (e.g., Libya in 2011).

### Heterogeneity and decomposition results
- Share of country-year observations with MAE improvements is highest for functions predicting negative impacts for all countries (HS 2025, COACCH, DICE 2023, KMNPRY 2021).
- High-impact functions (KLW 2022, BK 2026, BHM 2015) show dispersed performance: large gains for some countries, large deteriorations for others.
- Decomposition (Figure 6): forecast improvements are driven primarily by reductions in the average error across countries (global component), not by improved country-specific performance. Several functions reduce performance in the country-deviation dimension even while improving global average error.

### Country-level reality check
- Example period 2015–2019 (using 2014 WEO forecasts):
  - Global mean surface temperature increased from approximately 0.9°C above pre-industrial levels in 2014 to 1.1°C in 2019.
  - BK 2026 predicts substantial GDP per capita reductions for several industrialized and lower-income countries (e.g., Canada, Japan, Egypt, Eritrea, Madagascar) inconsistent with observed positive growth—suggesting possible overstatement of near-term impacts.
  - BHM 2015 predicts smaller annual impacts but more pronounced accumulation over longer horizons.
  - Damage functions using annual country-level temperature variation (KW 2020, KLW 2022) can yield volatile GDP projections for high-income countries that exceed observed trajectory volatility.

### Performance-weighted ensemble (Europe, 2010–2023)
- Performance weight construction:
  - For each damage function s compute R_s = (1/5) Σ_{τ=2010}^{2014} (MAE_{τ,baseline} − MAE_{τ,s}) / MAE_{τ,baseline} (Equation 20).
  - Exclude functions with R_s ≤ 0 and those showing clear deterioration in country-deviation dimension.
  - Weights: w_s = R_s / Σ_{j∈S*} R_j (Equation 21).
- Retained specifications and weights (R_s > 0; no country-deviation deterioration):
  - HS 2025: 0.55
  - COACCH: 0.24
  - DICE 2023: 0.10
  - BHM 2015: 0.06
  - KMNPRY 2021: 0.06
  - (Table 5)
- Chaining one-year-ahead forecasts to 2023 and applying weighted damages yields:
  - ∆^2023_EU = −1.0%. (Equation 22)
- Geographic pattern (EU27): pronounced north–south gradient; Southern European countries experience the largest negative impacts; Northern Europe shows much smaller losses. BHM 2015 can imply large positive impacts in northern countries but receives a lower weight.

### Discussion — implications and limitations (key points)
- Methodological contribution: professional forecasts (WEO) serve as climate-naïve counterfactuals allowing validation of damage functions while mitigating omitted-variable bias from predictable country-specific trends.
- Main empirical implication: climate damage functions can explain meaningful but modest portions of IMF forecast errors; best-performing functions reduce MAE by 0.1–0.4 pp (≈1–6% of baseline forecast error; at most 3% of average annual growth).
- Heterogeneity across specifications:
  - Bottom-up models (COACCH) and specifications smoothing climate variation perform more consistently.
  - Some high-SCC implying functions (e.g., Bilal and Känzig (BK 2026) with SCC exceeding $1,000 per ton CO2) predict near-term contractions inconsistent with observed data—suggesting potentially upward-biased short-term sensitivity.
- Main limitations:
  - Cannot definitively decompose forecast errors into climate vs. non-climate components; coincidentally signed non-climate shocks could contribute.
  - Validation period (2011–2019) covers modest warming (~0.2°C globally) — results pertain to near-term impacts and may not generalize to larger warming.
  - Cannot fully adjudicate functional forms governing long-term damage accumulation; accumulated small annual biases can compound over decades.
  - Exclusion of crisis years (2008–2010, 2020–2023) avoids contamination but may miss periods of salient climate impacts.
  - Focuses on GDP growth impacts and excludes non-market/non-use values (health, ecosystems, well-being).

### Conclusion (concise)
- Using WEO forecasts as climate-naïve counterfactuals, damage functions can modestly improve forecast accuracy (MAE reductions of 0.1–0.4 pp), indicating climate variables add information beyond standard economic indicators.
- Substantial heterogeneity exists across damage functions; several widely used high-impact functions imply near-term outcomes difficult to reconcile with professional forecasts and observed data.
- For near- to medium-term policy analysis, more moderate damage functions that align better with historical experience may provide more reliable guidance, while extreme damage estimates (e.g., implying SCC > $1,000 per ton) warrant cautious interpretation.

*Source: 3.2 Forecast error and climate impact evaluation measures, wpiea2026085-source-pdf*

### References

### References

### Core literature on macroeconomic impacts of climate change
- Akyapı, Berkay, Matthieu Bellon, and Emanuele Massetti, “Estimating Macrofiscal Effects of Climate Shocks from Billions of Geospatial Weather Observations,”American Economic Journal:  Macroeconomics, July 2025,17(3), 114–159.
- Bilal,  Adrien  and  Diego  K ̈anzig,  “Does  Unilateral  Decarbonization  Pay  For  Itself?,” Technical Report, National Bureau of Economic Research, Cambridge, MA 2025.
- and Diego R K ̈anzig, “The Macroeconomic Impact of Climate Change:  Global Versus Local Temperature*,”The Quarterly Journal of Economics, February 2026, p. qjag011.
- Burke, Marshall and Kyle Emerick, “Adaptation to Climate Change:  Evidence from US  Agriculture,”American  Economic  Journal:   Economic  Policy,  August  2016,8(3), 106–140.
- , Solomon M. Hsiang, and Edward Miguel, “Global non-linear effect of temperature on economic production,”Nature, November 2015,527(7577), 235–239.
- Carleton,  Tamma,  Amir  Jina,  Michael  Delgado,  Michael  Greenstone,  Trevor Houser,  Solomon  Hsiang,  Andrew  Hultgren,  Robert  E  Kopp,  Kelly  E  McCusker, Ishan Nath, James Rising, Ashwin Rode, Hee Kwon Seo, Arvid Viaene, Jiacan Yuan, and Alice Tianbo Zhang, “Valuing the Global Mortality Consequences of Climate Change Accounting for Adaptation Costs and Benefits*,”The Quarterly Journal of Economics, April 2022, p. qjac020.
- Dell, Melissa, Benjamin F Jones, and Benjamin A Olken, “Temperature Shocks and Economic Growth:  Evidence from the Last Half Century,”American Economic Journal: Macroeconomics, July 2012,4(3), 66–95.
- Desbordes,  Rodolphe and Markus Eberhardt,  “Climate change and economic prosperity:  Evidence from a flexible damage function,”Journal of Environmental Economics and Management, 2024,125, 102974.
- Drouet,  Laurent,  Valentina  Bosetti,  Simone  A.  Padoan,  Lara  Aleluia  Reis, Christoph Bertram, Francesco Dalla Longa, Jacques Despr ́es, Johannes Emmerling,  Florian  Fosse,  Kostas  Fragkiadakis,  Stefan  Frank,  Oliver  Fricko, Shinichiro  Fujimori,  Mathijs  Harmsen,  Volker  Krey,  Ken  Oshiro,  Larissa  P. Nogueira, Leonidas Paroussos, Franziska Piontek, Keywan Riahi, Pedro R. R. Rochedo,  Roberto Schaeffer,  Jun’ya Takakura,  Kaj-Ivar van der Wijst,  Bob van der Zwaan,  Detlef van Vuuren,  Zoi Vrontisi,  Matthias Weitzel,  Behnam Zakeri,  and Massimo Tavoni,  “Net zero-emission pathways reduce the physical and economic risks of climate change,”Nature Climate Change, November 2021,11(12), 1070–1076.
- Emmerling,  Johannes,  Pietro  Andreoni,  and  Massimo  Tavoni,  “Global  inequality consequences of climate policies when accounting for avoided climate impacts,”Cell Reports Sustainability, January 2024,1(1), 100008.  Publisher:  Elsevier.
- Kahn,  Matthew E.,  Kamiar Mohaddes,  Ryan N. C. Ng,  M. Hashem Pesaran, Mehdi  Raissi,  and  Jui-Chung  Yang,  “Long-term  macroeconomic  effects  of  climate change:  A cross-country analysis,”Energy Economics, December 2021,104, 105624.
- Kalkuhl, Matthias and Leonie Wenz, “The impact of climate conditions on economic production. Evidence from a global panel of regions,”Journal of Environmental Economics and Management, September 2020,103, 102360.
- Kotz,  Maximilian,  Anders  Levermann,  and  Leonie  Wenz,  “The  effect  of  rainfall changes on economic production,”Nature, January 2022,601(7892), 223–227.
- Morris, Jennifer, Steven K. Rose, John Reilly, Angelo Gurgel, Sergey Paltsev, and C. Adam Schlosser, “Reconciling widely varying estimates of the global economic impacts from climate change,”Nature  Climate  Change, February 2025,15(2), 124–127. Publisher:  Nature Publishing Group.
- Nath, Ishan B., Valerie A. Ramey, and Peter J. Klenow, “How Much Will Global Warming Cool Global Growth?,” July 2024.
- Newell, Richard G., Brian C. Prest, and Steven E. Sexton, “The GDP-Temperature relationship:  Implications for climate change damages,”Journal  of  Environmental  Economics and Management, March 2021, p. 102445.
- Piontek, Franziska, Laurent Drouet, Johannes Emmerling, Tom Kompas, Aur ́elie M ́ejean, Christian Otto, James Rising, Bjoern Soergel, Nicolas Taconet, and Massimo Tavoni, “Integrated perspective on translating biophysical to economic impacts of climate change,”Nature Climate Change, June 2021.
- Takakura,  Jun’ya,  Shinichiro  Fujimori,  Naota  Hanasaki,  Tomoko  Hasegawa, Yukiko Hirabayashi, Yasushi Honda, Toshichika Iizumi, Naoko Kumano, Chan Park,  Zhihong Shen, Kiyoshi Takahashi,  Makoto Tamura,  Masahiro Tanoue, Koujiro Tsuchida, Hiromune Yokoki, Qian Zhou, Taikan Oki, and Yasuaki Hijioka, “Dependence of economic impacts of climate change on anthropogenically directed pathways,”Nature Climate Change, October 2019,9(10), 737–741.
- Tol,  Richard  S.J.,  “A  meta-analysis  of  the  total  economic  impact  of  climate  change,”Energy Policy, 2024,185, 113922.

### Climate damage functions, integrated assessment models, and social cost estimates
- Barrage,  Lint  and  William  Nordhaus,  “Policies,  projections,  and  the  social  cost  of carbon:  Results  from  the  DICE-2023  model,”Proceedings  of  the  National  Academy  of  Sciences of the United States of America, 2024,121(13), e2312030121.
- DICE 2023 (referenced multiple times within figures and captions).
- Desbordes, Rodolphe and Markus Eberhardt, “Climate change and economic prosperity: Evidence from a flexible damage function,”Journal of Environmental Economics and Management, 2024,125, 102974.
- Gortan, Marco, Lorenzo Testa, Giorgio Fagiolo, and Francesco Lamperti, “A unified dataset for pre-processed climate indicators weighted by gridded economic activity,”Scientific data, 2024,11(1), 533.
- Lemoine, Derek, Catherine Hausman, and Jeffrey G. Shrader, “A Guide to Climate Damages,”  Technical  Report  w34348,  National  Bureau  of  Economic  Research  October 2025.
- Mohaddes,   Kamiar  and  Mehdi  Raissi,   “Rising  temperatures,   melting  incomes: Country-specific macroeconomic effects of climate scenarios,”PLOS Climate, 2025,4(9), e0000621.
- Rennert,  Kevin,  Frank  Errickson,  Brian  C.  Prest,  Lisa  Rennels,  Richard  G. Newell,  William  Pizer,  Cora  Kingdon,  Jordan  Wingenroth,  Roger  Cooke, Bryan  Parthum,  David  Smith,  Kevin  Cromar,  Delavane  Diaz,  Frances  C. Moore,   Ulrich  K.  M ̈uller,   Richard  J.  Plevin,   Adrian  E.  Raftery,   Hana ˇ Sevˇc ́ıkov ́a,  Hannah  Sheets,  James  H.  Stock,  Tammy  Tan,  Mark  Watson, Tony E. Wong, and David Anthoff, “Comprehensive Evidence Implies a Higher Social Cost of CO2,”Nature, September 2022, pp. 1–3.  Publisher:  Nature Publishing Group.
- Ricke, Katharine, Laurent Drouet, Ken Caldeira, and Massimo Tavoni, “Country-level social cost of carbon,”Nature Climate Change, October 2018,8(10), 895–900.
- van der Wijst, Kaj-Ivar, “MIMOSA: Integrated Assessment Model for Cost-Benefit Anal-ysis:  GitHub repository.https://github.com/UtrechtUniversity/mimosa/,” 2024.
- van der Wijst, Kaj-Ivar, Francesco Bosello, Shouro Dasgupta, Laurent Drouet, Johannes  Emmerling,   Andries  Hof,   Marian  Leimbach,   Ramiro  Parrado, Franziska  Piontek,  Gabriele  Standardi,  and  Detlef  van  Vuuren,  “New  damage curves and multimodel analysis suggest lower optimal temperature,”Nature Climate Change, March 2023.
- Tol,  Richard  S.  J.,  “Social  cost  of  carbon  estimates  have  increased  over  time,”Nature Climate Change, June 2023,13(6), 532–536.

### Forecasting accuracy, IMF/WEO process, and evaluation studies
- Artis,  Michael J, “How Accurate Is the World Economic Outlook?  A Post Mortem on Short-Term Forecasting at the International Monetary Fund,” in “World Econonomic and Financial Surveys, 1988,” International Monetary Fund, 1988.
- Celasun,  Oya,  Jungjin Lee,  Mico Mrkaic,  and Allan Timmermann,  “An evaluation of world economic outlook growth forecasts, 2004–17,” Technical Report 2021/216, International Monetary Fund 2021.
- Dreher, Axel, Silvia Marchesi, and James Raymond Vreeland, “The political economy of IMF forecasts,”Public Choice, October 2008,137(1), 145–171.
- Eicher,  Theo  S.  and  Yuan  Gao  Rollinson,  “The  accuracy  of  IMF  crises  nowcasts,” International Journal of Forecasting, January 2023,39(1), 431–449.
- Gatti, Roberta, Daniel Lederman, Asif M. Islam, Ha Nguyen, Rana Lotfi, and Mennatallah  Emam  Mousa,  “Data  transparency  and  GDP  growth  forecast  errors,” Journal of International Money and Finance, February 2024,140, 102991.
- Genberg, Hans, Andrew Martinez, and Michael Salemi, “The imf/weo forecast process,”Independent Evaluation Office of the International Monetary Fund Background Paper No. BP/14/03, Washington, DC., 2014.
- ,,  Carlos  de  Resende,  Francesco  Luna,  and  Franz  Loyola,  “IMF  Forecasts: Process, Quality, and Country Perspectives,”Independent Evaluation Office of the International Monetary Fund Evaluation Report, Washington, DC., 2014.
- Hamilton,  James  D.,  “Why  You  Should  Never  Use  the  Hodrick-Prescott  Filter,”The Review of Economics and Statistics, December 2018,100(5), 831–843.
- Ranger,  Nicola Ann,  Olivier Mahul,  and Irene Monasterolo,  “Assessing financial risks from physical climate shocks,” Technical Report 168725, The World Bank, Washington, D.C 2022.
- Usman, Sehrish, Guzm ́an Gonz ́alez-Torres Fern ́andez, and Miles Parker, “Going NUTS: The regional impact of extreme climate events over the medium term,”European Economic Review, September 2025,178, 105081.
- Figures and appendix material on forecast errors and WEO bias:
  - “The annual WEO bias (averaged across countries) varies over time but is typically negative across all forecast horizons” (Figure S7 caption and panels a–c).
  - Ex-post bias panels showing values including ranges such as −0.75% to 0.00% and −1.5% to 0.0% across forecast horizons and base years (Figure S7).

### Methodology, datasets, and climate indicators used in damage functions
- Gortan, Marco, Lorenzo Testa, Giorgio Fagiolo, and Francesco Lamperti, “A unified dataset for pre-processed climate indicators weighted by gridded economic activity,”Scientific data, 2024,11(1), 533.
- Rohde, Robert A. and Zeke Hausfather, “The Berkeley Earth Land/Ocean Temperature Record,”Earth System Science Data, 2020,12(4), 3469–3479.
- Waidelich, Paul, Fulden Batibeniz, James Rising, Jarmo S. Kikstra, and Sonia I. Seneviratne, “Climate damage projections beyond annual temperature,”Nature Climate Change, June 2024,14(6), 592–599.  Publisher:  Nature Publishing Group.
- Figure S1 notes: “All variables are normalized to 2010 = 1 to enable comparison across different scales and units.  Local annual temperature and precipitation are used by BHM 2015,  KW 2020,  KLW 2022 and KMNPRY 2021.  Global temperature is used by BK 2026.  Global mean surface temperature (GMST) anomaly relative to 1850-1900 is used by DICE 2023 and COACCH. The ABM 2025 variables include drought index (PDSI<-4), temperature stress (9-12 months), and extreme heat days (days>35°C).”

### Meta-analyses, damage estimation guidance, and synthesis studies
- Howard, Peter H. and Thomas Sterner, “Few and Not So Far Between: A Meta-analysis of Climate Damage Estimates,”Environmental and Resource Economics, September 2017,68(1), 197–225.
- and, “Methodology Matters:  A Careful Meta-Analysis of Climate Damages,”Environmental and Resource Economics, 2025.
- Tol,  Richard  S.  J.,  “Social  cost  of  carbon  estimates  have  increased  over  time,”Nature Climate Change, June 2023,13(6), 532–536.
- Waidelich, Paul, Fulden Batibeniz, James Rising, Jarmo S. Kikstra, and Sonia I. Seneviratne, “Climate damage projections beyond annual temperature,”Nature Climate Change, June 2024,14(6), 592–599.  Publisher:  Nature Publishing Group.
- Lemoine, Derek, Catherine Hausman, and Jeffrey G. Shrader, “A Guide to Climate Damages,”  Technical  Report  w34348,  National  Bureau  of  Economic  Research  October 2025.

### Appendix and figure-specific content referenced
- Appendix A includes multiple figures and panels presenting:
  - Figure S1: Climate Variables Used in Damage Functions for the United States (2010-2019) with normalization to 2010 = 1.
  - Figure S2: Aggregated performance by climate damage function based on different definitions of the forecast error; top panel uses T=5 cumulative effect, bottom panel shows averaged improvement in year-by-year growth rates.
  - Figure S3: Distribution of MAE improvements by damage function and base year by country.
  - Figure S4: Performance by evaluation window and country (panels a–c show share of country-year observations across windows 2011–2019 and average improvement bins [−0.1,−0.025], (−0.025,−0.005], (−0.005,0], (0,0.005], (0.005,0.025], (0.025,0.1]).
  - Figure S5: Weighted ensemble estimates of climate change impacts on GDP per capita in 2023 for EU27 countries; Europe Avg. −1.5% displayed with country-level estimates and weighted mean values.
  - Figure S6: Full ensemble estimates of climate change impacts on GDP per capita in 2023 in Europe (damage functions listed: ABM 2025, BHM 2015, BK 2026, COACCH, DICE 2023, HS 2025, KLW 2022, KMNPRY 2021, KW 2020).
  - Figure S7: WEO forecast error by time horizon and window, panels showing average forecast error (residual) in GDPpc growth p.a. across horizons 1–5 and base years 2010–2014 with noted bias ranges.

*Content derived exclusively from the supplied “References” section and accompanying appendix figure captions.*

### Appendix B    Additional information on implementing

### Appendix B    Additional information on implementing damage functions

### B.1 BHM
- Regression model used:
  - ln(y_it) − ln(y_i,t−1) = β1 T_it + β2 T_it^2 + β3 P_it + β4 P_it^2 + γ_i + α_t + θ_i,1 t + θ_i,2 t^2 + ε_it (Equation 23)
- Projection approach:
  - Annual growth impact (log scale) relative to baseline mean temperature:
    - δ_BHM_it = [β1 T_it + β2 T_it^2] − [β1 T_i,baseline + β2 T_i,baseline^2] (Equations 24–25)
  - Parameters: β1 = 0.012718353 and β2 = −0.00048709 (from Extended Data Table 1, col. 1)
  - Baseline choice: 2006–2010 average mean temperature (to be close to 2010 start year and smooth year-to-year variation)
- Conversion and cumulation:
  - Cumulative impact in logarithmic changes since base year τ:
    - ∆_BHM,ln_it = Σ_{s=τ+1}^t δ_BHM_is (Equation 26)
  - Convert logarithmic cumulative change to % of GDPpc:
    - ∆_BHM_it = exp(∆_BHM,ln_it) − 1 (Equation 27)
- Key assumption:
  - Original BHM project damages as y_{t−1} × (1 + g_t + δ_t), implying growth impacts are in % of GDPpc; authors convert via logarithmic cumulation to align methods.

### B.2 COACCH
- Damage function (region-specific, quadratic) depends on shift in annual global mean surface temperature vis-`a-vis 1986–2005 average:
  - ∆_COACCH_it = a_r [ b_{r,1} ∆T_{global,t,1986−2005} + b_{r,2} ∆T_{global,t,1986−2005}^2 ] (Equation 28)
  - 26 IMAGE regions r; central specification uses a_r = 1 ∀ r
- Implementation details:
  - Map IMAGE regions to countries using matching files from van der Wijst (2024)
  - Use region-specific parameters b_{r,1} and b_{r,2} from https://zenodo.org/records/5546264
  - Use damage functions that do NOT include sea level rise (for comparability)
- Units and assumptions:
  - COACCH returns impacts in % of GDP (no log-to-% conversion needed)
  - Assume GDP impacts ≡ GDPpc impacts (i.e., negligible climate-driven population impacts)
- Isolation of post-forecast impacts:
  - Only consider impacts due to increases in global mean surface temperature after the WEO forecast year τ:
    - ∆_COACCH_it = [b_{r,1} ∆T_{global,t,1986−2005} + b_{r,2} ∆T_{global,t,1986−2005}^2] − [b_{r,1} ∆T_{global,τ,1986−2005} + b_{r,2} ∆T_{global,τ,1986−2005}^2] (Equation 29)

### B.3 KW 2020
- Regression model (ADM1-level fixed effects; dependent variable: first difference of log gross regional income per capita):
  - ln(y_it) − ln(y_i,t−1) = β1 ∆T_it + β2 ∆T_it T_{i,t−1} + β3 ∆T_{i,t−1} + β4 ∆T_{i,t−1} T_{i,t−1} + other precipitation and fixed effects (Equation 30)
  - T_it and P_it denote ADM1-level annual mean temperature (°C) and annual precipitation (mm)
- Projection methodology:
  - KW 2020 use only the four temperature first-difference terms for projections:
    - δ_KW_it = β1 ∆T_it + β2 ∆T_it T_{i,t−1} + β3 ∆T_{i,t−1} + β4 ∆T_{i,t−1} T_{i,t−1} (Equation 31)
  - Coefficients: β1 = 0.00641, β2 = −0.00109, β3 = 0.00345, β4 = −0.000718
  - Coefficients applied at country level (ADM1→country simplification validated)
- Cumulation and conversion:
  - ∆_KW_it = exp(Σ_{s=τ+1}^t δ_KW_is) − 1 (Equation 32)

### B.4 KLW 2022
- Regression model (ADM1-level; adds day-to-day variability, extreme rainfall, monthly deviations, wet days; many terms in levels):
  - ∆ln(y_it) = β^T terms for ∆T + β^P terms for P levels + β̃_T T̃ + β_RD terms for wet days and extremes + β_RM terms + α_i + δ_t + ε_it (Equation 33)
  - T̃: day-to-day temperature variability; RD_{x,t}: annual number of wet days with daily precipitation ≥ 1 mm; ŘD_{x,t}: extreme daily rainfall; RM_{i,t}: standardized monthly rainfall deviation
- Projection approach:
  - KLW 2022 do not provide projections directly; follow Kotz et al. (2024) re-application and Waidelich et al. (2024)
  - Use KW 2020 methodology applied to KLW 2022 temperature terms:
    - δ_KLW22_it = β_{T1} ∆T_it + β_{T2} ∆T_it T_{i,t} + β_{T3} ∆T_{i,t−1} + β_{T4} ∆T_{i,t−1} T_{i,t−1} (Equation 34)
  - Coefficients: β_{T1} = 0.000960192, β_{T2} = −0.002273751, β_{T3} = −0.0010594136, β_{T4} = −0.0006545396
  - Only annual temperature used for projections (other climate indicators have low signal-to-noise)
- Cumulation and conversion:
  - ∆_KLW22_it = exp(Σ_{s=τ+1}^t δ_KLW22_is) − 1 (Equation 35)
- Assumption:
  - Implement ADM1-level estimates directly at country level (per Emmerling et al., 2024)

### B.5 ABM 2025
- Regression model (country-level GDPpc growth in log changes) with LASSO-selected climate variables:
  - ∆ln(y_it) = β1 ∆Tx35_{i,t} + β2 ∆T9to12_{i,t} + β3 ∆PDSI_{i,t} + α_t (Equation 36)
  - Independent variables standardized as z-scores (divided by in-sample standard deviation)
- Annual impact:
  - δ_ABM_it = β1 ∆Tx35_{i,t} + β2 ∆T9to12_{i,t} + β3 ∆PDSI_{i,t} (Equation 37)
  - Coefficients: β1 = −0.00168, β2 = 0.00144, β3 = −0.00225 (see Table 1, column A)
- Cumulation and conversion:
  - ∆_ABM_it = exp(Σ_{s=τ+1}^t δ_ABM_is) − 1 (Equation 38)

### B.6 BK 2026
- Use regional impulse response function coefficients for global temperature shocks (from BK replication package)
- Regional mapping:
  - Match BK 2026 regions to countries within macro-regions and continents (Table S1 lists BK regions and ISO3 codes)
- Annual impact for region r:
  - δ_BK_it = Σ_{l=0}^{10} β_{r,l} T^{shock}_{global,t−l} (Equation 39)
  - T^{shock}_{global} is year-specific global mean surface temperature shock variable (“gtmpnoaaawdtfe2s”) from BK replication package, based on NOAA anomaly data
- Conversion to % of GDPpc:
  - ∆_BK_it = exp(δ_BK_it) − 1 (Equation 40)
- Notes on temporal persistence:
  - Approach calculates impacts based on previous 10 years of shocks; effects disappear after ten years, making long-term results substantially more conservative relative to structural-model projections.

### B.7 DICE 2023
- Global reduced-form quadratic damage function based on shift in global mean surface temperature since pre-industrial:
  - ∆_DICE_global,t = β1 * ∆T_{global,t,1850−1900}^2 (Equation 41)
  - Parameter: β1 = −0.003467 (derived from meta-analysis)
- Implementation:
  - Apply global impact uniformly to all countries
  - Isolate impacts attributable to warming after base year τ:
    - ∆_DICE_global,t = β1 * [∆T_{global,t,1850−1900}^2 − ∆T_{global,τ,1850−1900}^2] (Equation 42)
  - Note: DICE returns impact in % of output; assume equivalence to % of GDPpc (negligible population impacts)

### B.8 HS 2025
- Global damage function from meta-analysis (Howard and Sterner, 2025), expressed as share of global GDP relative to baseline temperature:
  - ∆_HS_global,t = f(∆T_{global,t,1850−1900}) − f(∆T_{global,τ,1850−1900}) (Equation 43)
  - f(·) denotes the meta-analytic damage function from Howard and Sterner (2025)
- Downscaling global damages to countries:
  - Follow OECD (2025) approach using Tol (2024) downscaling: allocate global damages based on current climate conditions and GDP per capita using 2006–2010 average as reference for baseline climate and income characteristics

### B.9 KMNPRY 2021
- Regression model (half-panel jackknife estimator) projecting impacts via deviations from historical temperature norms:
  - ∆ln(y_{i,t}) = α_i + Σ_{l=1}^4 γ_l ∆ln(y_{i,t−l}) + Σ_{j=0}^4 β_j ˜T_{i,t−j} + ε_{i,t} (Equation 44)
  - ˜T_{i,t} = |T_{i,t} − (1/m) Σ_{l=1}^m T_{i,t−l}| (Equation 45)
- Projection mechanics:
  - GDPpc losses for year t due to warming since t = 0:
    - Σ_{j=1}^t (g_{1,j} − g_0) × ĥψ(t−j) (Equation 46)
  - g_0 and related analytic expressions defined using standard normal Φ(·) and φ(·) functions (Equations 47–51)
  - μ_0 = m + 1/2 β_0 (Equation 48); ω_0 = [σ_0^2 × (1 + 1/m)]^{0.5} (Equation 49)
  - μ_{1,j} = m + 1/2 × (β_0 + j × d_{RCP}) (Equation 50)
  - ĥψ(L) = γ(L)^{-1} β(L) (Equation 51)
- Implementation choices:
  - Use m = 30 historical norm
  - Take country-specific β_0 and ω_0 from KMNPRY 2021 Table A.7 and central ĥψ(t−j) for t−j = 0,1,...,100 from KMNPRY 2021 replication package (Version 1.0.1)
- Adjustment for projection window:
  - Original KMNPRY compared 1960–2014 trends vs. 2015–2100 with RCP2.6 and d_{RCP8.5}
  - For this implementation, shorten baseline from 2014 to 2010 and change projection period from 2015–2100 to 2011–2019
  - Use Berkeley Earth GMST trends: 0.047 °C p.a. for 2011–2019, 0.017 °C p.a. for 1960–2014, 0.017 °C p.a. for 1960–2010
  - Conclude 2011–2019 warming aligns most closely with SSP5-RCP8.5; therefore use original RCP8.5 d_{RCP} and original μ_0 and ω_0 estimates from replication package without adjustment

### Appendix C — Sample and exclusions
- WEO data covers N = 196 economies
  - Two economies (Macao SAR and Hong Kong SAR) not included in climate data by Gortan et al. (2024)
  - An additional 27 economies omitted from forecast error evaluation because at least one damage function cannot be implemented (e.g., cannot match to COACCH region or missing KMNPRY parameters)
- Economies with missing climate data or missing impacts are listed in Table S2 (summary in source). Economies with missing climate data are excluded from placebo regressions; economies with missing impacts are excluded from forecast performance evaluation.

_Italic source attribution: When Forecasts Meet Reality: Assessing Climate Damage Functions — Working Paper No. WP/2026/085 (Appendix B)_

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026085-source-pdf.pdf_